Daniel Mata Flores

Jean-Paul Ampuero

Anthony Sladen

Devant Le

Professeur Olivier Coutant

Président Du

Professeur Miguel González Herráez

Professeur Céline Hadziioannou

Marine Denolle

Philippe Jousset

Eléonore Stutzmann

Thanks

Françoise Courboulex

Jenny Trévisan

Bertrand Delouis

Jean-Mathieu Nocquet

Frédérique Also

Louis Leclerc

De Barros

Carlo Mologni

Christelle Saliby

Frichnel Mamfoumbi

Hugo Lestrelin

Sébastien Bonnieux

Christophe Matonti

Pablo Lara

Daniel Pacheco

Marie Baillet

Ariana Astorga

Estelle Delouche

Thibaut Cardinal

Guillaume Clement

Anna Maria Sklodowska

Hugo Sánchez Reyes

Jorge Jara

Henry Cárdenas

Rafael Requena

Orian Hernández

Luis Arturo K Brunicardi

Lucho

Application des mesures acoustiques sur câble fibre optique à l'étude de l'interface terre-mer et du milieu marin

Keywords: fiber optic cable, Distributed Acoustic Sensing, seafloor, ocean current, cable waves, vortex-induced vibration v

Oceans are in the middle of a technological dichotomy: they are poorly explored and studied due to the lack of dedicated instrumentation and, yet, they are traversed by a complex network of fiber optic cables mostly used for telecommunications. Recently, a photonic-based technique known as Distributed Acoustic Sensing (DAS) has demonstrated potential to improve the spatial coverage of observations in Earth Sciences, by turning telecom fiber optic cables into dense arrays of sensors. Harnessing DAS along underwater telecom fibers, spanning tens-to-hundreds of kilometers, for applications in physical oceanography becomes crucial to improve our understanding of the ocean dynamics and to increase the spatial coverage of physical observations of the ocean. However, seafloor telecom fiber optic cables are expected to feature heterogeneous mechanical coupling with the seabed. This aspect, although formerly noticed, has not been evaluated in detail in terms of the type of signals recorded by DAS along cable sections with a poor coupling to the sea bottom.

In this work, I investigate two vibration regimes of underwater fiber optic cables recorded by DAS, along cable sections of three submarine fibers featuring heterogeneous mechanical coupling to the seafloor. I demonstrate that the first regime, characterized by a frequency content lower than 1 Hz, is generated by Vortex-Induced Vibrations of cable segments presumably suspended in the water column. In particular, I show that the amplitude-dependent frequency of the cable oscillations can be used to obtain time series of ocean current speeds in deep environments. This may offer a new method for physical oceanography at depths rarely studied before. To validate my results, I systematically compare the DAS-based time series with the current speeds recorded by a nearly located current meter. I further reveal that the second regime excites frequencies higher than 2 Hz, due to the passage of seismic waves along cable sections seemingly pinned between two points of the seafloor. I notice that this high-frequency fiber oscillations are dominated by cable waves that introduce highly monochromatic noise to the DAS recordings. The results on this second regime suggest that cable waves may indicate cable segments unsuitable for the analysis of seismic waves, for DAS-based underwater seismology. Overall, this PhD research helps understanding how seafloor features affect DAS recordings, which opens the way to novel applications of submarine DAS in oceanography and seismology.

Résumé

Les océans sont actuellement au coeur d'une dichotomie technologique: ils sont peu explorés et étudiés à cause du manque d'instrumentation dédiée et, pourtant, ils sont traversés par un réseau complexe de câbles à fibre optique servant aux télécommunications. Récemment, la technique connue comme "Détection Acoustique Distribuée" (DAS, en anglais) a montré qu'elle pourrait améliorer la couverture spatiale des observations en Sciences de la Terre, en transformant des câbles de télécommunications en réseau dense de capteurs. Comprendre comment utiliser le DAS le long des câbles à fibre optique sous-marins devient, donc, essentiel pour mieux étudier la dynamique océanique, et pour augmenter la couverture spatiale de nos observations des océans. Néanmoins, on s'attend à une fluctuation du couplage mécanique des câbles à fibre optique sous-marins, tout au long de leurs trajectoires -communément de plusieurs kilomètres de longueur -sur le fond marin. Bien que ce problème soit largement reconnu, son impact sur les signaux DAS reste encore peu étudié.

Dans ce travail de thèse, je présente deux régimes de vibration des câbles à fibre optique sous-marins enregistrés par DAS, le long des sections de câble ayant un couplage mécanique hétérogène avec le fond marin. Je montre que le premier régime est généré par des Vibrations de Von Karman le long de segments de câble présumés suspendus, avec des fréquences d'oscillation inférieures à 1 Hz. Notamment, je constate que ces fréquences dépendent de l'amplitude d'oscillation et qu'elles peuvent être utilisées pour suivre l'amplitude des courants océaniques sur le fond marin. Pour valider mes résultats, je compare les séries temporelles obtenues par DAS avec les courants océaniques enregistrés par un courantomètre placé proche du câble. Je montre également la présence d'un deuxième régime de vibration aux fréquences supérieures à 2 Hz, lié à l'arrivée des ondes sismique sur certaines sections du câble. Ces oscillations hautes fréquences sont dominées par des ondes de câble, qui introduisent du bruit monochromatique aux enregistrements DAS. A priori, ces ondes de câble sont limitées à des segments de câble bordés par des points d'appui sur le fond marin. Ces résultats suggèrent que les ondes de câble, vues par le DAS, permettent d'identifier des segments inappropriés pour l'analyse des ondes sismiques. Globalement, ce travail de thèse aide à comprendre comment les caracteristiques du fond marin impactent les enregistrements DAS, ce qui ouvre de nouvelles applications du DAS en océanographie et sismologie.

Mots

2.1

Photon-scattering mechanisms of light. A beam of light of frequency "f " propagates along a material with density fluctuations that scattered the incident light (a). The spectrum of the scattered light includes Rayleigh (frequency peak at the incident light frequency "f "), Brillouin and Raman scattering (both with shifted frequency peaks respect to "f ") (b). Stokes and Anti-Stokes light is generated when the scattered light is emitted at lower or higher frequency than the incident light, respectively (Modified from [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]) . . . . . . . . .

2.2

Representation of Rayleigh scattering in fiber optic cables. A coherent laser (input light) is injected into a fiber core protected by claddings. As the laser interacts with a density heterogeneity of the cable (black circle), backscattered and reflected light is generated and propagates back to the interrogator and forward along the fiber, respectively. (taken from [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]) . . . . . . . . .

2.3

General sketch of an OTDR system. A pulsed laser is injected into the cable by the interrogator unit (Receiver), which also detects the Rayleigh backscattered signal (curved arrows). Imperfections in the cable, at locations indicated by the yellow and red boxes, decrease the power of the reflected light. (Modified from [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Raman Amplification applied to a short fiber (span length < 50 km). DAS signal levels of backscattered light from a continuous 39-km-long fiber (a) without and (b) with (co-propagating) Raman amplification. The former shows exponential decay due to attenuation, while in the latter high signal levels are maintained more uniformly and over a longer distance. (Taken from [START_REF] Wilson | Distributed acoustic sensing of long subsea tie-backs[END_REF]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5 Raman Amplification applied to a long fiber (span length > 100 km). Optical power of Φ-OTDR traces recorded along a 120 km-long fiber: without amplification (a), and using first-order bidirectional Raman amplification (b).

Raman amplification increases the range from 50 to 120 km. (Taken from [START_REF] Martins | Distributed vibration sensing over 125 km with enhanced snr using phi-otdr over a urfl cavity[END_REF]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.6 Sketch of geophysical sensing based on offshore SOP. Light is injected into a seafloor fiber through an optical transmitter, and its State of Polarization (SOP) is continuously monitored along the cable (a). Minimal perturbations of the input signal (red star) generate a stable output of SOP (blue dots) on the Poincaré sphere (b). Storms, tsunami/earthquake waves or ocean swells produce SOP anomalies by shaking or pressuring the cable (c). As the Stoke parameters S 1 , S 2 and S 3 are commonly normalized to 1, only two are independent. A typical practice in SOP sensing is to rotate the Stoke parameters to one pole of the Poincaré sphere (the north pole in this example) and focus on analyzing the independent parameters after rotation (d). (Modified from [START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF]) . 20 2.7 Time-and-frequency domain analysis of SOP signals. M W 6.8 intermediatedepth earthquake recorded by SOP along a transoceanic cable (10 500 km long). Stoke traces, S 2 , are bandpass-filtered between 0.8 -3 Hz (a), and between 0.3 -0.8 Hz (b). The vertical red, blue and green lines highlight the earthquake origin time, theoretical P and S wave arrival times, respectively. (c) Spectrogram for S 2 showing a package of seismic energy between 0.8 -3 Hz, and potentially Scholte waves at lower frequencies. (Modified from [START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF]) . . . . 21

2.8 Diagram of Fabry-Perot Interferometer (FPI) sensors in fiber optic cables.

Two types of FPI sensors can be found in fibers: the extrinsic type (a), and the intrinsic type (b). Commonly, the optical cavity of the extrinsic FPI is an airgap, whereas the optical cavity of the intrinsic FPI is the fiber itself. (Modified from [START_REF] Joe | A review on optical fiber sensors for environmental monitoring[END_REF]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 xviii 2.9 Tidal currents detected by Ultrastable Laser-based Interferometry. [START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF] performed laser-based interferometry along a transoceanic fiber cable connecting Southport, UK and Halifax, Canada. They observed narrowband components excited in two frequency ranges: A first between 1 and 5 Hz, repeating approximately every 6 h, that they associated with tidal currents in the Irish Sea (A, B); and a second, between 0.5 and 1. 5 Hz with a 12-h repeating pattern, attributed to tidal currents in the MAR area (D). Interactions with ocean currents due to the changing MAR bathymetry were also recorded (E, F). D in the right column stands for depth. (Taken from [START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF]) . . . . . .

Representation of the Double Crucible Method.

A fiber optic cable is fabricated from a rod tube (or "preform") that is drawn out from the bottom of two crucibles. The preform is composed by a core glass inside of a tube of cladding glass. (Modified from (Al-Azzawi, 2017)) . . . . . . . . . . . . . . . . . . . .

3.2

Cross section and schematic view of a typical fiber optic cable. Core-cladding fiber optic cables are obtained from a preform. During the drawing process of the preform, a protective layer of plastic -the so-called jacket -is coated on the surface of the cladding. (Taken from (Al-Azzawi, 2017)) . . . . . . . . . . . . 3.5 Optical loss vs. wavelength of the light travelling in standard fibers. The wavelength of optical sources is usually chosen around 1.5 µm to avoid the Fiber Loss peak at 1.39 µm, and infrared absorption. (Taken from [START_REF] Murata | Handbook of optical fibers and cables[END_REF]))

3.6 Cross-sectional view of a high-density fiber cable. Optical fibers are embedded within a jelly filled, and separated from an outer layer of silicon gel by a loose tube. A final jacket covers the entire unit. (Modified from [START_REF] Murata | Handbook of optical fibers and cables[END_REF]))

3.7 Absorption loss in Jelly-filled and Non-jelly-filled fiber optic cables due to water infiltration. Below the freezing temperature of water, attenuation due to absorption loss strongly increases in Non-jelly-filled fibers. While, absorption loss remains the same in Jelly-filled optical fiber despite the temperature drop.

(Modified from [START_REF] Murata | Handbook of optical fibers and cables[END_REF] (Modified from Technical Specifications of Submarine Cables, Alcatel-Lucent) . 47

3.13 Portion of the route followed by a submarine fiber optic cable in the Methoni Bay, southwestern Greece. A designed cable path (red line) traverses different geological features -ripples, rock fragments, sandy mud, rocky bed and rocky outcrops -that were identified by bathymetry surveys and geotechnical assessments during the planning of the cable trajectory. Ocean currents of speed "U " hit a suspended cable of diameter "D", which leads to vortices shedding off from the cable at a frequency "f v ". (Modified from [START_REF] Williamson | A brief review of recent results in vortex-induced vibrations[END_REF]) . . . . . . . . . . . . . . . . . . . . 53 4.3 Two behaviors of the vortex shedding frequencies observed during a VIV experiment. Vortex shedding frequencies (circles) in the lock-out regime (yellow area) are well described by the Strouhal number equation (black line, eq. 4.1). While, in the lock-in regime (green area), vortex shedding frequencies approach the natural frequency of the vibrating object (downward triangles).

Low-amplitude and high-amplitude oscillations (upward triangles) are typically observed in the lock-out regime and lock-in regime, respectively. (Modified from [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF] A cutoff frequency of 2 Hz is used to filter the strain rate. Uniform quasi-harmonic oscillations of fiber strain occur around a seafloor valley. (e) Spectrogram of strain rate at the center of the vibrating section featuring a time-dependent characteristic frequency, varying from 0.1 to 0.4 Hz, and the second-order pressure peak caused by sea surface waves near 0.5 Hz [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF]. Higher harmonic frequencies of VIV are excited during two periods in July 16th and 17th, accompanied by large strain amplitudes. (b, d and f) Same as a, c and e, but for a cable section laid across a change of seafloor slope (thick blue lines in b), in Segment 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.6

Evidence of Vortex-Induced Vibrations (VIV) on a suspended underwater cable. Maximum absolute value of the fiber strain rate at the center of segment 3, during 14.5 days, over two-minutes-long sliding windows, plotted as a function of the dominant frequency of the fiber oscillations (density of points). Each blue box represents the median fiber strain (red), its 25 th and 75 th percentiles (bottom and top edges) by frequency, respectively. The whiskers extend to the most extreme data points that are not considered outliers (dashed black lines). The amplitude increases exponentially up to a frequency close to 0.35 Hz, then more steeply as the frequency approaches 0.40 Hz. Considering that VIV frequencies are linearly related to current speeds through the Strouhal relation (blue horizontal scale), this behavior is consistent with that observed in controlled VIV experiments (triangles: experimental data of [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF], rescaled in amplitude and frequency to match the peak of the DAS data).

A harmonic excited during the lock-in regime of VIV is seen around 0.79 Hz.

Box-and-whiskers are not represented for the low-amplitude cluster at 0.45-0.50 Hz, which is associated with the second-order pressure peak caused by sea surface waves (the persistent peak in (a) Ocean current speed recorded by MII current meter between 11-July-2019 00:00:00 UTC and 31-July-2019 00:00:00 UTC (gray circles), its median over 2-hours-long sliding windows (black curve), current speed derived from Strouhal frequencies sensed by DAS in a hanging section between km 37.06 and 37.18 (cyan circles) and its median over 2-hours-long sliding windows (blue line). Horizontal segments of the curves correspond to data gaps. (b) Power Spectral Density of raw MII (black) and DAS (blue) oceanic current speeds from 19-July-2019 22:09:04 to 29-July-2019 06:14:45. A 17-hours peak is observed in both spectra. The energy power of the DAS spectrum (P (f )) decays with increasing frequency from a period T < 17 hours to T = 4 hours following P (f ) ≈ 1/f p , with p = 2.5. For reference, the red lines show the spectral decay slope for two values of the decay exponent "p". . . . . . . . . . . . . . 64

4.8 Impact of the ocean dynamics on current speeds measured by DAS. (a) Low-pass filtered ocean current speeds: recorded by the current meter (black) and DAS-derived from the same cable section as in Fig. 4.7 (blue), from July 11th to July 31st, 2019. We low-pass filtered both time series with a cutoff period of 10 h. (b) Expected time-shift between ocean current speeds at the MII current meter location and along the hanging cable section (red squares), derived from MII current meter data. The red line is the median expected timeshift averaged over a 2-hours sliding window. Circles: time-shift calculated by cross-correlation between MII current meter and DAS time series over a 50hours sliding window, only shown for windows without data gaps. Coherence is shown in color scale. Ocean current direction recorded by the current meter (ϕ current , green squares). The green line is the median-ϕ current averaged over 2-hours-long sliding windows. 5.17 Normal modes of Low-Frequency (LF) oscillations compared to longitudinal strain predicted by the beam theory. (red and cyan) Dominant normal modes of LF oscillations recorded by DAS along the NESTOR and HCMR cable, respectively. (black) Longitudinal strain (ε(x)) of a long and slender beam predicted by Timoshenko's beam theory as a function of the beam's deflection (y(x)) and bending (y ′′ (x)), assuming that fibres have mode-shapes given by a sine function: y(x) = sin(πx/L). Amplitudes in the vertical and horizontal axis are normalized by the maximum strain rate and the cable span length (L), respectively. The relation ε(x) = y ′′ (x)y(x) explains well the zero strain at both ends of the dominant normal modes, and the absence of strain nodes within the vibrating span. However, it predicts a maximum of strain at the midspan, which is different from the quasi-uniform strain of the observed dominant normal modes.

General Introduction

"Until recent years much more was known about the surface of the moon than about the vast areas that lie beneath three-fourths of the surface of our own planet", stated the sedimentologist Francis Parker Shepard in 1948. Similarly, the oceanographer Paul Snelgrove claimed during his 2011's TED talk (go to TED talk) "We know more about the surface of the Moon and about Mars than we do about [the deep sea floor] ...". This last statement, although astonishing in our days, was delivered by the head scientist of the Census of Marine Life project: a 10-year work that invested US$ 650 million and 540 expeditions to assess the diversity, distribution, and abundance of marine life. It is then worth asking: How can we know so much less about something we have so much closer? Especially, after decades of research and technological progress.

The key to answer this question relies on a simple dogma in science: observations. Scientists have collected either more data or better data on the Moon than in the Earth's oceans, as suggested by the US$ 280 billion spent only by the Apollo Program between 1963 and 1972 to recover 400 kg of lunar samples1 .

Oceans represent around two thirds of the total area of our planet's surface, as depicted in Figure 1.1. They cover approximately 3.61 × 10 8 km 2 [START_REF] Ye | Submarine Optical Cable Engineering[END_REF], one order of magnitude larger than the surface area of the Moon. Moreover, the average depth of the ocean being over 4000 m (Figure 1.1), its vast territory is extremely difficult to access. Besides, oceans block the propagation of most electromagnetic waves, which prevents from using instrumentation relying on electromagnetism to communicate their data wirelessly. It should not be surprising then that most of the ocean -particularly its deepest parts -lacks still of instrumentation, resulting in a barely explored environment despite its crucial role in climate change [START_REF] Galland | The ocean and climate change policy[END_REF]. Over the last decades, physical oceanography has relied on major technological advances to improve instrumentation and data coverage. Prior to 1980, the progress in electronics allowed for low power circuitry and high energy density batteries, which made possible several-years worth of oceanographic campaigns [START_REF] Eriksen | Instrumentation for physical oceanography: the last two decades and beyond[END_REF]. According to [START_REF] Baker | Ocean instruments and experiment design[END_REF], the first era of modern instrumentation came in the early 1980's with the deployment of deep-sea moorings and neutrally buoyant floats, thanks to the development of more sophisticated navigation systems. Another big step was made by satellite-based measurement systems, which provide regional and global views of the spatial structure of the ocean since SEASAT, the first satellite for remote sensing of Earth's oceans, was put in orbit in 1978 [START_REF] Eriksen | Instrumentation for physical oceanography: the last two decades and beyond[END_REF]. Unfortunately, anchoredbased systems, like moorings and bottom mounted instruments, offer "local" observations at the deployment location which are hardly representative of entire ocean basins [START_REF] Eriksen | Instrumentation for physical oceanography: the last two decades and beyond[END_REF]. Although satellite-based measurement systems provide a good spatial coverage, they have three main weaknesses: they are extremely expensive to develop, limited to observing the sea surface, and managed by space agencies rather than oceanographers [START_REF] Eriksen | Instrumentation for physical oceanography: the last two decades and beyond[END_REF].

Distributed Acoustic Sensing (DAS) is a novel photonic technology that transforms seafloor fiber optic cables into dense arrays of sensors. DAS exploits the interaction of light prop-agating along telecom cables, with the defects along the fiber generated during the manufacturing of its silica core [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. This groundbreaking sensing method provides [START_REF] Zhan | Distributed acoustic sensing turns fiber-optic cables into sensitive seismic antennas[END_REF]. Source: Web of Science Clarivate, Dec. 2022) recordings of longitudinal fiber strain each few meters along fiber cables spanning tens to hundreds of kilometers [START_REF] Zhan | Distributed acoustic sensing turns fiber-optic cables into sensitive seismic antennas[END_REF]. The adoption of DAS among seismologists is expanding dramatically thanks to its proven capabilities of seismic wave detection, both on-land [START_REF] Lindsey | Fiber-optic network observations of earthquake wavefields[END_REF][START_REF] Jousset | Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features[END_REF][START_REF] Li | Rapid response to the 2019 ridgecrest earthquake with distributed acoustic sensing[END_REF] and offshore [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF][START_REF] Williams | Distributed sensing of microseisms and teleseisms with submarine dark fibers[END_REF][START_REF] Lior | On the Detection Capabilities of Underwater Distributed Acoustic Sensing[END_REF]. Research based on DAS data in Earth Sciences is increasing rapidly (Figure 1.2) and proving that DAS is useful in a variety of applications in both on-land and submarine environments.

The network of submarine fiber cables currently traversing the oceans may be exploited with DAS to observe the oceans with unparalleled spatial coverage. Since high-purity silica fibers were invented in 1970 by Corning Glass Works [START_REF] Murata | Handbook of optical fibers and cables[END_REF], the deployment of underwater fiber optic cables has rapidly increased due to the continuous growing demand of telecommunications. Eventually, that complex system of seafloor fibers led to a spider web of cables crisscrossing almost every ocean on Earth (Figures 1.3). This network, in principle, offers today a potential array of DAS-based sensors around the world. This opens the way to broaden the spatial coverage of physical observations of the ocean to a level unreachable by any other technology. Recent studies have already suggested oceanography applications of DAS along seafloor fiber optic cables. They range from the detection of post-low-tide bores and storm-induced sediment transport [START_REF] Lindsey | Illuminating seafloor faults and ocean dynamics with dark fiber distributed acoustic sensing[END_REF] to the measurement of ocean current velocities [START_REF] Williams | Surface gravity wave interferometry and ocean current monitoring with ocean-bottom das[END_REF]. Moreover, [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF] have reported the detection by DAS of ocean surface gravity waves in coastal environments, while [START_REF] Guerin | Quantifying microseismic noise generation from coastal reflection of gravity waves recorded by seafloor das[END_REF] Figure 1.3 -Worldwide network of submarine fiber optic cables. Active and planned underwater fiber cables traversing the ocean (orange lines) are depicted together with their landing points (white dots). Landing points in Greenland (1), South-East of Brazil (2), and North of Mozambique (3) are highlighted. Data downloaded from www.submarinecablemap.com were used to generate the figure .  proposed that ocean-solid Earth interactions, such as the reflection of gravity waves and coastal microseismic sources, can be monitored through DAS data.

Despite fast growing interest on DAS applications in oceanography and geophysics, one crucial aspect that remains to be assessed is the impact of the mechanical coupling between the cable and the seafloor on the signals recorded by DAS along underwater fibers. Submarine fiber cables are expected to feature heterogeneous mechanical coupling to the seabed [START_REF] Worzyk | Submarine power cables: design, installation, repair, environmental aspects[END_REF]. Indeed, to decrease deployment costs, seafloor fiber cables are typically buried only along the first kilometers of the cable path close to the shore. Therefore, most of the cable is commonly exposed to the ocean dynamics. The aim of this PhD thesis is to analyze DAS recordings collected along three seafloor fiber optic cables located in the Mediterranean Sea, to answer the following questions: Can we quantify the impact of the mechanical cable/seafloor coupling on DAS-recordings? Do seabed features affect DAS recordings? How can we harness the answers of these questions for DAS applications in oceanography and geophysics?

Organization of the Manuscript

The content of this manuscript is divided into two main parts:

-Part One, or state-of-the-art, offers a wide vision of the elements that can have an impact on DAS measurements. It is composed of Chapters 2 and 3. The concept of "Distributed Optical Sensing" is discussed in Chapter 2, together with the physical principles of DAS. This dissertation ends with a section presenting the general conclusions obtained from this PhD project. Future lines of research, that can be explored based on the results presented in Chapters 4 and 5, are also suggested as perspectives of this work.

Chapter 2

Principles of DAS

Chapter 2 introduces a current cutting edge approach for sensing in geophysics: Distributed Acoustic Sensing (DAS). The first half of the chapter explains how a DAS system operates, its physical principle and the main parameters involved in a DAS acquisition. The second half of the chapter describes an approach typically used to improve the quality of DAS signals, and compares the performance of DAS to that of other optical-based sensing techniques available in the market. Chapter 2 was conceived to reach two goals: first, to introduce the basics to someone new to DAS data; and second, to describe in a comprehensible way for a geophysicist the dense and vast domain of optical sensing, while focusing on DAS. The backbone of this PhD thesis is the technique called Distributed Acoustic Sensing (DAS). It is one of the several ways to perform Distributed Sensing, i.e. to measure a physical quantity simultaneously at multiple points of an optical fiber, yielding a large array of discrete sensors positioned regularly along the fiber [START_REF] Glisic | Fiber optic sensors for subsea structural health monitoring[END_REF]. Distributed Sensing relies on an optical phenomenon known as scattering.

Optical Scattering

When light travels through matter (solid, liquid or gas), various scattering mechanisms can occur along its path [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF], as shown in Figure 2.1. The one exploited by DAS is called Rayleigh Scattering, and arises in optics when a source of light interacts with an inhomogeneous medium that contains spatial variations of its refractive index of length scales much shorter Stokes and Anti-Stokes light is generated when the scattered light is emitted at lower or higher frequency than the incident light, respectively (Modified from [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF] than the wavelengths of the light source. In optical fibers, such heterogeneities result from the manufacturing of the glass that is used to fabricate the fiber (more about this in Chapter 3). During the assembling process, the fiber is drawn and its material is softened at a very high temperature, which produces fluctuations in the density of the material over distances of the order of 100 nm [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. These density variations are fixed in the fiber, forming a threedimensional roughness of the refractive index that acts as a collection of scatterers when light propagates through it.

In Rayleigh scattering the energy of the scattered photons is the same as that of the incident ones. This is known as elastic scattering -similar to the elastic collisions between solidsand guarantees that the frequency of both scattered and incident photons is identical [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. To illustrate the phenomenon, consider a coherent laser with a wavelength (λ) of 1550 nm that propagates along a fiber core protected by claddings, as depicted in Figure 2.2. As Figure 2.2 -Representation of Rayleigh scattering in fiber optic cables. A coherent laser (input light) is injected into a fiber core protected by claddings. As the laser interacts with a density heterogeneity of the cable (black circle), backscattered and reflected light is generated and propagates back to the interrogator and forward along the fiber, respectively. (taken from [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF] the laser travels along the cable, it is scattered by density anomalies in the fiber core having length scales of the order of 100 nm. Due to the total internal reflection at the core-cladding interface (discussed in Chapter 3), the light generated after the scattering can travel following just two directions: forward down the fiber or backward toward the light source [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. The forward Rayleigh scattered light continues its journey along with the incident light, while the Rayleigh backscattered light returns to the interrogator unit, providing the raw data for the instrumental technique used for DAS: the Optical Time-Domain Reflectometry (more details in the next section).

Two other forms of optical scattering used for Distribued Sensing are Brillouin and Raman scattering, as depicted in Fig. 2.1. According to [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF], the former can be equivalently considered as the scattering of light from acoustic phonons. In silica optical fibers, the inelastic interaction between photons and phonons leads to a frequency shift of the (Brillouin) scattered light, that depends on the velocity of the sound wave [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. Brillouin scattering due to variations of the refractive index along fibers, typically occurs in the hypersonic frequency range (10-30 GHz) [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Raman scattering is also an inelastic scattering phenomenon, and is generated when pumped photons excite electronic vibrational states of an atom or molecule, leading to the re-emission of scattered photons at a different frequency [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. Molecular vibrations producing Raman scattering occur at very high frequency (∼ 10 THz) [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. In both Brillouin and Raman scattering, energy is exchanged between the incident wave and the material, which causes a frequency shift. Both Brillouin and Raman scattering are utilized for distributed optical sensing but tend to have a more limited range of applications than DAS: their back-scattered signal is usually weaker and less sensitive to perturbations. Applications of these two types of inelastic scattering for distributed sensing, their pros and cons, will be described in section 2.4.3.

Optical Time-Domain Reflectometry

Optical Time-Domain Reflectometry (OTDR) is a technique initially proposed in the late 1970s to monitor the operational health of optical transmission lines [START_REF] Dakin | Distributed optical fiber sensors[END_REF]. By analizing the amplitude of the Rayleigh backscattered signal of a high-power light pulse propagating along the fiber, OTDR detects attenuating/reflective faults or imperfections in the cable [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF], as illustrated in Figure 2.3. Nowadays, OTDR has been extended to a number of Figure 2.3 -General sketch of an OTDR system. A pulsed laser is injected into the cable by the interrogator unit (Receiver), which also detects the Rayleigh backscattered signal (curved arrows). Imperfections in the cable, at locations indicated by the yellow and red boxes, decrease the power of the reflected light. (Modified from [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF].) applications ranging from the location of breaks or high point-losses in the fiber to the identification of mismatches in the properties of fibers at joints [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF], axial variation of diameter [START_REF] Conduit | High-resolution measurement of diameter variations in optical fibres by the backscatter method[END_REF][START_REF] Eriksrud | Application of the backscattering technique to the determination of parameter fluctuations in multimode optical fibers[END_REF], numerical aperture [START_REF] Eriksrud | Application of the backscattering technique to the determination of parameter fluctuations in multimode optical fibers[END_REF], chromatic dispersion [START_REF] Murdoch | Distributed measurement of the chromatic dispersion of an optical fiber using a wavelength-tunable otdr[END_REF] or impurity distribution of the cable [START_REF] Conduit | Spectral-and length-dependent losses in optical fibres investigated by a two-channel backscatter technique[END_REF].

A typical OTDR sensor launches a series of short optical pulses (probe pulses) into a fiber, and averages the changes in time of the probe intensity over multiple probe pulses [START_REF] Dakin | Distributed optical fiber sensors[END_REF][START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. It is necessary to separate the forward probe light from the backscattered light, which is accomplished internally by recent interrogator units [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. The recorded data is usually represented on a plot of optical power as a function of distance along the fiber relative to the location of the OTDR sensor, as shown in Figure 2.3. Fiber locations featuring sharp transitions of the refractive index, such as fiber breaks or connectors, decrease sharply the reflected power. Such sudden fluctuations of the optical power are visible for a data interpreter evaluating the integrity of the fiber.

The sensitivity of an OTDR system is a function of the injected pulse width: wider pulse widths provide better sensitivity [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. The spatial resolution (δx) of an OTDR sensor results from the convolution of the impulse responses of the probe pulse, the receiver and acquisition devices, and the fiber that is interrogated. As a first approximation, δx can be modelled considering the group velocity of the probe pulse (V g ), the duration of the impulse response of the pulse (τ p ), the receiver (τ rx ) and the fiber (τ f ), by [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]:

δx = 1.087 • V g 2 • τ 2 p + τ 2 rx + τ 2 f (2.1)
OTDR for telecommunication network troubleshooting typically uses a pulse width of 10 ns, corresponding to 1-m of spatial resolution, and achieves a high dynamic range [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF].

Phase-sensitive Optical Time-Domain Reflectometry

Rayleigh backscattering has been discussed above for a generic source of light, that is, incoherent light containing waves that do not oscillate at the same frequency. In this general framework, scattered light has the same phase as the incident photons. Now, when a coherent source is used, i.e. a beam of photons propagating at the same frequency, the phase of the incident light is consistent within a resolution cell (i.e. within the footprint of the incident light pulse), and so too are the phases of the scattered light [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. The scattered light is the sum of several scattered electric fields that have a stable, although random, phase relationship [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. The phase-sensitive Optical Time-Domain Reflectometry, also referred to as Φ-OTDR ("phase-OTDR"), is similar to traditional OTDR but uses a narrow linewidth laser with a stable frequency (coherent light) as a source [START_REF] Martins | Phase-sensitive optical time domain reflectometer assisted by first-order raman amplification for distributed vibration sensing over> 100 km[END_REF][START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF].

A Φ-OTDR system exploits the temporal changes in the relative phases between the multiple coherent back-scattered light pulses generated by different scattering centers within the incident pulse width, which are sensitive to strain and temperature disturbances [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. The detected signal is proportional to the backscattered power (intensity or amplitude) returned from each point along the fiber, which varies at the disturbance location [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF][START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. The disturbance location and amplitude can be inferred by comparing undisturbed and disturbed Φ-OTDR traces [START_REF] Zinsou | Recent progress in the performance enhancement of phase-sensitive otdr vibration sensing systems[END_REF][START_REF] Rao | Recent advances in phase-sensitive optical time domain reflectometry (ϕ-otdr)[END_REF].

Distributed Optical Fiber Sensors based on Φ-OTDR, such as fiber cables exploiting DAS, measure the phase difference (∆Φ) of the backscattered light between two points, separated by a distance known as the gauge length [START_REF] Karrenbach | Fiber-optic distributed acoustic sensing of microseismicity, strain and temperature during hydraulic fracturing[END_REF]. The optical phase change ∆Φ is proportional to the elongation of the fiber (∆L) over the gauge length (L). It is related to the strain in the direction of the fiber axis (ε f iber = ∆L/L), the refractive index of the fiber (n c ) and the wavelength of the backscattered light (λ l ) through the following equation [START_REF] Karrenbach | Fiber-optic distributed acoustic sensing of microseismicity, strain and temperature during hydraulic fracturing[END_REF][START_REF] Bakhtiari Gorajoobi | Long range raman-amplified distributed acoustic sensor based on spontaneous brillouin scattering for large strain sensing[END_REF]:

∆Φ = 0.78 × 4πn c λ l ∆L = 0.78 × 4πn c λ l Lε f iber (2.2)
Through equation 2.2, recordings of fluctuations in the phase of the backscattered light can readily be converted into strain in the direction of the fiber [START_REF] Karrenbach | Fiber-optic distributed acoustic sensing of microseismicity, strain and temperature during hydraulic fracturing[END_REF].

Φ-OTDR traces will also be sensitive to ongoing variations of temperature (∆T ), which manifest as a local temporal delay affecting the recordings. The temporal delay (∆t) is related to the pulse central frequency (ν 0 ), the pulse width (τ p ) and the maximal excursion of the instantaneous frequency (δν p ), by (R. [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF]:

1 ν 0 δν p τ p ∆t ≈ 6.92 × 10 -6 • ∆T (2.3)
Φ-OTDR is appropriate for vibration detection [START_REF] Fu | Ultra-long-distance hybrid botda/ϕ-otdr[END_REF][START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. In vibration sensing, Φ-OTDR traces display, in the same pulse, strain perturbations synchronized with the vibration frequency between two neighboring fiber segments [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]. Nowadays, several applications ranging from the monitoring of long-distance pipelines to seismic monitoring along wellbores exploit the Φ-OTDR technique through DAS [START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF][START_REF] Dean | The effect of gauge length on axially incident p-waves measured using fibre optic distributed vibration sensing[END_REF]. DAS is a specific application of Φ-OTDR along fiber optic cables.

Parameters involved in Φ-OTDR

In a distributed sensor relying on Φ-OTDR, every point of the fiber contributes to the final measurement via a complex interplay between optical and instrumental parameters. A detailed description of all the parameters involved in DAS is given by [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Here I provide a brief description of the most crucial ones:

Principles of DAS -The measurement resolution, also known as measurand resolution, is the capacity of the instrument to discriminate small phase changes. It is a function of the distance along the cable length, since light is increasingly attenuated as it propagates away from its source (Figure 2.3).

-The range is the maximum length of fiber that can be probed.

-The pulse repetition rate is the inverse of the time between consecutive laser pulses injected into the fiber. To avoid overlap between the back-scattered light from consecutive pulses, the time between pulses must be longer than time of propagation forth and back along the entire cable length.

-The optical resolution is the minimum distance along which two punctual strain perturbations applied to the fiber can be independently measured (R. [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF]. It can be calculated through equation 2.1.

-The sampling resolution is the distance between two sensing locations along the fiber.

It is proportional to speed of light propagation on the fiber and to the time step at which the light signals are sampled. Typical values of the sampling resolution range from a few to tens of meters.

-The gauge length. Φ-OTDR extracts the average phase of the reflected signal occupied by a pulse, since the density of the scatterers in a fiber is too high to be individually discriminated [START_REF] Hartog | Vertical seismic optical profiling on wireline logging cable[END_REF]. To avoid the highly nonlinear transfer function of the change in phase of the backscattered signal, the phase difference between two points along the cable length is calculated [START_REF] Hartog | Vertical seismic optical profiling on wireline logging cable[END_REF], as briefly mentioned in 2.2.1. The distance separating these two points is known as the gauge length, and it is one of the most important parameters during a DAS acquisition. A small gauge length generates recordings with a low signal-to-noise ratio (SNR), while a large gauge length improves the SNR but reduces the measurement resolution [START_REF] Dean | The effect of gauge length on axially incident p-waves measured using fibre optic distributed vibration sensing[END_REF]. Common values of gauge length range from 7 to 60 m [START_REF] Hartog | Vertical seismic optical profiling on wireline logging cable[END_REF][START_REF] Mateeva | Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling[END_REF][START_REF] Dean | The effect of gauge length on axially incident p-waves measured using fibre optic distributed vibration sensing[END_REF]. The gauge length (GL) is often expressed as a multiple of the sampling resolution (SR): GL = N • SR, usually with N > 4.

Quality of the signal in Φ-OTDR systems

A Φ-OTDR system relies on back-scattered light, whose amplitude is very weak. Moreover, the fiber is sensitive to several processes in the surroundings of the cable [START_REF] Zhu | Enhancement of snr and spatial resolution in φ-otdr system by using two-dimensional edge detection method[END_REF]. Therefore, the signal-to-noise ratio (SNR) in Φ-OTDR can be low, and the background noise can fluctuate due to many uncertain reasons such as laser frequency drift and/or environmental temperature fluctuations [START_REF] Izumita | Fading noise reduction in coherent otdr[END_REF][START_REF] Zhu | Enhancement of snr and spatial resolution in φ-otdr system by using two-dimensional edge detection method[END_REF]. The issue of low SNR in Φ-OTDR systems is addressed by both data processing and acquisition tuning.

During the acquisition, Φ-OTDR systems average measurements over many consecutive laser pulses: they acquire multiple backscatter waveforms and sum them up point-by-point. The SNR improves proportionally to the square root of the number of waveforms averaged [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. SNR can also be improved by increasing the power of the laser source. However, this is limited by source availability, nonlinear optical effects, and security considerations including eye safety and risk of explosion [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. For long-span cables, SNR can also be improved by using wider pulse durations. This increases the probe energy and reduces the bandwidth of the acquisition, which decreases the noise in the Φ-OTDR system [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. A more recent approach to enhance the quality of Φ-OTDR signals is optical amplification. Several techniques are available for that purpose. Raman Amplification is one technique described in the next section, and employed to collect one of the DAS datasets used in this work.

In terms of data processing, different techniques have been proposed to reduce random noise and highlight the difference among Φ-OTDR traces. For instance, [START_REF] Lu | Distributed vibration sensor based on coherent detection of phase-otdr[END_REF] obtained an improvement of 6.5 dB in their Φ-OTDR system by applying moving averaging and moving differential methods with a spatial resolution of 5 m, and [START_REF] Qin | High sensitivity distributed vibration sensor based on polarization-maintaining configurations of phase-otdr[END_REF] improved the performance of their Φ-OTDR system by 7.6 dB with 1-m spatial resolution by using polarization-maintaining configurations of the fiber for higher frequency response. More advanced approaches have been proposed to enhance the SNR or the spatial resolution of Φ-OTDR systems, such as the wavelet signal processing method introduced by Qin et al. ( 2012) and the Two-Dimensional Edge Detection method proposed by [START_REF] Zhu | Enhancement of snr and spatial resolution in φ-otdr system by using two-dimensional edge detection method[END_REF]. The aforementioned references (and references therein) provide a detailed description of data denoising in Φ-OTDR systems.

Raman Amplification: boosting DAS signals

The power of a pulsed laser attenuates with propagation distance along an optical fiber (Figure 2.3), which restricts the range and decreases the SNR of Φ-OTDR. To compensate attenuation losses, the pulse width and/or the pulse power can be increased, as indicated in section 2.2.3. But both approaches have limitations: increasing the pulse width reduces the spatial resolution of the system, while boosting the pulse power can introduce nonlinear impairments such as modulation instability [START_REF] Wilson | Distributed acoustic sensing of long subsea tie-backs[END_REF]. Distributed Raman Amplification, commonly referred to as Raman Amplification, is an alternative technique for optical amplification that distributes a gain profile along the span of the fiber (Figure 2.4) without compromising the spatial resolution or introducing nonlinear optical effects [START_REF] Rodríguez-Barrios | Distributed brillouin fiber sensor assisted by first-order raman amplification[END_REF]. Raman amplification is based on Raman scattering. Like Rayleigh-based Φ-OTDR is used to sense vibrations at acoustic frequencies (Zhu et al., 2013a), Raman and Brillouin scattering can be employed in Φ-OTDR. The former detects temperature variations along optical fibers [START_REF] Dakin | Distributed optical fibre raman temperature sensor using a semiconductor light source and detector[END_REF], while the latter can interrogate very long fibers up to a cm-scale spatial resolution [START_REF] Dominguez-Lopez | Resolving 1 million sensing points in an optimized differential time-domain brillouin sensor[END_REF]. Raman or Brillouin scattering can also be used together with Rayleigh-based Φ-OTDR to amplify both the probe pulse and the backscattered light as they propagate along the fiber [START_REF] Masoudi | Long range distributed optical acoustic sensor based on in-line raman amplification[END_REF][START_REF] Bakhtiari Gorajoobi | Long range raman-amplified distributed acoustic sensor based on spontaneous brillouin scattering for large strain sensing[END_REF].

Although Raman amplification is the core of this section, all its principles operate equivalently for Brillouin amplification. Raman amplification has been employed in optical communication systems for more than two decades for several long-distance applications [START_REF] Aoki | Properties of fiber raman amplifiers and their applicability to digital optical communication systems[END_REF][START_REF] Alahbabi | 150-km-range distributed temperature sensor based on coherent detection of spontaneous brillouin backscatter and in-line raman amplification[END_REF][START_REF] Martins | 300 km-ultralong raman fiber lasers using a distributed mirror for sensing applications[END_REF]. During an experiment of Rayleigh-based Φ-OTDR, such as DAS data acquisitions, Raman amplification is applied by activating an optional module called Raman Pump (Figure 2.5). This device consists of a single (first-order) Raman amplifier, or cascaded (higher order) levels of Raman amplification that are superimposed to reach a desired gain profile along the fiber span [START_REF] Wilson | Distributed acoustic sensing of long subsea tie-backs[END_REF]. The Raman pump can be coupled for boosting the DAS pulse along its propagation direction (copropagating amplification), for amplifying the signal in the direction of the backscattered light (counter-propagating amplification), or both directions (co-and counter-propagating amplification) [START_REF] Wilson | Distributed acoustic sensing of long subsea tie-backs[END_REF]. Although Raman amplification can effectively offset the attenuation losses in the transmission fiber, the DAS interrogator's pulse repetition rate remains limited by the total length of the sensing fiber, which still impacts the SNR of the collected data and the obtained acoustic bandwidth after amplification [START_REF] Wilson | Distributed acoustic sensing of long subsea tie-backs[END_REF].

In terms of technical limitations, the excessive use of high Raman pump powers can lead to degradation or thermal damage of the optical connectors (R. [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF][START_REF] Wilson | Distributed acoustic sensing of long subsea tie-backs[END_REF]. Moreover, a continuous operation of a Raman pump amplifies the probe pulse close to the injection point of the fiber, which can generate probe pulse powers beyond the maximum allowable for linear acquisitions [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. One of the main concerns of using Raman amplification is the noise introduced by the Raman pump to the signal, mainly Relative Intensity Noise (RIN) [START_REF] Bristiel | New model of noise figure and rin transfer in fiber raman amplifiers[END_REF][START_REF] Nuño | Rin transfer in random distributed feedback fiber lasers[END_REF]. Despite its limitations, this technique of optical amplification has proven capability to extend the range beyond 100 km [START_REF] Martins | Distributed vibration sensing over 125 km with enhanced snr using phi-otdr over a urfl cavity[END_REF][START_REF] Pastor-Graells | Chirped-pulse phase-sensitive reflectometer assisted by first-order raman amplification[END_REF], as shown in Figure 2.5.

DAS compared to other optical sensing techniques for offshore research

Sections 2.1, 2.2 and 2.3 presented the basics of Distributed Sensing, with special focus on DAS. I now compare DAS's performance with that of other common optical-based sensing techniques applied to offshore research.

The vast majority of the ocean remains today poorly instrumented, hindering fundamental investigation on a variety of submarine dynamics and oceanography processes. To fill the data gap, geophysical sensing techniques relying on different optical-based methods are emerging with distinct scopes, sensitivity ranges, coverage and spatial resolution [START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF]. DAS has proven its capabilities in physical oceanography [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF][START_REF] Lindsey | Illuminating seafloor faults and ocean dynamics with dark fiber distributed acoustic sensing[END_REF][START_REF] Williams | Surface gravity wave interferometry and ocean current monitoring with ocean-bottom das[END_REF], but is not the only available option to exploit underwater telecommunication cables for that purpose.

In this section, three other photonics-based techniques using seafloor fiber optic cables are briefly described. These techniques have some advantages over DAS but it is important to highlight their limitations which prevent the investigation of submarine processes as presented in Section 4 and 5.

Sensing the State of Polarization of light

Polarization is an intrinsic characteristic of light which describes the oscillation direction of its electric field and highlights its transverse nature [START_REF] Pedrotti | Introduction to optics[END_REF]. Since polarization is uncorrelated with the other properties of the light, it provides an additional information channel for several applications ranging from super-resolution imaging and optical magnetic recording [START_REF] Xie | Harnessing the point-spread function for high-resolution far-field optical microscopy[END_REF][START_REF] Li | Superresolution-focal-volume induced 3.0 tbytes/disk capacity by focusing a radially polarized beam[END_REF][START_REF] Wang | Generation of uniformly oriented in-plane magnetization with near-unity purity in 4π microscopy[END_REF], to enhanced nonlinear effects [START_REF] Li | Three-dimensional modulations on the states of polarization of light fields[END_REF][START_REF] Gong | Optical forces of focused femtosecond laser pulses on nonlinear optical rayleigh particles[END_REF]. In conventional optics, optical components allow to manipulate the State of Polarization (SOP or SoP) when light travels a distance much larger than its wavelength, based on the accumulated phase delay between two orthogonal and polarized electric fields [START_REF] Pedrotti | Introduction to optics[END_REF].

Mechanical perturbations along fibers can be detected through the monitoring of the SOP of an injected light, as depicted in Figure 2.6 [START_REF] Cantono | Subhertz spectral analysis of polarization of light in a transcontinental submarine cable[END_REF][START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF]. While the output SOP of onland fibers can be chaotic and hard to interpret due to substantial temperature variations and/or human-induced vibrations along the cable, the SOP for submarine cables is significantly more stable since extreme temperature fluctuations are not expected in the ocean nor electromagnetic or acoustic perturbations [START_REF] Cantono | Subhertz spectral analysis of polarization of light in a transcontinental submarine cable[END_REF][START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF]. The output of a SOP acquisition is represented by the so-called Stokes parameters S 1 , S 2 and S 3 [START_REF] Ding | Recent advances in polarization-encoded optical metasurfaces[END_REF]. To better discriminate different signal components, spectral analysis is usually performed on Stoke traces [START_REF] Cantono | Subhertz spectral analysis of polarization of light in a transcontinental submarine cable[END_REF][START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF], as shown in Figure 2.7.

Sensing the SOP of light along transoceanic fiber cables has proven capabilities for recording large earthquakes and detecting ocean swells produced by distant storms [START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF]. However, the current state-of-the-art of the method imposes technical limitations. Firstly, the SOP-based sensing integrates the detected perturbations over the entire optical length, which produces a single SOP time series per Stokes parameter for the whole cable [START_REF] Dejdar | Trains detection using state of polarization changes measurement and convolutional neural networks[END_REF][START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF]. This integrated sensing, as opposed to Distributed Sensing, is not favorable for certain applications, such as the picking of seismic waves and the location of seismic sources, especially for large events that have long rupture durations [START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF]. Due to its integrated measure, the spatial resolution of SOP sensing is much coarser than the one delivered by DAS. Moreover, the noise floor of SOP recordings is determined by the background noise integrated over the entire cable length, which prevents from detecting small-sized earthquakes and observing other signals of interest such as tsunami waves [START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF][START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF].

Laser-based Interferometry

Laser interferometry relies on light transmission and interference. During an interferometry experiment, the light coming from a single source is split into two optical fibers: the so-called sensing arm, exposed to the environment to be sensed, and the reference arm [START_REF] Joe | A review on optical fiber sensors for environmental monitoring[END_REF]. The light propagating along the sensing arm is sensitive to environmental perturbations, such as temperature fluctuations, that change the refractive index in the fiber [START_REF] Udd | Fiber optic sensors: an introduction for engineers and scientists[END_REF][START_REF] Eickhoff | Real-time precision refractometry: new approaches[END_REF]. Once the light travelling in the two optical paths reaches the end of the cable, it is recombined [START_REF] Joe | A review on optical fiber sensors for environmental monitoring[END_REF]. The interference signals of the combined light, that result from the phase difference between the transmitted light in the two arms, contain the information of the environmental perturbations affecting the sensing arm [START_REF] Joe | A review on optical fiber sensors for environmental monitoring[END_REF].

Several configurations of sensors can be used for laser interferometry. The Fabry-Perot interferometer (FPI) (Figure 2.8), is one of the most common in physical oceanography and underwater seismology [START_REF] Marra | Ultrastable laser interferometry for earthquake detection with terrestrial and submarine cables[END_REF][START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF]. The FPI in optical fibers consists of two reflection mirrors and an optical cavity formed between them that produces the interference signals by reflecting the light at both end surfaces of the cavity [START_REF] Yoshino | Fiber-optic fabry-perot interferometer and its sensor applications[END_REF][START_REF] Joe | A review on optical fiber sensors for environmental monitoring[END_REF]. As physical characteristics of the environment vary (fluctuations of temperature, pressure, displacement or stress), the length or refractive index of the cavity becomes deflected, which induces a phase shift in the interference signals [START_REF] Islam | Chronology of fabryperot interferometer fiber-optic sensors and their applications: a review[END_REF][START_REF] Joe | A review on optical fiber sensors for environmental monitoring[END_REF]. Changes as small as a few femtoseconds can be measured by FPI sensors [START_REF] Marra | Ultrastable laser interferometry for earthquake detection with terrestrial and submarine cables[END_REF].

Recent studies of laser interferometry on fiber optic cables have reported the detection of seismically-induced signals from a local (M L 3.4, 89 km away from the cable location) and remote (M W 7.5) earthquakes along underwater long-fibers sensed through laser-based interferometry [START_REF] Marra | Ultrastable laser interferometry for earthquake detection with terrestrial and submarine cables[END_REF][START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF]. Storms and tidal currents have also been observed by spectral analysis of the recorded environmental noise, as depicted in Figure 2.9 [START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF]. However, the recorded signal integrates the detected perturbations over the entire optical path, which leads to similar limitations of spatial resolution and SNR as for SOP. [START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF] proposed a new approach by doing interferometry over 46 km-long sections in between repeaters of a 5860 km-long transoceanic optical fiber. However, the SNR decreased due to an accumulated amplified spontaneous emission (ASE) noise generated by repeaters increasingly distant from the transmitting end. While this technique has a much larger range than DAS, its spatial resolution (46 km) is much coarser.

Distributed Strain and Temperature Sensing

Section 2.1 introduced the concept of scattering, and the three types of scattering (Rayleigh, Brillouin and Raman) generated by light propagation in an inhomogeneous medium. As dis- cussed in Section 2.1, Rayleigh scattering is directly related to the laser source wavelength and very sensitive to strain anomalies across the fiber [START_REF] Miah | A review of hybrid fiber-optic distributed simultaneous vibration and temperature sensing technology and its geophysical applications[END_REF]. But Brillouin and Raman scattering have special attributes too. In the Stokes band -a spectral feature generated when light is scattered at a frequency lower than the one of the incident light (Figure 2.1) -Brillouin and Raman scattering are independent of temperature and strain variations. In contrast, in the Anti-Stokes band, Raman scattering is temperature-dependent while Brillouin scattering is both strain-and-temperature-dependent. This band arises when energy is transferred from the medium to the light, leading to scattered photons at a higher frequency than that of the incident light (Figure 2.1) [START_REF] Kimbell | History and analysis of distributed acoustic sensing (DAS) for oilfield applications[END_REF]. The characteristics of Brillouin and Raman scattering make them attractive for strain and temperature sensing across long fibers [START_REF] Hayashi | Brillouin gain spectrum dependence on large strain in perfluorinated graded-index polymer optical fiber[END_REF][START_REF] Mizuno | Potential of brillouin scattering in polymer optical fiber for strain-insensitive high-accuracy temperature sensing[END_REF].

While Brillouin and Raman scattering are both appropriate for temperature sensing, there are at least two main advantages of using the former as a basis for distributed sensing. First, the incident and Brillouin wavelengths experience almost identical attenuation, which allows increasing the spatial range of the measurement by keeping the loss at a minimum. Second, Brillouin signals are one order of magnitude stronger than Raman's and are resilient to wavelength-dependent loss, which guarantees a higher SNR and allows improving the sensor spatial resolution and the sensing range.

Brillouin-based sensing techniques are capable of simultaneous monitoring of temperature and strain. The approach is called Distributed Strain and Temperature Sensing (DSTS), and has been used to monitor large structures such as pipelines, dams and dikes [START_REF] Inaudi | Development of distributed strain and temperature sensing cables[END_REF], and to detect hot-spots in high-power cables [START_REF] Inaudi | Reliability and field testing of distributed strain and temperature sensors[END_REF]. DSTS is affected by cross-sensitivity between strain and temperature measurements, i.e. changes in the Brillouin frequency due to strain and temperature anomalies cannot be distinguished unless an independent measurement of one of these quantities is used. To overcome this limitation, a methodology relying on "loose" and "tight" fibers is commonly exploited. The former are packaged in loose tubes to prevent strain transfer to the fiber, while the latter are coupled to the cable structure to allow the recording of strain [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Unfortunately, the loose-and-tight fiber procedure requires dedicated cables and excludes standard telecom cables. [START_REF] Miah | A review of hybrid fiber-optic distributed simultaneous vibration and temperature sensing technology and its geophysical applications[END_REF] proposed a combination of Rayleigh and Brillouin scattering for DSTS, an optical combo of Φ-OTDR and Brillouin-OTDR (B-OTDR). Using a coherent narrow laser as the source of light, laser pulses of different width and intensity are encoded to generate a pulse-train that is injected into the fiber repeatedly for dynamic vibration (strain) and temperature monitoring. However, combining Φ-OTDR and B-OTDR comes with the cost of dealing with the limitations of both techniques. B-OTDR for distributed temperature sensing requires complex processing at the receiver end [START_REF] Miah | A review of hybrid fiber-optic distributed simultaneous vibration and temperature sensing technology and its geophysical applications[END_REF]. Hence, its spatial resolution depends on the pulse width. In fact, mixing two different pulse patterns (one for Φ-OTDR, the other for B-OTDR) increases the overall pulse width, which coarsens the spatial resolution and decreases the sample repetition rate. Moreover, an extended DSTS campaign over a long fiber may induce spurious nonlinear noise effects leading to both spontaneous Brillouin scattering (SpBS) and stimulated Brillouin scattering (SBS), which reduce SNR.

Peláez Quiñones et al. ( 2022) have shown that the low-frequency signal of seafloor DAS is mainly influenced by temperature varations, effectively transforming optical fibers into dense arrays of temperature anomaly sensors. This approach has significantly higher sensitivity than DSTS (mK instead of K) but is usually limited by the need to update the laser reference. Recent work has shown the possibility to overcome this laser reference problem [START_REF] Vidal-Moreno | Cancellation of reference updateinduced 1/f noise in a chirped-pulse DAS[END_REF].

Advantages and disadvantages of DAS

DAS has several advantages over other types of sensors, namely [START_REF] Sabri | Fiber optic sensors: short review and applications[END_REF]:

-Distributed sensing provides dense spatial sampling, a unique benefit in comparison to conventional single-point sensors and integrated measurements. DAS campaigns deliver datasets with a spatial resolution that ranges from a few to several meters along thousands of meters of fiber optical cables, which generates a density of distributed sensors unreachable by conventional sensor arrays.

-DAS is a non-invasive sensing technique because it relies on passive monitoring and, in many cases, existing telecom cables. When cables have to be specifically deployed, they are usually thin cables with a limited environmental impact.

-The physical principle governing DAS is not affected by high temperatures or pressures or by chemically reactive environments along the cable, which makes this technique ideal for monitoring in harsh and hostile environments such as boreholes or the deep ocean.

-Electrical passiveness and electromagnetic immunity: DAS can be used in volatile environments and is not impacted by radio frequency or electromagnetic interference.

-DAS has the capability to detect strain perturbations with great sensitivity and wide dynamic range. This can be exploited in several applications ranging from the monitoring of objects of great length exposed to continuous stress (pipelines, railways, highways, bridges), to seismic monitoring of boreholes, underwater seismology and physical oceanography (e.g. [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF][START_REF] Gorshkov | Scientific applications of distributed acoustic sensing: State-of-the-art review and perspective[END_REF].

-The longest range currently achieved by a single DAS acquitision system on standard fiber is about 150 kilometers. The range can be extended if bi-directional repeaters can be added along the cable [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF].

-DAS interrogator units are relatively portable, compact and light (the size of a large desktop computer) allowing for rapid deployments.

-Research and Development on DAS moves extremely fast, which helps to overcome current technical limitations, such as sensitivity or sensing range, in few years [START_REF] Dorize | Advanced fiber sensing leveraging coherent systems technology for smart network monitoring[END_REF][START_REF] Vidal-Moreno | Cancellation of reference updateinduced 1/f noise in a chirped-pulse DAS[END_REF]. It is expected that the cost of DAS interrogators will decrease with the progress of telecom components and the increasing competition between DAS manufacturers.

-DAS offers measurements in real time, which allows real-time decision making for several monitoring applications. Since the acquisition is done at the speed of the light, any application on DAS can readily be turned into an operational solution, including earthquake early warning systems [START_REF] Lior | Harnessing distributed acoustic sensing for earthquake early warning: Magnitude estimation and ground motion prediction[END_REF].

However, there are still challenges and weaknesses of DAS that constrain its application:

-Low SNR compared to geophones: DAS data collected on-land are much noisier than geophone data [START_REF] Li | Current and future applications of distributed acoustic sensing as a new reservoir geophysics tool[END_REF]. DAS noise is a mixture of random noise coming from the interrogator unit, the time-variant optical noise that occurs on all receivers and the spike-like noise [START_REF] Bakku | Monitoring hydraulic fracturing using distributed acoustic sensing in a treatment well[END_REF]. The contribution of all the noise sources hinders the detection of low-amplitude signals, especially on microseismic applications [START_REF] Li | Current and future applications of distributed acoustic sensing as a new reservoir geophysics tool[END_REF]. [START_REF] Westbrook | Enhanced optical fiber for distributed acoustic sensing beyond the limits of rayleigh backscattering[END_REF] have proposed the use of engineered fibers called "enhanced fibers" to increase the signal-to-noise ratio of Rayleigh backscattered signals.

However, that would require the deployment of new fiber cables rather than exploiting the existing network of optical fibers.

-Deficient sensitivity to transverse waves: by default, DAS measures the strain along the axis of the fiber but hardly the strain perpendicular to the cable [START_REF] Li | Current and future applications of distributed acoustic sensing as a new reservoir geophysics tool[END_REF]. Thus, DAS measurements are more sensitive to waves deforming the cable longitudinally, which prevents from tracking certain waves depending on their direction of motion and propagation. To reduce the dependence of DAS on incidence angles the fiber can be wound helically around a mandrel, which increases the fiber's broadside sensitivity [START_REF] Wuestefeld | How to twist and turn a fiber: Performance modeling for optimal das acquisitions[END_REF]. This approach, although convenient for more systematic detection of direct waves, does not always allow separating transverse and radial components of a recorded wavefield.

-It is challenging to permanently deploy an interrogator unit under extreme environmental conditions [START_REF] Li | Current and future applications of distributed acoustic sensing as a new reservoir geophysics tool[END_REF]. The quality of recorded signals is usually degraded if the interrogator unit is exposed to high temperatures or continuous sunlight, which can compromise the stability of the laser source.

-The mechanical coupling between the fiber and its solid environment (e.g. the surface where the cable lays on) has a strong impact on the quality of DAS data [START_REF] Lindsey | Illuminating seafloor faults and ocean dynamics with dark fiber distributed acoustic sensing[END_REF][START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF][START_REF] Williams | Distributed sensing of microseisms and teleseisms with submarine dark fibers[END_REF]. This point will be addressed in Sections 4 and 5.

Chapter 3

Technical Aspects of Fiber Optic Cables

Understanding the composition of fiber optic cables, their fabrication and deployment processes, and light propagation along them can be a complex task. This is partly due to the enormous rainfall of technical terminology involved, that gets even more complicated when it comes to seafloor fiber optic cables. Chapter 3 is an effort to summarize all those topics by answering four questions: 1) What are the basic steps to manufacture fiber cables? 2) How does light propagate along fibers? 3) What fiber cables look like? and 4) How are fiber cables deployed on the seafloor? Contents Fiber optic cables have a direct impact on our daily life. Yet, most people take for granted the numerous activities relying on them. The list is vast and includes a large spectrum of dayto-day tasks or hobbies, ranging from watching a match of our favorite sport on streaming, to attending from home a conference hosted in the other corner of the Earth. What do these activities have in common? They need the internet connection that fiber optic cables supply to our homes.

The worldwide array of underwater fiber optic cables (Figure 1.3) delivers international telecommunication services -such as e-mail, phone calls, video content -in the most efficient fashion [START_REF] Cariolle | Telecommunication submarine-cable deployment and the digital divide in sub-saharan africa[END_REF]. These complex spider webs crisscrossing the ocean are, in fact, the connection point to the internet for most countries around the world. But, what are optical cables made of? How do telecom companies deploy fiber cables in the ocean? What prevents underwater fiber cables from being damaged by human activities like fishing? Answers to these and other related questions are found in this chapter and provide a general context and specific information to better apprehend the next chapters.

The art of manufacturing optical fibers

Fiber cables are substantially distinct from other cables transmitting data, such as the copperbased coaxial cable, since they offer higher bandwidth, lower data losses and higher data transmission rates over long distances. But all the advantages offered by fiber optic cables depend on the success of a sophisticated and extremely delicate manufacturing process, that must be performed with accuracy and precision.

The fabrication of fiber optic cables relies on a single chemical compound that assures low optical loss, a mixture of high-silica glasses consisting primarily of fused silica (SiO 2 ). Other materials are commonly added to the silica to finely tune its final refractive index, until reaching the necessary index of refraction to guide the light along the fiber [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. These materials, known as dopants, include germanium dioxide (GeO 2 ) and phosporus pentoxide (P 2 O 5 ) to increase the refractive index, and boron trioxide (B 2 O 3 ) and fluorine (F ) to decrease it [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Tuning the refractive index must be performed in a way that other properties of the silica are not affected. Moreover, the final diameter of the silica core must be monitored with high precision (Al-Azzawi, 2017). Therefore, a method in compliance with both criteria is crucial to manufacture fibers of high quality. The most popular techniques to fabricate fiber optic cables are briefly presented in the next subsection.

Production methods of fiber optic cables

Since the invention of a low-loss fiber in the 1970's by Corning Glass Works, researchers have invested economic and academic resources to develop a fiber manufacturing method that defeats Corning's [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. It has been a long journey, and today two methods are common:

Double Crucible Method

The double crucible method uses two platinum melting pots, one inside the other, to generate a core-cladding fiber. The process is illustrated in Figure 3.1. As described by Al-Azzawi (2017), two molten compounds -core glass and cladding glass -are poured in the inner and the outer crucible, respectively. To guarantee a successful operation, the temperature of the melting pots must remain between 1850 and 2000 • C. The two glass-compounds flow separately and are mixed at the base of the outer crucible, forming a rod tube that is drawn out from the melting pots. The rod tube is composed by a core glass inside of a tube of cladding glass: the preform of the fiber cable. Then, a first quality control is performed to verify the diameter of the fiber and to detect possible heterogeneities generated during the drawing process. The fiber is then covered by a colored jacket, and a second quality control checks its new diameter. The process ends by attaching the fiber termination to a steadily rotating spool. A final quality control tests operational parameters of the fiber, such as attenuation, dispersion and any other requirements specified by the customer.

Chemical Vapor Deposition processes

Chemical vapor deposition (CVD) is a technique originally designed for the manufacturing of semiconductors. It shares most of the fabrication steps described in 3.1.1.1 for the double crucible method [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. CVD synthesizes high-silica glasses directly into the preform, by oxidizing initial halide compounds in a liquid state [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. A halide is a chemical compound including a halogen atom (fluorine (F ), chlorine (Cl), bromine (Br), iodine (I) or astatine (At)) and another element less electronegative than the halogen. CVD relies on thermochemical reactions in the vapor phase that form oxides from a starting mixture of dopants. After evaporation, the resulting oxide is deposited in consecutive layers of high-purity silica. CVD produces extremely pure glasses whose features are under the total control of the manufacturer (Al-Azzawi, 2017). There are several ways to fabricate preforms during the vapor deposition process. The most common methods are presented in Table 3.1.

Fiber drawing

The final optical fiber is obtained by drawing the preform from the furnace, as depicted in Figure 3.1. The drawing is a critical process, since the fiber diameter must be uniform -diameter variations cannot surpass 0.1% -and the mechanical strength of the drawn fiber must allow practical use [START_REF] Al-Azzawi | Advanced Manufacturing for Optical Fibers and Integrated Photonic Devices[END_REF][START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Usually, the fiber is drawn at the higher temperatures of the range indicated in section 3.1.1.1, as close as possible to the melting temperature of silica, approximately 1900 °C [START_REF] Murata | Handbook of optical fibers and cables[END_REF].

Manufacturing defects, such as surface cracks, can be easily generated during drawing since the surface temperature of both the preform and the final fiber are high [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Moreover, external agents (dust, moisture) in contact with the fiber can alter its surface conditions. To avoid contamination caused by environmental agents and manufacturing defects, a plastic layer known as jacket is coated on the surface of the cladding-core fiber immediately after drawing [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. The jacket has important features designed to protect the core and cladding, such as bending ability, abrasion resistance, static fatigue protection, moisture resistance, and capacity to be stripped (Al-Azzawi, 2017). Figure 3.2 displays the typical structure of a fiber optic cable, after the drawing process.

Fiber optic cables can be fabricated in a variety of diameters. Standard dimensions of the core, cladding and jacket of four commonly used fiber optic cables are presented in The initial compound together with a carrier gas (O 2 ) and a fuel gas (H 2 ) are made to blow, which generates a starting rod of silica. Then the initial rod is pulled off, dehydrated and vitrified in a heating furnace to form a preform rod.

No limit size of preforms, fast procedure and all synthetic fibers can be manufactured.

High risk of contamination due to impurities and high risk of structural irregularities at the center of the core.

Vapor-Phase Axial Deposition (VAD)

SiCl 4 or GeCl 4
The initial compound together with O 2 and H 2 are blown in the lower end of a rotating silica boule, which produces a soot rod. The soot rod is pulled up while being rotated, and then dehydrated and consolidated in a furnace to form a preform.

The preform is continuously fabricated in an endless span and low-loss fibers are easily obtained.

Hard to control the flame and difficult to manufacture broad bandwidth fibers. The initial compound and O 2 flow into a rotating silica tube, and are heated with oxyhydrogen flames from the outside. A first oxidizing reaction starts and produces glass soots. After consecutive rounds of heating, a preform is generated in the furnace.

Low risk of contamination due to impurities and easy to control the refractive index of the fiber.

Long fibers cannot be produced, risk of low refractive index at the center of the core and slow process. The source of heat is easily controlled (easier to manage the fiber core profile)

The silica tube must be preheated, long fibers cannot be produced and larger equipment is required. Table 3.1 -Typical methods to fabricate preforms of fiber optic cables through Chemical Vapor Deposition (CVD). The initial com-pound is used in its vapor phase. Information extracted from [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Table 3.2 -Typical diameters of cores, claddings and jackets in fiber optic cables. Values taken from Al-Azzawi (2017).

Types of optical fibers

Fiber optic cables are used for several applications, ranging from telecommunication and data collection systems to scanning and sensing. Despite this large variety of uses, only three types of optical fibers are commonly needed for industrial purposes: single-mode, multimode, and graded-index fiber cables. Their main features are described below:

Single-Mode Step-Index Fiber Cable. This optical fiber, commonly known as single-mode fiber cable, has the smallest core diameter out of the three types which allows transmitting signals for long distances with low loss. The refractive index of their core is slightly larger than that of the cladding [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Single-mode fibers are typically used for communication systems. The number of modes -i.e. the electromagnetic field pattern of the propagating wave -that can travel along single-mode fibers inversely depends on the square of the wavelength of the optical source. Fewer modes will propagate across the fiber with increasing wavelengths, until reaching a limit value for transmitting a unique mode (Al-Azzawi, 2017), as depicted in Figure 3.3(a). Transmission with single-mode fibers usually starts with wavelength values close to the core diameter. The bandwidth of single-mode fibers is typically larger than 10 GHz/km [START_REF] Murata | Handbook of optical fibers and cables[END_REF].

Multimode

Step-Index Fiber Cable. This fiber type is usually referred to as multimode fiber cable, since the light travelling across the fiber reflects at different angles generating distinct propagation modes [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. A schematic view of a multimode fiber is depicted in Figure 3.3(b). The composition of multimode fiber cables can vary: a glass core and a glass cladding, a glass core and a plastic cladding, or a plastic core and a plastic cladding [START_REF] Al-Azzawi | Advanced Manufacturing for Optical Fibers and Integrated Photonic Devices[END_REF]. In this type of fiber, the refractive index of the core is constant [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Despite multimode fibers have the longest range, their optical loss is higher than that of single-mode fibers. Multimode fiber cables are also affected by modal dispersion due to the spreading of light rays in different paths (Al-Azzawi, 2017), as shown in Figure 3.3(b). One disadvantage of multimode fibers is that the modes propagate at different group velocities along the core [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Therefore, light rays will reach the termination point of the fiber at several arrival times, which has an impact on the information-carrying capacity of the fiber [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. The bandwidth of multimode fibers is typically around 50 MHz/km [START_REF] Murata | Handbook of optical fibers and cables[END_REF].

Multimode Graded-Index Fiber Cable. Also known as graded-index fiber cable (GRIN), this fiber type has similar diameters than multimode fiber cables. A remarkable feature of GRIN fibers is their core: it is composed of concentric layers of silica with progressively decreasing refraction index, from the center of the core to the core-cladding interface [START_REF] Al-Azzawi | Advanced Manufacturing for Optical Fibers and Integrated Photonic Devices[END_REF][START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Hence, the light is continuously reflected in a pseudo-sinusoidal pattern from each layer of the fiber core, which produces propagation modes travelling along quasi-parabolic light rays [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Figure 3.3(c) displays light rays travelling across a GRIN fiber cable. Light rays propagating close to the fiber center travel with slower velocities than those propagating near the outside of the core (Al-Azzawi, 2017). Subsequently, all rays tend to reach the termination point of the fiber at the same time. GRIN fiber cables are popularly used to reduce the modal dispersion of optical fibers. The bandwidth of GRIN fibers is typically between 0.5 and 3 GHz/km [START_REF] Murata | Handbook of optical fibers and cables[END_REF].

Characteristics of light transmission in optical fibers

Propagation of light along fiber cables

Ideally, light travels following a straight line in an homogeneous medium [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. However, the propagation of light in fibers is introduced in section 3.1.3 as the spreading of rays following several paths. Light rays are generated across a fiber due to the difference in the refractive index (n) between its core and cladding [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. The core has a refractive index higher than that of the cladding, which traps the input light within a defined cone of acceptance at the fiber input [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. As a result, light propagates in fibers as guided waves.

To understand the propagation of light in optical fibers as guided waves, the Snell-Descartes law of refraction of light can be used. Consider light injected in a fiber's core of refractive index n 1 which is surrounded by a cladding of refractive index n 2 such as n 1 > n 2 , as depicted in so-called angle of incidence), and is refracted by an angle β from the normal (i.e. angle of refraction), following the Snell-Descartes relation [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]:

n 1 sin (θ) = n 2 sin (β) (3.1)
Since n 1 > n 2 then necessarily β > θ [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF], as shown in Figure 3.4(a). Light arriving at the core-cladding interface at larger θ will be naturally refracted at larger β (Figure 3.4(b)). At a particular angle θ c = sin -1 (n 2 /n 1 ), known as the critical angle of incidence, the refracted light travels parallel to the core-cladding interface, i.e. β = π/2 (Figure 3.4(c)) [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF][START_REF] Al-Azzawi | Advanced Manufacturing for Optical Fibers and Integrated Photonic Devices[END_REF]. Beyond θ c , all the incident light at the core-cladding interface is reflected back into the fiber's core (Figure 3.4(d)), a phenomenon called total internal reflection [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF][START_REF] Al-Azzawi | Advanced Manufacturing for Optical Fibers and Integrated Photonic Devices[END_REF]. Thus, light propagating at angles lower than θ f = π/2 -θ c relative to the fiber axis will be guided by the refractive index contrast between the core and the cladding [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Since the angles of incidence and refraction are the same, the light will continuously bounce along the span of the fiber cable, as represented in Figure 3.4(e).

According to Al-Azzawi (2017), the propagation of light in optical fibers is governed by technical parameters that can be controlled by manufacturers/operators, such as:

-The wavelength of the optical source.

-The angle of incidence of the optical source at the input of the fiber.

-The indices of refraction, size and design of the core and cladding.

-The total span of the cable.

-The bending radius of the cable.

-The transmission modes.

-The temperature, environmental conditions, strength and flexibility of the fiber.

Mechanisms of optical loss in fiber cables

Among all the properties making fiber optic cables an attractive medium for data transmission, manufacturers and operators highlight one: the low optical loss of silica fibers. According to [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF], cutting edge optical fibers lose only 20% of the injected light after transmission through 5 km. Optical loss is an important phenomenon that deserves attention, especially during the design of fiber optic cables. Two main mechanisms of optical loss, attenuation and dispersion [START_REF] Ye | Submarine Optical Cable Engineering[END_REF], are described below.

Attenuation

As light of input power P in propagates along a fiber optic cable, the output signal power P out decays exponentially with propagation distance L [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF][START_REF] Ye | Submarine Optical Cable Engineering[END_REF]:

P out = P in e -αL (3.2)
The parameter α, known as attenuation, determines the spacing between repeaters in telecommunication cables. Repeaters are devices that increase the reach of an optical source by (1) reducing its inherent optical loss due to attenuation, and by (2) rectifying distorted signals (decreasing dispersion). There are mainly three processes that generate attenuation of optical signals [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]:

1. Absorption loss: it involves optical loss through the absorption of light energy, as the optical source propagates along the fiber [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. Absorption loss is usually a function of the wavelength at which the light travels [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. In high-purity silica fibers, the wavelength range for low-loss transmission lies between the ultraviolet and infrared absorption [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Figure 3.5 displays the wavelength range of low-loss transmission for a typical fiber. To guarantee optimal values of absorption loss in fiber cables (around 0.2 dB/km), the wavelength of optical sources are commonly selected around 1.5 µm. Shorter wavelengths are strongly absorbed by SiOH bonds that are generated by the diffusion of hydrogen into the glass (Fiber Loss at 1.39 µm in Figure 3.5), while larger wavelengths enter into the zone of infrared absorption [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Additional absorption due to the SiOH impurities can be generated, with less intensity, around 0.95 and 1.24 µm, as depicted in Figure 3.5.

2. Scattering loss: as discussed in section 2.2, scattering occurs when light travels through an inhomogeneous medium. In fibers, the heterogeneities arise from fluctuations in the density of the glass that are generated during the fabrication process [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. There are mainly four types of scattering loss for optical fibers: Mie, Brillouin, Raman and Rayleigh scattering [START_REF] Murata | Handbook of optical fibers and cables[END_REF][START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Optical loss due to the first three types of scattering is commonly neglected, since it is approximately 1 % of that generated by Rayleigh scattering [START_REF] Murata | Handbook of optical fibers and cables[END_REF].

The Rayleigh scattering loss (α R ) in silica fibers is given by the relation [START_REF] Murata | Handbook of optical fibers and cables[END_REF][START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]:

α R = 8π 3 3π 4 n 8 C 2 p k B β T F = A λ 4 (3.3)
where, n : refractive index C p : constant of optical elasticity k B : Boltzmann's constant β : isothermal compressibility A : coefficient of Rayleigh scattering loss λ : wavelength of the optical source According to [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF], 0.016% of the incident light is lost every meter of fiber due to Rayleigh scattering, considering a wavelength of 1000 nm.

3. Bending loss: fiber optic cables are usually bent as they are stored in the winding spool, or during deployment. Bending generates a leakage of the light energy, from the fiber core towards the cladding, resulting in additional optical loss [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF][START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. The "tighter" the bend, the smaller its radius of curvature, and the larger the loss due to the external force bending the fiber [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF].

According to [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF], the bend radius should not be larger than a few centimeters in order to keep low levels of bending loss. Moreover, it has been observed that bending loss is higher with optical sources at 1550 nm than at 1310 nm, which suggests that bending loss can be highly wavelength-dependent [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF]. The International Telecommunication Union (ITU)-T standards indicate that an additional loss due to bending at 1550 nm is expected between 0.5-1.0 dB, for 100 turns of fiber wound with a bend radius of 37.5 mm [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF].

Dispersion

The duration of optical signals can vary during their transit across optical fibers. In fact, different spectral components of the injected light may propagate at distinct velocities in the fiber [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF][START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. Thus, as previously discussed for multimode fibers in section 3.1.3, each wavelength of the transmitted light will arrive at the receiver at a different time. This phenomenon, known as dispersion, may distort the optical signal that propagates in the fiber. Generally, dispersion leads to broadening of the signal pulse, which induces interference due to overlapping front and rear pulses [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF][START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. Dispersion restricts the bandwidth and the effective propagation distance of signal pulses along the fiber [START_REF] Ye | Submarine Optical Cable Engineering[END_REF].

Dispersion in optical fibers is usually related to the fiber compounds, but also to the propagating modes and the type of optical signal travelling along the cable [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. Multimode fibers, for instance, are generally more impacted by dispersion of the propagating modes, while single-mode fibers are mainly affected by optical dispersion of the cable materials [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. Another case of dispersion in fibers arises due to the nature of light. The energy of a propagating pulse is commonly split into two orthogonally polarized modes, which have slightly different propagation constants [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF]. Since fibers are inhomogeneous media, the refractive index may not be exactly the same at two perpendicular directions. Therefore, polarized light travelling across a fiber might be distorted. This phenomenon is called Polarization-Mode Dispersion, and theoretically is similar to the pulse spreading observed in multimode fibers but much weaker [START_REF] Ramaswami | Optical networks: a practical perspective[END_REF].

Design of fiber optic cables

Optical fibers include an insulating layer composed of a silicon gel, a sort of jelly, that separates the core-cladding fiber from outer securing layers. It is also common to find corecladding fibers embedded in the gel. The fiber-jelly matrix is then covered by an outer plastic coating that is directly applied to the silicon gel [START_REF] Horima | Jelly-filled optical cable[END_REF]. Figure 3.6 displays a jelly-filled fiber optic cable. Jelly-filled fibers are protected against the infiltration of H 2 , and have less risk of damage due to water infiltration [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Fiber cables with no gel protection tend to accumulate moisture, which freezes with decreasing temperatures. Consequently, the attenuation along the fiber increases due to microbending loss [START_REF] Murata | Handbook of optical fibers and cables[END_REF], as can be observed in Figure 3.7.

In addition to insulating layers, the structure of optical fibers can also include copper conductors. The current state-of-the-art of fiber cables hinders the transmission of electrical power through the cable [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Therefore, copper conductors installed along the fiber are commonly used for power transmission (Figure 3.8). Electrical power is regularly demanded in telecommunication fiber systems to assure the proper operation of repeaters, for monitoring, or for emergency use [START_REF] Murata | Handbook of optical fibers and cables[END_REF]. Copper conductors or cables increase the total weight of a fiber. A trade-off between the structural element providing strength to the fiber and the copper conductor is therefore needed, in order to guarantee an operational fiber optic cable [START_REF] Murata | Handbook of optical fibers and cables[END_REF].

Submarine optical fibers

Previous sections in Chapter 3 illustrate the most common fabrication processes of fiber optic cables. Through those pages, the reader explored the fiber's manufacturing procedure from the very starting step (the silica glass), until reaching the final shape of a telecommunication fiber system. Now, section 3.4 describes the crucial element of the research project presented by this PhD thesis: the submarine fiber optic cable.

Underwater fiber optic cables are essentially the modern highways for communication and data transmission. As depicted in Figure 1.3, seafloor fiber cables are the only cost-efficient way to transmit data between distant locations. The oceans are currently crossed by multiple submarine fiber cables. I will explain here how those fibers differ from the ones already described, and how they are deployed in the deepest ocean.

Armoured cables

During the Middle Ages, knights used to wear armors to protect themselves in combat. Similarly, submarine fiber optic cables are covered by different types of armouring, as those displayed in Figure 3.8. Underwater fiber cables are not conceived for combat, but they traverse a hostile environment, the deep ocean, that can compromise the integrity of the cable. According to the "Submarine Cable Map 2022" by TeleGeography1 , fishing net entanglement, dropped anchors, and other human activities account for almost 70% of the cases of seafloor cable damage. Protective layers are then vital to prevent submarine fibers from mechanical failure.

Usually, most seafloor fibers share a common type of cable, the so-called lightweight (LW) cable. This type of fiber serves as the starting structure over which consecutive layers of protection are added. The number and characteristics of the external layers depends primarily on the seabed conditions traversed by the cable, but also on the client's requirements. Figure 3.9 displays a typical LW cable. To protect the cable against abrasion, fishing activities and fish bites2 , it is common to cover the insulating sheath of the LW cable by a metallic tape, and then add a second sheath of high density polyethylene. The resulting cable is referred to as lightweight protected (LWP) cable. A common LWP cable is shown below: A regular practice during the deployment of submarine fiber cables is to use heavier armoured cables as the trajectory of the fiber approaches the shore. These type of fibers are composed by a central-core LW cable, which is covered by external layers of metallic protection. There are two popular models of heavy-armoured submarine fiber cables: single armoured (SA) cable (Figure 3.11) and double armoured (DA) cable (Figure 3.12).

Deployment of underwater fiber cables

Once a submarine fiber optic cable is manufactured and armoured, it is ready to be laid out on the seafloor. The deployment of seafloor fiber cables is a delicate procedure that involves a meticulous planning of the cable route.

The installation of underwater fiber cables begins out of the sea, since an appropriate landing point must be selected. Optimal landing points are usually close to the on-land facility harboring the cable, but also need to be easily reached by the vessel that takes over the deployment offshore [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. After a suitable landing point is chosen, the cable route in the sea is planned. To avoid unfavorable seabed topography (reefs, scarps, deep valleys) and geological hazards (submarine landslides, turbidity, active fractures, high seismic activity), bathymetry surveys and geotechnical studies are performed along the preliminary cable path [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. Figure 3.13 displays the main geological features identified by a bathymetry and geotechnical assessment, along a planned cable path in the Mediterranean Sea. Supplemen-Figure 3.13 -Portion of the route followed by a submarine fiber optic cable in the Methoni Bay, southwestern Greece. A designed cable path (red line) traverses different geological features -ripples, rock fragments, sandy mud, rocky bed and rocky outcrops -that were identified by bathymetry surveys and geotechnical assessments during the planning of the cable trajectory. (Taken from METHONI EMSO Submarine Cable System -As Built Report by ELETTRA, 2015) tary studies deliver meteorological, hydrologic and biologic information of the sea conditions, such as maximum and average wind speeds, frequency of waves and current speeds at different depths, and marine flora and fauna that could be potentially dangerous to the cable [START_REF] Ye | Submarine Optical Cable Engineering[END_REF].

Offshore operations for the installation of seafloor fiber cables are performed, supervised and monitored from special vessels. Submarine cable ships are equipped with drum cable machines and storage tanks for laying or stocking the fibers, when needed [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. To avoid deviations from the planned cable route and handle the laying of the cable with the appropriate speed, deployment vessels rely on modern navigation systems and control management softwares. Moreover, specialized equipment for underwater installations are typically on board, such as cable burial machines and remotely operated vehicles (ROVs) [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. Cable burial machines are mostly utilized in the first kilometers of the offshore cable trajectory, with burial depths ranging from 1.5 to 3.0 m [START_REF] Ye | Submarine Optical Cable Engineering[END_REF]. ROVs are commonly used for the inspection and recovery of damaged cable sections.

The deployment of submarine fiber cables is a multistep operation that is performed with extreme caution, to prevent cable damage. Yet, suspended cable sections can occur, due to irregular seafloor and steep underwater slopes [START_REF] Worzyk | Submarine power cables: design, installation, repair, environmental aspects[END_REF]. Figure 3.14 shows hanging sections identified by an ROV, during the inspection of a submarine fiber cable deployed in southwestern Greece. Chapters 4 and 5 introduce and describe particular signals recorded by DAS, along cable sections presumably suspended of three underwater fiber cables located in the Mediterranean Sea: the MEUST cable in Toulon, France, and the NESTOR and HCMR cables in southwest Greece.

Key Points of Vortex-Induced Vibrations

Steady and low-speed winds hitting overhead power lines produce an audible "whistling". This sound is appreciated as the power lines vibrate. Whistlings and vibrations are connected in a particular way. Indeed, oscillations of elongated bodies -such as power cables -are generated when a stable fluid (wind in this case) hits them, which produces vortices that shed off from the vibrating structure (Figure 4.1). Whistlings result from the vortex shedding pattern triggered by the power line oscillations, a phenomenon referred to as Vortex-Induced Vibrations (VIV). VIV is the backbone of Chapter 4, and key points of underwater VIV will be given below (more detailed information in [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF], [START_REF] Williamson | A brief review of recent results in vortex-induced vibrations[END_REF], and the references therein). Underwater flexible structures with bluff cross sections are also susceptible to VIV due to ocean currents hitting them. Risers and moorings lines immersed in ocean currents, as well as suspended sections of telecom fiber optic cables deployed at the seafloor, are exposed to high-amplitude oscillations triggered by underwater VIV. Such vibrations amplify the mean drag forces acting on the body, which may lead to fatigue damage and failure of the structure (Bourguet and Triantafyllou, 2015). VIV of slender deformable structures due to steady ocean current flows is a well-known problem in ocean engineering (Bourguet and Triantafyllou, 2015).

Ocean current speeds and vortex shedding frequencies excited during VIV are linearly related through the Strouhal number equation. When an ocean current flow of speed "U " hits a slender object -such as hanging sections of seafloor telecom fibers -of diameter "D", vortices will shed off from the upper and lower part of the body (Figure 4.2). The Figure 4.2 -Underwater VIV of a fiber cable segment suspended in the water column. Ocean currents of speed "U " hit a suspended cable of diameter "D", which leads to vortices shedding off from the cable at a frequency "f v ". (Modified from [START_REF] Williamson | A brief review of recent results in vortex-induced vibrations[END_REF])) frequency at which vortices are generated is known as the vortex shedding frequency "f v ", and is related to U and D through the Strouhal constant "S t ", by the Strouhal number equation [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF]:

f v = S t U D (4.1)
Equation 4.1 leads to a linear dependency between the vortex shedding frequency and the ocean current speed that triggers VIV.

Two behaviors of the vortex shedding frequencies generated by VIV have been reported experimentally and numerically [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF][START_REF] Williamson | A brief review of recent results in vortex-induced vibrations[END_REF]Bourguet and Triantafyllou, 2015). The first -known as the "lock-out regime" -manifests as low-amplitude oscillations that generate vortex shedding frequencies well described by equation 4.1 (yellow area in Figure 4.3). During lock-out, f v is usually far away from the natural frequency "f n " of the vibrating body. On the contrary, the second behaviorcommonly referred to as the "lock-in regime" -arises when f v approaches or equals f n . During lock-in, vortex shedding frequencies depart from the Strouhal number equation and high-amplitude oscillations are usually observed (Bourguet and Triantafyllou, 2015), as depicted by the green area in Figure 4.3. The lock-out and the lock-in regimes have been identified in VIV experiments using wind and water flows. current speeds may be used for investigating several processes in oceanography.

Introduction

Understanding ocean circulation is crucial for climate change modeling. Oceans play a determinant role in the climate system: they contain Earth's dominant reservoirs of heat and freshwater in near equilibrium with the atmosphere and cryosphere, and can trigger and non-linearly amplify climate change via multiple mechanisms [START_REF] Wunsch | Global ocean integrals and means, with trend implications[END_REF][START_REF] Semtner | Modeling ocean circulation[END_REF][START_REF] Rahmstorf | Ocean circulation and climate during the past 120,000 years[END_REF]. In addition, ocean currents are one of the main sources of turbulent energy contributing to mix the ocean and controlling the sediment distribution of marine deposits [START_REF] Munk | Abyssal recipes ii: Energetics of tidal and wind mixing[END_REF][START_REF] Bryden | Changing currents: a strategy for understanding and predicting the changing ocean circulation[END_REF]). Yet, observations of ocean currents are rare, especially in deep seafloor environments, due to the cost of instrumentation. The scarcity of deep ocean current data leads to incomplete observational time series of ocean dynamics, which hinders the establishment of long-term trends of ocean circulation [START_REF] Rahmstorf | Ocean circulation and climate during the past 120,000 years[END_REF]. Moorings and gliders are a first good approach to fill the data gap but their energy and cost budgets hold back the deployment of additional sensors [START_REF] Bryden | Changing currents: a strategy for understanding and predicting the changing ocean circulation[END_REF]. The Argo program floats have been expanding the coverage of deep oceanographic data, but they are limited to a profiling depth of approximately 2000 m, leaving half of the deep ocean unsampled [START_REF] Bryden | Changing currents: a strategy for understanding and predicting the changing ocean circulation[END_REF]. Moreover, the combination of ships-of-opportunity and float dispersion is not sufficient to sample regions of the globe with difficult access [START_REF] Roemmich | The argo program: Observing the global ocean with profiling floats[END_REF].

Underwater telecommunication cables, the only infrastructure already crisscrossing the ocean floors, could be leveraged to enhance ocean monitoring. The SMART (Science Monitoring And Reliable Telecommunications) initiative has proposed to constrain ocean circulation by temperature sensors integrated into the repeaters of undersea telecommunication cables [START_REF] Howe | Smart cables for observing the global ocean: science and implementation[END_REF], but it does not address the recording of ocean currents. Analysis of the state of polarization (SOP) of regular optical telecommunication channels can be used to monitor ocean swells produced by distant storms [START_REF] Zhan | Optical polarization-based seismic and water wave sensing on transoceanic cables[END_REF] but has two main limitations: the low signal-tonoise ratio of the interferometry and its very coarse spatial resolution, as the measurement is integrated over the whole cable length. Long-distance optical interferometry across transoceanic cables has been proposed to monitor tidal currents [START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF], but would also have limited spatial resolution of several tens of km, the distance between cable repeaters. Among the different photonics-based metrology techniques, Distributed Acoustic Sensing (DAS) has been rapidly and widely adopted, with demonstration of a large potential of applications in physical oceanography [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF][START_REF] Lindsey | Illuminating seafloor faults and ocean dynamics with dark fiber distributed acoustic sensing[END_REF][START_REF] Williams | Surface gravity wave interferometry and ocean current monitoring with ocean-bottom das[END_REF]. DAS probes changes in the Rayleigh back-scattering pattern along tens of kilometers of fiber optic cables, effectively turning cables into arrays of thousands of strain sensors [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. DAS typically records nano variations of strains, enabling the detection of a wide range of processes. Underwater cables are interrogated by DAS from their on-shore termination points, which may allow uninterrupted monitoring of the ocean dynamics from land.

Underwater fiber cables commonly traverse a variety of seafloor conditions, which leads to an uneven mechanical coupling between the cable and the ocean bottom. On rough seafloor bathymetry, some cable portions might be suspended and thus susceptible to Vortex-Induced Vibrations (VIV) driven by deep ocean currents. Along slender objects exposed to water currents, VIV manifests as high-amplitude oscillations with characteristic frequencies associated to the periodicity of vortex shedding. The phenomenon has been previously reported at scales ranging from deep-water oil and gas facilities, such as risers, to Ocean Bottom Seismometers (OBS) antennas [START_REF] Trim | Experimental investigation of vortexinduced vibration of long marine risers[END_REF][START_REF] Hong | Vortex-induced vibrations and control of marine risers: A review[END_REF][START_REF] Duennebier | Current-generated noise recorded on ocean bottom seismometers[END_REF][START_REF] Stähler | A self-noise model for the german depas obs pool[END_REF]. The relation between DAS, VIV, and ocean currents has been previously cited [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF] but, to the best of our knowledge, no quantitative link has been established in preceding works. We report here observations of VIV along a seafloor fiber cable monitored with DAS in the Mediterranean Sea, for which independent measurements of ocean currents at the sea bottom are available as validation data.

Here, we examine the potential of DAS to monitor deep-sea currents, using the fundamental frequency of quasi-harmonic oscillations recorded along sections of an underwater telecommunication cable located in southern France. We first identify cable segments featuring the oscillations, which we interpret as cable portions suspended and exposed to VIV. Using VIV theory, we convert the cable oscillation frequencies into an ocean current speed time series. We further show that DAS-derived current speeds are comparable to speeds recorded by a current meter deployed 3.75 km away, also on the deep seafloor. The spectral content of the DASderived time series offers insight into oceanographic processes involving ocean circulation and stratification in the Mediterranean Sea.

Data Overview

The electro-optic cable monitored in this study is located offshore Toulon, south of France (Figure 4.4.a). It is part of the MEUST-NUMerEnv project (Mediterranean Eurocentre for Underwater Sciences and Technologies-Neutrino Mer Environnement) [START_REF] Lamare | The meust deep sea infrastructure in the toulon site[END_REF] and is used to transmit the data acquired at its underwater end by the KM3NeT/ORCA (Oscillation Research with Cosmics in the Abyss) neutrino detector [START_REF] Coyle | KM3NeT-ORCA: Oscillation Research with Cosmics in the Abyss[END_REF]. The cable trajectory slightly differs from the one described in [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF] due to maintenance works performed in October 2018, which involved the replacement of the distant half of the cable. All cable sections analyzed here are from this replaced part of the cable which traverses different oceanic features, from the continental slope to the abyssal plain, that may allow hanging sections (Figure 4.4.b). According to technical specifications provided during the maintenance works, the diameter of the cable segments presented here is 2.75 cm. [START_REF] Coyle | KM3NeT-ORCA: Oscillation Research with Cosmics in the Abyss[END_REF].

DAS strain data (strain parallel to the cable axis) were collected from July 11 th to July 31 st , 2019, using an Aragon Photonics HDAS interrogator. Distributed Raman amplification was used to ensure low variations of the instrumental noise floor (< 5 dB) over the whole cable length [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF][START_REF] Williams | Distributed sensing of microseisms and teleseisms with submarine dark fibers[END_REF][START_REF] Pastor-Graells | Single-shot distributed temperature and strain tracking using direct detection phase-sensitive otdr with chirped pulses[END_REF][START_REF] Lior | On the Detection Capabilities of Underwater Distributed Acoustic Sensing[END_REF]. The cable is equipped with Corning© LEAF (Large Effective Area Fiber) optic fibers with very low attenuation (<0.19 dB/km), which improves the detection range. The instrumental strain noise floor is < 100 picostrain/sqrt (Hz), comparable to optimal laboratory measurements for long fibers [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF][START_REF] Lior | On the Detection Capabilities of Underwater Distributed Acoustic Sensing[END_REF]. The pulse wavelength was set at 1550 nm, with 100 ns width (equivalent to a spatial resolution of 10 m), 1 GHz spectral content and 50 mW peak power. The DAS strain data were sampled at a rate of 100 Hz during the first 10 days of the experiment and 500 Hz in the remaining part of the campaign.

The gauge length was set at 10 m, leading to a network of 4480 equally-spaced strain sensors. To mitigate the 1/f noise that affects strain recordings at low frequencies f (R. [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF], we converted the strain data to strain rate by finite-difference time derivation.

A range of environmental sensors are located on the Interface Instrumented Module (MII) at the end of the cable [START_REF] Coyle | KM3NeT-ORCA: Oscillation Research with Cosmics in the Abyss[END_REF]. We will use for comparison with the DAS measurements the data recorded by an ADCP current meter, an Aquadopp DW from Nortek, located on the MII (red triangle, Figure 4.4.b). cable oscillations can be readily detected by three distinguishing features in the DAS recordings:

Results

(1) they have amplitudes larger than those of any other background noise, (2) they coherently extend between sharply-defined points along the cable, and ( 3) their Fourier spectra show a characteristic frequency lower than 1 Hz, which is time-dependent. Cable oscillations can last from hours to days, separated by periods without oscillations that range from a few hours to almost half a day. Several cable segments of different lengths can vibrate simultaneously with different amplitudes. Hence, we analyze hour-long DAS recordings to identify cable segments presenting the three features previously described.

Quasi-harmonic oscillations are easily recognized along the MEUST cable. We observe them along three segments located at different depths (Figure 4.4.b). We focus here on two cable portions in segments labeled as 3 and 2 in Figure 4.4, since they display fundamental frequencies that extend during days and harmonics are barely observed (Figure 4.5.c,d;Supporting Figure 4.11 shows oscillations of a cable section along the segment labeled as 1 in Figure 4.4). These cable sections span 210 and 70 m, respectively, they are 10 km apart and their depth differs by less than 120 m (Figure 4.5.a,b, magenta line). The former crosses a deep ocean valley (segment 3) and the latter a change of the seafloor slope (segment 2). Both cable portions oscillate at the same time between July 14th at 06:00 and July 17th at 18:00. Between July 16th at 18:00 and July 17th at 18:00, the cable oscillations in segment 3 have amplitudes ranging from 600 to 2300 nstrain/s, one to two orders of magnitude larger than the background noise recorded by DAS. During the same period, the amplitudes of the cable oscillations along segment 2 remain between 10 and 15 nstrain/s, slightly above the background noise. The oscillations of both cable portions have a characteristic frequency lower than 1 Hz, which fluctuates through time (Figure 4.5.e,f). Harmonics are identified in segment 3, when the strain rate amplitude reaches its maximum between July 14th 06:00 and July 17th 18:00 (Figure 4.5.e,f).

The origin of the cable oscillations is explained by comparing their signal properties with experimental observations of VIV. We analyze 14.5 days of fiber cable oscillations detected between July 12th at 02:10:26 and July 29th at 23:31:28 along cable segment 3 in Fig. 4.5(a). The fundamental frequency of the oscillations was present during several days in this cable portion, and harmonics were barely observed. The amplitude of the cable oscillations changes systematically as a function of the changing frequency. The maximum absolute value of the fiber strain rate increases exponentially with increasing dominant frequency, up to approximately 0.35 Hz (Figure 4.6). From 0.35 to 0.40 Hz, the amplitude increases more steeply, then reaches a maximum. Similarly, published experimental results on VIV show that the amplitude of oscillations increases with the frequency at which vortices shed off from elongated structures [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF][START_REF] King | A review of vortex shedding research and its application[END_REF]Bourguet et al., 2015). This frequency, also known as the vortex shedding frequency, describes the periodic pattern of the wake formed when a fluid -commonly wind in VIV experiments -flows about a stationary and slender object [START_REF] King | A review of vortex shedding research and its application[END_REF]. The steepen-Figure 4.6 -Evidence of Vortex-Induced Vibrations (VIV) on a suspended underwater cable. Maximum absolute value of the fiber strain rate at the center of segment 3, during 14.5 days, over two-minutes-long sliding windows, plotted as a function of the dominant frequency of the fiber oscillations (density of points). Each blue box represents the median fiber strain (red), its 25 th and 75 th percentiles (bottom and top edges) by frequency, respectively. The whiskers extend to the most extreme data points that are not considered outliers (dashed black lines). The amplitude increases exponentially up to a frequency close to 0.35 Hz, then more steeply as the frequency approaches 0.40 Hz. Considering that VIV frequencies are linearly related to current speeds through the Strouhal relation (blue horizontal scale), this behavior is consistent with that observed in controlled VIV experiments (triangles: experimental data of Feng, 1968, rescaled in amplitude and frequency to match the peak of the DAS data). A harmonic excited during the lock-in regime of VIV is seen around 0.79 Hz. Box-and-whiskers are not represented for the low-amplitude cluster at 0.45-0.50 Hz, which is associated with the second-order pressure peak caused by sea surface waves (the persistent peak in Figure 4.5.e) ing of the VIV amplitude growth before reaching the maximum amplitude is also observed in experiments [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF]. The similarity of the amplitude versus frequency relation between the cable oscillations and that reported in the literature on VIV suggests that the characteristic oscillations recorded by seafloor DAS along segment 3 are indeed VIV of the cable induced by deep ocean currents. To trigger VIV along underwater fibers, seafloor ocean currents must interact with hanging sections of the cable. Hence, the cable oscillations presented here may be used to identify spatial variations in the mechanical coupling between the cable and the seafloor, particularly to detect suspended sections of underwater fiber cables.

A persistent signal with stationary frequency is also observed along cable sections undergoing VIV, which we associate with sea surface gravity waves. Between July 14th at 06:00 and July 17th at 18:00, a frequency permanently excited can be identified in Figure 4.5 (e,f). This frequency is about 0.4 and 0.8 Hz in the cable sections located at segments 3 and 2, respectively. This frequency has been previously reported as featuring water-depth dependence and being related to second-order pressure fluctuations caused by sea surface gravity waves, which are at the origin of secondary microseism [START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF][START_REF] Guerin | Quantifying microseismic noise generation from coastal reflection of gravity waves recorded by seafloor das[END_REF]. This signal has a clear and persistent signature and does not interfere with the analysis of the oceanic VIV.

Current Speed Monitoring in Deep Ocean Environments

Cable oscillations caused by VIV are expected to have frequencies proportional to ocean current speeds, as long as the vortex shedding frequency is not close to the natural vibration frequency of the suspended cable segment. Vortex shedding frequencies near or equal to one of the natural frequencies of the hanging section may trigger a vibration of the cable in resonance, a phenomenon called "lock-in" [START_REF] Worzyk | Submarine power cables: design, installation, repair, environmental aspects[END_REF]. The effect of lock-in on cable oscillations recorded by DAS is discussed in the next section. Out of the lock-in regime, the cable oscillations are synchronized with the vortex shedding frequency (f vs ) (Bourguet and Triantafyllou, 2015), which is related to the ocean current speed (U c ) through the Strouhal number (S t ) equation:

f vs = S t U c D (4.2)
Given S t and the diameter of the cable (D), ocean current speeds can be estimated using equation (4.2) from the vortex shedding frequencies extracted from DAS data. The Strouhal number can be taken as 0.2 for seafloor cables and relevant current conditions [START_REF] Worzyk | Submarine power cables: design, installation, repair, environmental aspects[END_REF]. Experimental observations indicate that in the range of Reynolds numbers (R e ), 5 • 10 2 < R e < 5 • 10 5 , S t remains around 0.2. Numerical modeling of oceanic flows at basin scales commonly assumes R e around 10 2 [START_REF] Lin | A numerical study of low reynolds number 2-dimensional convective adjustment[END_REF][START_REF] Jiménez | A numerical study of the relative importance of wind and topographic forcing on oceanic eddy shedding by tall, deep water islands[END_REF], although R e values can exceed 10 4 in the ocean [START_REF] Thorpe | An introduction to ocean turbulence[END_REF][START_REF] Özgökmen | Reynolds number dependence of mixing in a lock-exchange system from direct numerical and large eddy simulations[END_REF][START_REF] Katopodes | Chapter 5 -viscous fluid flow[END_REF].

Here, we validate the proposed VIV speed-meter concept by comparing the ocean current speeds derived from vibration frequencies recorded by DAS to those independently recorded by the nearby current meter (station MII). We focus on the vibrating cable section in segment 3 in Figure (4.5.a), which is the closest to the current meter (3.75 km away) and is located at a similar depth (2390 m). The corresponding DAS data are low-pass filtered below 0.35 Hz to avoid the second-order pressure peak (near 0. 5 Hz,Fig. 4.5.e) and the observed lockin frequency around 0.4 Hz (Figure 4.6). We picked a value of f vs at every minute, as the Ocean current speed recorded by MII current meter between 11-July-2019 00:00:00 UTC and 31-July-2019 00:00:00 UTC (gray circles), its median over 2-hours-long sliding windows (black curve), current speed derived from Strouhal frequencies sensed by DAS in a hanging section between km 37.06 and 37.18 (cyan circles) and its median over 2-hours-long sliding windows (blue line). Horizontal segments of the curves correspond to data gaps. (b) Power Spectral Density of raw MII (black) and DAS (blue) oceanic current speeds from 19-July-2019 22:09:04 to 29-July-2019 06:14:45. A 17-hours peak is observed in both spectra. The energy power of the DAS spectrum (P (f )) decays with increasing frequency from a period T < 17 hours to T = 4 hours following P (f ) ≈ 1/f p , with p = 2.5. For reference, the red lines show the spectral decay slope for two values of the decay exponent "p". frequency corresponding to the maximum amplitude of the Fourier spectra over 2-min sliding windows with 1-min overlap. Using equation ( 4.2) and the cable diameter of 2.75 cm, we derive a time series of ocean current speeds from the time series of f vs , with resulting values ranging from 1.11 to 5.45 cm/s (Figure 4.7.a). The precision of our current speed estimates, ∆U , is controlled by the window size, T window = 120 s, of the Fourier spectral analysis: ∆U = D St•T window ≈ 1 mm/s. We compare the resulting DAS-derived time series to the current meter time series smoothed with a 2-hour sliding median (Figure 4.7.a). Before July 27th, the two time series agree well during periods without data gaps. Afterwards, the DAS-derived current speeds are lower by more than 1 cm/s than the speeds recorded by the current meter. This deviation may be due to local perturbations affecting the ocean current speeds or their direction in the vicinity of the cable (different seafloor features, local turbulence). We further observe that the DAS-derived and current meter speeds share a common dominant period near 17 h (see the spectral peak in Figure 4.7.b). The implications of this detected dominant period are discussed in Section 4.3.5. Figure 4.8 shows both time series low-pass filtered with a cutoff frequency f cutof f = (10 h) -1 , to focus on the dominant period. A time-dependent time-shift is clearly observed between the two low-pass filtered time series, as expected for oceanic currents measured several kilometers away (Figure 4.8.a). We measure the time-dependent time-shift by cross-correlation over 50-hours-long sliding windows between July 20th and July 27th, a period with no data gaps (Figure 4.8.b). We compare it with an expected time-shift derived from:

∆T = ∆X U • cos α (4.3)
where ∆X ∼3.75 km is the distance between the current meter and the selected cable section, U the ocean current speed, and α the smallest angle between the cable azimuth (ϕ cable =101 • ) and the azimuth of the ocean current direction (ϕ current ). Both U and ϕ current were recorded by the current meter. The measured and expected time-shifts agree during periods when the ocean current features a dominant orientation (Figure 4.8.b). Between July 21st and 22nd the current meter recordings show a change of the ocean current orientation, which corresponds to a decrease in the coherence between the time series from July 22nd to 23rd.

Limitations Imposed by the Lock-in Regime

Oscillation frequencies recorded during lock-in, i.e. while the cable vibration is in resonance with vortex shedding, cannot be readily exploited to estimate ocean current speeds. Lock-in involves large-amplitude excitation of the natural frequencies of the cable [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF]Bourguet et al., 2015). The cable vibration frequency is then no longer controlled by the Strouhal number recorded by the current meter (black) and DAS-derived from the same cable section as in Fig. 4.7 (blue), from July 11th to July 31st, 2019. We low-pass filtered both time series with a cutoff period of 10 h. (b) Expected time-shift between ocean current speeds at the MII current meter location and along the hanging cable section (red squares), derived from MII current meter data. The red line is the median expected time-shift averaged over a 2-hours sliding window. Circles: time-shift calculated by cross-correlation between MII current meter and DAS time series over a 50-hours sliding window, only shown for windows without data gaps. Coherence is shown in color scale. Ocean current direction recorded by the current meter (ϕ current , green squares). The green line is the median-ϕ current averaged over 2-hours-long sliding windows. The time-shift sign fluctuates according to whether oceanic currents are measured first by MII current meter (negative) or by DAS (positive). relation, equation (4.2), but by the cable resonance frequency. [START_REF] Stähler | A self-noise model for the german depas obs pool[END_REF] observed harmonic signals (fundamental and overtones) in OBS recordings at 20 m depth in the Baltic Sea, and associated them to lock-in generated by ocean currents strumming the head-buoy cable of the OBS. The multiple harmonics observed in Fig. 4.5(e) in July 16th at 18:00 and in July 17th between 06:00 and 18:00, suggest VIV is operating in the lock-in regime during these time periods. We rarely observe such higher-harmonics in the DAS data recorded in segment 3. Therefore, we consider the lock-in regime does not dominate the VIV along this cable section.

Lock-in imposes an upper bound on the current speed that can be estimated by VIV on DAS data. The natural frequencies (f n ) of a hanging cable portion depend on its span length (l), mass per unit length (m) and horizontal tension (T ) as

f n = n 2l T m
, where n is an integer [START_REF] Irvine | The linear theory of free vibrations of a suspended cable[END_REF]. The maximum amplitude of the ocean current speed that can be constrained before lock-in emerges, i.e. that satisfies the condition f vs < f 1 , is:

U max = D 2S t T m 1 l (4.4)
More precisely, lock-in occurs over a range of frequencies around f 1 , roughly from 0.94f 1 to 1.25f 1 in the experiments reported by [START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF]. In principle, current speeds could also be measured if they are above the lock-in range associated to f 1 , i.e. above ∼ 1.25f 1 . However, the sequence of lock-in ranges related to the higher modes f n would make this impractical. Thus, in practice equation (4.4) gives the maximum current speed that can be measured by our proposed method.

The maximum measurable speed can be estimated from known cable properties. Using the relation T = mgl 2 8d [START_REF] Irvine | The linear theory of free vibrations of a suspended cable[END_REF], where g is the gravitational acceleration and d the sag of the cable, equation (4.4) becomes:

U max = D √ 2g 8S t 1 d 1/2 (4.5)
If d/l ≤ 1/8, as expected in submarine cables, the sag d is related to the curvilinear length of the suspended cable by [START_REF] Irvine | The linear theory of free vibrations of a suspended cable[END_REF]. We further assume that length L and span l are related by a cable layout parameter: the slack reported during the cable deployment, [START_REF] Bibliography Abidin | Subsea cable laying problem[END_REF]. We then obtain:

L ≈ l 1 + 8 3 d l 2 (Irvine
S = L/l -1 ≈ 8 3 d l 2 (
U max = A n l 1/2 (4.6)
where A n = nA 1 and

A 1 = D √ 2g 4 √ 24S 24 S S t . (4.7)
Equation ( 4.6) provides an estimate of the largest current speed accessible with a given span length l of suspended cable, given two geometrical parameters of the cable, its diameter D and its slack S. Conversely, it provides the longest suspended cable span length, l max = (A n /U max ) 2 , that can be utilized to monitor seafloor current speeds up to a given target value U max .

According to equation (4.6), detecting faster currents requires shorter suspended cable sections. Figure 4.9 displays the permissible range of span lengths and current speeds in the MEUST cable, assuming the same values of D and S t as for equation ( 4.2). The peak current speeds reached by various oceanography processes are also indicated in Figure 4.9. Considering suspended cable sections of different lengths, DAS observations should allow to monitor a wide range of oceanography processes: tsunami-induced geostrophic vortices [START_REF] Nosov | Horizontal motions of water in the vicinity of a tsunami source[END_REF] using kilometers-long cable spans, sea-bottom currents, convective plumes motion and tsunami-induced perturbations [START_REF] Camden-Smith | A preliminary report on long-term bottom-current measurements and sediment transport/erosion in the agulhas passage, southwest indian ocean[END_REF][START_REF] Margirier | Characterization of convective plumes associated with oceanic deep convection in the northwestern mediterranean from high-resolution in situ data collected by gliders[END_REF][START_REF] Mikada | New discoveries in dynamics of an m8 earthquake-phenomena and their implications from the 2003 tokachi-oki earthquake using a long term monitoring cabled observatory[END_REF] with meters-long cable spans, turbidity currents, such as benthic storms and tsunamiinduced currents [START_REF] Mikada | New discoveries in dynamics of an m8 earthquake-phenomena and their implications from the 2003 tokachi-oki earthquake using a long term monitoring cabled observatory[END_REF][START_REF] Admire | Observed and modeled currents from the tohoku-oki, japan and other recent tsunamis in northern california[END_REF], using centimeters-long cable spans. More DAS campaigns are needed to validate the capability of the VIV-speedmeter method to properly monitor this wide spectrum of oceanography processes.

VIV Under Oblique Seafloor Currents

Under certain conditions, equation ( 4.2) is expected to be valid also when the current hits the cable obliquely, if U c is defined as the cable-normal component of the current speed, i.e. the projection of the current speed vector onto the plane perpendicular to the cable axis. The literature on oblique-VIV commonly examines the accuracy of attributing VIV frequencies and flow dynamics to the component of the current speed perpendicular to the axis of the oscillating body (Bourguet et al., 2015). The so-called Independence Principle (IP) or cosine law postulates that the physical quantities of oblique and normal VIV (fluid forces, vortex shedding, vibration amplitudes) should match if the normal component of the current speed is the same (Bourguet et al., 2015). Numerical simulations show that the IP is valid as long as the incidence angle relative to the plane perpendicular to the cable axis is smaller than 60 degrees (Bourguet et al., 2015).

To investigate this Independence Principle, we compare the cable-normal component of the current meter speed to the DAS-derived time series. To do so, we calculate the angle θ between the ocean current direction recorded by the current meter and the plane perpendicular to the cable. We then compute the cable-normal component of the current meter speed (U M II • cos(θ)) and compare it to the DAS-derived speed (U DAS ) (Supporting Figure 4.11). The resulting time series are not in agreement (U M II • cos(θ) ̸ = U DAS ), which does not support the IP. We cannot attribute this negative result to the validity range of θ: the IP is expected to fail if θ > 60 degrees (Bourguet et al., 2015;Bourguet and Triantafyllou, 2015;[START_REF] Lucor | Effects of oblique inflow in vortex-induced vibrations[END_REF], but here θ ranges from 24 to 82 degrees. Our negative result could be biased by the high variability of θ, and the non-negligible distance between the cable and the reference current meter (3.75 km). Dedicated instrument deployment is therefore needed to study the limitations of the IP in predicting physical quantities of oblique VIV recorded by DAS.

Observing Internal Gravity Waves in the Mediterranean Sea

Spectral analysis of DAS-derived ocean current speed time series provides quantitative information about internal gravity waves generated in the Mediterranean Sea. The Power Spectral Density estimates (PSD's) of DAS-derived and current meter speed time series between July 19th at 22:09:04 and July 29th at 06:14:45 show a strong peak around a period of 17 hours (Figure 4.7.b). This peak has been previously observed in ocean current speed time series recorded in the Mediterranean Sea [START_REF] Van Haren | Seasonality of internal gravity waves kinetic energy spectra in the ligurian basin[END_REF]. It has been associated with nearinertial waves generated in the Mediterranean basin during summer, i.e. internal gravity waves with periods close to the so-called local inertial period (T inertial ), which is primarily controlled by Earth's rotation rate (Ω ∼ 2π/24hours) and location latitude (φ). The theoretical value at the current meter location (φ = 42.805°) is T inertial = 2π/f coriolis = 17.66 hours, using the Coriolis frequency [START_REF] Van Haren | Seasonality of internal gravity waves kinetic energy spectra in the ligurian basin[END_REF]:

f coriolis = 2 Ω sin φ (4.8)
The difference of 0.60 µHz between our theoretical and observed frequencies is smaller than the uncertainty in our determination of the observed frequency, which is given by the frequency sampling of our PSD's, 1.75 µHz (based on 158-hours-long sliding windows).

The spectrum of the DAS-derived speed decays in a way consistent with ocean stratification processes. Between T < 17 hours and T ≈ 4.02 hours it decays as P (f ) ≈ 1/f 2.5 (Figure 4.7.b). This is consistent with the weak turbulence theory that predicts a variety of power laws for the energy spectrum of internal gravity waves generated in the ocean [START_REF] Garrett | Internal waves in the ocean[END_REF][START_REF] Lvov | Oceanic internal-wave field: Theory of scale-invariant spectra[END_REF]. Previous observations by [START_REF] Van Haren | Seasonality of internal gravity waves kinetic energy spectra in the ligurian basin[END_REF] show that the kinetic-energy spectra of near-inertial waves decay as P (f ) ≈ 1/f p , with p a seasonal parameter that fluctuates between 1.5 and 2.5 during summer in the Mediterranean sea. According to [START_REF] Van Haren | Seasonality of internal gravity waves kinetic energy spectra in the ligurian basin[END_REF], the seasonal variation of the ocean stratification is the process at the origin of the fluctuations of the p value. The DAS-derived current speed spectrum over longer times should be able to capture the seasonal variation of p, which can offer novel opportunities to monitor the dynamics of ocean stratification. The permissible frequency range of internal gravity waves is f coriolis < f < N , with N the Buoyancy frequency that depends on the ocean depth and stratification [START_REF] Garrett | Internal waves in the ocean[END_REF]. [START_REF] Van Haren | Seasonality of internal gravity waves kinetic energy spectra in the ligurian basin[END_REF] have estimated N ≈ 3f coriolis at 1100 m depth, from density-depth profiles recorded by moorings during summer in the Mediterranean Sea, while Van Haren (2014) suggested that deeper, around 2200 m, N ≈ 4f coriolis . The spectrum decay of the DAS-derived current speeds detected at 2390 m depth is described by the power law down to a period of 4.02 hours (Figure 4.7.b), which is in agreement with the expected lower bound period T = 4.42 hours that results from N ≈ 4f coriolis .

Conclusions

We investigated the potential of Distributed Acoustic Sensing (DAS) to monitor deep sea currents along suspended sections of underwater fiber optic cables. We demonstrated that oblique Vortex Induced Vibrations (VIV) can be recorded by DAS along cable sections presumably hanging due to irregular seafloor conditions. The oscillations showed time-dependent amplitudes larger than those of any other background noise and amplitude-dependent characteristic frequencies, as expected for VIV, lower than 1 Hz at different depths.

To the best of our knowledge, this is the first quantitative analysis of seafloor circulation using DAS data along hanging cable sections. The measured ocean currents speed recovered in this study ranged from 1.11 to 5.45 cm/s and matched those of a current meter located 3.75 km away but at a similar depth. Both time series showed a similar dominant period and correlation after time shift. The DAS-derived current speed time series displays features, such as characteristic periods and spectral decay, associated with known oceanographic processes: the generation of internal gravity waves and weak turbulence. Thus, DAS offers novel opportunities to monitor oceanographic processes at depths barely studied with the current instrumentation.

Our estimates of current speeds from vortex shedding frequencies recorded by DAS were derived through the Strouhal number equation. This approach is valid in the range of Reynolds numbers where the Strouhal constant remains close to 0.2. Since vortex shedding frequencies close to lock-in are not described by the Strouhal relation, we limited our analysis to conditions where the lock-in frequency is the upper limit of the method. The possibility to monitor the currents beyond the lock-in frequency is left for further studies. Also, more experiments are still needed to determine the lower limit of ocean current speeds that DAS is able to record, and if the Independence Principle holds for small incidence angles of the current on the cable.

The DAS-based monitoring of deep ocean currents presented here may be useful to investigate a variety of oceanography processes. We suggest to perform DAS experiments along controlled sections of suspended underwater cables, to validate the contribution of DAS-recorded VIV in the monitoring of several submarine processes. If the cable used in this study had nearby hanging cable segments with different orientations, we hypothesize that they could be used as an antenna to track changes in orientation of the ocean circulation. (a) Time variation of the angle " θ" between the ocean currents registered by MII current meter and the plane perpendicular to the cable axis (red circles), from 11-July-2019 00:00:00 UTC to 31-July-2019 00:00:00 UTC. The red line indicates the median angle averaged over a 2-hours sliding window. (b) Median of ocean currents registered by MII current meter averaged over 2-hours-long sliding windows (black), its vertical component respect to the plane perpendicular to the cable axis (magenta) and DAS-derived ocean currents (blue), during the same time in (a). The angle " θ" fluctuates between 24 and 82 degrees during the campaign. The vertical component of the MII current meter and DAS-derived ocean current time series do not match, which invalidates the IP. We believe that the high variability of " θ" may lead the IP to fail predicting the component of the oceanic current speed contributing to the VIV. channels have a spacing of a few meters across tens of kilometers, providing dense arrays of sensors for several applications, such as on-land/offshore seismology or physical oceanography, at low relative cost with a spatial resolution unreachable by the current instrumentation [START_REF] Mateeva | Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling[END_REF][START_REF] Lindsey | Fiber-optic network observations of earthquake wavefields[END_REF][START_REF] Martin | A seismic shift in scalable acquisition demands new processing: Fiber-optic seismic signal retrieval in urban areas with unsupervised learning for coherent noise removal[END_REF][START_REF] Zhan | Distributed acoustic sensing turns fiber-optic cables into sensitive seismic antennas[END_REF].

Underwater DAS relies on fibre optic cables traversing different seafloor features, which conditions the quality of the recorded signals. Commonly, underwater fibre cables are designed to connect an on-land facility with either deep ocean instruments or another coastal facility. Cables often cross several bathymetry features from the coast to the abyssal plain, including steep fluctuations of the continental slope and deep valleys on the seafloor. To decrease the deployment cost, offshore cables are often buried only on the first kilometers near the coast. Hence, most of the cables are exposed to the ocean dynamics and the irregularities of the bathymetry, which may lead to cable segments mechanically decoupled from the seafloor or even cable sections hanging in the water column (Mata Flores et al., 2022) 1 . A significant correlation between irregular bathymetry and unfavorable DAS measurements has been noted by [START_REF] Lior | On the Detection Capabilities of Underwater Distributed Acoustic Sensing[END_REF], for seismology applications of seafloor DAS. They concluded that bathymetry dictates the quality of DAS recordings. It has been also reported that the variation of the mechanical cable/seafloor coupling across long underwater fibre optic cables has an impact on the amplitude of the strain rate and the type of seismic waves recorded by DAS [START_REF] Lindsey | Illuminating seafloor faults and ocean dynamics with dark fiber distributed acoustic sensing[END_REF][START_REF] Sladen | Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables[END_REF][START_REF] Williams | Distributed sensing of microseisms and teleseisms with submarine dark fibers[END_REF].

The mechanical coupling between the cable and the seafloor is expected to fluctuate along underwater fibre optic cables. Although this variation determines whether a cable section is useful or not for DAS applications in seismology, the detection of unsuitable cable portions through DAS has not been previously addressed. Maintenance works of seafloor fibre optic cables usually supply real-time images of the cable conditions. However, the cost of these direct inspections is commonly high and increases with the type of remotely operated underwater vehicle (ROV) surveying the cable. Moreover, ROV inspections are not regularly scheduled, which prevents monitoring the temporal evolution of the mechanical cable/seafloor coupling. This situation calls for generic approaches based on fibre sensing techniques capable of continuous monitoring, considering that seafloor fibre optic cables are exposed to ocean dynamics or areas with high rates of marine erosion/sediment deposition. A method identifying underwater cable sections featuring unfavorable coupling with the sea bottom is then crucial to harness offshore DAS for seismology applications. We report here observations of two vibration regimes recorded by DAS across seafloor fibre optic cables: high-frequency and low-frequency oscillations. We associate the former with cable segments pinned at their ends by seafloor features and the latter with suspended cable sections.

In this study, we identify seismic waves exciting high-frequency oscillations of three seafloor fibre optic cables located in the Mediterranean sea. We extract normal modes of these oscillations by Proper Orthogonal Decomposition and we compare them with those of a 1D wave propagation model. We further calculate the speed of trapped waves propagating along the cable portions featuring the oscillations. Then, we compare the high-frequency oscillations to low-frequency oscillations detected along presumably hanging cable segments. Our results suggest that the spatio-temporal evolution of the mechanical coupling between fibre cables exposed to the ocean dynamics and the seafloor can be monitored through the two vibration regimes presented here. This article is organized as follows. In the next section, the DAS recordings and their main characteristics are described. Then, in Section 5.3, the high-frequency oscillations are analyzed, their normal modes are extracted and the cable waves generated during the vibrations are studied. In Section 5.4, the high-frequency oscillations are compared to the low-frequency oscillations. Finally, we discuss the implications of the two vibration regimes on the mechanical cable/sea bottom coupling and on the type of seismic waves recorded by DAS.

Data overview

This study uses DAS data acquired in the Mediterranean sea along three underwater electrooptic fibre cables: one located in Toulon, south of France, and two situated offshore Methoni, southwest Greece. The three cables were deployed to power and retrieve data from instruments installed at their offshore ends [START_REF] Coyle | KM3NeT-ORCA: Oscillation Research with Cosmics in the Abyss[END_REF][START_REF] Aggouras | A measurement of the cosmic-ray muon flux with a module of the nestor neutrino telescope[END_REF][START_REF] Anassontzis | Deep-sea station connected by cable to shore[END_REF]. The cable trajectories and bathymetry profiles presented here are estimated using the cable deployment coordinates and bathymetry maps taken from the EMODnet (European Marine Observation and Data Network) platform, with a cell size of ∼111 m. Due to oceanography processes, such as deep-sea currents, or bathymetry irregularities, the real cable locations may differ from the ones adopted here. We provide more details on the cables and associated DAS measurement campaigns below.

DAS experiment on the HCMR and NESTOR cables

DAS strain rate data were acquired along the contiguous HCMR (Hellenic Center for Marine Research) and NESTOR (Neutrino Extended Submarine Telescope with Oceanographic Research) fibre optic cables (Figure 5.1), located offshore Methoni at the deepest part of the Mediterranean in Greece, southwest of the Peloponnese [START_REF] Collaboration | Nestor: A neutrino particle astrophysics underwater laboratory for the mediterranean[END_REF][START_REF] Anassontzis | Status of nestor, a deep sea neutrino telescope in the mediterranean[END_REF][START_REF] Aggouras | A measurement of the cosmic-ray muon flux with a module of the nestor neutrino telescope[END_REF]. The HCMR cable communicates an on-land facility with an oceanography laboratory. The cable is 13.2 km long and includes 12 single-mode fibres protected by a Single Armouring (SA) of galvanized steel wires. The NESTOR cable was deployed for data transmission of a deep sea neutrino telescope, but it was abandoned after several failures on the cable. It is composed of 18 single-mode fibres that are protected by a Heavy Armouring (HV) made of two layers of galvanized steel wires along the first 12.5 km, and from there to its terminal point at 26.2 km by a Light Armouring (LA) made of one layer of galvanized steel wires. Both cables are buried for the first 2 km inside the Methoni Bay, following parallel paths, at a depth ranging from 0.5 to 1.5 m below the seabed. Outside the bay, the cables lay on the seafloor following different directions. The HCMR cable mostly points to the West, reaching a depth of 1530 m. The NESTOR cable points to the South-West and reaches a depth of 3820 m [START_REF] Lior | On the Detection Capabilities of Underwater Distributed Acoustic Sensing[END_REF].

The HCMR and NESTOR cables were sensed in 2019, between 18-April 16:20:22 UTC and 25-April 04:30:15 UTC, by a Febus Optics A1-R DAS interrogator unit. The former was interrogated on the first 48 h of the experiment, and the latter during the rest of the DAS campaign. The A1-R DAS unit interrogates the fibre using a single-pulse phase-based system that generates strain rate recordings. Longitudinal cable strains are obtained by the optical dephasing between two points along the fibre cable, at a specified gauge length distance. We set the DAS interrogator to acquire with a pulse width of 5 m, a spatial resolution of 3.2 m, and pulse rate frequencies of 500 Hz on the HCMR cable, and 1400 and 1000 Hz for the first and last 4 days on the NESTOR cable, respectively. The gauge length was set to 19.2 m for both cables, generating an array of 688 and 1365 equally-spaced sensors along the HCMR and NESTOR cables, respectively. Two earthquakes recorded by DAS along the HCMR and NESTOR cables are used in this study. A M L -3.7 earthquake (epicenter, cyan star in Figure 5.1) identified by the EMSC (European Mediterranean Seismological Centre), with origin time 18-April-2019 21:44:42 UTC, was clearly observed in the DAS-data recorded along the HCMR cable. Similarly, a M L -3.3 earthquake was recorded across the NESTOR cable (epicenter, red star in Figure 5.1). This earthquake was cataloged by the Athens University, with origin time 22-April-2019 19:26:06 UTC.

DAS experiment in Toulon, France

DAS strain data were collected along the MEUST (Mediterranean Eurocentre for Underwater Sciences and Technologies) optic fibre cable, situated offshore Toulon, south of France (Figure 5.1). The cable bridges landward a multi-physics-and-communication station and the KM3NeT/ORCA (Oscillation Research with Cosmics in the Abyss) neutrino detector located at the cable underwater termination point, as part of the MEUST-NUMerEnv (NeUtrino Mer Environment) project [START_REF] Lamare | The meust deep sea infrastructure in the toulon site[END_REF][START_REF] Coyle | KM3NeT-ORCA: Oscillation Research with Cosmics in the Abyss[END_REF]. The MEUST cable spans 44.8 km and its armouring progressively changes oceanward, as follows: a Double Armouring (DA) of two layers of galvanized steel wires along the first 2.1 km offshore, then a Single Armouring (SA) of one layer of galvanized steel wires for the next 15.1 km, and finally a metallic screen until the cable termination point. Only the first 500 m of cable are buried offshore. Afterward, the cable lays on the seafloor and traverses different oceanic features until reaching a maximum depth of 2420 m.

The MEUST cable was sensed combining a DAS-interrogator from Aragon Photonics (HDAS) with Raman amplification. Distributed Raman amplification guarantees longitudinal (along the cable axis) strain recordings with an instrumental noise floor variation of < 5 dB [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF][START_REF] Williams | Distributed sensing of microseisms and teleseisms with submarine dark fibers[END_REF][START_REF] Pastor-Graells | Single-shot distributed temperature and strain tracking using direct detection phase-sensitive otdr with chirped pulses[END_REF][START_REF] Lior | On the Detection Capabilities of Underwater Distributed Acoustic Sensing[END_REF]. The instrumental noise floor was observed to be below 100 picostrain/

√

Hz along the cable, which is comparable to optimal laboratory measurements for long fibres [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF][START_REF] Lior | On the Detection Capabilities of Underwater Distributed Acoustic Sensing[END_REF]. During the DAS experiment performed between 11-July-2019 13:12:16 UTC and 31-July-2019 08:19:25 UTC, the pulse wavelength was set to 1550 nm, with 100 ns width (equivalent to a spatial resolution of 10 m), 1 GHz spectral content and 50 mW peak power.

Corning© LEAF (Large Effective Area Fiber) optic fibres featuring a light attenuation (<0.19 dB/km) are integrated in the MEUST cable, which also improved the detection range. The longitudinal strain was sampled at a rate of 100 Hz during the first 10 days of the experiment and 500 Hz in the remaining part of the campaign. The gauge length was set at 10 m, creating a network of 4480 equally-spaced strain sensors across the cable. To prevent low-frequency noise affecting the strain recorded by DAS, as suggested by R. [START_REF] Fernández-Ruiz | Teleseisms monitoring using chirped-pulse φotdr[END_REF], we converted the strain data to strain rate by computing its finite-difference time derivative. The data set used here is composed of strain rate recordings comparable to the ones collected during the Greek experiment.

A M L -3.9 earthquake recorded by DAS along the MEUST cable is used in this study. The epicenter of the earthquake (green star in Figure 5.1) was identified by the IGN ("Instituto Geográfico Nacional", Spanish for "National Geographic Institute") at northern Algeria, with origin time 22-July-2019 16:23:07 Local Time.

5.3 Fibre optic cable oscillations triggered by earthquakes 5.3.1 Detection of High-Frequency oscillations DAS recordings show that the passage of earthquake seismic waves along underwater fibre optic cables excites high-frequency oscillations that remain trapped within certain cable sections. We analyze the strain rate recorded by DAS along the NESTOR, HCMR and MEUST cables, at the time of the three earthquakes aforementioned, low-pass filtered with a cutoff frequency of 20 Hz. Oscillations with frequencies above 2 Hz appear simultaneously in cable portions with different span lengths, at the same time as the passage of seismic waves, as shown in Fig. 5.2(c) for the NESTOR cable. We refer to these oscillations as "high-frequency oscilla- tions" or HF oscillations. Figure 5.2 shows an example during a M L -3.3 earthquake recorded by DAS in the NESTOR cable (Figure 5.2.a). HF oscillations are confined within some cable segments. We select a 1-min window, 40 s after the origin time of the earthquake, in which HF oscillations are visible, and calculate the Fourier spectrum for each channel. The spectra show fundamental and harmonic frequencies excited above 2 Hz (Figure 5.2.c). HF oscillations are not visible on 1-min windows 90 s before and 180 s after the origin time of the earthquake. In contrast, signals with frequency lower than 1 Hz exist at all times on certain cable segments (Figure 5.2.b,d): these low-frequency oscillations are related to a different process discussed later on. A similar behavior is observed for earthquakes recorded along the HCMR and MEUST cables (Supplementary Figures 5.9 and 5.10).

The relation between the frequencies of HF oscillations and the span lengths of the cable portions that host them suggests they are made of waves trapped along the cable. We measure the fundamental frequencies of the HF oscillations excited by the three earthquakes, and plot them as a function of the span length L of their hosting cable segment (Figure 5.3). We find that they follow the equation:

f n = nV 2L (5.1)
that describes the natural frequency f n of the n-th normal mode of wave propagation in a 1D elastic medium with fixed ends, wave speed V and length L [START_REF] Thompson | Dispersion of flexural elastic waves in honeycomb sandwich panels[END_REF][START_REF] Yigit | Vibration confinement in flexible structures via alteration of mode shapes by using feedback[END_REF]. Fundamental frequencies (n = 1) recorded along different segments of the MEUST, HCMR and NESTOR cables are consistent with a wave speed V = 4000 m/s ± 400 m/s (Figure 5.3). Similarly, the first and second harmonics (n = 2, 3) in the NESTOR cable are in agreement with eq. ( 5.1) and the same wave speed (Figure 5.3). The implications of the wave speed value obtained are described in section 5.3.3.

Normal modes of the High-Frequency oscillations

Modal analysis further supports that the propagation of longitudinal waves along a vibrating string is one of the simplest model to explain the HF oscillations. Modal analysis is commonly used to characterize the normal modes of a vibrating structure, and the Proper Orthogonal Decomposition (POD) is a popular technique for examining modal activity [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]. The POD method, also known as Karhunen-Loève decomposition, is a statistical approach to obtain optimal distributions of energy from a set of recordings [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]. It has been widely used to generate empirical modes for modal reduction of nonlinear systems (Kappagantu andFeeny, 1999, 2000), to yield a measure of spatial coherence [START_REF] Cusumano | Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree of freedom impact oscillator[END_REF]Cusumano et al., 1993), and for modal analysis [START_REF] Feeny | On the physical interpretation of proper orthogonal modes in vibrations[END_REF]. POD results in a family of proper orthogonal modes (POMs) that are extracted from the correlation matrix of a set of time series [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]. We extract normal modes from 1-min windows of the HF oscillations described in 5.3.1, using POD. The correlation matrix used for the POD calculations is composed of the strain rate recorded by DAS along the cable segments featuring HF oscillations.

We compare normal modes extracted by POD from HF oscillations to those of a 1D wave propagation structure with fixed ends. The normal modes (Φ n ) of a vibrating string fixed at its ends are described by:

Φ n (x) = sin nπx L (5.2)
with n and L as defined for eq. ( 5.1), and x ∈ [0, L] the relative location along the span length [START_REF] Yigit | Vibration confinement in flexible structures via alteration of mode shapes by using feedback[END_REF]. We calculate the spatial derivative ∂Φ n (x)/∂x of eq. ( 5.2), which provides the modes expected for strain rate data. The fundamental mode derived from the cable vibrations by POD has the same shape as the theoretically expected fundamental mode (Figure MEUST cable between km 18.90 and 19.18 (green), NESTOR cable between km 14.13 and 14.78 (red), and HCMR cable between km 9.69 and 10.04 (cyan). Vertical and horizontal axes are normalized by the maximum amplitude of the Normal Mode derivative and the span length L, respectively. (b) Sames as a, but for the Proper Orthogonal first-harmonic-Mode of NESTOR and HCMR cables. (c, d and e) Fourier spectra of the POD-extracted fundamental and first-harmonic mode time series |F(P OC(t) 1 )| and |F(P OC(t) 2 )| (blue and magenta, respectively) compared to the Fourier spectra of the 1-min fibre cable oscillations indicated in a and b, band-pass filtered between 2 and 20 Hz (gray). Proper Modes extracted through POD of the fibre strain oscillations recorded by DAS are in agreement with those of a 1D vibrating structure fixed at its ends. 5.4.a), regardless of the cable location and the DAS-interrogator used (POMs calculations in the Supplementary Material). Similarly, the first harmonic mode extracted from the NESTOR and HCMR cable oscillations by POD is in agreement with the model prediction (Figure 5.4.b).

Natural frequencies recorded by DAS during HF oscillations are in agreement with the ones extracted by POD. POMs derived from POD can be used as basis functions to define proper orthogonal modal coordinates (POCs). Each time-dependent POC represents the amplitude time series associated to its corresponding POM, and its frequency content provides information of the number of active modes [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]. We calculate the Fourier transform of the POCs derived from the POMs of Fig. 5.4(a), for cable segments of the MEUST, NESTOR and HCMR cables that span 280.00, 652.80 and 345.60 m, respectively. We compare them with the Fourier spectra obtained from vibrating cable spans at relative positions (i.e. distance along span normalized by span length) of 0.125, where the fundamental and first harmonic normal modes should have non-zero amplitude according to Fig. 5.4(a,b). We observe that the fundamental frequency of the HF oscillations recorded by DAS in the three cables is in agreement with the one extracted by POD (Figure 5.4.c,d,e). In the case of the NESTOR and HCMR fibre cables, harmonic frequencies were also measured during the cable vibrations. We note that those harmonic frequencies correspond as well to the ones derived from the POCs' spectra.

Cable waves in underwater fibre optic cables

Cross-correlation analysis of DAS data indicates that the HF oscillations are composed of waves traveling along the cable and trapped within bounded cable spans. We calculate crosscorrelation functions between strain rate time series of pairs of DAS channels along cable spans featuring HF oscillations. To avoid high-frequency noise, the strain rate data were band-pass filtered between 2 and 20 Hz. Then, cross-correlations were computed over 60-s-long consecutive windows, using as reference trace the first oceanward DAS channel featuring the oscillations. The cross-correlation traces show waves traveling back and forth along segments of all three cables: Figure 5.5(c,e) shows examples from two sections of the NESTOR cable, while examples for the MEUST and HCMR cables can be found in Supplementary Figures 5.11 and 5.12. For all three cables, the trapped waves travel at speeds ranging from 3939 to 4080 m/s (Figure 5.5.c,e,Supplementary Figures 5.11.c,e and 5.12.c,e), consistent with the speed obtained in Fig. 5.3, and close to the compressional speed of stainless steel ∼ 5000 m/s [START_REF] Haynes | crc handbook of chemistry and physics[END_REF]. This observation is in agreement with the property that longitudinal waves in a composite cable are primarily controlled by the characteristics of the stiffer and denser material, here the steel armouring of the cable [START_REF] Miller | Das and dts at brady hot springs : Observations about coupling and coupled interpretations[END_REF]. The fact that cable waves are trapped indicates that there are changes in the mechanical cable/seafloor coupling along the cable. Local seafloor conditions affect the mechanical coupling between underwater fibre cables and the sea bottom. Indeed, cable sections can be partially or completely buried, just laying on the seafloor, or even hanging (Mata Flores et al., 2022). As previously reported in borehole DAS data, fibre cable segments that are decoupled from the borehole wall can host the propagation of longitudinal vibrations along the cable, the so-called "cable waves" detected by [START_REF] Munn | Novel cable coupling technique for improved shallow distributed acoustic sensor vsps[END_REF]. However, to the best of our knowledge, cable waves have not been previously reported in the literature of underwater DAS. [START_REF] Chang | Investigation of time-lapse changes with das borehole data at the brady geothermal field using deconvolution interferometry[END_REF] observed similar waveforms and wave speeds than the ones we present in Fig 5 .5, for a borehole DAS experiment. They attributed the waveforms to waves likely propagating in the stainless steel cable jacket or the steel well-casing. They also observed similar normal mode shapes and natural frequencies for cable or casing waves than those we obtain from the POD of the HF oscillations presented here. We detect the cable waves along cable segments traversing steep continental slopes or deep ocean valleys (Figure 5.5.b,d,respectively), which may allow cable spans pinned between two points of the sea bottom.

Cable waves generated by earthquakes may reveal cable segments that are unsuitable for DAS applications in seismology. The detection of earthquake-triggered cable oscillations indicates cable spans affected by monochromatic noise due to the generation of cable waves. Figure 5.6.(c) shows DAS-strain rate recordings across the NESTOR cable, collected during the arrival of the seismic waves generated by the M L -3.3 earthquake of Fig. 5.1. We selected two DASchannels on the NESTOR cable separated by 110 m (Figure 5.6.(a,b)): the first at km 19.70 in window W1 containing cable waves and the second at km 19.81 in window W2 without cable waves. Assuming that the variability of the incidence angle and epicentral distance effects of the earthquake are weak at this scale, both DAS-channels should record similar waveforms. Highly monochromatic noise affects the DAS-trace at km 19.70 after the arrival of seismic waves, while the DAS-recordings at km 19.81 are unaffected by this type of noise. We associate the noise in W1 with the propagation of cable waves along this segment. The high-amplitude noise introduced by the cable waves prevents from detecting latter seismic phases across cable sections featuring HF oscillations. Therefore, the detection of cable waves by DAS may help to evaluate the usability of certain cable segments for DAS-applications in underwater seismology.

Low-Frequency oscillations compared to High-Frequency oscillations

As mentioned in section 5.3.1, fibre cable oscillations at frequencies lower than 1 Hz are also detected by DAS. We refer to these oscillations as "low-frequency oscillations" (LF oscillations), since their fundamental frequencies are lower than those of the HF oscillations. We observe LF oscillations that extend coherently between pairs of points along the MEUST, NESTOR and HCMR cables. As previously reported by Mata Flores et al. ( 2022), LF oscillations can last from hours to days and they occur along hanging sections of underwater fibre cables exposed to Vortex-Induced Vibrations (VIV) driven by deep ocean currents. We occasionally observe harmonics of these oscillations (Supplementary Figure 5.13). In this study, we examine the vibration modes and calculate cross-correlations along the cable spans featuring LF oscillations in order to compare the results with the ones already obtained for the HF oscillations.

The LF oscillations show a dominant normal mode shape with quasi-uniform strain rate, a box-car shape. The same normal mode shape is retrieved by POD analysis from the three cables, during periods containing LF oscillations, which we call the "dominant normal mode" (Figure 5.7). The LF dominant normal mode does not correspond with the fundamental mode of strain along a vibrating string, presented in Fig. 5.4(a), since it does not feature nodes along the cable span. Spectral analysis of the POC derived from the dominant normal mode shows a dominant frequency, which corresponds with the one recorded by DAS during the LF oscillations.

Key aspects of the box-car shape featured by dominant normal modes can be interpreted by beam theory deformation under VIV. Bourguet and Triantafyllou (2015) reported box-car shaped root-mean-square (RMS) displacements in numerical simulations of VIV along a flexible cylinder fixed at both ends. However, a box-shaped RMS displacement does not imply a box-shaped strain rate. More useful insight is derived here from beam theory. According to classical beam theory, the longitudinal strain ε (x) of a long and slender beam -a component designed to support transverse load by bending only -laying on two supports, is proportional to its deflection y(x) through its curvature κ: ε [START_REF] Timoshenko | 1 heory of elasticity[END_REF][START_REF] Kelly | Solid mechanics part i: An introduction to solid mechanics[END_REF]. Assuming that the slope of the deflection curve is small (y ′ (x) << 1), which is expected for small deformations of fibre cables, leads to κ ≈ y ′′ (x), and the longitudinal strain of the beam becomes proportional to its bending as [START_REF] Kelly | Solid mechanics part i: An introduction to solid mechanics[END_REF]:

(x) = -κ y(x) , with κ = y ′′ (x) (1+y ′ (x) 2 ) 3/2 (Timoshenko
ε (x) ≈ -y ′′ (x) y(x)
(5.3) We considered the fibre segments featuring LF oscillations as beams that bend due to the transverse oscillating load induced by the drag forces during VIV. Moreover, we assumed that the tensioned fibres have mode-shapes given by a sine function y(x) = A sin(nπx/L), with L the cable span length and A an unknown amplitude, as suggested by [START_REF] Lie | Modal analysis of measurements from a large-scale viv model test of a riser in linearly sheared flow[END_REF] for a riser manifesting VIV due to a linearly sheared flow. Under those assumptions, equation (5.3) shows that the dominant normal modes for longitudinal strain should have a sine-square shape (Supplementary Figure 5.17). Equation ( 5.3) explains well the zero strain at both ends of the dominant normal modes, and the absence of strain nodes within the oscillating span, two features that cannot be explained by the vibrating string theory. However, it predicts a maximum of strain at the mid-span, which is different from the quasi-uniform strain of the observed dominant normal mode. More investigation is needed to completely elucidate what physical process controls the shape of the dominant normal mode extracted from DAS-recorded LF oscillations.

Evidence suggests that the HF and LF oscillations presented here are associated with different conditions of the mechanical cable/seafloor coupling. These two types of oscillations have different frequency content and normal mode shapes. Besides, LF oscillations have been associated with deep ocean currents hitting suspended fibre cable spans, which generate vortexinduced vibrations (Mata Flores et al., 2022). The ocean-driven origin of the LF oscillations contrasts with the earthquake-triggered HF oscillations presented in this study. We calculate cross-correlation traces from cable segments featuring LF oscillations. To prevent highfrequency noise, the strain rate data were first low-pass filtered at 2 Hz. Then, cross-correlations were computed over 30-min-long windows, using as reference trace the first oceanward DAS channel featuring the oscillations. The cross-correlation traces do not show cable waves (Supplementary Figure 5.14), thus LF oscillations cannot be used to identify fibre cable spans pinned between two points along the seafloor. Further work is warranted to locate suspended sections of seafloor fiber cables with precision, by combining the detection of the LF oscillations we present here with a detailed bathymetry model along the fibre cable path. We suspect that the assessment of fibre cable spans likely to suffer damage due to overload could be performed through the detection of LF fibre cable oscillations.

Discussion

Our results suggest that LF and HF oscillations can be detected on seafloor fibre optic cables regardless of the geographic location and the interrogator used for the DAS acquisition. The data analyzed here was recorded on three underwater fibre cables deployed in two different locations of the Mediterranean sea. The datasets were acquired by DAS interrogators that use distinct optical measurement principles. Yet, HF oscillations were observed in all cases. Similarly, LF oscillations were recorded along both the Toulon and Methoni cables. We expect the two vibration regimes can be detected in any seafloor fibre cable interrogated by DAS, since they are generated by mechanisms that are independent of the optical properties of DAS.

LF and HF oscillations result from independent mechanisms. We showed here that HF oscillations are triggered by seismic waves from earthquakes, while Mata Flores et al. (2022) showed that LF oscillations are driven by ocean currents. We found here that the frequency content of LF and HF oscillations is well separated and their occurrence is not correlated, which suggests distinct sources for each vibration regime. The frequencies of HF oscillations depend on span length (Figure 5.3) and, for the three steel-armoured fiber cables used in this study, are higher than 2 Hz and lower than 18 Hz, along span lengths ranging from 115.20 to 748.80 m. On the other hand, the frequency content of LF oscillations observed in this study rarely exceeds 1 Hz nor depends on span length. LF and HF oscillations can be recorded simultaneously, as shown in Fig. 5.2.c, without their characteristics being affected, which suggests the two vibration regimes are not mutually exclusive. Nevertheless, further work should be aimed to determine if HF oscillations occur on longer cable spans than those found here, at frequencies that overlap with LF oscillations.

We propose that LF and HF oscillations can be used to assess the mechanical coupling between offshore fibre cables and the seafloor. LF oscillations require hanging cable segments, as documented by Mata Flores et al. (2022). We interpret here that HF oscillations require two pinning points that prevent longitudinal motion of the cable and trap compressional cable waves along a finite span length. The identification of fibre cable segments featuring LF or HF oscillations can supply information of the mechanical cable/seafloor coupling without deploying additional instruments or resources. We propose to use the detection of LF and HF oscillations to monitor the spatial distribution of the mechanical coupling between offshore fibre cables and the sea bottom. Tracking the amplitude of strain rate via its standard deviation in the LF band is a convenient approach to identify cable sections that are presumably hanging and thus might suffer damage due to overload or fatigue, as shown in Fig. 5.8 for the NESTOR and HCMR cables. The identification of HF oscillations can pinpoint the cable segments that are least appropriate where suspended portions of the fibre cable are expected, 6 segments featuring quasi-uniform strain rate correlate with an increase of the maximum positive strain rate and the standard deviation of the strain rate.

for seismological purposes due to high noise made of trapped cable waves. On the other hand, the temporal evolution of the mechanical cable/seafloor coupling may also be tracked through the detection of LF oscillations. Submarine slopes starting at the edge of continental shelves are usually eroded into deep canyons and other small channels that accumulate sediments, until they become unstable and initiate erosion by sedimentary mass flows such as turbidity currents [START_REF] Shepard | Submarine canyons: multiple causes and long-time persistence[END_REF][START_REF] Mitchell | Interpreting long-profiles of canyons in the usa atlantic continental slope[END_REF]. In submarine canyons, erosion may alternate locally with sediment deposition [START_REF] Menard | Some rates of regional erosion[END_REF], which exposes underwater fibre cables traversing continental slopes to different rates of sediment accumulation. Most of the suspended sections we identified in this study are located along cable segments that cross continental slopes, as shown in Fig. 5.8 for the cables in the Methoni bay. Hence, sediment deposition may progressively bury hanging sections until LF oscillations are no longer detectable. We suggest to conduct longer DAS-experiments in fibre cables traversing continental slopes, preferably in areas with high erosion/deposition rates, to verify the relation between sedimentation and the vanishing of LF oscillations in time.

Conclusions

We identified and characterised two vibration regimes of underwater fibre optic cables recorded by DAS along three cables situated in the Mediterranean sea. We observed that seismic waves excite high-frequency oscillations, with fundamental frequencies > 2 Hz, composed of longitudinal waves that remain trapped along cable segments presumably pinned between two points in the seafloor. The frequency vs length relation and normal mode shapes extracted from high-frequency oscillations are consistent with 1D wave propagation in a structure with fixed ends. Cross-correlation shows that these waves travel along the cable structure with a speed ranging from 3939 to 4080 m/s, close to that of longitudinal waves propagating along the steel armouring of the cables. We have also identified fibre cable segments featuring low-frequency oscillations, with fundamental frequencies < 1 Hz, which have been previously associated to vortex-induced vibration of suspended cable sections caused by deep sea currents. We further showed that these low-frequency oscillations feature quasi-uniform strain rates along each vibrating section. This is the first study, to our knowledge, assessing the mechanical coupling between offshore fibre cables and the seafloor based on the detection of high-frequency cable waves and lowfrequency vortex induced vibrations. We propose to use the detection of high-frequency and low-frequency oscillations to monitor the spatio-temporal evolution of the mechanical coupling between fibre cables and the seafloor. The former may help to identify the most appropriate cable segments for seismology purposes, and the latter may supply a non-invasive method to monitor cable sections likely to suffer damage due to overload or fatigue.

Each modal co-ordinate represents the dynamics in the axis of its corresponding POM [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]. ) and bending (y ′′ (x)), assuming that fibres have mode-shapes given by a sine function: y(x) = sin(πx/L). Amplitudes in the vertical and horizontal axis are normalized by the maximum strain rate and the cable span length (L), respectively. The relation ε(x) = y ′′ (x)y(x) explains well the zero strain at both ends of the dominant normal modes, and the absence of strain nodes within the vibrating span. However, it predicts a maximum of strain at the mid-span, which is different from the quasi-uniform strain of the observed dominant normal modes.

General Conclusions

Summary of Key Results

-Two vibration regimes of underwater fibers are recorded by DAS: High-Frequency oscillations (HF) with frequencies > 2 Hz and Low-Frequency oscillations (LF) with frequencies < 1 Hz.

-LF oscillations are generated by Vortex-Induced Vibrations (VIV) of cable segments presumably suspended. They feature time-dependent amplitudes and amplitude-dependent characteristic frequencies.

-Time series of ocean current speeds can be obtained using a linear relationship between the frequency of LF oscillations and current speed.

-HF oscillations are triggered by the passage of earthquake seismic waves along cable portions pinned between two seabed points, and are composed of trapped cable waves bouncing back and forth.

-Cable waves introduce highly monochromatic noise, which prevents the analysis of seismic waves.

DAS is a photonics-based technology increasingly popular in the Earth Science community. Scientists started to grow interest on this sensing technique due to its proven capabilities to deliver real time measurements, with unprecedented spatial resolution, in environments otherwise difficult to instrument (seafloor, glaciers, volcanoes...). First applications of DAS were focused on terrestrial cables, and only more recently research on submarine fibers has revealed its potential for the monitoring of deep oceanographic processes, seismic imaging and underwater seismology. The current state-of-the-art of DAS allows sensing seafloor fibers spanning 80 km or more from the coast (up to 150 km on unrepeated cables), which may facilitate worldwide early warning systems and offshore geophysical observatories relying on the telecom cables already crisscrossing the Earth's oceans. However, any growing domain in science has poorly explored corners. In the case of DAS, one remaining central question is the effect of the seabed and cable structure on the DAS recordings. A majority of submarine cables are only buried along their first few kilometers from shore, while the vast majority is subject to a variety of changes in the bathymetry.

During this PhD project, I analyzed DAS recordings collected along three submarine fiber optic cables located in the Mediterranean Sea -one offshore Toulon, in south of France, and two others departing from the Methoni Bay, South-West Greece -all with lengths of ten-ofkilometers. I focused on understanding how different seafloor conditions, from the shore to the abyssal plain, determine the type of signal recorded by DAS across armoured submarine fibers similar to those used for telecommunications. Indeed, I observed that cable segments traversing deep valleys or sudden changes of the seafloor slope correlated with cable oscillations recorded by DAS along the Toulon cable, which suggests those sections are suspended in the water column. I noticed that the cable oscillations feature amplitude-dependent frequencies lower than 1 Hz and larger than any other background noise. Based on those observations, I was able to link these oscillations to vortex-induced vibrations generated by deep ocean currents. Using a theoretical linear relationship, I related the frequency of vibration to the speed of the ocean current causing the cable oscillations. This approach opens the way for scaling up oceanography measurements of deep environments that are barely studied, due to the lack of dedicated instrumentation. More data of deep ocean currents, such as the one provided by the DAS-based current meter concept described here, may help understanding delicate processes including deepwater flows and weak turbulence, and may contribute to improve our current models of climate change.

Additionally, I focused my work on another type of cable oscillations recorded by DAS, but specifically after the passage of earthquake seismic waves. The frequency of these earthquaketriggered oscillations was higher than the ones of the vortex-induced cable vibrations, and showed dependency on the length of the cable segment hosting the vibration. I also noticed these high-frequency cable oscillations were composed of trapped cable waves, propagating back and forth along cable segments presumably anchored between seabed features. The detection of such cable waves in the three submarine fibers allowed to pinpoint cable sections that featured a highly monochromatic noise, which prevented from identifying latter seismic phases possibly generated by the earthquake. It is vital for future applications of DAS in underwater seismology -either for earthquake seismic wave detection or seismic imaging -to discriminate cable sections recording cleaner data from noisier ones. The observation of cable waves may help to easily and rapidly point to noisy sections, without deploying further resources.

The outcomes of this PhD work show valuable insight on a central issue in many seafloor DAS applications: the nature and impact of the mechanical cable/seabed coupling. First, the results I presented suggest that bathymetry does have an impact on the type and quality of signal recorded by DAS. Diverse seafloor conditions may generate different mechanical coupling between the cable and the sea bottom. In this study, I characterized signals recorded by DAS along specific bathymetry features that can be used for applications in physical oceanography and underwater seismology. Further research may help identifying other bathymetry conditions than the ones identified here, that might also influence DAS recordings in deep environments. Second, the cable vibrations analyzed in this PhD research indicate two possible configurations of mechanical coupling between submarine fibers and the sea bottom: suspended and pinned cable portions. Valuable information regarding the mechanical properties of operational fibers may be obtained in real time by detecting those cable vibrations using DAS. Indeed, cable portions susceptible to failure due to overload or supporting points exposed to abrasion due to the ocean dynamics may be potentially detected, by identifying hanging or anchored cable segments, respectively. This may be a solution for the monitoring of seafloor fibers in operation, with no additional equipment or intervention from land, since the data acquisition, processing and interpretation can be done from the on-land end point of the cable.

Future investigations may explore several aspects of the vortex-induced cable vibrations recorded by DAS. First, their large amplitudes may be exploited for automatic detection, via supervised or unsupervised algorithms. Observing those cable vibrations in real time may be useful for applications ranging from tsunami-source detection and early warning to the temporal monitoring of cable portions with high risk of damage. Moreover, field experiments in a different location than the Mediterranean Sea are necessary to determine the applicability of the DAS-based current meter concept described here, for ocean current speeds with amplitudes larger than 5 cm/s. The Thermohaline Front, a large-scale pattern of ocean circulation well known by oceanographers, flows across the Atlantic and Indian oceans. Table A1 displays previous campaigns performed at Greenland (North Atlantic), South-East of Brazil (South Atlantic) and North of Mozambique, in South-East Africa (Indian), that recorded deep ocean currents with amplitudes ranging from 23.77 to 73.66 cm/s. Those locations also correspond to the landing points of several underwater fiber cables (Figure 1.3), that might be exploited by DAS to monitor the Thermohaline circulation at water depths ranging from 500 to 3464 m. This may offer the opportunity to validate the DAS-based method presented in this PhD research, for estimating in a wide range of water depths ocean current speeds with amplitudes 4 to 14 times larger than the ones obtained by this work. Additionally, investigations on the capabilities of DAS to record VIV triggered by wind or freshwater along hanging fibers in air and rivers, could potentially expand the concept proposed here to the monitoring of storms and natural flowing watercourses. ∼ 60 850 [START_REF] Ullgren | Observations of strong ocean current events offshore pemba, northern mozambique[END_REF] Table A1 -Ideal locations for the monitoring of large-scale ocean circulation by DAS along seafloor fiber optic cables. The Thermohaline front -a large-scale pattern of deep ocean circulation -flows near to these three locations, which correspond to the landing points of several underwater fibers (Figure 1. 3). The amplitude of ocean current speeds represents the maximum value recorded by previous oceanography campaigns.

Location

Further research on earthquake-triggered cable oscillations recorded by DAS may explore techniques to suppress the monochromatic noise introduced by cable waves. The moving averaging/moving differential methods proposed by [START_REF] Lu | Distributed vibration sensor based on coherent detection of phase-otdr[END_REF] and the wavelet-based data processing suggested by [START_REF] Qin | Wavelet denoising method for improving detection performance of distributed vibration sensor[END_REF] (Section 2.2.3), may help increasing the signal-tonoise ratio of signals associated to earthquake seismic waves. Cleaning the DAS signal of fiber cable sections featuring cable waves noise may lead to a fully use of seafloor fibers traversing pinning bathymetry features. Field experiments with enhanced fibers anchored between two seabed points may also supply valuable insight of their sensitivity to earthquake-induced noise.

Finally, DAS provides an amount of data that challenges our current tools for data processing and analysis. It is then essential to optimize our techniques for data management and data storage, in order to effectively exploit all the advantages that DAS datasets may offer. Research evaluating how much data is actually necessary to efficiently use terrestrial or submarine fiber cables sensed by DAS might supply a clue to such remaining open subjects. In my opinion, these are important matters that sooner or later will impact the way science on DAS is performed.

  -clés: câble de télécommunication, Mesure acoustique distribuée, fond marin, vibrations vii de câble, courants marins, ondes de câble, vibrations induites par vortex viii List of Figures 1.1 Hypsometric (area-altitude, area-depth) curve of the Earth. Oceans represent around 70% of the Earth's surface total area. Yet, most of the ocean's extension is barely instrumented leading to a lack of oceanography measurements, especially below the average depth of the ocean. (Modified from (Ye et al., 2018)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Number of DAS-related publications between 2011 and 2022. DAS-related publications and citations (gray) and, since 2013, DAS-related publications and citations in earthquake (cyan) and ocean (red) works are increasing quickly and steadily. (Inspired in (Zhan, 2020). Source: Web of Science Clarivate, Dec. 2022) 1.3 Worldwide network of submarine fiber optic cables. Active and planned underwater fiber cables traversing the ocean (orange lines) are depicted together with their landing points (white dots). Landing points in Greenland (1), South-East of Brazil (2), and North of Mozambique (3) are highlighted. Data downloaded from www.submarinecablemap.com were used to generate the figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3. 3 3 . 4

 334 Schematic view of the three main types of fiber optic cables. 2D crosssectional view of: (a) a single-mode, (b) a multimode, and (c) a graded-index fiber optic cable. As a reference, the injected input signal is represented together with the expected output signal, for each type of fiber. Modal dispersion affects the amplitude of the retrieved signal in multimode fiber optic cables. (Modified from (Al-Azzawi, 2017)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propagation of light along fiber optic cables. (a) Light arrives at the corecladding interface at an angle θ and is refracted at an angle β. (b) If θ increases, then β becomes larger. (c) At a particular θ (i.e. critical angle of incidence, θ c ), the refracted light travels across the core-cladding interface. (d) Beyond θ c , all the incident light is reflected back into the core, a phenomenon known as total internal reflection. (e) Light propagates in fiber cables following the total internal reflection along the entire cable span. (Modified from (Al-Azzawi, 2017))

  (Taken from METHONI EMSO Submarine Cable System -As Built Report by ELETTRA, 2015) . . . . . 48 3.14 Images taken during a ROV inspection along the NESTOR cable, southwest of Greece. (a) Obstacles or (b, c) irregular seafloor can generate suspended sections of submarine fiber optic cables. . . . . . . . . . . . . . . . . 49 4.1 Sketch of Vortex-Induced Vibrations (VIV). Vortices are shed off from an eloganted body due to VIV generated by a steady fluid (blue arrows). (Modified from (Williamson and Govardhan, 2008)) . . . . . . . . . . . . . . . . . . . . 52 4.2 Underwater VIV of a fiber cable segment suspended in the water column.

4 . 4

 44 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 xx Location and bathymetry model of the underwater MEUST cable. The optic fiber cable depicted in (a) offshore Toulon, France, traverses different seafloor features throughout its 44.8-km length (b). Nine hanging sections were identified along three segments of the cable trajectory (1 in Segment 1, 6 in Segment 2 and 2 in Segment 3). The red triangle represents the position of an Acoustic Doppler Current Profiler (MII current meter) deployed next to the cable end (Coyle, 2017). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Vortex-Induced Vibrations (VIV) recorded by seafloor DAS. We show two examples, in segments 3 (left) and 2 (right). (a) Bathymetry profile along the cable path (VE stands for Vertical Exaggeration) and (c) 84 hours-long recording of low-pass filtered strain rate, along a portion of Segment 3.

4 . 7

 47 Figure 4.5.e) . . . . . . . . . . . . . . . . xxi Deep ocean currents sensed by DAS compared to MII current meter records.

5 . 5 5 . 8

 5558 (a) Bathymetry profile along the MEUST cable path (VE stands for Vertical Exaggeration) and (b) 84 hours-long recording of low-pass filtered strain rate, along a cable portion of Segment 1. A cutoff frequency of 2 Hz is used to filter the strain rate. Uniform quasi-harmonic oscillations of fiber strain occur around a seafloor valley. (c) Spectrogram of strain rate at the center of the vibrating section featuring a time-dependent characteristic frequency, varying from 0.13 to 0.16 Hz. Higher harmonic frequencies of VIV are excited during different periods, accompanied by large strain amplitudes. . . . . . . . . . . .4.11 Validity of the Independence Principle (IP) for oblique Vortex-Induced Vibrations registered by underwater DAS. (a) Time variation of the angle " θ" between the ocean currents registered by MII current meter and the plane perpendicular to the cable axis (red circles), from 11-July-2019 00:00:00 UTC to 31-July-2019 00:00:00 UTC. The red line indicates the median angle averaged over a 2-hours sliding window. (b) Median of ocean currents registered by MII current meter averaged over 2-hours-long sliding windows (black), its vertical component respect to the plane perpendicular to the cable axis (magenta) and DAS-derived ocean currents (blue), during the same time in (a). The angle " θ" fluctuates between 24 and 82 degrees during the campaign. The vertical component of the MII current meter and DAS-derived ocean current time series do not match, which invalidates the IP. We believe that the high variability of " θ" may lead the IP to fail predicting the component of the oceanic current speed contributing to the VIV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Location of the underwater HCMR, NESTOR and MEUST electro-optic fibre cables. (yellow rectangle) The 13.2-km-long Hellenic Center for Marine Research (HCMR) and the 26.2-km-long Neutrino Extended Submarine Telescope with Oceanographic Research (NESTOR) fibre cables, situated offshore Methoni Bay, Greece. DAS data were acquired in HCMR and NESTOR cables between 18-April-2019 16:20:22 UTC and 25-April-2019 04:30:15 UTC. (cyan and red stars) Epicenters of: a M L -3.7 earthquake recorded along HCMR cable, origin time 18-April-2019 21:44:42 UTC, and a M L -3.3 earthquake recorded along NESTOR cable, origin time 22-April-2019 19:26:06 UTC, respectively (Lior et al., 2021). (red rectangle) The 44.8-km-long Mediterranean Eurocentre for Underwater Sciences and Technologies (MEUST) fibre cable, located offshore Toulon, France. A DAS experiment was conducted along the MEUST cable between 11-July-2019 13:12:16 UTC and 31-July-2019 08:19:26 UTC. (green star) Epicenter of a M L -3.9 earthquake recorded along the MEUST cable, origin time 22-July-2019 16:23:07 Local Time. . . . . . . . . . . . . . . . xxiii 5.2 High-frequency vibrations triggered along the NESTOR fibre cable after a M L -3.3 earthquake is recorded by DAS. (a) Low-pass filtered strain rate between km 12.48 and 19.20 along the NESTOR cable, from 22-April-2019 19:24:45 to 19:30:15 UTC. Strain rate is filtered below 20 Hz. (red star) Origin time of the M L -3.3 earthquake of Fig.5.1 is indicated as reference (Lior et al., 2021). (red rectangles) Waves trapped along certain cable sections can be observed after the arrival of seismic waves. (b), (c) and (d) Fourier Spectra between km 12.48 and 19.20 of a 1-min window starting: 90 s before the earthquake (1), 40 s after the earthquake (2) and 180 s after the earthquake (3), respectively. Red lines in (c) indicate the cable sections highlighted by red rectangles in (a). Fourier spectra before (b) and after (d) the earthquake are dominated by excited frequencies lower than 1 Hz. Fundamental-and-harmonic frequencies higher than 2 Hz appear after the arrival of seismic waves along different cable spans (c), from km 12.48 to 19.20. . . . . . . . . . . . . . . . . 83 5.3 Natural frequencies of earthquake-triggered oscillations as a function of underwater fibre cable spans. Natural frequencies recorded by DAS during EQ-triggered fibre cable oscillations are represented as a function of the cable span length featuring the vibration for the MEUST (green), NESTOR (red) and HCMR (cyan) cables. Error bars indicate half of the gauge length used during each DAS experiment. The black continuous lines follow the equation f n = nV /2L of the n-th natural frequency f n of a 1D elastic medium with fixed ends, wave speed V and length L. Values of n = 1, 2, 3 represent the fundamental mode, the first and the second harmonic, respectively. A wave speed V = 4000 m/s (solid lines) with a deviation of ± 10% (dashed lines) is consistent with the natural frequencies of MEUST, HCMR and NESTOR cables. . . . . . . . . . 85 5.4 Proper Orthogonal Decomposition (POD) of high-frequency fibre cable oscillations compared to Normal Modes of a vibrating string. (a) Spatial derivative ∂Φ n (x)/∂x of the normal modes Φ n (x) = sin(nπx/L) of a vibrating string (black) compared to the Proper Orthogonal fundamental-Modes extracted from a 1-min-long window of fibre oscillations recorded during an EQ in: MEUST cable between km 18.90 and 19.18 (green), NESTOR cable between km 14.13 and 14.78 (red), and HCMR cable between km 9.69 and 10.04 (cyan). Vertical and horizontal axes are normalized by the maximum amplitude of the Normal Mode derivative and the span length L, respectively. (b) Sames as a, but for the Proper Orthogonal first-harmonic-Mode of NESTOR and HCMR cables. (c, d and e) Fourier spectra of the POD-extracted fundamental and first-harmonic mode time series |F(P OC(t) 1 )| and |F(P OC(t) 2 )| (blue and magenta, respectively) compared to the Fourier spectra of the 1-min fibre cable oscillations indicated in a and b, band-pass filtered between 2 and 20 Hz (gray). Proper Modes extracted through POD of the fibre strain oscillations recorded by DAS are in agreement with those of a 1D vibrating structure fixed at its ends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 xxiv Longitudinal trapped waves detected by DAS along cable segments featuring earthquake-triggered vibrations. (a) Band-pass filtered strain rate between km 13.82 and 17.28 along the NESTOR cable, from 22-April-2019 19:26:46 to 19:27:46 UTC. Strain rate is filtered between 2 and 20 Hz. (red rectangles) Two 60-s-long windows of 883.2 (1) and 960 m (2) width are indicated as reference. (b) Bathymetry profile between km 14 and 15 along the cable path (VE stands for Vertical Exaggeration). The red line highlights the location of window 1 in (a). (c) Cross-correlation traces calculated over window 1 in (a), and relative to the trace reference number 5, km 14.13 along the cable. Amplitudes are normalized by the maximum of the cross-correlation traces. A longitudinal trapped wave bouncing forward and backward along the cable span with a speed of 4080 m/s can be clearly observed (black dashed lines). (d and e) Same as b, and c, but for a cable section presumably suspended between km 16 and 17, window 2 in (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Noise generated by cable waves in DAS-strain rate recordings of the NESTOR cable. (a) 120-s-long traces of band-pass filtered strain rate between km 18.24 and 21.12 along the NESTOR cable. Traces are filtered between 1 and 12 Hz and are represented each 57.6 m. (dashed line) Arrival of seismic waves due to the M L -3.3 earthquake of Fig. 5.1. (red and blue rectangles) As reference, 60-s-long windows of 172.8 m width indicate whether cable waves are detected (W1) or absent (W2), respectively. (b) Fourier spectra between km 18.24 and 21.12 of a 60-s-long window starting at the same time of W1 in (a). (red and blue rectangles) Frequency content of W1 and W2, respectively. (c) 15-s-long traces of strain rate along: km 19.70, in W1 (red) and km 19.81, in W2 (blue). Amplitudes are normalized by the maximum strain rate of each DAS-channel. Cable waves are clearly recorded in W1, which may explain the high monochromatic noise that dominates the signal along the DAS-trace in km 19.70, after the arrival of seismic waves, compared to the DAS-trace in km 19.81. . . . . . . . 5.7 Dominant normal mode of Low-Frequency oscillations recorded by DAS. (a) Proper Orthogonal fundamental Modes of the NESTOR (red), HCMR (cyan) and MEUST (green) cables, extracted through POD of LF oscillations. (b, c and d) 1-h-long windows of low-pass filtered strain rate featuring LF oscillations along the MEUST, HCMR and NESTOR cable, respectively. Strain rate is filtered below 2 Hz. (black rectangles) 30-min-long windows of strain rate along cable spans of 180.00, 345.60 and 806.40 m selected in the MEUST, HCMR and NESTOR cable, respectively, for POD calculations. The dominant normal mode obtained from the three cables exhibits a quasi-uniform strain rate along the cable span featuring the oscillation, similar to a box-car shape. . . . . . . . xxv Fibre segments of the NESTOR and HCMR cables presumably vibrating are highlighted by Low-Frequency Oscillations. (a) NESTOR and HCMR cable trajectories offshore Methoni Bay, Greece (black), and location of the detected vibrating sections (magenta). Positive and negative values indicate the distance along the cable path in kilometers and the seafloor depth in meters, respectively. (b) Low-pass filtered strain rate along NESTOR cable between km 5 and 26, from 19-April-2019 18:18:38 to 18:20:38 UTC (black and white), compared with the variation across the cable of the maximum positive strain rate (blue) and the standard deviation of the strain rate (red). Strain rate is lowpass filtered below 2 Hz. (c) Same as b, but from 24-April-2019 02:43:46 to 02:45:46 UTC. Throughout the continental slope between km 10 and 20 across the NESTOR fibre in (c), where suspended portions of the fibre cable are expected, 6 segments featuring quasi-uniform strain rate correlate with an increase of the maximum positive strain rate and the standard deviation of the strain rate. 95 5.9 High-frequency vibrations triggered along the HCMR fibre cable after a M L -3.7 earthquake is recorded by DAS. (a) Low-pass filtered strain rate between km 7.48 and 10.96 along the HCMR cable, from 18-April-2019 21:43:07 to 21:48:47 UTC. Strain rate is filtered below 20 Hz. (cyan star) Origin time of the M L -3.7 earthquake of Fig.5.1 is indicated as reference. Waves trapped along certain cable sections can be observed in Window 2, after the arrival of seismic waves. (b), (c) and (d) Fourier Spectra between km 7.48 and 10.96 of a 1-min-long window starting: 90 s before the earthquake (1), 40 s after the earthquake (2) and 180 s after the earthquake (3), respectively. Fourier spectra before (b) and after (d) the earthquake are dominated by excited frequencies lower than 1 Hz. Fundamental-and-harmonic frequencies higher than 2 Hz appear after the arrival of seismic waves along different cable spans (c), from km 7.48 to 10.20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.10 High-frequency vibrations triggered along the MEUST fibre cable after a M L -3.9 earthquake is recorded by DAS. (a) Low-pass filtered strain rate between km 16.50 and 19.70 along the MEUST cable, from 22-July-2019 16:23:00 to 16:39:00 UTC. Strain rate is filtered below 20 Hz. (green star) Origin time of the M L -3.9 earthquake of Fig.5.1 is indicated as reference. Waves trapped along certain cable sections can be observed in Window 2, after the arrival of seismic waves. (b), (c) and (d) Fourier Spectra between km 16.50 and 19.70 of a 1-min-long window starting: 2 min, 16 s after the earthquake (1), 7min, 29 s after the earthquake (2) and 14 min, 34 s after the earthquake (3), respectively. No significant signals are appreciated in Fourier spectra (b) and (d). Fundamental frequencies higher than 2 Hz appear after the arrival of seismic waves along different cable spans (c), from km 16.50 to 19.70. . . . . . . . . . . . . . 102 xxvi 5.11 Longitudinal trapped waves detected by DAS along cable segments of the HCMR cable featuring earthquake-triggered vibrations. (a) Low-pass filtered strain rate between km 7.48 and 10.20 along the HCMR cable, from 18-April-2019 21:45:27 to 21:46:27 UTC. Strain rate is filtered below 20 Hz. (red rectangles) Two 60-s-long windows of 172.80 (1) and 345.60 m (2) width are indicated as reference. (b) Bathymetry profile between km 7.45 and 7.95 along the cable path (VE stands for Vertical Exaggeration). The red line highlights the location of window 1 in (a). (c) Cross-correlation traces calculated over window 1 in (a), and relative to the trace reference number 5, km 7.60 along the cable. Amplitudes are normalized by the maximum of the cross-correlation traces. A longitudinal trapped wave bouncing forward and backward along the cable span with a speed of 4008 m/s can be clearly observed (black dashed lines). (d and e) Same as b, and c, but for a cable section traversing the continental slope between km 9.5 and 10.2, window 2 in (a). . . . . . . . . . . . . . . . . . . . 5.12 Longitudinal trapped waves detected by DAS along cable segments of the MEUST cable featuring earthquake-triggered vibrations. (a) Low-pass filtered strain rate between km 16.75 and 17.90 along the MEUST cable, from 22-July-2019 16:30:35 to 16:31:35 UTC. Strain rate is filtered below 20 Hz. (red rectangles) Two 60-s-long windows of 420 (1) and 370 m (2) width are indicated as reference. (b) Bathymetry profile between km 16.84 and 17.36 along the cable path (VE stands for Vertical Exaggeration). The red line highlights the location of window 1 in (a). (c) Cross-correlation traces calculated over window 1 in (a), and relative to the trace reference number 5, km 16.94 along the cable. Amplitudes are normalized by the maximum of the cross-correlation traces. A longitudinal trapped wave bouncing forward and backward along the cable span with a speed of 3974 m/s can be clearly observed (black dashed lines). (d and e) Same as b, and c, but for a cable section presumably suspended between km 17.43 and 17.90, window 2 in (a). . . . . . . . . . . . . . . . . . . . . . . . . 5.13 Harmonics of Vortex-Induced Vibrations (VIV) recorded by DAS along suspended sections of submarine fibre cables. Low-pass filtered strain rate between km 7.52 and 7.84 from 18-April-2019 19:20:23 to 22:20:23 UTC along the HCMR cable (a), between km 12.17 and 12.41 from 19-April-2019 22:42:41 to 20-April 04:42:41 UTC along the NESTOR cable (b), and between km 37.02 and 37.22 from 25-July-2019 08:30:00 to 15:00:00 along the MEUST cable (c). DAS-strain rate data are filtered below 5 Hz. Black lines indicate the center of the cable segment featuring Low-Frequency (LF) oscillations. (d, e, f) Spectrograms of strain rate at A, B and C, respectively. Higher harmonic frequencies of VIV are excited along cable segments displaying LF oscillations. 5.14 Cross-correlation analysis of underwater fibre cables displaying Low-Frequency oscillations. Low-pass filtered strain rate between km 7.52 and 7.90 from 18-April-2019 20:25:47 to 21:25:47 UTC along the HCMR cable (a), between km 12.17 and 12.41 from 20-April-2019 00:12:41 to 01:12:41 UTC along the NESTOR cable (b), and between km 37.02 and 37.22 from 25-July-2019 10:00:00 to 11:00:00 along the MEUST cable (c). DAS-strain rate data are filtered below 2 Hz. (red rectangles) 30-min-long windows of strain rate of 345.60 (window 1), 230.40 (window 2) and 190 (window 3) m width for the HCMR, NESTOR and MEUST cable, respectively. (d, e and f) Cross-correlation traces calculated over window 1, 2 and 3 respectively. Dashed red lines in a, b and c indicate the reference traces used for cross-correlation. Amplitudes are normalized by the maximum of the cross-correlation traces. The cross-correlation of cable segments featuring Low-Frequency oscillations does not reveal cable waves. . . 106 5.15 Noise generated by cable waves in DAS-strain rate recordings of the HCMR cable. (a) 120-s-long traces of band-pass filtered strain rate between km 6.72 and 8.45 of the HCMR cable. Traces are filtered between 1 and 12 Hz and are represented each 38.4 m. (dashed line) Arrival of seismic waves due to the M L -3.7 earthquake of Fig.5.1. (blue and red rectangles) As reference, 60-s-long windows of 172.80 m width indicate whether cable waves are absent (W1) or detected (W2), respectively. (b) Fourier spectra between km 6.72 and 8.45 of a 60-s-long window starting at the same time of W1. (red and blue rectangles) Frequency content of W1 and W2, respectively. (c) 15-s-long traces of strain rate along: km 7.53 in W1 (blue), and km 7.62 in W2 (red). Amplitudes are normalized by the maximum strain rate of each channel. Cable waves are clearly recorded in W2, which may explain the high monochromatic noise that dominates the signal along the DAS-trace in km 7.62, after the arrival of seismic waves, compared to the DAS-trace in km 7.53. . . . . . . . . . . . . . . . . . 107 5.16 Noise generated by cable waves in DAS-strain rate recordings of the MEUST cable. (a) 120-s-long traces of band-pass filtered strain rate between km 18.80 and 20.20 of the MEUST cable. Traces are filtered between 1 and 12 Hz and are represented each 20 m. (dashed line) Arrival of seismic waves due to the M L -3.9 earthquake of Fig.5.1. (red and blue rectangles) As reference, 60-slong windows of 180 m width indicate whether cable waves are detected (W1) or absent (W2), respectively. (b) Fourier spectra between km 18.80 and 20.20 of a 60-s-long window starting at the same time of W1. (red and blue rectangles) Frequency content of W1 and W2, respectively. (c) 15-s-long traces of strain rate along: km 19.46 in W1 (red), and km 19.62 in W2 (blue). Amplitudes are normalized by the maximum strain rate of each channel. Cable waves are clearly recorded in W1, which may explain the high monochromatic noise that dominates the signal along the DAS-trace in km 19.46, after the arrival of seismic waves, compared to the DAS-trace in km 19.62. . . . . . . . . . . . . 108

Figure 1

 1 Figure 1.1 -Hypsometric (area-altitude, area-depth) curve of the Earth. Oceans represent around 70% of the Earth's surface total area. Yet, most of the ocean's extension is barely instrumented leading to a lack of oceanography measurements, especially below the average depth of the ocean. (Modified from (Ye et al., 2018)).

Figure 1

 1 Figure 1.2 -Number of DAS-related publications between 2011 and 2022. DAS-related publications and citations (gray) and, since 2013, DAS-related publications and citations in earthquake (cyan) and ocean (red) works are increasing quickly and steadily. (Inspired in (Zhan, 2020). Source: Web of Science Clarivate, Dec. 2022)

Figure 2

 2 Figure 2.1 -Photon-scattering mechanisms of light. A beam of light of frequency "f " propagates along a material with density fluctuations that scattered the incident light (a). The spectrum of the scattered light includes Rayleigh (frequency peak at the incident light frequency "f "), Brillouin and Raman scattering (both with shifted frequency peaks respect to "f ") (b).Stokes and Anti-Stokes light is generated when the scattered light is emitted at lower or higher frequency than the incident light, respectively (Modified from[START_REF] Lu | Distributed optical fiber sensing: Review and perspective[END_REF]

Figure 2 . 4 -

 24 Figure 2.4 -Raman Amplification applied to a short fiber (span length < 50 km). DAS signal levels of backscattered light from a continuous 39-km-long fiber (a) without and (b) with (co-propagating) Raman amplification. The former shows exponential decay due to attenuation, while in the latter high signal levels are maintained more uniformly and over a longer distance. (Taken from (Wilson et al., 2022))

Figure 2 . 5 -

 25 Figure 2.5 -Raman Amplification applied to a long fiber (span length > 100 km). Optical power of Φ-OTDR traces recorded along a 120 km-long fiber: without amplification (a), and using first-order bidirectional Raman amplification (b). Raman amplification increases the range from 50 to 120 km. (Taken from (Martins et al., 2015))

Figure 2

 2 Figure 2.6 -Sketch of geophysical sensing based on offshore SOP. Light is injected into a seafloor fiber through an optical transmitter, and its State of Polarization (SOP) is continuously monitored along the cable (a). Minimal perturbations of the input signal (red star) generate a stable output of SOP (blue dots) on the Poincaré sphere (b). Storms, tsunami/earthquake waves or ocean swells produce SOP anomalies by shaking or pressuring the cable (c). As the Stoke parameters S 1 , S 2 and S 3 are commonly normalized to 1, only two are independent. A typical practice in SOP sensing is to rotate the Stoke parameters to one pole of the Poincaré sphere (the north pole in this example) and focus on analyzing the independent parameters after rotation (d). (Modified from (Zhan et al., 2021))

Figure 2

 2 Figure 2.7 -Time-and-frequency domain analysis of SOP signals. M W 6.8 intermediatedepth earthquake recorded by SOP along a transoceanic cable (10 500 km long). Stoke traces, S 2 , are bandpass-filtered between 0.8 -3 Hz (a), and between 0.3 -0.8 Hz (b). The vertical red, blue and green lines highlight the earthquake origin time, theoretical P and S wave arrival times, respectively. (c) Spectrogram for S 2 showing a package of seismic energy between 0.8 -3 Hz, and potentially Scholte waves at lower frequencies. (Modified from (Zhan et al., 2021))

Figure 2

 2 Figure 2.8 -Diagram of Fabry-Perot Interferometer (FPI) sensors in fiber optic cables. Two types of FPI sensors can be found in fibers: the extrinsic type (a), and the intrinsic type (b). Commonly, the optical cavity of the extrinsic FPI is an air-gap, whereas the optical cavity of the intrinsic FPI is the fiber itself. (Modified from (Joe et al., 2018))

Figure 2

 2 Figure 2.9 -Tidal currents detected by Ultrastable Laser-based Interferometry. Marra et al. (2022) performed laser-based interferometry along a transoceanic fiber cable connecting Southport, UK and Halifax, Canada. They observed narrow-band components excited in two frequency ranges: A first between 1 and 5 Hz, repeating approximately every 6 h, that they associated with tidal currents in the Irish Sea (A, B); and a second, between 0.5 and 1.5 Hz with a 12-h repeating pattern, attributed to tidal currents in the MAR area (D). Interactions with ocean currents due to the changing MAR bathymetry were also recorded (E, F). D in the right column stands for depth. (Taken from[START_REF] Marra | Optical interferometrybased array of seafloor environmental sensors using a transoceanic submarine cable[END_REF]

Figure 3 .

 3 Figure 3.1 -Representation of the Double Crucible Method. A fiber optic cable is fabricated from a rod tube (or "preform") that is drawn out from the bottom of two crucibles. The preform is composed by a core glass inside of a tube of cladding glass. (Modified from (Al-Azzawi, 2017))

3

 3 Similar to MCVD, but a plasma flame is used instead of oxyhydrogen flames.

Figure 3 .

 3 Figure 3.2 -Cross section and schematic view of a typical fiber optic cable. Core-cladding fiber optic cables are obtained from a preform. During the drawing process of the preform, a protective layer of plastic -the so-called jacket -is coated on the surface of the cladding. (Taken from (Al-Azzawi, 2017))

Figure 3 . 3 -

 33 Figure 3.3 -Schematic view of the three main types of fiber optic cables. 2D cross-sectional view of: (a) a single-mode, (b) a multimode, and (c) a graded-index fiber optic cable. As a reference, the injected input signal is represented together with the expected output signal, for each type of fiber. Modal dispersion affects the amplitude of the retrieved signal in multimode fiber optic cables. (Modified from (Al-Azzawi, 2017))

Figure 3 .

 3 Figure 3.4(e). The light arrives at the core-cladding interface at an angle θ to the normal (the

Figure 3 . 4 -

 34 Figure 3.4 -Propagation of light along fiber optic cables. (a) Light arrives at the corecladding interface at an angle θ and is refracted at an angle β. (b) If θ increases, then β becomes larger. (c) At a particular θ (i.e. critical angle of incidence, θ c ), the refracted light travels across the core-cladding interface. (d) Beyond θ c , all the incident light is reflected back into the core, a phenomenon known as total internal reflection. (e) Light propagates in fiber cables following the total internal reflection along the entire cable span. (Modified from (Al-Azzawi, 2017))

Figure 3 . 5 -

 35 Figure 3.5 -Optical loss vs. wavelength of the light travelling in standard fibers. The wavelength of optical sources is usually chosen around 1.5 µm to avoid the Fiber Loss peak at 1.39 µm, and infrared absorption. (Taken from (Murata, 2001))

Figure 3 .

 3 Figure 3.6 -Cross-sectional view of a high-density fiber cable. Optical fibers are embedded within a jelly filled, and separated from an outer layer of silicon gel by a loose tube. A final jacket covers the entire unit. (Modified from (Murata, 2001))

Figure 3 .

 3 Figure 3.7 -Absorption loss in Jelly-filled and Non-jelly-filled fiber optic cables due to water infiltration. Below the freezing temperature of water, attenuation due to absorption loss strongly increases in Non-jelly-filled fibers. While, absorption loss remains the same in Jellyfilled optical fiber despite the temperature drop. (Modified from (Murata, 2001))

Figure 3 .

 3 Figure 3.8 -Different types of armoured fiber cables deployed offshore. A copper tube used for power transmission (2) separates the jelly-filled fibers (1) from different types of armouring used in underwater fibers (3). (Taken from (Ye et al., 2018))

Figure 3 .

 3 Figure 3.9 -Aspect and 2D cross-sectional view of a Lightweight (LW) cable. (Modified from Technical Specifications of Submarine Cables, Alcatel-Lucent)

Figure 3 .

 3 Figure 3.10 -Aspect and 2D cross-sectional view of a Lightweight Protected (LWP) cable. (Modified from Technical Specifications of Submarine Cables, Alcatel-Lucent)

Figure 3 .

 3 Figure 3.11 -Aspect and 2D cross-sectional view of a Single Armoured (SA) cable. (Modified from Technical Specifications of Submarine Cables, Alcatel-Lucent)

Figure 3 .

 3 Figure 3.12 -Aspect and 2D cross-sectional view of a Double Armoured (DA) cable. (Modified from Technical Specifications of Submarine Cables, Alcatel-Lucent)

Figure 3 .

 3 Figure 3.14 -Images taken during a ROV inspection along the NESTOR cable, southwest of Greece. (a) Obstacles or (b, c) irregular seafloor can generate suspended sections of submarine fiber optic cables.

Figure 4 .

 4 Figure 4.1 -Sketch of Vortex-Induced Vibrations (VIV). Vortices are shed off from an eloganted body due to VIV generated by a steady fluid (blue arrows). (Modified from (Williamson and Govardhan, 2008))

Figure 4 . 3 -

 43 Figure 4.3 -Two behaviors of the vortex shedding frequencies observed during a VIV experiment. Vortex shedding frequencies (circles) in the lock-out regime (yellow area) are well described by the Strouhal number equation (black line, eq. 4.1). While, in the lock-in regime (green area), vortex shedding frequencies approach the natural frequency of the vibrating object (downward triangles). Low-amplitude and high-amplitude oscillations (upward triangles) are typically observed in the lock-out regime and lock-in regime, respectively. (Modified from[START_REF] Feng | The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders[END_REF]

Figure 4 . 4 -

 44 Figure 4.4 -Location and bathymetry model of the underwater MEUST cable. The optic fiber cable depicted in (a) offshore Toulon, France, traverses different seafloor features throughout its 44.8-km length (b). Nine hanging sections were identified along three segments of the cable trajectory (1 in Segment 1, 6 in Segment 2 and 2 in Segment 3). The red triangle represents the position of an Acoustic Doppler Current Profiler (MII current meter) deployed next to the cable end (Coyle, 2017).

4. 3 . 1

 31 Observation of Vortex-Induced Vibrations along Hanging Cable Sections Our DAS datasets feature quasi-harmonic oscillations of fiber strain along cable sections laid on irregular bathymetry or where suspended sections are expected (Figure 4.5.a,b). These

Figure 4 . 5 -

 45 Figure 4.5 -Vortex-Induced Vibrations (VIV) recorded by seafloor DAS. We show two examples, in segments 3 (left) and 2 (right). (a) Bathymetry profile along the cable path (VE stands for Vertical Exaggeration) and (c) 84 hours-long recording of low-pass filtered strain rate, along a portion of Segment 3. A cutoff frequency of 2 Hz is used to filter the strain rate. Uniform quasi-harmonic oscillations of fiber strain occur around a seafloor valley. (e) Spectrogram of strain rate at the center of the vibrating section featuring a time-dependent characteristic frequency, varying from 0.1 to 0.4 Hz, and the second-order pressure peak caused by sea surface waves near 0.5 Hz (Sladen et al., 2019). Higher harmonic frequencies of VIV are excited during two periods in July 16th and 17th, accompanied by large strain amplitudes. (b, d and f) Same as a, c and e, but for a cable section laid across a change of seafloor slope (thick blue lines in b), in Segment 2.

Figure 4 .

 4 Figure 4.7 -Deep ocean currents sensed by DAS compared to MII current meter records. (a)Ocean current speed recorded by MII current meter between 11-July-2019 00:00:00 UTC and 31-July-2019 00:00:00 UTC (gray circles), its median over 2-hours-long sliding windows (black curve), current speed derived from Strouhal frequencies sensed by DAS in a hanging section between km 37.06 and 37.18 (cyan circles) and its median over 2-hours-long sliding windows (blue line). Horizontal segments of the curves correspond to data gaps. (b) Power Spectral Density of raw MII (black) and DAS (blue) oceanic current speeds from 19-July-2019 22:09:04 to 29-July-2019 06:14:45. A 17-hours peak is observed in both spectra. The energy power of the DAS spectrum (P (f )) decays with increasing frequency from a period T < 17 hours to T = 4 hours following P (f ) ≈ 1/f p , with p = 2.5. For reference, the red lines show the spectral decay slope for two values of the decay exponent "p".

Figure 4 .

 4 Figure 4.8 -Impact of the ocean dynamics on current speeds measured by DAS. (a) Low-pass filtered ocean current speeds:recorded by the current meter (black) and DAS-derived from the same cable section as in Fig.4.7 (blue), from July 11th to July 31st, 2019. We low-pass filtered both time series with a cutoff period of 10 h. (b) Expected time-shift between ocean current speeds at the MII current meter location and along the hanging cable section (red squares), derived from MII current meter data. The red line is the median expected time-shift averaged over a 2-hours sliding window. Circles: time-shift calculated by cross-correlation between MII current meter and DAS time series over a 50-hours sliding window, only shown for windows without data gaps. Coherence is shown in color scale. Ocean current direction recorded by the current meter (ϕ current , green squares). The green line is the median-ϕ current averaged over 2-hours-long sliding windows. The time-shift sign fluctuates according to whether oceanic currents are measured first by MII current meter (negative) or by DAS (positive).

Figure 4 .

 4 Figure 4.9 -Permissible range of suspended cable span lengths and current speeds imposed by the lock-in condition in the MEUST cable. Maximum span lengths are shown as a function of expected peak current speeds detected by DAS, together with the lock-in range reported by Feng (1968) (black lines and pink rectangle, respectively). Adjusting the span length of a suspended section in cable segment 3, from kilometers-long to centimeters-long, may allow detecting peak current speeds associated to several processes in oceanography (circles).

Figure 4 .

 4 Figure 4.11 -Validity of the Independence Principle (IP) for oblique Vortex-Induced Vibrations registered by underwater DAS.(a) Time variation of the angle " θ" between the ocean currents registered by MII current meter and the plane perpendicular to the cable axis (red circles), from 11-July-2019 00:00:00 UTC to 31-July-2019 00:00:00 UTC. The red line indicates the median angle averaged over a 2-hours sliding window. (b) Median of ocean currents registered by MII current meter averaged over 2-hours-long sliding windows (black), its vertical component respect to the plane perpendicular to the cable axis (magenta) and DAS-derived ocean currents (blue), during the same time in (a). The angle " θ" fluctuates between 24 and 82 degrees during the campaign. The vertical component of the MII current meter and DAS-derived ocean current time series do not match, which invalidates the IP. We believe that the high variability of " θ" may lead the IP to fail predicting the component of the oceanic current speed contributing to the VIV.

Figure 5 .

 5 Figure 5.1 -Location of the underwater HCMR, NESTOR and MEUST electro-optic fibre cables. (yellow rectangle) The 13.2-km-long Hellenic Center for Marine Research (HCMR) and the 26.2-km-long Neutrino Extended Submarine Telescope with Oceanographic Research (NESTOR) fibre cables, situated offshore Methoni Bay, Greece. DAS data were acquired in HCMR and NESTOR cables between 18-April-2019 16:20:22 UTC and 25-April-2019 04:30:15 UTC. (cyan and red stars) Epicenters of: a M L -3.7 earthquake recorded along HCMR cable, origin time 18-April-2019 21:44:42 UTC, and a M L -3.3 earthquake recorded along NESTOR cable, origin time 22-April-2019 19:26:06 UTC, respectively (Lior et al., 2021). (red rectangle) The 44.8-km-long Mediterranean Eurocentre for Underwater Sciences and Technologies (MEUST) fibre cable, located offshore Toulon, France. A DAS experiment was conducted along the MEUST cable between 11-July-2019 13:12:16 UTC and 31-July-2019 08:19:26 UTC. (green star) Epicenter of a M L -3.9 earthquake recorded along the MEUST cable, origin time 22-July-2019 16:23:07 Local Time.

Figure 5 .

 5 Figure 5.2 -High-frequency vibrations triggered along the NESTOR fibre cable after a M L -3.3 earthquake is recorded by DAS. (a) Low-pass filtered strain rate between km 12.48 and 19.20 along the NESTOR cable, from 22-April-2019 19:24:45 to 19:30:15 UTC. Strain rate is filtered below 20 Hz. (red star) Origin time of the M L -3.3 earthquake of Fig.5.1 is indicated as reference (Lior et al., 2021). (red rectangles) Waves trapped along certain cable sections can be observed after the arrival of seismic waves. (b), (c) and (d) Fourier Spectra between km 12.48 and 19.20 of a 1-min window starting: 90 s before the earthquake (1), 40 s after the earthquake (2) and 180 s after the earthquake (3), respectively. Red lines in (c) indicate the cable sections highlighted by red rectangles in (a). Fourier spectra before (b) and after (d) the earthquake are dominated by excited frequencies lower than 1 Hz. Fundamental-and-harmonic frequencies higher than 2 Hz appear after the arrival of seismic waves along different cable spans (c), from km 12.48 to 19.20.

Figure 5 . 3 -

 53 Figure 5.3 -Natural frequencies of earthquake-triggered oscillations as a function of underwater fibre cable spans. Natural frequencies recorded by DAS during EQ-triggered fibre cable oscillations are represented as a function of the cable span length featuring the vibration for the MEUST (green), NESTOR (red) and HCMR (cyan) cables. Error bars indicate half of the gauge length used during each DAS experiment. The black continuous lines follow the equation f n = nV /2L of the n-th natural frequency f n of a 1D elastic medium with fixed ends, wave speed V and length L. Values of n = 1, 2, 3 represent the fundamental mode, the first and the second harmonic, respectively. A wave speed V = 4000 m/s (solid lines) with a deviation of ± 10% (dashed lines) is consistent with the natural frequencies of MEUST, HCMR and NESTOR cables.

Figure 5 . 4 -

 54  of high-frequency fibre cable oscillations compared to Normal Modes of a vibrating string. (a) Spatial derivative ∂Φ n (x)/∂x of the normal modes Φ n (x) = sin(nπx/L) of a vibrating string (black) compared to the Proper Orthogonal fundamental-Modes extracted from a 1-min-long window of fibre oscillations recorded during an EQ in: MEUST cable between km 18.90 and 19.18 (green), NESTOR cable between km 14.13 and 14.78 (red), and HCMR cable between km 9.69 and 10.04 (cyan). Vertical and horizontal axes are normalized by the maximum amplitude of the Normal Mode derivative and the span length L, respectively. (b) Sames as a, but for the Proper Orthogonal first-harmonic-Mode of NESTOR and HCMR cables. (c, d and e) Fourier spectra of the POD-extracted fundamental and first-harmonic mode time series |F(P OC(t) 1 )| and |F(P OC(t) 2 )| (blue and magenta, respectively) compared to the Fourier spectra of the 1-min fibre cable oscillations indicated in a and b, band-pass filtered between 2 and 20 Hz (gray). Proper Modes extracted through POD of the fibre strain oscillations recorded by DAS are in agreement with those of a 1D vibrating structure fixed at its ends.

Figure 5 . 5 -

 55 Figure 5.5 -Longitudinal trapped waves detected by DAS along cable segments featuring earthquake-triggered vibrations. (a) Band-pass filtered strain rate between km 13.82 and 17.28 along the NESTOR cable, from 22-April-2019 19:26:46 to 19:27:46 UTC. Strain rate is filtered between 2 and 20 Hz. (red rectangles) Two 60-s-long windows of 883.2 (1) and 960 m (2) width are indicated as reference. (b) Bathymetry profile between km 14 and 15 along the cable path (VE stands for Vertical Exaggeration). The red line highlights the location of window 1 in (a). (c) Cross-correlation traces calculated over window 1 in (a), and relative to the trace reference number 5, km 14.13 along the cable. Amplitudes are normalized by the maximum of the cross-correlation traces. A longitudinal trapped wave bouncing forward and backward along the cable span with a speed of 4080 m/s can be clearly observed (black dashed lines). (d and e) Same as b, and c, but for a cable section presumably suspended between km 16 and 17, window 2 in (a).

Figure 5 .

 5 Figure 5.6 -Noise generated by cable waves in DAS-strain rate recordings of the NESTOR cable. (a) 120-s-long traces of band-pass filtered strain rate between km 18.24 and 21.12 along the NESTOR cable. Traces are filtered between 1 and 12 Hz and are represented each 57.6 m. (dashed line) Arrival of seismic waves due to the M L -3.3 earthquake of Fig. 5.1. (red and blue rectangles) As reference, 60-s-long windows of 172.8 m width indicate whether cable waves are detected (W1) or absent (W2), respectively. (b) Fourier spectra between km 18.24 and 21.12 of a 60-s-long window starting at the same time of W1 in (a). (red and blue rectangles) Frequency content of W1 and W2, respectively. (c) 15-s-long traces of strain rate along: km 19.70, in W1 (red) and km 19.81, in W2 (blue). Amplitudes are normalized by the maximum strain rate of each DAS-channel. Cable waves are clearly recorded in W1, which may explain the high monochromatic noise that dominates the signal along the DAS-trace in km 19.70, after the arrival of seismic waves, compared to the DAS-trace in km 19.81.

Figure 5 .

 5 Figure 5.7 -Dominant normal mode of Low-Frequency oscillations recorded by DAS. (a) Proper Orthogonal fundamental Modes of the NESTOR (red), HCMR (cyan) and MEUST (green) cables, extracted through POD of LF oscillations. (b, c and d) 1-h-long windows of low-pass filtered strain rate featuring LF oscillations along the MEUST, HCMR and NESTOR cable, respectively. Strain rate is filtered below 2 Hz. (black rectangles) 30-min-long windows of strain rate along cable spans of 180.00, 345.60 and 806.40 m selected in the MEUST, HCMR and NESTOR cable, respectively, for POD calculations. The dominant normal mode obtained from the three cables exhibits a quasi-uniform strain rate along the cable span featuring the oscillation, similar to a box-car shape.

Figure 5 .

 5 Figure 5.8 -Fibre segments of the NESTOR and HCMR cables presumably vibrating are highlighted by Low-Frequency Oscillations. (a) NESTOR and HCMR cable trajectories offshore Methoni Bay, Greece (black), and location of the detected vibrating sections (magenta). Positive and negative values indicate the distance along the cable path in kilometers and the seafloor depth in meters, respectively. (b) Low-pass filtered strain rate along NESTOR cable between km 5 and 26, from 19-April-2019 18:18:38 to 18:20:38 UTC (black and white), compared with the variation across the cable of the maximum positive strain rate (blue) and the standard deviation of the strain rate (red). Strain rate is low-pass filtered below 2 Hz. (c) Same as b, but from 24-April-2019 02:43:46

Figure 5 .

 5 Figure 5.9 -High-frequency vibrations triggered along the HCMR fibre cable after a M L -3.7 earthquake is recorded by DAS.

Figure 5 .

 5 Figure 5.10 -High-frequency vibrations triggered along the MEUST fibre cable after a M L -3.9 earthquake is recorded by DAS. (a) Low-pass filtered strain rate between km 16.50 and 19.70 along the MEUST cable, from 22-July-2019 16:23:00 to 16:39:00 UTC. Strain rate is filtered below 20 Hz. (green star) Origin time of the M L -3.9 earthquake of Fig.5.1 is indicated as reference. Waves trapped along certain cable sections can be observed in Window 2, after the arrival of seismic waves. (b), (c) and (d) Fourier Spectra between km 16.50 and 19.70 of a 1-min-long window starting: 2 min, 16 s after the earthquake (1), 7min, 29 s after the earthquake (2) and 14 min, 34 s after the earthquake (3), respectively. No significant signals are appreciated in Fourier spectra (b) and (d). Fundamental frequencies higher than 2 Hz appear after the arrival of seismic waves along different cable spans (c), from km 16.50 to 19.70.

Figure 5 .

 5 Figure 5.11 -Longitudinal trapped waves detected by DAS along cable segments of the HCMR cable featuring earthquaketriggered vibrations. (a) Low-pass filtered strain rate between km 7.48 and 10.20 along the HCMR cable, from 18-April-2019

Figure 5 .

 5 Figure 5.12 -Longitudinal trapped waves detected by DAS along cable segments of the MEUST cable featuring earthquake-triggered vibrations. (a) Low-pass filtered strain rate between km 16.75 and 17.90 along the MEUST cable, from 22-July-2019 16:30:35 to 16:31:35 UTC. Strain rate is filtered below 20 Hz. (red rectangles) Two 60-s-long windows of 420 (1) and 370 m (2) width are indicated as reference. (b) Bathymetry profile between km 16.84 and 17.36 along the cable path (VE stands for Vertical Exaggeration). The red line highlights the location of window 1 in (a). (c) Cross-correlation traces calculated over window 1 in (a), and relative to the trace reference number 5, km 16.94 along the cable. Amplitudes are normalized by the maximum of the cross-correlation traces. A longitudinal trapped wave bouncing forward and backward along the cable span with a speed of 3974 m/s can be clearly observed (black dashed lines). (d and e) Same as b, and c, but for a cable section presumably suspended between km 17.43 and 17.90, window 2 in (a).

Figure 5 .

 5 Figure 5.13 -Harmonics of Vortex-Induced Vibrations (VIV) recorded by DAS along suspended sections of submarine fibre cables. Low-pass filtered strain rate between km 7.52 and 7.84 from 18-April-2019 19:20:23 to 22:20:23 UTC along the HCMR cable

  and 12.41 from 19-April-2019 22:42:41 to 20-April 04:42:41 UTC along the NESTOR cable (b), and between km 37.02 and 37.22 from 25-July-2019 08:30:00 to 15:00:00 along the MEUST cable (c). DAS-strain rate data are filtered below 5 Hz. Black lines indicate the center of the cable segment featuring Low-Frequency (LF) oscillations. (d, e, f)Spectrograms of strain rate atA, B and C, respectively. Higher harmonic frequencies of VIV are excited along cable segments displaying LF oscillations.

Figure 5 .

 5 Figure 5.14 -Cross-correlation analysis of underwater fibre cables displaying Low-Frequency oscillations. Low-pass filtered strain rate between km 7.52 and 7.90 from 18-April-2019 20:25:47 to 21:25:47 UTC along the HCMR cable (a), between km 12.17 and 12.41 from 20-April-2019 00:12:41 to 01:12:41 UTC along the NESTOR cable (b), and between km 37.02 and 37.22 from 25-July-2019 10:00:00 to 11:00:00 along the MEUST cable (c). DAS-strain rate data are filtered below 2 Hz. (red rectangles) 30-min-long windows of strain rate of 345.60 (window 1), 230.40 (window 2) and 190 (window 3) m width for the HCMR, NESTOR and MEUST cable, respectively. (d, e and f) Cross-correlation traces calculated over window 1, 2 and 3 respectively. Dashed red lines in a, b and c indicate the reference traces used for cross-correlation. Amplitudes are normalized by the maximum of the cross-correlation traces. The cross-correlation of cable segments featuring Low-Frequency oscillations does not reveal cable waves.

Figure 5 .

 5 Figure 5.15 -Noise generated by cable waves in DAS-strain rate recordings of the HCMR cable. (a) 120-s-long traces of band-pass

Figure 5 .

 5 Figure 5.16 -Noise generated by cable waves in DAS-strain rate recordings of the MEUST cable. (a) 120-s-long traces of band-pass filtered strain rate between km 18.80 and 20.20 of the MEUST cable. Traces are filtered between 1 and 12 Hz and are represented each 20 m. (dashed line) Arrival of seismic waves due to the M L -3.9 earthquake of Fig.5.1. (red and blue rectangles) As reference, 60-s-long windows of 180 m width indicate whether cable waves are detected (W1) or absent (W2), respectively. (b) Fourier spectra between km 18.80 and 20.20 of a 60-s-long window starting at the same time of W1. (red and blue rectangles) Frequency content of W1 and W2, respectively. (c) 15-s-long traces of strain rate along: km 19.46 in W1 (red), and km 19.62 in W2 (blue). Amplitudes are normalized by the maximum strain rate of each channel. Cable waves are clearly recorded in W1, which may explain the high monochromatic noise that dominates the signal along the DAS-trace in km 19.46, after the arrival of seismic waves, compared to the DAS-trace in km 19.62.

Figure 5 .

 5 Figure 5.17 -Normal modes of Low-Frequency (LF) oscillations compared to longitudinal strain predicted by the beam theory. (red and cyan) Dominant normal modes of LF oscillations recorded by DAS along the NESTOR and HCMR cable, respectively. (black) Longitudinal strain (ε(x)) of a long and slender beam predicted by Timoshenko's beam theory as a function of the beam's deflection (y(x)) and bending (y ′′ (x)), assuming that fibres have mode-shapes given by a sine function: y(x) = sin(πx/L). Amplitudes in the vertical and horizontal axis are normalized by the maximum strain rate and the cable span length (L), respectively. The relation ε(x) = y ′′ (x)y(x) explains well the zero strain at both ends of the dominant normal modes, and the absence of strain nodes within the vibrating span. However, it predicts a maximum of strain at the mid-span, which is different from the quasi-uniform strain of the observed dominant normal modes.

  Different types of armoured fiber cables deployed offshore. A copper tube used for power transmission (2) separates the jelly-filled fibers (1) from different types of armouring used in underwater fibers(3). (Taken from[START_REF] Ye | Submarine Optical Cable Engineering[END_REF]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.9 Aspect and 2D cross-sectional view of a Lightweight (LW) cable. (Modified from Technical Specifications of Submarine Cables, Alcatel-Lucent) . . . . . . 46 3.10 Aspect and 2D cross-sectional view of a Lightweight Protected (LWP) cable. (Modified from Technical Specifications of Submarine Cables, Alcatel-Lucent) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.11 Aspect and 2D cross-sectional view of a Single Armoured (SA) cable. (Modified from Technical Specifications of Submarine Cables, Alcatel-Lucent) . . . . 47 3.12 Aspect and 2D cross-sectional view of a Double Armoured (DA) cable.

) . . . . . . . . . . . . . . . . . . . . . . . . . . xix 3.8

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

	List of Tables
	3.1 Typical methods to fabricate preforms of fiber optic cables through Chemical
	Vapor Deposition (CVD). The initial compound is used in its vapor phase. In-
	formation extracted from Murata (2001). . . . . . . . . . . . . . . . . . . . .
	3.2 Typical diameters of cores, claddings and jackets in fiber optic cables. Values
	taken from Al-Azzawi (2017). . . . . . . . . . . . . . . . . . . . . . . . . . .
	A1 Ideal locations for the monitoring of large-scale ocean circulation by DAS
	along seafloor fiber optic cables. The Thermohaline front -a large-scale pat-
	tern of deep ocean circulation -flows near to these three locations, which cor-
	respond to the landing points of several underwater fibers (Figure 1.3). The
	amplitude of ocean current speeds represents the maximum value recorded by
	previous oceanography campaigns. . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1

Table 3 .

 3 2.

	(OVD)	Deposition	Vapor	Outside		Method
			GeCl 4	SiCl 4 or	compound	Initial
						General description
						Advantages
						Disadvantages

sources: https://nssdc.gsfc.nasa.gov/planetary/lunar/apollo.html and https: //www.planetary.org/space-policy/cost-of-apollo

Map available in https://submarine-cable-map-2022.telegeography.com/

Sharks are known to be particularly attracted by underwater fiber optic cables. Real attacks have been documented. For an example, go to https://www.youtube.com/watch?v=1ex7uTQf4bQ

Acknowledgements

I would like to thank all those who -in one way or another -have contributed or helped for bringing this PhD thesis to safe port. Thanks to:

Acknowledgments

The work of D.M.F. was funded by a joint fellowship of the Observatory of Côte d'Azur (OCA) and Region Sud. The MEUST-NUMerEnv project is sponsored by CNRSIN2P3, the Region Sud, France (CPER), the State (DRRT), and the Europe (FEDER). This work was partially supported by the SEAFOOD project, funded by grant ANR-17-CE04-0007 of the French Agence Nationale de la Recherche and the Doeblin Federation (FR2800 CNRS).

Acknowledgments

The work of D.M.F. was funded by a joint fellowship of the Observatory of Côte d'Azur (OCA) and Region Sud. The MEUST-NUMerEnv project is sponsored by CNRSIN2P3, the Region Sud, France (CPER), the State (DRRT), and the Europe (FEDER). This work was partially supported by the SEAFOOD project, funded by grant ANR-17-CE04-0007 of the French Agence Nationale de la Recherche and the Doeblin Federation (FR2800 CNRS).

Data Availability Statement

The fiber optic DAS datasets used to generate are available in the following OSF repository: https://osf.io/cfwb3/.

Data Availability

The DAS-strain rate recordings used to generate figures 5.2 -5.8 are available in the following OSF repository: https://osf.io/srv76/.

Abstract

Underwater fiber optic cables commonly traverse a variety of seafloor conditions, which leads to an uneven mechanical coupling between the cable and the ocean bottom. On rough seafloor bathymetry, some cable portions might be suspended and thus susceptible to Vortex-Induced Vibrations (VIV) driven by deep ocean currents. Here, we examine the potential of Distributed Acoustic Sensing (DAS) to monitor deep-sea currents along suspended sections of underwater telecom fiber optic cables undergoing VIV. Oscillations of a seafloor fiber optic cable located in southern France are recorded by DAS along cable sections presumably hanging. Their characteristic frequencies are lower than 1 Hz, at different ocean depths, and have an amplitude-dependency consistent with the driving mechanism being VIV. Based on a theoretical proportionality between current speed and VIV frequencies, we derive ocean current speed time series at 2390 m depth from the vortex shedding frequencies recorded by DAS. The DAS-derived current speed time series is in agreement with recordings by a current meter located 3.75 km away from the hanging cable section (similar dominant period, high correlation after time shift). The DAS-derived current speed time series displays features, such as characteristic periods and spectral decay, associated with the generation of internal gravity waves and weak oceanic turbulence in the Mediterranean Sea. The results demonstrate the potential of DAS along hanging segments of fiber optic cables to monitor a wide range of oceanography processes, at depths barely studied with current instrumentation.

Plain Language Summary

Ocean current speed recordings are rare below 1500 meters depth due to the cost of instrumentation in deep ocean environments. In this study, we demonstrate that deep-sea current speeds can be obtained using measurements of deformation along suspended sections of seafloor fiber optic cables by a technique called Distributed Acoustic Sensing (DAS). As ocean currents hit hanging cable segments, they generate vortex that shed off from the cable at a frequency called "vortex shedding frequency". We show field evidence that the resulting cable oscillations can be recorded by seafloor DAS. We infer ocean current speed time series from the vortex shedding frequencies recorded by DAS across a hanging section of an underwater fiber optic cable in southern France. The DAS-derived time series is in agreement with the one recorded by a nearby current meter. Our results demonstrate the potential of DAS to monitor the generation of internal gravity waves in the Mediterranean Sea at depths barely studied with the current instrumentation, and suggest that the technique presented here to estimate seafloor Chapter 5

Identification of Two Vibration Regimes of Underwater Fiber Optic Cables by DAS

Chapter 5 addresses the issue of heterogeneous mechanical fiber/seabed coupling, and offers a method to detect underwater cable segments that are unsuitable for submarine seismology. This chapter was written in collaboration with E. Diego Mercerat, Jean-Paul Ampuero, Diane Rivet and Anthony Sladen, and was submitted for peer-reviewing to "Geophysical Journal International", under the title "Identification of two vibration regimes of underwater fibre optic cables by Distributed Acoustic Sensing".

Abstract

Distributed Acoustic Sensing (DAS) enables data acquisition for underwater Earth Science with unprecedented spatial resolution. Submarine fibre optic cables traverse sea bottom features that can lead to suspended or decoupled cable portions, and are exposed to the ocean dynamics and to high rates of marine erosion or sediment deposition, which may induce temporal variations of the cable's mechanical coupling to the ocean floor. Although these spatio-temporal fluctuations of the mechanical coupling affect the quality of the data recorded by DAS, and determine whether a cable section is useful or not for geophysical purposes, the detection of unsuitable cable portions has not been investigated in detail. Here, we report on DAS observations of two distinct vibration regimes of seafloor fibre optic cables: a high-frequency (> 2 Hz) regime we associate to cable segments pinned between seafloor features, and a low-frequency (< 1 Hz) regime we associate to suspended cable sections. While the low-frequency oscillations are driven by deep ocean currents, the high-frequency oscillations are triggered by the passage of earthquake seismic waves. Using Proper Orthogonal Decomposition, we demonstrate that high-frequency oscillations excite normal modes comparable to those of a finite 1D wave propagation structure. We further identify trapped waves propagating along cable portions featuring high-frequency oscillations. Their wave speed is consistent with that of longitudinal waves propagating across the steel armouring of the cable. The DAS data on cable sections featuring such cable waves are dominated by highly monochromatic noise. Our results suggest that the spatio-temporal evolution of the mechanical coupling between fibre optic cables exposed to the ocean dynamics and the seafloor can be monitored through the combined analysis of the two vibration regimes presented here, which provides a DAS-based method to identify underwater cable sections unsuitable for the analysis of seismic waves.

Introduction

Distributed Acoustic Sensing (DAS) is a revolutionary technology that transforms ordinary telecommunication fibre cables into dense high-resolution strainmeter arrays. Relying on the principles of φ-OTDR (phase-Optical Time Domain Reflectometry), DAS probes fibre optic cables through an interrogator unit that sends a pulsed coherent laser signal and records the Rayleigh backscattered light [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. Measurements of longitudinal strain or strain rate are derived from the phase difference of the light traveling back to the interrogator, using the speed of light and refractive index of the fibre [START_REF] Hartog | An introduction to distributed optical fibre sensors[END_REF]. The strain (or strain rate) is averaged over a predetermined cable span whose length is known as the gauge length. DAS

Appendix -Supporting Figures & Calculations

Proper Orthogonal Decomposition based on DAS-recorded time series of strain rate: According to [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF], Proper Orthogonal Decomposition (POD) is a statistical method that is used to find optimal distributions of energy from a set of time series. POD is commonly applied to a dataset of dynamical quantities recorded at M locations [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]. Here, M stands for the number of channels along the fibre cable that record DAS-strain rate (ε) from a time t 1 to t N , such as ε i = (ε i (t 1 ), ε i (t 2 ), ..., ε i (t N )) T , for i = 1, 2, ..., M . Prior to POD calculations, time series of DAS-strain rate are used to generate a N x M matrix, as follows [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]:

Then, a M x M correlation matrix R = (1/N )E T E is formed, from which eigenvectors (v) and eigenvalues (λ) are extracted. The correlation matrix R is real and symmetric, which guarantees that v and λ are orthogonal [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]. Moreover, v contains the proper orthogonal modes (POMs) and λ the proper orthogonal values (POVs) of R, i.e. the principal axes of inertia of the DAS-data and the signal power of each corresponding POM, respectively [START_REF] Lumley | The structure of inhomogeneous turbulent flows[END_REF][START_REF] Cusumano | Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree of freedom impact oscillator[END_REF]Cusumano et al., 1993;[START_REF] Berkooz | The proper orthogonal decomposition in the analysis of turbulent flows[END_REF][START_REF] Feeny | On the physical interpretation of proper orthogonal modes in vibrations[END_REF].

POMs can be used as basis functions to decompose the dynamics of the DAS-recordings into modal co-ordinates q(t) [START_REF] Han | Enhanced proper orthogonal decomposition for the modal analysis of homogeneous structures[END_REF]. To do so, a proper orthogonal modal matrix V is defined, as follows [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]:

(5.5)

Then, modal co-ordinates with elements q i (t), i = 1, 2, ..., M are defined, such that [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]:

(5.6)

The proper orthogonal coordinates (POCs) time series q i (t) can be extracted from [START_REF] Feeny | On proper orthogonal co-ordinates as indicators of modal activity[END_REF]:

(5.7)