domain: chim spi

text:
Miguel Sanchez Mendez

Khley Cheng

Khay Chhor

Mounir Mamadou Traore

Ben Amar

Andrei Kanaev
email: andrei.kanaev@lspm.cnrs.fr

Sauro Pierucci

Jiří Jaromír Klemeš

Laura Piazza

Novel Synthesis of Mixed Oxide Nanoparticles for Photocatalysis

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Natural resources have reached nowadays a high level of pollution, between which air and water pollution contribute most important in the balance of the ecosystem. The pollutants are usually toxic organic compounds like dyes, detergents and surfactants, agro wastes like insecticides and herbicides, etc. In order to solve this problem, the development of clean and green processes is under way, among which photocatalysis takes a special place (Fox and Dualy, 1993;[START_REF] Ohtani | Photocatalysis A to Z -What we know and what we do not know in a scientific sense[END_REF]. One of most effective photocatalysts, TiO 2 , has been a subject of numerous studies since many decades [START_REF] Hashimoto | TiO 2 photocatalysis: A historical overview and future prospects[END_REF][START_REF] Schneider | Understanding TiO2 Photocatalysis: Mechanisms and Materials[END_REF][START_REF] Fagan | A review of solar and visible light active TiO 2 photocatalysis for treating bacteria, cyanotoxins and contaminants of emerging concern[END_REF][START_REF] Chianese | Photodegradation of diclofenac sodium salt in water solution: Effect of HA, NO 3 and TiO 2 on photolysis performance[END_REF][START_REF] Lovino | Triclosan photolysis: operating condition study and photo-oxidation pathway[END_REF]. Because of rather high band gap energy, i.e. E g =3.0-3.2 eV, this material cannot be activated with visible light. Consequently, many studies have been performed to decrease its absorption onset by the compositional modification. Another issue in preparation of an effective photocatalyst concerns the decrease of the photoinduced charges recombination, whose solution can be found in preparing composites of TiO 2 with other metal oxides, as e.g. TiO 2 -ZrO 2 [START_REF] Reddy | Recent advances on TiO 2 -ZrO 2 mixed oxides as catalysts and catalyst supports[END_REF]. One of important problems in this respect is the control of its compositional homogeneity at nanoscale, since inhomogeneous domains and elements clustering can affect material properties and effectiveness in the photocatalytic process [START_REF] Tieng | New homogeneously doped Fe(III)-TiO 2 photocatalyst for gaseous pollutant degradation[END_REF]. Vanadium pentoxide (V 2 O 5 ) is one relevant material with semiconducting properties and relatively narrow bang-gap E g =2.2 eV, which could be potentially used in photocatalysis with the visible light activation (Kruef et al., 2017;[START_REF] Li | Vanadium pentoxide nanobelts and nanorolls: from controllable synthesis to investigation of their electrochemical properties and photocatalytic activities[END_REF]. However, a high probability of the photogenerated electron-hole pair recombination was a serious drawback limiting its effectiveness. A possible solution to overcome this problem is to prepare mixed-oxide materials. Several compositions of V 2 O 5 with other semiconductors have been realized so far: V 2 O 5 /SiO 2 [START_REF] Amano | Steady-state photocatalytic epoxidation of propene by O 2 over V 2 O 5 /SiO 2 photocatalysts[END_REF], V 2 O 5 /BiVO 4 [START_REF] Su | Macroporous V 2 O 5 -BiVO 4 composites: Effect of heterojunction on the behavior of photogenerated charges[END_REF], V 2 O 5 /Al 2 O 3 [START_REF] Teramura | Study of the reaction mechanism of selective photooxidation of cyclohexane over V 2 O 5 /Al 2 O 3[END_REF] and TiO 2 / V 2 O 5 [START_REF] Jianhua | Preparation and Characterization of the TiO 2 /V 2 O 5 photocatalyst with visible light activity[END_REF], which have not been effective in the photocatalytic process. However, as it has been recently shown [START_REF] Cheng | Photocatalytic nanoparticulate Zr x Ti 1-x O 2 coatings with controlled homogeneity of elemental composition[END_REF], an effective mixed-oxide photocatalysts can be prepared following a bottom-up approach from size-and composition-selected nanoparticles by controlling their nucleationgrowth process in chemical reactors with ultra-rapid micromixing [START_REF] Azouani | Elaboration of Doped and composite nano-TiO 2[END_REF][START_REF] Azouani | Elaboration of pure and doped TiO 2 nanoparticles in sol-gel reactor with turbulent micromixing: Application to nanocoatings and photocatalysis[END_REF]. In particular, mixing of most effective titanium oxide with vanadium oxide at the molecular level may lead to the nucleation of the mixed-oxide nanoparticles that permits preparation of novel effective photocatalysts with the visible light activation. An evaluation of the ternary Ti-V-O system via thermodynamic CALPHAD modeling [START_REF] Yang | An assessment of the Ti-V-O system[END_REF] has predicted several stable compositions, which needs further experimental verification. In present communication, we report on the influence of micromixing conditions on nucleation-growth of vanadium oxide and mixed oxide Ti-V nanoparticles. The synthesis was achieved using sol-gel method either manually or in a chemical reactor with ultra-rapid micromixing. Improved particle size homogeneity and interaction between titanium and vanadium oxide species were shown in the micromixing conditions at the nucleation stage.

Experimental

Material preparation

The metal oxide nanoparticles, either single oxide vanadium oxo-alkoxy (VOA) and titanium oxo-alkoxy (TOA) or mixed-oxide vanadium-titanium-oxo-alkoxy (VTOA), were prepared in this study via sol-gel method either manually with a magnetic stirring or in a chemical reactor with ultra-rapid micromixing. The reactor used for the synthesis of the metal oxide nanoparticles has been described in our previous studies (Rivalin et al., 2005[START_REF] Azouani | Elaboration of pure and doped TiO 2 nanoparticles in sol-gel reactor with turbulent micromixing: Application to nanocoatings and photocatalysis[END_REF]. In brief, two solutions of 50 mL each containing A) precursors of vanadium(V) oxytripropoxide (98%, Sigma Aldrich) in n-propanol (99.5%, Sigma Aldrich) and B) distilled water filtered twice (syringe filter 0.1 µm porosity PALLs Acrodisc) in n-propanol were prepared in a LABstar glove box workstation MBraun (O 2 ≤80 ppm, H 2 O≤0.5 ppm), in order to avoid any contamination by air humidity and dust particles promoting heterogeneous precipitation of the reactive colloids. The precursor concentrations were C v =0.3 mol/l and 0.145 mol/l and hydrolysis ratio H=C w /C v varied between 1.0 and 2.5, where C V and C w are concentration of vanadium precursor and water. The series of experiments were repeated. In experiments of VTOA mixed oxides preparation, titanium tetraisopropoxide (TTIP, 98%, Sigma-Aldrich) was used as the precursor of Ti-containing species. Each solution A and B were transferred in glass syringes of a volume 50 ml to the reactor containers maintained under dry nitrogen gas flow, in order to prevent any contamination of the reactive media from the atmosphere. The preparation and transfer of the reactive solutions took from about 20 to 40 minutes. The preparation of the reactive medium was achieved by a simultaneous injection of the stock solutions A and B in a static T-mixer with exocentric input arms of 1 mm diameter and an output tube of 2 mm diameter. The injection was triggered by applying a dry nitrogen gas pressure to the reactor containers by synchronous valves opening. The injected fluids flow with a rate of 10 m/s (at the applied pressure of 4 bar) exhibited a strong turbulence through the mixed zone with a Reynolds number Re=4Qp/πηd, equal to 6000, where Q, p and η are flow rate, density and dynamic viscosity of the fluid respectively, which forces the solutions to mix at the molecular level. The reactor was maintained at the temperature of 20 °C with a thermocryostat Haake DC10K15. The optimal operating regime of the sol-gel reactor is attributed to the Damköhler number Da≤1, which means that the time of the fluid composition homogenized before the chemical reactions complete nucleation of species, which permits the narrowest polydispersity of the produced nanoparticles.

Material characterization

Dynamic Light Scattering (DLS) method was used for the particle size measurements. A home-made monomode optical fiber probe was introduced in the reaction volume to monitor scattered light from a volume ~10 -6 cm 3 , which avoided multiple scattering events and allowed measurements in concentrated solutions. A 40 mW/640 nm single-frequency laser Cube 640-40 Circular (Coherent) was used as a coherent light source and signal was analyzed with 48 bits 288 channels photon correlator Photocor-PC2 (Photocor Instruments). Each mean radius was obtained from the least-squared fit of the respective autho-correlation curve (ACF) accumulated during 60 s. The confidence range of the experimental was evaluated from spread of R(t) points. Thermal studies of the vanadium oxide nanopowders were done on a SETARAM TG-DTA 92 device operating simultaneously in thermal gravimetric analysis (TGA) and differential thermal analysis (DTA) in the following conditions: powders of a mass between 40 and 50 mg were introduced into the sample holder and then heated from 50°C to 1000°C with a rising speed of 10°C per minute under argon gas (1 bar). X-ray diffraction (XRD) patterns of powders after heat treatment during 4 hours were analyzed with a benchtop X-ray diffractometer (EQUINOX 1000-Inel) with CoKα source (λ=0.1788976 nm). The prepared samples were characterized using a Zeiss Supra 40 VP SEM-FEG scanning electron microscopy (SEM). The microscopy was performed in a high vacuum mode and low acceleration voltage.

Results and Discussion

Before addressing the mixed-oxide system, the nucleation-growth process of the single oxides has to be documented as a reference point. The similar approach has already proven its effectiveness in studies of Zr x Ti 1-x O 2 solids in a broad range of compositions 0≤x≤1 (Cheng et al. 2017a). The nucleation-growth of titanium-oxo-alkoxy (TOA) species has been previously reported [START_REF] Azouani | Elaboration of pure and doped TiO 2 nanoparticles in sol-gel reactor with turbulent micromixing: Application to nanocoatings and photocatalysis[END_REF]Cheng et al. 2017b). In the same time, no related information concerning VOA species is available in literature. First observation of the nucleation-growth process of VOA species is presented below.

As it has been shown, inhomogeneous reaction conditions of the sol-gel process generally lead to the appearance of strongly polydispersed species. In contrast, point-like reaction conditions in chemical reactors with ultrarapid (t<10 ms) micromixing permit the process with low Damköhler numbers (Da≤1) resulting in the formation of size selected nanoparticles, among which a nucleus (basic unit of the growing solids) can be firmly identified. For example, DLS and TEM measurements have evidenced the basic TOA unit with radius of R TOA =1.6 nm (Cheng at al., 2017b). Because only general information exists about reactivity of metal-oxoalkoxy species [START_REF] Livage | Sol-gel chemistry of transition metal oxides[END_REF], different injection conditions in a T-mixer were tried, leading to the nucleation of VOA species. The size evolution of VOA species prepared manually and in the reactor at different Reynolds numbers (Re) of the injected fluids is shown respectively in Figures 1a and1b As one can see, the radius of VOA particles prepared manually evolves from ~120 nm at the beginning to ~1 μm at the precipitation point. In contrast, the VOA particles prepared in the reactor are significantly smaller and have R 0 =40 nm after injection; however, their growth kinetics depends on Re value. For relatively low Re<3.6⋅10 3 the particles grow up to ~1 μm and precipitate (like with manual preparation), while at higher Re the particles remain much finer (R<100 nm) and stable for a long time (days) in colloids. This may infer the homogeneous nucleation of VOA species. We therefore concluded that Re=6⋅10 3 correspond to the criteria of Da≤1 and conduct further experiments in these injection conditions. The zoom on the very process beginning permits to define a VOA nucleus that begins the growth process: the extrapolation of experimental kinetics in Figure 2a to a common starting point provides the particle radius of R 0 =20 nm. The VOA growth kinetics confirms mechanism of the sol-gel process earlier validated on Ti, Zr and Ti-Zr oxo-alkoxy species [START_REF] Rivallin | Sol-Gel reactor with rapid micromixing: modelling and measurements of titanium oxide nano-particle growth[END_REF][START_REF] Azouani | Stability and growth of titanium-oxo-alcoxy Ti x O y (OiPr) z clusters[END_REF][START_REF] Labidi | Nucleation and growth kinetics of zirconiumoxo-alkoxy nanopparticles[END_REF]Cheng et al., 2017a). The induction stage takes place at H above a critical value h * , which is apparently smaller than the experimental values 1.80, … 2.20 (Figure 2b). The SEM images evidence morphological differences of VOA powders prepared manually (Figure 3a) and in micromixing conditions (Figure 3b), consisting in significantly smaller size of the last, which is in agreement with the DLS observations. The TGA-DTA measurements in Figure 4a confirm results of vanadium oxides structural evolution. The mass loss of ~17 wt% are connected to the departure of surface alkoxy and hydroxyl groups at T<300 °C. The exothermic peak at 280 °C corresponds to VOA particles crystallization into V 2 O 5 metal oxide and the endothermic peak at 675 °C corresponds to the crystalline material melting. The XRD patterns in Figure 4b evidence structural changes of VOA powders. The powders remain amorphous at temperatures T≤200 °C and show crystalline peaks at 300 °C and higher temperatures, which corresponds to the orthorhombic phase of V 2 O 5 (JCPDS 01-089-0612). The diffraction peaks become sharper after the heat treatment at a higher temperature, indicating crystalline domains growth. However, narrower peaks were also observed in nanopowders prepared in the micromixing reactor at the crystallization onset (Figure 4e). This may be explained by an easy thermal fusion of small VOA nanoparticles and connected to the morphological modification of the material. Afterwards, the first synthesis of mixed-oxide VTOA nanoparticles in micromixing conditions was carried out.

The measured autho-correlation curves (ACF) in reactive media containing pure V and V-Ti precursors are shown in Figure 5. The ACF in the mixture Ti:V=0.05:0.95 (Figure 5a) fitted with two-exponential decay indicates the bimodal population with particle sizes of R 1 =7.9 nm and 75 nm. Comparing the respective amplitudes A 1 and A 2 and taking into account that the scattering light intensity I∝R 6 in the Rayleigh domain of particle sizes, one can conclude the population ratio p(R 1 ) / p(R 2 ) ≈ 2⋅10 6 , which shows a strong preference of the small nanoparticles formation in the reaction conditions. In contrast, removal of Ti precursor in similar reaction conditions (Figure 5b) results in a very weak (noisy) signal corresponding to rare particles of radius R 0 =160 nm. We also notice that using pure Ti precursor in similar reaction conditions lead to the formation of monodispersed TOA particles of radius 1.6 nm [START_REF] Azouani | Stability and growth of titanium-oxo-alcoxy Ti x O y (OiPr) z clusters[END_REF]. The observed difference indicates a strong interaction between the two V and Ti systems apparently leading to the nucleation of mixed oxide VTOA nanoparticles. Most probably, because of the strong reactivity and rapid formation, Ti species nucleate first and serve condensation centers for V species. .6, n-propanol solvent, 20°C).

The interaction between the vanadium and titanium systems can be confirmed by TGA-DTA measurements of VTOA nanopowder shown in Figure 6. In fact, the exothermic peak of the amorphous-anatase phase transition appears at 505 °C, which is significantly higher than that 380 °C observed in pure titania nanopowders.

Conclusions

This communication is devoted to a critical step in the preparation of mixed-oxide photocatalysts with a homogeneous composition at nanoscale. The nucleation-growth process of vanadium-oxo-alkoxy (VOA) and vanadium-titanium-oxo-alkoxy (VTOA) species was studied in a chemical reactor with an ultra-rapid mixing of the reactive medium. It was shown that the micromixing has a strong impact on the material morphology and structure. First evidence of the formation of VTOA nanoparticles was given. At small hydrolysis ration, VTOA seems to form starting with titanium oxo-alkoxy (TOA) species, which grow by consuming small hydrolyzed VOA species. The optimization of this process is under way.

  .

Figure 1 :

 1 Figure 1: Mean radius of VOA particles prepared manually (a) and in micromixing reactor (b) with different Reynolds numbers (inset) of the injected reactive fluids (C V =0.30 mol/l, H=1.9, 20 °C).

Figure 2 :

 2 Figure 2: Growth kinetics of VOA nanoparticles in micromixing reactor: particle size versus time for different H (a) and induction rate versus H (b) (C V = 0.30 mol/l, 20 °C, Re=6000).

Figure 3 :

 3 Figure 3: SEM images of VOA nanopowders prepared manually (a) and in micromixing reactor (b) (C V =0.30 mol/l, H=2.0, heat treatment at T=300 °C for 4 h).

Figure 4 :

 4 Figure 4: TGA-DTA (a) measurements of VOA powders prepared in the reactor (C V =0.15 mol/l, H=15, 20 °C, Re=6000) and XRD patterns (b) of V 2 O 5 powder prepared manually (a-d) and in micromixing reactor (e) heat treated at 25 °C (a), 200 °C (b), 300 °C (c, e) and 600 °C (d).

Figure 5 :

 5 Figure 5: ACF curves of VTOA (a) and VOA (b) nanoparticles in reactive solutions: C Ti =0.285 mol/l, C V =0.015 mol/l (a) and C Ti =0 mol/l, C V =0.015 mol/l (b) (H=1.6, n-propanol solvent, 20°C).

Figure 6 :

 6 Figure 6: TGA-DTA measurements of VTOA powders with elemental ratio Ti:V=0.9:0.1.

Acknowledgments

Miguel Sanchez is grateful to CONACYT for the financial support of his PhD work.


Fabrice Hadziioannou

Ardhuin

L Gualtieri

E Stutzmann

C Juretzek

C Hadziioannou

F Ardhuin

Global scale analysis and modeling of primary microseisms

Keywords: Seismic noise, Numerical modeling, Computational seismology, Theoretical Seismology

Global scale analysis and modeling of primary microseisms

INTRODUCTION

Ambient seismic noise recorded worldwide between about 0.05 and 0.08 Hz is called primary microseism, and it can be generated by ocean gravity waves propagating over the seafloor in shallow water [START_REF] Hasselmann | A statistical analysis of the generation of microseisms[END_REF]. Seismic waves have the same frequency as ocean waves, and therefore primary microseisms are sometimes called single-frequency microseisms. While ambient seismic noise at higher frequencies (secondary microseisms) and lower frequencies (seismic 'hum') has been widely studied, very little has been done about primary microseisms.

Early studies identified sources of primary microseisms in near-shore regions by comparing spectra of microseisms and swells (e.g. [START_REF] Haubrich | Comparative spectra of microseisms and swell[END_REF] or by frequency-wavenumber analysis (e.g. [START_REF] Haubrich | Microseisms: coastal and pelagic sources[END_REF][START_REF] Cessaro | Sources of primary and secondary microseisms[END_REF]. More recent studies also used beamforming analysis to infer the location of the sources of Rayleigh and Love waves in the primary microseism frequency band (e.g. [START_REF] Juretzek | Where do ocean microseisms come from? A study of Loveto-Rayleigh wave ratios[END_REF][START_REF] Juretzek | Linking source region and ocean wave parameters with the observed primary microseismic noise[END_REF][START_REF] Gal | Matched field processing of 3 component seismic array data applied to Rayleigh and Love microseisms[END_REF]. Primary microseisms recorded on the vertical-component seismograms are dominated by the fundamental mode of Rayleigh waves (e.g. [START_REF] Haubrich | Microseisms: coastal and pelagic sources[END_REF][START_REF] Schimmel | Polarized Earth's ambient microseismic noise[END_REF]. The energy ratio between Rayleigh and Love waves on the horizontal components is still under debate and may vary with the location of the seismic station (e.g. [START_REF] Friedrich | Ocean-generated microseismic noise located with the Gräfenberg array[END_REF][START_REF] Nishida | Background Love and Rayleigh waves simultaneously generated at the Pacific Ocean floors[END_REF][START_REF] Juretzek | Linking source region and ocean wave parameters with the observed primary microseismic noise[END_REF]. Several of these studies were conducted assuming that the coast responsible for primary microseism generation was the closest one along the source direction given by the beamforming analysis.

The coupling of surface gravity waves and seafloor topography simplifies in the case of a constant slope [START_REF] Hasselmann | A statistical analysis of the generation of microseisms[END_REF] or a fine-scale random topography [START_REF] Ardhuin | Large-scale forces under surface gravity waves at a wavy bottom: A mechanism for the generation of primary microseisms[END_REF]. Using the first approach extended to slowly varying topography, [START_REF] Ardhuin | How ocean waves rock the Earth: Two mechanisms explain microseisms with periods 3 to 300 s[END_REF] modeled the amplitude of the vertical-component primary microseisms. They showed that the power spectral density (PSD) of primary microseisms could be well modeled at three stations in Europe considering sources in shallow water close to the ocean-continent boundary and assuming a constant ocean-bottom slope and a uniform ocean floor topography along the coast. In that case, ocean waves can be considered to be perpendicular to the topography. Therefore, in agreement with previous theoretical studies (e.g. [START_REF] Hasselmann | A statistical analysis of the generation of microseisms[END_REF][START_REF] Saito | Love-wave excitation due to the interaction between a propagating ocean wave and the sea-bottom topography[END_REF], they considered ocean waves perpendicular to the topography in shallow water as the main factor responsible for the generation of primary microseism. Small deviations from the perpendicular direction due to 3D topographic effects are not taken into account.

In this paper, we perform the analysis and modeling of one year of continuous seismic data recorded on the vertical component of 24 seismic stations of the Geoscope network located worldwide.

We focus on frequencies between 0.05 and 0.08 Hz. In section 2 we describe the analysis workflow applied to our seismic dataset and we detail the method used for modeling seismic PSDs. In section 3, we show maps of sources of primary microseisms, and we compare our modeling with observations Global scale analysis and modeling of primary microseisms 3 as a function of time and frequency. We also locate the sources that mostly contribute to primary microseisms at each station by inferring the source region that on its own can explain the spectrum of primary microseisms. To asses the robustness of our approach, in Appendix A we present the modeling of another year of data using the same method discussed in Section 2.

DATA AND METHOD

We analyze vertical continuous seismic data recorded at 24 seismic stations (triangles in Figure 2) of the Geoscope network in 2013. We use the vertical component long-period (LHZ) seismograms, with a sampling rate of 1 Hz. The instrumental response is deconvolved from raw seismograms in order to get ground displacement, and the PSD (in dB with respect to 1 m 2 /Hz) is computed every three hours, considering 50% overlapping time windows of 1024 s. To avoid earthquakes and retain only ambient seismic noise, we keep the minimum value of the PSD every 24 hours.

We model the vertical component PSD at the same 24 seismic stations, following the theoretical framework proposed by [START_REF] Hasselmann | A statistical analysis of the generation of microseisms[END_REF] and [START_REF] Ardhuin | How ocean waves rock the Earth: Two mechanisms explain microseisms with periods 3 to 300 s[END_REF]. To evaluate the location and amplitude of the sources, we use the numerical ocean wave model WAVEWATCH III, version 5.12, as implemented by [START_REF] Ardhuin | A numerical model for free infragravity waves: Definition and validation at regional and global scales[END_REF] with output available at ftp://ftp.ifremer.fr/ifremer/ ww3/HINDCAST. The model is forced by winds from the European Center for Medium-Range Weather Forecast (ECMWF) every three hours. Extended sources are discretized in a grid of point sources each 0.5 • both in latitude and in longitude. The amplitude of the sources is expressed as pressure PSD induced by ocean waves propagating over the seafloor. The ocean wave spectrum is evaluated along the shorelines, and only waves in the direction perpendicular to the shore -both towards and away from the shore -are taken into account [START_REF] Ardhuin | How ocean waves rock the Earth: Two mechanisms explain microseisms with periods 3 to 300 s[END_REF]. Following [START_REF] Hasselmann | A statistical analysis of the generation of microseisms[END_REF], we do not consider shallow depths that have no nearby coastline.

The simplified model of [START_REF] Ardhuin | How ocean waves rock the Earth: Two mechanisms explain microseisms with periods 3 to 300 s[END_REF] based on a large scale sloping seafloor may require unrealistic large bottom slopes where small-scale topographic features (with wavelengths similar to those of ocean waves, typically 50 to 500 m) have large amplitudes [START_REF] Ardhuin | Large-scale forces under surface gravity waves at a wavy bottom: A mechanism for the generation of primary microseisms[END_REF]. The coupling between these topographic features and ocean waves along the perpendicular direction is a possible source of primary microseisms. However, these features are not generally known, making it impossible to take them into account at the global scale. In general, the energy level of ocean waves in directions perpendicular to shore is highly correlated to the energy in other directions so that the theoretical sources used here are a good proxy for general sources caused by all types of bottom topographies. In that theoretical model, the source PSD is proportional to an effective slope, called s in [START_REF] Ardhuin | How ocean waves rock the Earth: Two mechanisms explain microseisms with periods 3 to 300 s[END_REF] (expressed in percentage form) and in [START_REF] Ardhuin | Physics of ambient noise generation by ocean waves[END_REF] (expressed in decimal form), which is not well known in the frequency band of primary microseisms due to uncertainties on bottom topography at scales under 5 km. However, as we shall see in the following, our first-order modeling of primary microseisms does not take into account local site effects at the source (e.g., sediments (e.g. [START_REF] Gualtieri | On the shaping factors of the secondary microseismic wavefield[END_REF][START_REF] Koper | The fine structure of double-frequency microseisms recorded by seismometers in North America[END_REF], fine-scale seafloor roughness (e.g. [START_REF] Ardhuin | Large-scale forces under surface gravity waves at a wavy bottom: A mechanism for the generation of primary microseisms[END_REF]) and 3D propagation effects (e.g., scattering at the ocean-continent boundary, focusing and defocusing at heterogeneities (e.g. Ziane & Hadziioannou, 2019)). Both of these aspects are not negligible at the frequencies of primary microseisms. Therefore, we define an effective fitting parameter γ (expressed in percentage form), which accounts for effects that are not known (e.g., large-scale bathymetric effects, that is the slope factor s of [START_REF] Ardhuin | How ocean waves rock the Earth: Two mechanisms explain microseisms with periods 3 to 300 s[END_REF] and [START_REF] Ardhuin | Physics of ambient noise generation by ocean waves[END_REF], and small-scale topographic effects as in [START_REF] Ardhuin | Large-scale forces under surface gravity waves at a wavy bottom: A mechanism for the generation of primary microseisms[END_REF] or not taken into account in our modeling (source-site and 3D propagation effects). We point out that our effective fitting parameter γ weakly varies with frequency and therefore can be assumed constant (see section 3.4 for a more detailed explanation). This assumption is justified by the fact that we consider a narrow frequency band (0.05-0.08 Hz) and, as we will see in the next section, the spectrum of primary microseisms expressed in displacement varies within a few dB over this frequency band.

A pressure source acting over a given surface at the ocean seafloor in shallow water is equivalent to a vertical force applied on a flat Earth surface. Assuming a homogeneous half space, the vertical component PSD of the total displacement u(f ) [m 2 /Hz] recorded at a seismic station at a given time can be written as the integral over the displacement PSDs due to each vertical point force (e.g. [START_REF] Kanamori | Use of long-period surface waves for rapid determination of earthquake-source parameters[END_REF]:

u(f ) = γ 2π 0 π 0 (2π) 2 f c 2 ρ 2 c β 5 c F p (f ) e -ω∆R Q(f )U (f ) Rsin∆ R 2 sin φ dλ dφ (1)
where f is the seismic frequency, ρ c = 2600 kg/m 3 is the density of the crust, β c = 2.8 km/s is the S-wave velocity in the crust, R = 6371 km is the radius of the Earth, ∆ is the spherical distance between source and receiver, and λ and φ are the longitude and colatitude of the sources, respectively.

The adimensional coefficient c accounts for the (resonance) site effect due to the ocean depth at the source [START_REF] Longuet-Higgins | A theory of the origin of microseisms[END_REF]. We observe that at frequencies between 0.05 and 0.08 Hz and in shallow water, where the sources of primary microseisms are located [START_REF] Ardhuin | How ocean waves rock the Earth: Two mechanisms explain microseisms with periods 3 to 300 s[END_REF], the coefficient c is only relevant to the fundamental mode of Rayleigh waves (c 1 in [START_REF] Longuet-Higgins | A theory of the origin of microseisms[END_REF], his Fig-

ure 1) and it is nearly constant with frequency and ocean depth (unlike for secondary microseisms, e.g. [START_REF] Gualtieri | Modelling secondary microseismic noise by normal mode summation[END_REF]). Therefore, the coefficient c in our computation is set to the corresponding constant value, c 0.2. The attenuation Q(f ) and the group velocity U (f ) are computed for the fun- Global scale analysis and modeling of primary microseisms 5 damental mode of Rayleigh waves in the frequency band 0.05-0.08 Hz using the QL6 model [START_REF] Durek | A radial model of anelasticity consistent with long-period surfacewave attenuation[END_REF] and the continental version of the PREM model [START_REF] Dziewonski | Preliminary reference Earth model[END_REF].

The term e -ω∆R Q(f )U (f ) accounts for minor-arc propagation. At the frequencies of primary microseisms, major-arc and multi-orbit propagation can be neglected.

As already discussed, the displacement PSD u(f ) depends on the value of the effective fitting parameter γ, which includes effects due to the slope of the seafloor over which ocean waves propagate, as well as local source site effects and propagation effects. While the latter aspects are not included in our first-order modeling, the bathymetric and slope effects are unknown for two main reasons.

First, the source magnitude is the result of a complex interference between surface ocean waves and the bottom topography. Second, the ocean floor geometry is generally not known to a level of detail sufficient to estimate the contribution of the slope or the fine-scale bathymetric roughnesses to γ.

Therefore, to achieve the first-order modeling of primary microseisms, we estimate an effective fitting parameter γ for each station minimizing the L1 norm between one year of observed and synthetic PSDs, considering their minimum value every 24 hours. Figure 1 shows two examples of the misfit as a function of the effective fitting parameter γ for the station a) CAN (Canberra, Australia) and b) IVI (Ivittuut, Greenland). The minimum misfit (blue dot) is clearly identified in both cases. The effective fitting parameter γ estimated for each station is shown in Figure 3 and listed in Table 1 in the Supplementary Materials.

Assessing an effective fitting parameter γ for each station allows us to perform the first-order modeling of primary microseisms. This parameter includes both local and propagation effects, which cannot be distinguished with the present first-order modeling. In the following section, we will discuss the main outcomes of our modeling. We will also present a strategy to refine the estimate of the effective fitting parameter by inverting for fitting parameters that vary with a given source area.

RESULTS

Worldwide modeling

In Figure 2, we show a map of the median pressure PSD of primary microseisms. The value of the PSD of each source is the median value over 2013 and in the frequency band 0.05-0.08 Hz. We observe that sources on the eastern side of ocean basins at mid-latitudes (i.e., western coasts of Europe and the US) are stronger than sources on the western side. This evidence is due to the prevalence of westerly winds at mid-latitudes. We also observe that many small islands worldwide are associated with sources of primary microseisms.

A few observations of sources of primary microseisms have been documented in the literature by triangulation of azimuths to the incoming waves. For example, [START_REF] Cessaro | Sources of primary and secondary microseisms[END_REF] observed persistent

primary microseism sources in the North Pacific Ocean near the west coast of the Queen Charlotte Islands (Canada) and the North Atlantic Ocean near the coast of Newfoundland (Canada). In both these regions, the pressure PSD computed from the ocean wave model (Figure 2) shows a large amplitude.

The surrounding insets in Figure 2 show the PSD (in dB with respect to 1 m 2 /Hz) as the median over the PSDs computed every 3 hours in 2013 and as a function of frequency. In the case of missing data, we consider only the portion of the synthetics for which we have data. Data are in blue and synthetics in red. Overall, synthetic and observed PSDs have the same amplitude, shape, and slope.

The fit between data and synthetic is within a few dB, up to a maximum error of about 4 dB at the station PPTF in French Polynesia. At some stations (e.g., PAF and FOMA in the Indian Ocean) we get a perfect match at all frequencies.

Each synthetic PSD is computed by searching the value of the effective fitting parameter γ that minimizes the L1 norm between continuous observed and synthetic records averaged between 0.05 and 0.08 Hz over the year 2013. The effective fitting parameter γ for each station is shown in Figure 3 (color scale) and Table 1 in the Supplementary Materials. Being affected by source (e.g., local site effects due to sediments and fine-scale seafloor roughness) and propagation effects (e.g., scattering at the ocean-continent boundary, focusing and defocusing at heterogeneities), other than by the slope of the bathymetry at the coast, the effective fitting parameter γ in Figure 3 than 1. This means that the features that we do not take into account in our modeling (see Section 2) contribute to the PSD recorded at the seismic stations. In Appendix A, we show that these effective fitting parameters estimated using data in 2013 are time independent, and they allow us to model another year of data with high accuracy.

Seasonal variations

In Figure 4, we investigate the seasonality of primary microseisms. Figure 4a and4b show maps of primary microseism sources in January and July 2013, respectively. Sources are defined as the median pressure PSD F p (f ) between 0.05 and 0.08 Hz. In the northern hemisphere, sources are stronger during the local winter (January, Figure 4a) than during the local summer (July, Figure 4b), notably on both East and West sides of the North Atlantic Ocean, on the coasts of Greenland and the Mediterranean Sea. Weaker variability is observed on both sides of the North Pacific ocean. In the southern hemisphere, seasonal variability is less pronounced, with only some confined regions (e.g., Pacific coasts of South America) clearly showing stronger sources during the southern hemisphere winter (July, Figure 4b). The amplitude of sources around Antarctica varies in response to local effects, such Major peaks and seasonality are well modeled.

as the presence of sea ice, and therefore does not follow a regular seasonal variability, as also observed for secondary microseisms (e.g. [START_REF] Stutzmann | Global climate imprint on seismic noise[END_REF][START_REF] Grob | Observations of the seasonality of the antarctic microseismic signal, and its association to sea ice variability[END_REF][START_REF] Stutzmann | Modelling long-term Downloaded from[END_REF].

A peculiar case is represented by the sources along the coasts of India. Despite being located on the northern hemisphere, they show a larger amplitude in July than in January. As already observed for secondary microseisms (e.g. [START_REF] Koper | Seasonal anisotropy in short-period seismic noise recorded in south asia[END_REF][START_REF] Stutzmann | Modelling long-term Downloaded from[END_REF][START_REF] Davy | Sources of secondary microseisms in the Indian Ocean[END_REF], the sources around India experience a strong seasonality typical of the southern hemisphere.

The seasonality of the sources is reflected in the seasonality of the recorded primary microseisms.

Figure 4c shows time series of RMS minimum displacement integrated over the 0.05 -0.08 Hz frequency band. We keep the minimum value every 24 hours to remove earthquakes. The time series are plotted as a function of the latitude of the stations (y-axis). The time evolution of data (blue) and synthetics (red) is in good agreement, and many strong peaks are well reproduced by our modeling.

Moreover, the ground-displacement time series show a pronounced seasonal variability, especially at stations in the northern hemisphere, where the amplitude of the primary microseism ground displacement is larger in January-February than in July-August. Stations in the southern hemisphere exhibit less seasonal variability -although we still observe higher ground-displacement in January-February than in July-August -in agreement with the time-varying behavior of the source amplitude in the southern hemisphere. A similar seasonality can be observed in 2017 (see Appendix A, Figure A1a).

Dominant source regions

To understand where primary microseisms recorded at each station come from, we perform simulations considering subsets of the sources. We divide the global-scale source distribution into 12 regions, as shown in Figure 5. Then we model the amplitude of the spectrum and the time evolution of the ground displacement considering each one of these source subregions separately. For each station, we use the same effective fitting parameter γ used for the global-scale simulations (Table 1 in the Supplementary Materials). In such a way, a direct comparison with the global scale simulations can be performed. Triangles in Figure 5 denote seismic stations, and their color reflects the dominant source region. Triangles showing two colors represent stations where primary microseisms are due to two different source regions.

Figure 6 shows the median PSD in 2013 (Figure 6a) and the time evolution of the RMS displacement at 0.08 Hz (Figure 6b) and 0.05 Hz (Figure 6c) at the station CAN (Canberra, Australia).

Figure 7 shows the same quantities at the station IVI (Ivittuut, Greenland). The color of the solid lines reflects the source subregion (Figure 5) used to compute the synthetic spectra and RMS minimum displacement. Dashed lines denote data (blue) and synthetics computed considering the global-scale distribution of sources (red).

At the station CAN (Figure 6a), sources from all around Australia (black line) dominate at all frequencies, while the contribution of the other regions decreases with distance. This occurs all year round, as shown in Figure 6b at frequency f = 0.08 Hz, and in Figure 6c at frequency f = 0.05 Hz.

We observe that the fit is particularly good at f = 0.08 Hz, while at f = 0.05 Hz the modeled time series of RMS minimum displacement (dashed red line) shows larger amplitudes than observations (blue dashed line), especially during the local winter. The same observation can be made for 2017 (see Appendix A, Figure A2). Detailed investigation of this evidence can be found in section 3.4.

At IVI (Figure 7a), the dominant source region is frequency dependent: sources around Greenland (yellow) give the largest contribution at f > 0.06 Hz, and sources on the west coasts of North America dominate at f < 0.06 Hz. Although the sources along the east coast of North America (dark red) are located closer to the station IVI, they give a smaller contribution. The time series of RMS minimum displacement at f = 0.08 Hz (Figure 7b) due to sources around Greenland (yellow) is the largest contribution throughout the year, with some sporadic dominant contributions due to sources around Europe (e.g., in April). At f = 0.05 Hz (Figure 7c), the contribution due to sources on the western (Pacific) coasts of North America (distance beyond 2800 km) is the largest on average, although several individual peaks are due to sources around Greenland (e.g. in May), and Europe (e.g. in November).

Primary microseisms at about 83% of the stations can be explained by a unique source region at all frequencies (color of triangles in Figure 5a and spectra in Figures S1-S4 in the Supplementary materials). Some stations are located in the middle of their dominant source regions (e.g. INU in Japan, TAM in Algeria, KIP and NOUC on islands in the Pacific Ocean), while some others are located close L. Gualtieri et al. to edge of their dominant source regions (e.g., HDC in Costa Rica, AIS, PAF and CRZF on islands in the Indian Ocean).

On the other hand, primary microseisms at about 17% of the stations -FDF and MPG along the eastern coasts of the central Atlantic, IVI in Greenland, CLF and SSB in France -are characterized by two main dominant source regions for varying frequency (triangles showing two colors in Figure 5 and spectra in Figure S4 in the Supplementary Materials). Some of the stations are characterized by adjacent dominant source regions: SSB and CLF in France where the dominant source regions are Europe and Africa. Primary microseisms at stations in Antarctica, CCD and DRV, show instead dominant sources located around Australia. Some other stations are characterized by local and distant source regions: IVI in Greenland where the dominant source regions are Greenland and the coasts of northwest America, and FDF and MPG along the eastern central Atlantic coasts where the dominant source regions are southeast and southwest America. At high frequency (f 0.08 Hz), the closest subregion always dominates, while at low frequency (f 0.05 Hz), it is the subregion located further away that dominates (see Figure 7a and Figure S4). Notably, at low frequency (f 0.05 Hz), the dominant source region is located beyond about: 2000 km from the station FDF, 2750 km from MPG, 1220 km from CLF, 880 km from SSB, and 2820 km from IVI. This evidence demonstrates that primary microseisms recorded at a seismic station can also be generated at distant coasts, especially around 0.05 Hz.

Source-dependent effective fitting parameter

In our computations, a constant effective fitting parameter γ has been used for simulating synthetic PSDs at each seismic station. The effective fitting parameter is defined as the value that minimizes the misfit between data and synthetics. In Figures 6 and7, we observed a remarkably good fit between synthetic and observed minimum displacement all year round. An exception is the station CAN at 0.05 Hz (Figure 6c), for which the synthetic minimum displacement shows a systematic larger amplitude than the observed one. The same discrepancy at 0.05 Hz at CAN is also observed in 2017 (see Appendix A). In Figure S9 and S10 in the Supplementary Materials, we investigate the frequency dependence of the effective fitting parameter. We observe that the parameter γ is weakly frequency dependent at the major part of the stations. In a few cases, the effective fitting parameter varies with frequency (e.g. AIS, NOUC), although the misfit does not vary significantly around the minimum value. As a consequence, the observed overestimation at the station CAN at 0.05 Hz cannot be explained by our assumption of a constant effective fitting parameter.

To investigate this discrepancy between observations and synthetics at 0.05 Hz at the station CAN, we let the effective fitting parameter γ vary over macro source areas of 500 km and we use simulated Global scale analysis and modeling of primary microseisms 15 annealing to find the local effective fitting parameters that allow a better fit. By iterating over source points, each parameter γ is slightly modified, and changes are accepted if they improve the fit. If the fit worsens, changes are still accepted with decreasing probability for increasing iteration number. The extension of the macro areas, each of which include about 100 source locations, is chosen to reduce the number of parameters and thus the computational time. To resolve detailed local changes of the effective fitting parameter γ, we minimize the L2 norm between data and synthetics.

We allow the local effective fitting parameter to vary symmetrically around the initial constant value used in the previous simulations, that is γ = 8 for the station CAN (see Figure 3 and Table 1 in the Supplementary materials). Figure 8a shows the RMS minimum displacement obtained for varying the fitting parameter (final model, black) compared to the RMS minimum displacement obtained with a constant effective fitting parameter (initial model, red) and the observed RMS minimum displacement (blue), all at 0.05 Hz. The histograms of the residuals between data and synthetics at 0.05 Hz computed at each time step (Figure 8b) shows that the final model is much closer to the observations (histogram with empty black bars) than the initial model (histogram with light blue bars). The local effective fitting parameter that allows us to obtain the final model reveal a clear spatial pattern, as shown in Figure 8c.

With respect to the starting value (γ = 8), the amplitude of the effective fitting parameter drops on the south-western side of Australia and around New Zealand, it increases on the north-eastern side of Australia and remains unchanged in the Philippine Sea and around Indonesia. Possible causes for this pattern are local structure effects (bathymetry, sediments) and propagation effects (heterogeneities) or other factors in the actual source amplitude that our model does not take into account. For example, we observe that the region where the effective fitting parameter is higher than average (yellow dots in Figure 8c) correlate well with the area of the southwestern Pacific Ocean where tropical cyclones develop. Underestimation of the ECMWF wind forcing in high wind conditions [START_REF] Pineau-Guillou | Strong winds in a coupled wave-atmosphere model during a north atlantic storm event: evaluation against observations[END_REF]) (e.g., tropical cyclones) can lead to errors in the ocean wave height (see Figure S11 in the Supplementary Materials and [START_REF] Rascle | A global wave parameter database for geophysical applications. Part 2: Model validation with improved source term parameterization[END_REF]). In turn, hight wind conditions correspond to long period ocean waves, which generate long period seismic noise (0.05 Hz in this case). This can result in an underestimation of the source amplitude in this region [START_REF] Gualtieri | Global scale analysis and modeling of primary microseisms 19 of tropical cyclones in ambient seismic noise[END_REF], which would justify the need for a higher effective fitting parameter in our modeling.

DISCUSSION AND CONCLUSIONS

In this paper, we showed that our understanding of the generation theory of primary microseisms, combined with state-of-the-art ocean wave models, allows us to model the amplitude of the spectrum of primary microseisms successfully at worldwide-located seismic stations and for varying time.

The pressure source PSD of primary microseisms varies with season, notably in the northern hemisphere. This seasonality is reflected in the seasonality of the recorded displacement as a function of time. The major part of the stations is sensitive to sources located in adjacent subregions, while some of the stations also need source regions located far away to explain the PSD of primary microseisms.

For example, the PSD at the station IVI can be explained by sources situated around Greenland at Global scale analysis and modeling of primary microseisms 17 high frequency (f > 0.06 Hz), while they require sources on the western coasts of North America to explain the data at low frequency (f < 0.06 Hz). The east coast of North America, the closest coast moving west from IVI, gives a negligible contribution to the actual noise level (see Figure 7a). The same behavior is observed at the stations FDF and MPG, with dominant sources on the eastern coasts of South America at high frequency and on the western coasts of South America at low frequency.

The much closer eastern coasts of North America give a negligible contribution (see Figure S4).

One key aspect of the generation of primary microseisms is the slope of the bathymetry in shallow water, where ocean waves propagate. In our modeling, the effect of the slope in shallow water is included in the effective fitting parameter γ (see Figure 3 and Table 1 in the Supplementary materials), which is assessed for each station by minimizing the L1 norm between data and synthetics. This parameter also includes source site effects (e.g., sediments [START_REF] Gualtieri | On the shaping factors of the secondary microseismic wavefield[END_REF][START_REF] Koper | The fine structure of double-frequency microseisms recorded by seismometers in North America[END_REF], fine-scale seafloor roughness) and 3D propagation effects (e.g., scattering at the oceancontinent boundary, focusing and defocusing at heterogeneities), which are not taken into account in our 1D modeling. The effective fitting parameter estimated for each station is time independent. The same values can be used to compute synthetics PSDs of primary microseisms during other periods of time (Appendix A). A simple test for sources around Australia recorded at the station CAN at 0.05 Hz -taken as a case study because of the systematic discrepancy between data and modeling -revealed that local variations of the effective fitting parameter can improve the fit between data and synthetics.

To investigate this aspect in depth, a regional study will follow.

  The detailed expression of the pressure PSDF p (f ) [Pa 2 •m 2 •s]at the seafloor is given by Ardhuin et al. (2015) (Supplementary materials, equation S22) and in Ardhuin et al. (2019) (Equation 3.16).

Figure 1 .

 1 Figure 1. L1-norm misfit between observed and modeled PSDs as a function of the effective fitting parameter γ for the station a) CAN (Canberra, Australia) and b) IVI (Ivittuut, Greenland). The blue dot in each panel highlights the value of the effective fitting parameter γ at which the misfit is minimum.

Figure 2 .Figure 3 .

 23 Figure 2. Map (central inset) showing the pressure PSD F p (Ps 2 • m 2 • s, see Equation1) of primary microseisms in 2013 (color). Pressure PSD is the median over time, integrated between 0.05 and 0.08 Hz. Surrounding insets show the observed (blue) and synthetic (red) seismic displacement PSDs (in dB with respect to 1 m 2 /Hz) of primary microseisms as a function of frequency at 24 seismic stations (black triangles in the map) in 2013.

Figure 4 .

 4 Figure 4. Pressure PSD F p (Ps 2 • m 2 • s) of primary microseisms as the median over time and frequency in a) January 2013 and b) July 2013. c) Observed (blue) and synthetic (red) seismic displacement in 2013 at eight seismic stations (triangles in a and b) as a function of time (x-axis). The time series are normalized with respect to the standard deviation at each station and sorted by station latitude (y-axis) to enhance seasonal patterns on both hemispheres. To avoid earthquakes, we keep the minimum value every 24 hours in both data and synthetics.

  This evidence is in agreement with observations at the global scale by[START_REF] Schimmel | Polarized Earth's ambient microseismic noise[END_REF] and in the Indian Ocean by[START_REF] Stutzmann | Global climate imprint on seismic noise[END_REF] and[START_REF] Davy | Sources of secondary microseisms in the Indian Ocean[END_REF], who showed weak seasonal variations of primary microseisms and pronounced seasonal variations of secondary microseisms. The high periodicity of secondary microseisms in the southern hemisphere was also observed in Australia by[START_REF] Aster | Multidecadal climate-induced variability in microseisms[END_REF] using a quantitative metric to asses seasonality over two decades and by[START_REF] Schimmel | Polarized Earth's ambient microseismic noise[END_REF] by computing the back azimuth to the incoming waves over eight years.

Figure 5 .

 5 Figure 5. Map showing the 12 chosen source subregions (dots) and the 24 seismic stations (triangles), whose color indicates the dominant source regions.

Figure 6

 6 Figure 6. a) Median PSD over 2013 and RMS minimum displacement at the station CAN (Canberra, Australia) at b) 0.08 Hz and c) 0.05 Hz. Solid colored lines are referred to synthetic spectra computed considering only sources in a given subregion (see Figure 5 for the definition of the different subregions). The red dashed line represents the synthetic spectra computed considering sources at the global scale, while the blue dashed line represents data. The legend on the bottom of the figure applies to the three panels. An enlarged version of figures b and c is shown in the Supplementary Materials, in Figures S5 and S6 respectively.

Figure 7

 7 Figure 7. a) Median PSD over 2013 and RMS minimum displacement at the station IVI (Ivittuut, Greenland) at b) 0.08 Hz and c) 0.05 Hz. Solid colored lines are referred to synthetic spectra computed considering only sources in a given subregion (see Figure 5 for the definition of the different subregions). The red dashed line represents the synthetic spectra computed considering sources at the global scale, while the blue dashed line represents data. The legend on the bottom of the figure applies to the three panels. An enlarged version of figures b and c is shown in the Supplementary Materials, in Figures S7 and S8 respectively.

  Downloaded from https://academic.oup.com/gji/advance-article-abstract/doi/10.1093/gji/ggz161/5421624 by Dupre Library Serials Dept user on 29 March 2019

Figure 8 .

 8 Figure 8. (a) Observed (red) RMS minimum displacement at 0.05 Hz recorded at the station CAN compared to the corresponding synthetic obtained with a constant effective fitting parameter s=8 and to the synthetic obtained varying the effective fitting parameters over macro areas. (b) Histogram of the residuals between data and synthetics (as shown in a) computed with a constant effective fitting parameter (light blue) and a varying effective fitting parameter (black contours). (c) Map showing the effective fitting parameter computed over macro areas of 500 km.

  Downloaded from https://academic.oup.com/gji/advance-article-abstract/doi/10.1093/gji/ggz161/5421624 by Dupre Library Serials Dept user on 29 March 2019

  Downloaded from https://academic.oup.com/gji/advance-article-abstract/doi/10.1093/gji/ggz161/5421624 by Dupre Library Serials Dept user on 29 March 2019

  Downloaded from https://academic.oup.com/gji/advance-article-abstract/doi/10.1093/gji/ggz161/5421624 by Dupre Library Serials Dept user on 29 March 2019

Downloaded from https://academic.oup.com/gji/advance-article-abstract/doi/10.1093/gji/ggz161/5421624 by Dupre Library Serials Dept user on 29 March 2019

ACKNOWLEDGMENTS

We thank the GEOSCOPE Observatory and the Incorporated Research Institutions for Seismology (IRIS) for providing openly available seismic data. The output of the ocean wave model can be found at ftp://ftp.ifremer.fr/ifremer/ww3/HINDCAST. L.G. acknowledges support from Princeton University. E.S. and F.A. acknowledge support through the ANR Project MIMOSA under Grant ANR-14-CE01-0012. C.J. acknowledges support through the Cluster of Excellence 'CliSAP' (EXC177), Universität Hamburg, funded through the German Science Foundation (DFG). CJ and CH acknowledge support by the Emmy Noether program (HA7019/1-1) of the German Research Foundation (DFG). The authors also wish to acknowledge useful discussions during the TIDES Training Schools, supported by the COST Action ES1401 (European Cooperation in Science and Technology). We thank two anonymous reviewers for their constructive comments that helped to improve the manuscript.

Table 1 in the Supplementary Materials). The location of the seismic stations is shown in Figures 4a and4b.

APPENDIX A: MODELING PRIMARY MICROSEISMS RECORDED IN 2017

To evaluate whether our results vary over time and assess the robustness of the effective fitting parameter, we compute synthetic PSDs in 2017 using the same effective fitting parameters estimated using data in 2013 (Table 1 in the Supplementary Materials and Figure 3). The overall shape and amplitude of the PSD are well reconstructed at all stations, with a fit within a few dB. We recall that the same effective fitting parameters found in section 2 using data in 2013 have been used to compute synthetics in 2017.

We also investigate the RMS of the displacement at the station CAN in 2017 for varying frequency.

Similarly to 2013 (Figures 6b and6c), we find that the fit between data and synthetics is particularly Global scale analysis and modeling of primary microseisms 23 good at f = 0.08 Hz (Figure A2a), while at f = 0.05 Hz (Figure A2b) the modeled time series (dashed red line) shows larger amplitudes than observations (blue dashed line). This persistent overestimation could indicate a recurrent overestimation of the source amplitude in this region (for example associated with tropical cyclones, see section 3.4) or to features that have been not taken into account in our modeling (e.g., sediments at the source).


Qiang Zhong
email: qzhong@mail.ustc.edu.cn

Haibo Chen
email: hbchen@ustc.edu.cn

Alain Le Bot
email: alain.le-bot@ec-lyon.fr

RADIATIVE ENERGY TRANSFER MODEL FOR PRE-STRESSED ORTHOTROPIC PLATE ON VISCO-ELASTIC FOUNDATION

Keywords: radiative energy transfer method, orthotropic plate, in-plane pre-stresses, visco-elastic foundation

In this study, we develop the radiative energy transfer method for pre-stressed orthotropic plate vibrational on visco-elastic foundation . For orthotropic plate system, the formula of the energy transfer depends not only on the distance between the observation point and source point, but also on the head angle of the wave. And the in-plane pre-stresses and visco-elastic foundation applied on the orthotropic plate can change the wave number, group velocity and input power. Some numerical simulations are performed for a typical tyre model to verify its validation. The simulation results, such as energy density distribution and energy flow field, are compared with the traditional modal superposition solutions for various frequencies and damping loss factors. We analyze the influence of elastic stiffness and pre-stresses on the dynamic response of the orthotropic plate by the proposed model.

Introduction

Methods related to high frequency wave propagation have been introduced into response analysis of structures in recent decades. Statistical energy analysis (SEA) represents a most popular method for analyzing the high-frequency response of bult-up structures under mechanical or acoustical load [START_REF] Lyon | Theory and Application of Statistical Energy Analysis[END_REF]. Power flow analysis (PFA) or Energy finite element method (EFEM) offer an alternative method to SEA wich does not present the detail local energy distribution in a subsystem [START_REF] Nefske | Power flow finite element analysis of dynamic systems: basic theory and application to beams[END_REF][START_REF] Dong | Parametric design sensitivity analysis of highfrequency structural-acoustic problems using energy finite element method[END_REF], but their effectiveness only exists in the high frequency vibration analysis of the one-dimensional system [START_REF] Bot | Geometric diffusion of vibrational energy and comparison with the vibrational conductivity approach[END_REF].

In order to simulate the energy flow in a high frequency vibrational orthotropic medium, D.-H. Prak and S.-Y. Hong [START_REF] Park | Power flow model of flexural waves in finite orthotropic plates[END_REF] established a model by developing the PFA from isotropic medium to orthotropic medium. Based on the study of D.-H. Prak and S.-Y. Hong, X. Y. Yan [START_REF] Yan | Energy Finite Element Analysis Developments for High Frequency Vibration Analysis of Composite Structures[END_REF] proposed the EFEM models of orthotropic and anisotropic plates to predict the highfrequency vibration response of composite structures. Later, Miaoxia Xie [START_REF] Xie | Initial Investigation of Energy Finite Element Validation on High-Frequency Flexural Vibration of Stiffened Thin Orthotropic Plates[END_REF] developed the EFEM model for thin orthotropic plate to analyze the high frequency vibration of a rectangular stiffened thin orthotropic plate. Noted that all these derivation results show that the power flow intensity is proportional to the gradient of the energy density in the orthotropic medium due to the reverberant wave field assumption, and it is consistent with the Fourier's law of heat conduction. However, Langley [START_REF] Langley | On the vibrational conductivity approach to high frequency dynamics for two-dimensional structural components[END_REF] and Aain Le Bot reveal [START_REF] Bot | Geometric diffusion of vibrational energy and comparison with the vibrational conductivity approach[END_REF] that the high frequency vibration response for a two-dimensional system is determined by the direct wave field, that is to say, EFEM has a large error in estimating the response of a two-dimensional system.

In general, the vibrational characteristics of orthotropic plates have been widely investigated from low frequency to high frequency. Howerver, the existing energy flow methods for high frequency vibrational orthotropic plate can not give a reliable local energy density response. Thus, the aim of this study is developing a RETM for pre-stressed orthotropic plate vibrating on visco-elastic foundation.

Basic theory of radiative energy transfer method 2.1 Statistical parameters

The governing equation for out-of-plane vibrations in a prestressed orthotropic plate resting on an elastic foundation excited by a harmonic point force located at

(x 0 , y 0 ) is[10]   D x ∂ 2 ∂x 2 + D y ∂ 2 ∂y 2 2 -T x ∂ 2 ∂x 2 + T y ∂ 2 ∂y 2 + c ∂ ∂t + k + m ∂ 2 ∂t 2   w = F e iωt δ(x-x 0 , y-y 0 ) (1)
where w(x, y, t) is the transverse displacement and m is the mass per unit area of the plate. D x and D y are the bending stiffness in xand y-directions, T x is the x-component of the tensile force, c is the viscous damping coefficient, k is the stiffness per unit area of the elastic foundation, F and ω are the amplitude and the circular frequency of excitation. By substituting a travelling wave solution and considering the undamped case (c = 0), we get the dispersion equation.

( D x cos 2 ϕ + D y sin 2 ϕ) 2 κ 4 + (T x cos 2 ϕ + T y sin 2 ϕ)κ 2 + k -mω 2 = 0 (2)
Phase velocity is defined as

c p (ϕ) = ω κ (3)
and group velocity is defined as

c g (ϕ) = ∂ω ∂κ (4)
The attenuation coefficient is defined as

m(ϕ) = ηω c g (ϕ) ( 5
)
where η is the structural damping loss factor. Eqs. ( 3), ( 4) and ( 5) are wave velocities and attenuation coefficient for the pre-stressed orthotropic plate vibrating on elastic foundation. The influence of elastic stiffness of the foundation and in-plane tension forces on the three variables are involved. And for orthotropic medium, they are functions of the direction angle of propagation wave is significant.

Radiative energy transfer method

The radiative energy transfer method is a high frequency theory of sound and vibration. This theory belongs to geometrical acoustics and therefore its validity is limited to short wavelengths (i.e. high frequencies). As such, the method neglects interference effects and only provides mean values of sound levels when sources are random. The theory is inspired from the so-called "view factor method" in thermics. The primary variables of the theory are energy density and energy flux in the domain (vibrating structure or acoustic room). The theory is based on a local energy balance on the boundary and aims to calculate the power reflected from the boundary. This leads to a boundary integral equation on the reflected power in the form of Fredholm equation of the second type, as shown in Eqs. ( 1) and ( 2). This may be solved by any standard algorithm such as the collocation or Galerkin method.

W (M ) = Ω ρ(S)G(S, M )dΩ + Γ σ(P, M )G(P, M )dΓ (6)
I(M ) = Ω ρ(S)H(S, M )dΩ + Γ σ(P, M )H(P, M )dΓ (7)
This method is basically equivalent to the ray-tracing method but requires a quite different implementation procedure. Among the advantages, it is possible to apply it to the vibration analysis of plates or shells even if they are coupled and their number is very large.

For weak anisotropic plate, we assume that the group velocity and phase velocity are in same direction. Rays propagating in different directions keep straight line, but the group velocity depends on the direction angle.

Discussion

For the values of physic parameters of the rectangular orthotropic plate, we can find in reference [START_REF] Bot | Statistical analysis of vibration in tyres[END_REF] for a tyre model as shown in Table. 1. The first example is given to show the difference of the wave fields between isotropic plate and orthotropic plate. When the stiffness of the two principal axes of the To further illustrate the accuracy of the model presented in this study, the energy responses at central lines (x-and y-direction) predicted by RETM are compared with the exact modal superposition solution. And to show the difference between the existing energy model and RETM for the orthotropic plate system, the results by RETM are also compared with the PFA solution [START_REF] Park | Power flow model of flexural waves in finite orthotropic plates[END_REF] as shown in Fig 4.

Using the parameters of the previous example, we calculated the energy distribution at f = 2500Hz and η = 0.05 as shown in Fig 5 . It can be seen that even with the application of in-plane pre-stress and elastic support, the response estimation model provided in this paper still has a good estimation result.

Conclusion

This study developed a radiative energy transfer method for pre-stressed orthotropic plate vibrating on visco-elastic foundation. Firstly, the present model gives a more accurate solution than the existing PFA solution for vibrational orthotropic plate under a high frequency hamornic point load. Secondly, the shape of wavefront for orthotropic plate is no longer cylindrical, it is elliptical.

Figure 1 :

 1 Figure 1: A prestressed rectangular orthotropic plate.

Table 1 :Figure 2 :Figure 3 :

 123 Figure 2: Energy distribution of isotropic plate D y = D x , f = 5000Hz, η = 0.1, (reference= 10 -12 J/m 2 ): (a) RETM; (b) Exact solution.

Figure 4 :

 4 Figure 4: Energy distribution at central line, f = 1000Hz, η = 0.05: (a) x-direction; (b) y-direction.

Figure 5 :

 5 Figure 5: Energy density distribution with both prestresses and elastic foundation effect, T x = 3 × 10 4 N/m, T y = 8 × 10 4 N/m, k w = 1.3 × 10 6 N/m 3 , f = 2500Hz, η = 0.05.

ICSV26, Montreal, 7-11 July 2019

ICSV26, Montreal, 7-11 July 2019


Modeste Assemien
email: nguetta.assemien@ec-lyon.fr

Alain Le Bot
email: alain.le-bot@ec-lyon.fr

INFLUENCE OF SLIDING SPEED ON ROUGHNESS NOISE

Keywords: roughness noise, sliding speed, vibratory level

This article presents an experiment and numerical simulation on friction noise. The noise emitted by a solid rubbing on a rough surface, also called roughness noise, results from a complex interaction between microscopic asperities of both surfaces. It is characterized by a wide band spectrum, a low noise levels and a weak mechanical interaction. The level is controlled by several external parameters such as surface roughness, normal load and sliding speed. The purpose of our study is to understand the evolution of roughness noise versus sliding speed. To achieve this goal, an experimental approach and numerical simulation have been used and the obtained results highlight the law between sound level and sliding velocity. The main conclusion of the study is that noise level versus sliding speed follows a power law with an exponent about 3/4.

Introduction

In the field of friction noise, the noise due to mechanical instabilities was largely studied in literature. But the role of roughness on friction noise has not received a so great attention, and its phenomenology is not yet fully explained. In literature, some experimental studies have proposed a relationship between the sound pressure level and the sliding speed [START_REF] Othman | Surface Roughness Measurement Using Dry Friction Noise[END_REF][START_REF] Othman | Experimental investigation of frictional noise and surfaceroughness characteristics[END_REF][START_REF] Abdelounis | An experimental study on roughness noise of dry rough flat surface[END_REF].

The study in this paper was realized in the case of flat-flat contact at a constant sliding speed and surface roughness. The dependence of vibration level L V (dB) with the sliding speed showed that L V is a logarithmic function. The objective is to clarify if the vibration level is an increasing function of the sliding speed according to the empiric following law:

L v (dB) ∝ 20 log 10 V n (1)
where the slope n varies between 0.6 and 1.1

[4-8].
This paper provides an experiment and numerical simulations to verify the relationship between the vibration level and the sliding velocity.

Experimental Setup

The experiment consists in rubbing two samples with rough surfaces and in recording the vibration of plate. Rubbing test were carried out for dry contact, under light load and with a varying sliding speed.

Principle of the experiment

Rigid slider is pulled by a small synchronous motor with a constant velocity V on a resonator (Figure 1). The base of the slider and the track on the resonator are rough. W denotes the weight of the slider. Table 1 shows the characteristics of the resonator and the slider. The resonator and the slider are made of stainless steel with Young's modulus E = 210 GPa, Poisson's ratio v= 0.3 and mass density ρ=7800 kg/m3.

The RMS value of the vibration velocity is measured within the frequency band [10 Hz-10 kHz] by a laser vibrometer with three velocity measuring ranges for maximum resolution up to 0.02 μm/s.

Protocol

Rubbing tests were carried out for samples having same surface roughness obtained by the same machining process. Before tests, samples are carefully degreased with heptane, acetone and isopropanol. Each friction test is repeated three times. The test is run in ambient atmosphere (relative humidity varied from 73 to 76% and room temperature from 21 to 23 °C). The slider (top solid) is moving in the xdirection at constant speed V in the range 1 ≤ V ≤ 1000 mm/s during friction test.

Experimental results

From vibrometer measurements, we can calculate the vibration level L V . This physical quantity is obtained from the following relationship:

L v = 20 log 10 V RMS V 0 (2)
Where V 0 = 10 -9 m/s and V RMS is the root mean square vibration speed.

The measurements show that 𝐿 𝑉 is linear increasing functions of the logarithm of 𝑉 (Figure 2).

Numerical simulation of roughness noise 3.1 Principle

The numerical approach used in this study is based on truncated modal decomposition of the vibration and central difference integration scheme and the penalty algorithm for contact [START_REF] Hung | Direct numerical simulation of dynamics of sliding surfaces[END_REF].

The simulation is based on a 3D model implemented in the software program ra3D. The top solid moves horizontally with à constant velocity V while the bottom solid is fixed at both ends. The solids have nominally flat surfaces.

Figure 3 shows the rough surfaces generated numerically by using spectral method with Berstrom's program [START_REF] Bergstrom | Rough surface generation & analysis[END_REF]. This surface is characterized by their standard parameters Ra, Rq, Rsk, Rku and λ for respectively arithmetic roughness, quadratic roughness, Skewness, Kurtosis and correlation length. The number of nodes is 8400x600 (Nx x Ny) and the step between tow nodes is 50 μm.

Protocol

Rubbing tests were carried out for samples having same surface roughness and each friction test is repeated three times. The numerical simulations are performed with the following parameters (Table 3):

Numerical results

Figure 6 shows that roughness noise is an increasing function of the logarithm of the sliding speed. Numerical results are in agreement with our experimental results. The simulation results also show that L V is linear increasing functions of the logarithm of 𝑉 (Figure 6) and the slope is 𝑛 = 0.77. This result is in agreement with the numerical simulation of the dynamics of sliding rough surfaces with 2D model of Hung and al [18].

Discussion

The results of experiment and numerical simulation of roughness noise in the study are in agreement with previous studies. The magnitude of vibration level obtained by simulation is greater than the values found experimentally. This gap could be explained by:

-The numerical model of the resonator -The value of the modal damping ratio -The boundary conditions of the resonator Another factor which affect strongly the vibration level and reduces sound level is dissipation in the roughness contact.

Conclusions

An experimental and numerical simulation investigation of friction noise between two rough and dry surfaces were carried out. The 3D model used for numerical simulation of roughness noise make realistic approach. The main conclusion of the study is that vibration level versus sliding speed follows a power law with an exponent about 3/4.

Figure 1 :

 1 Figure 1: (a): Principle of the experiment, (b): Experimental setup

Figure 2 :

 2 Figure 2: Evolution of vibration level L V versus sliding speed V The simulation results show that the vibration level L V is a linear increasing function of the logarithm of the 𝑉 (Figure 2) and the slope is 𝑛 = 0.76. This result is in agreement with the observations of Stoimenov and al [8] (0.7 ≤ 𝑛 ≤ 0.85), Nakai and yokoi [5] (0.6 ≤ 𝑛 ≤ 1.1), Abdelounis and al [7] (0.51 ≤ 𝑛 ≤ 0.78) for flat-flat contact.

Figure 3 :

 3 Figure 3: Rough surfaces generated numerically

Figure 6 :

 6 Figure 6: Evolution of vibration level Lv versus sliding speed V for surface roughness Ra = 5 µm

Table 1 :

 1 Characteristics of the slider and the resonator

		Resonator			Slider
	ζ	Size (mm)	Ra (µm)	Size (m)	V (mm/s)	Ra (µm)
	0.1%	450x300x2	5	20x20x5	1 -1000	5

Table 3 :

 3 Input and simulation parameters

				Input parameters				Simulation parameters
	Material			Resonator		Slider
	E	ρ	ν	ζ	Size (mm)	Size (mm)	Speed	Duration	Time-	Sampling	modes
	(GPa)	(kg/m 3 )					(mm/s)	(s)	step (s)	(Hz)
	210	7,800	0.3 0.1%	450x300x2	20x20x5	1 -1000	0.4	1e-6	44100	200

ICSV26, Montreal, 7-11 July 2019

Stoimenov, B., Maruyama, S., Adachi, K. and Kato K. The roughness effect on the frequency of frictional sound, Tribology International, 40, 659-664, (2007).