Le Roux-Mallouf

Gaëlle Le Roy
email: gaelle.le-roy@univ-grenoble-alpes.fr

A Helmstetter

D Amitrano

F Guyoton

R Le Roux-Mallouf

Seismic analysis of the detachment and impact phases of a rockfall and application for estimating rockfall volume and free-fall height

Seismic analysis of the detachment and impact phases of a rockfall and application for estimating rockfall volume and free-fall height

Introduction

Characterizing rock fall properties such as location, occurrence time, volume and propagation path, is a key point to improve the mitigation of the associated hazards and to better prevent them. Several approaches can be used to detect rockfalls and to assess erosion activity such as satellite imagery or terrestrial and airborne laser scanning. These methods can deliver accurate information on detachment and impact zones and on released volumes and thus provide volumefrequency relationships. However, temporal information is often limited as they rely on the survey lapse times (respectively 2.5, 0.5 and 1 year interval for [START_REF] Dewez | Probabilistic coastal cliff collapse hazard from repeated terrestrial laser surveys: case study from Mesnil Val (Normandy, northern France)[END_REF][START_REF] Kuhn | Coastal Cliff Monitoring and Analysis of Mass Wasting Processes with the Application of Terrestrial Laser Scanning: A Case Study of Rügen, Germany[END_REF][START_REF] D'amato | Influence of meteorological factors on rockfall occurrence in a middle mountain limestone cliff[END_REF]. Hence, with these approaches, it is impossible to resolve the gradual collapse of blocks released from the same location or to determine the relation between rockfalls occurrence and external triggers. This presents significant drawbacks for the knowledge of site activity (number and size of individual events, occurrence time, triggering factor, etc.). In addition, monitoring using DEMs is yet difficult to apply automatically and cannot be used for real-time detection and warning system of rockfalls.

Continuous seismic monitoring provides a solution for this shortcoming as rockfalls can be automatically detected and located from the seismic signal they generate [START_REF] Battaglia | Location of seismic events and eruptive fissures on the Piton de la Fournaise volcano using seismic amplitudes[END_REF][START_REF] Lacroix | Location of seismic signals associated with microearthquakes and rockfalls on the Séchilienne landslide, French Alps[END_REF][START_REF] Burtin | Continuous catchment-scale monitoring of geomorphic processes with a 2-D seismological array[END_REF][START_REF] Burtin | Seismic monitoring of torrential and fluvial processes[END_REF][START_REF] Levy | Friction weakening in granular flows deduced from seismic records at the Soufrière Hills Volcano, Montserrat[END_REF], Dietze et al., 2017a). According to the definition given by [START_REF] Varnes | Slope Movement Types and Processes[END_REF], a rockfall is a slope process that involves rock fragment detachment proceeding down the slope by free falling, bouncing, rolling, and sliding until their deposition. All these processes can be identified on the seismic signals. However, as gravitational mass wasting events are complex and composed of several processes occurring simultaneously, it is often difficult to determine the link between block dynamics and the seismic signal generated.

Seismic signals of rockfalls detachment have been identified in several studies [START_REF] Rousseau | Les signaux sismiques associés aux éboulements sur l'ile de la Réunion (océan indien) -étude de deux sites : la cascade de Mahavel et la cavité de la soufrière[END_REF][START_REF] Deparis | Analysis of rock-fall and rock-fall avalanche seismograms in the french Alps[END_REF][START_REF] Hibert | Slope instabilities in Dolomieu crater, Réunion Island: From seismic signals to rockfall characteristics[END_REF][START_REF] Dietze | Spatiotemporal patterns, triggers and anatomies of seismically detected rockfalls[END_REF]. However, the origin of these signals was linked to different processes: elastic rebound of the cliff [START_REF] Rousseau | Les signaux sismiques associés aux éboulements sur l'ile de la Réunion (océan indien) -étude de deux sites : la cascade de Mahavel et la cavité de la soufrière[END_REF]Deparis et al., 2009;[START_REF] Hibert | Slope instabilities in Dolomieu crater, Réunion Island: From seismic signals to rockfall characteristics[END_REF], fractures opening, and friction between the detached compartment and the cliff (Dietze et al., 2017a). In some cases, the detachment of a rockfall has been preceded by precursory signals. For instance, the 15 000 m 3 Illgraben rock avalanche (Rhone Valley, Switzerland) was preceded by seismic pulses lasting for a few seconds [START_REF] Zeckra | Automated detection and classification of rockfall induced seismic signals with Hidden-Markov-Models[END_REF].

Controlled experiments allow an accurate estimation of rockfall properties, and thus a better understanding of the processes generating the seismic signal. [START_REF] Vilajosana | Rockfall induced seismic signals: case study in Montserrat, Catalonia[END_REF] and [START_REF] Bottelin | Seismic and mechanical studies of the artificially triggered rockfall at Mount Néron (French Alps, December 2011)[END_REF] studied artificially triggered rockfall events. These studies allowed relating the most energetic seismic phases to boulder impacts after a free-fall and showed that impacts were characterized by waves packets with frequency contents over the range 1-50 Hz. Controlled releases of single blocks in a marl gully [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF] or in quarries (Saló et al., 2017) explored seismic amplitude and energy in relation to the kinetics of block impacts. [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF] inferred single block mass and velocity from local seismic records with a fair accuracy (median ratio between calculated and measured velocity of 0.2). In contrast, Saló et al. (2017) did not find a correlation between kinetic parameters of the blocks and measured seismic energies. All these studies highlight the large uncertainties on rockfall properties (volume, velocity, location, etc.) estimated from the associated seismic signal.

In the present study, we analyze Terrestrial Laser Scanning (TLS), photogrammetric and seismic data of natural rockfalls in order to investigate the relations between blocks dynamics and the associated seismic signal. The monitoring of two limestone cliffs, Mount Saint-Eynard and Mount Granier (Chartreuse massif, French Alps), allowed us to obtain numerous data on the characteristics of rockfalls (location, occurrence time, volume, failure mode, etc.).

We select 16 rockfalls from Mount Saint Eynard and Mount Granier that experienced a free fall phase and that were detected both by DEMs and seismic monitoring. We focus on the first part of the seismic signals (detachment and first impact), in order to better understand the link between seismic signals and rockfalls kinetics. This dataset allows us to establish scaling laws between seismic parameters (free-fall duration, frequency, seismic energy) and rockfall characteristics (volume, potential energy, free fall height).

A first data set of Mount Saint-Eynard rockfalls is used as a training data set to determine relations between rockfall properties and the characteristics of the seismic signals. These relations are then applied to a second data set of the Mount Granier rockfalls. Finally, we compare our results with two other sites, in order to test whether our relation could be applied to both smaller and larger rockfall volumes and for different geological settings. In the Yosemite area, we analyze the Happy Isle and Ahwiyah Point rockfalls to investigate volumes larger than 10 000 m 3 , while the controlled releases of block of [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF] extend the range of volumes down to 0.03 m 3 .

Study sites

Chartreuse massif

Our main study area is located in the sedimentary cover of the External Crystalline Massifs of the French Western Alps (Figure 1). The Chartreuse massif is mainly composed of limestone and marls forming a succession of synclines and anticlines. The eastern edge of this massif is characterized by long linear limestone cliffs overtopping marly talus slopes. Two major rock formations make up these cliffs: Tithonian stage limestone and Urgonian stage limestone, with near-horizontal beddings. This study area is interesting due to the frequent rockfall activity covering a large range of volumes, from less than 1 m 3 up to a few thousand cubic meters. Typical failure configurations and triggering factors of rockfalls have been studied in previous studies (Frayssines & Hantz, 2006;[START_REF] D'amato | Influence of meteorological factors on rockfall occurrence in a middle mountain limestone cliff[END_REF]. These studies inferred that rainfall and freezethaw cycles had triggered about half of the rockfall during the studied period (2013)(2014)(2015).

Mount Saint Eynard is located North East of Grenoble, Isère, French Alps (Figure 1a). Mount Granier (1933 m ASL), located north of the Chartreuse massif (Figure 1b), is an iconic mountain affected, in 1248, by one of the biggest landslides in Europe (500 million m 3 , [START_REF] Nicoud | Données nouvelles sur la nature et l'extension du glissement historique du Granier (Savoie, France)[END_REF]. Its north face, a 800 m high rock wall that appeared after the landslide, forms a natural geological cross section in Urgonian limestone, Hauterivian marls, Valanginian limestone and Berriasian marls. Formed by perched syncline oriented to the east, the Mount Granier presents numerous fractures and karst network.

Other sites

Yosemite Valley is a deep, glacier-carved valley bounded by steep granite cliffs. These steep cliffs produce numerous rockfalls and rockslides, which range from small boulders to massive events of several million cubic meters. In this study, we focus on three events exceptional due to their size and induced damages: the Happy Isles rockfall, which occurred on July 10, 1996 [START_REF] Morrissey | Air blasts generated by rockfall impacts: Analysis of the 1996 Happy Isles event in Yosemite National Park[END_REF][START_REF] Wieczorek | The unusual air blast and dense sandy cloud triggered by the July 10, 1996 rock fall at Happy Isles, Yosemite National Park, California[END_REF] for which two large rockfalls of combined volume estimated between 23 000 and 38 000 m 3 broke loose from cliffs adjacent to the Happy Isles Nature Center. The impact of these blocks generated pressure waves that downed over 1000 trees, destroyed a bridge and caused one fatality and several injuries. Finally, the unusually large rockfall (25 400 m 3 , which dislodged en route 21 300 m 3 ) occurred in 2009 near Ahwiyah Point. controlled release of single blocks within a soft-rock (black marls) gully of the Rioux Bourdoux torrent (French Alps). 28 blocks, with masses ranging from 76 kg to 472 kg For more details …. Blablabla …. see [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF]

Instrumentation

Mount-Saint-Eynard

Mount Saint-Eynard has been monitored since 2013 by several methods. The south of the Mount Saint-Eynard has been yearly surveyed by TLS since 2009, using an Optech Ilris-LR laser scanner, along a 750 m zone of interest [START_REF] Guerin | Investigating rockfall frequency using terrestrial laser scanner[END_REF][START_REF] D'amato | Influence of meteorological factors on rockfall occurrence in a middle mountain limestone cliff[END_REF]. In this study, we focus on rockfalls detected at the Mount Saint-Eynard cliffs between November 2013 and December 2015. In order to monitor a larger area, located between the seismic stations MOL and GAR (Figure 1c), and to reduce the delay between TLS surveys (once a year), we have carried out sporadic photogrammetric surveys over a larger area and to analyze specific events.

The cliffs are also monitored using an autonomously operating camera Canon EOS Rebel T3 1100D (Figure 1c) taking photographs every 10 min.

In 2013, four broad band 3-components seismometers (Guralp CMG40T, with a corner frequency of 0.1 Hz and a sampling frequency of 100 Hz) have been installed a few hundred meters apart, in order to detect rockfall activity. Stations MOL, RES and GAR are located at the cliff foot on top of scree, while station FOR is located on the cliff head, on top of rock (Figure 1c).

Mount Granier

There were no TLS or photographic time lapse surveys at Mount Granier. Therefore, we used sporadic photogrammetry surveys to reconstruct DEMs.

In 2016, a series of rockfalls occurred at Mount Granier with volumes up to 75 000 m 3 (Hobléa et al., 2018). In order to monitor the Mount Granier rockfall activity following these rockfalls, station, GRA, was installed on the cliff head of Mount Granier (Figure 1) in June 2016.The seismometer was a 3-component velocimeter with a corner frequency of 2 Hz. The signal was sampled at 250 Hz. When events were seismologically detected, complementary photogrammetric surveys were carried out within the next week.

Yosemite Park

Yosemite Park rockfall events are occasionally energetic enough to be detected by regional seismic sensors located several tens of kilometers away. Two notable examples are the 1996 Happy Isles rockfalls [START_REF] Wieczorek | The unusual air blast and dense sandy cloud triggered by the July 10, 1996 rock fall at Happy Isles, Yosemite National Park, California[END_REF][START_REF] Morrissey | Air blasts generated by rockfall impacts: Analysis of the 1996 Happy Isles event in Yosemite National Park[END_REF] and the 2009 Ahwiyah Point rockfall [START_REF] Zimmer | Rock fall dynamics and deposition: an integrated analysis of the 2009 Ahwiyah Point rock fall[END_REF] which are studied here.

In the case of the Happy Isles rockfalls, although the entire rock-fall event was not observed, rockfall characteristics used in this study were reconstructed by [START_REF] Morrissey | Air blasts generated by rockfall impacts: Analysis of the 1996 Happy Isles event in Yosemite National Park[END_REF] and [START_REF] Wieczorek | The unusual air blast and dense sandy cloud triggered by the July 10, 1996 rock fall at Happy Isles, Yosemite National Park, California[END_REF] from eyewitness accounts, seismic records and field evidence.

Airborne LiDAR data were collected in 2006 and in 2010 following the Ahwiyah Point rockfalls, by the National Center for Airborne Laser Mapping (NCALM). A complementary terrestrial LiDAR was carried out in May 2009, two months after the Ahwiyah Point rock fall, using a Riegl Z420i instrument, from two scan positions located 1150 m from the Ahwiyah Point rockfall source area [START_REF] Zimmer | Rock fall dynamics and deposition: an integrated analysis of the 2009 Ahwiyah Point rock fall[END_REF].

Methods

Topographic data analysis

Repeated topographic surveys allow identifying missing rock mass volumes, which can be interpreted as result of rockfalls and provide information on its detachment area, impact area, volume, free-fall height and failure mechanism. DEMs were constructed both by TLS for Mount-Saint-Eynard [START_REF] D'amato | Influence of meteorological factors on rockfall occurrence in a middle mountain limestone cliff[END_REF] and by photogrammetry (Mount Saint Eynard and Mount Granier, in this study).

Mount Saint-Eynard photogrammetric surveys were carried out using data sets of more than 500 photographs (camera Canon EOS 7D, resolution 5-9 cm/pixel) taken from 12 locations at the base of Mount Saint-Eynard. Three Mount Granier photogrammetric surveys were carried out between January and February 2017, providing a dataset of 100 photographs taken from eight locations (resolution < 8 cm/pixel).

Point clouds were constructed using Structure from motion (SfM) technics with Agisoft Photoscan software. Raw point clouds were cleaned, in order to remove vegetation noise and keep only the rock surface. They were georeferenced using a georeferenced point cloud of the site obtained by airborne laser scanning in 2011. The co-registration (or alignment) of the scans is achieved first by a manual alignment, which consists in identifying common points in the different point clouds. Following this rough matching, we applied an automated iterative procedure with a point-to-surface Iterative Closest Point (ICP) algorithm [START_REF] Besl | A method for registration of 3-D shapes[END_REF]Teza et al., 2007), in order to minimize the co-registration errors.

The quality of photogrammetric surveys is slightly coarser than TLS surveys (mean points distance for photogrammetric surveys: 15 cm, TLS surveys: 10 cm).

Once raw point clouds are cleaned from vegetation noise, they are georeferenced using a georeferenced 1 m spacing DEM of the site (from the IGN, French National Institute of Geography) and then meshed. We considered negative deviations larger than a threshold (TLS:10 cm; photogrammetry: 30 cm, corresponding to a 99.5% quantile of the noise distribution of the distance between the two point clouds) as rockfalls. The point clouds defining a fallen compartment are then meshed.

3D reconstructions provide constraints on the morphology of the fallen compartments. For each event, volume, surface and geometry (length, width, depth and gravity center) can be determined. For Mount-Saint Eynard area, this work was primarily carried out by D'Amato et al. (2016). They determined the volume and geometry of the detected events. We reprocessed these TLS point clouds to retrieve complementary information (volume uncertainty, free-fall height, cliff profile).

Based on these characteristics and by considering that the main force involved in the process is gravity, we can determine failure mechanisms. Depending on the weight vector characteristics (built from the gravity center, Figure 2a, 2b), two main types of failure were considered, (i) slide and (ii) free-fall or topple. When the weight vector intersects the cliff, the mechanism is a slide (Figure 2a). When it intersects a free face, the failure type is free-fall (Figure 2b) or topple. Topple involves a forward rotation out of the slope of the compartment about an axis below the center of gravity of the compartment [START_REF] Cruden | Landslides: investigation and mitigation. Chapter 3-Landslide types and processes[END_REF]. This kind of failure is likely to occur if the lower part of the compartment is intact whereas fractures are present in its upper part. For topple or free-fall detachment, no, or little, shear displacement takes place, contrary to slide failure. Topple and free-fall could not be distinguished in this study due to the lack of information on the repartition of fractures before failure. We thus use the term "free-fall" to designate both free-fall and topple mechanisms in the following. Some rockfalls experienced a free-fall after their detachment. In this case, the free-fall heights are obtained by measuring the distance HDEM between the gravity center of the compartments and their vertical projections on the cliff face. As illustrated in Figure 2b, ΔH the uncertainty on HDEM depends on the size of the compartment and on the angle of the slope, e.g., a steeper slope induces a larger uncertainty. The 25.11.2015 event underwent a 2 m slide after its detachment. In this case, the impact location and free-fall height were constrained by clear impact marks observed on the field. Using the DEMs, we can also calculate the potential energy of a rockfall EpDEM before its impact.

EpDEM = p VDEM g HDEM, ( 1
)
where VDEM is the volume, p is the density and g=9.82 m.s -2 is the gravity constant.

Detection and classification of seismic signals

A rockfall event is characterized by a series of pulses of ground velocity with frequency contents between 5 and 50 Hz and duration between several seconds and about one minute (Dietze et al., 2017a[START_REF] Provost | Towards a standard typology of endogenous landslide seismic sources[END_REF]. This characteristic pattern makes rockfalls distinct from other sources, such as earthquakes and anthropogenic noise. We have used the method of [START_REF] Helmstetter | Seismic monitoring of Séchilienne rockslide (French Alps): Analysis of seismic signals and their correlation with rainfalls[END_REF] in order to detect seismic events. The detection is performed by analyzing the seismic energy between 2 and 20 Hz averaged over all stations. An event is detected when the amplitude exceeds the long-term average by a factor of 3 or more. Events that are also detected by the regional seismic network Sismalp are automatically classified as earthquakes. We check all events in order to classify them based on the properties of rockfall seismic signals described in previous studies [START_REF] Helmstetter | Seismic monitoring of Séchilienne rockslide (French Alps): Analysis of seismic signals and their correlation with rainfalls[END_REF][START_REF] Provost | Towards a standard typology of endogenous landslide seismic sources[END_REF]. The configuration of the network, with large distances between stations, does not allow us to use the apparent velocity or the inter-trace correlation as classifying parameters. Earthquakes are characterized by distinct P and S waves, and have similar waveforms on all stations (amplitude, frequency content and shape of envelope). Rockfalls usually display a more complex envelope, with a succession of peaks corresponding to successive block rebounds. Events that are only visible at one station are likely noise (e.g., road traffic). Wind, rainfall and storms also generate seismic signals, which can be recognized by their relatively high-frequency content (mostly above 20 Hz) and by a large variability of signal properties between stations. For signals with ambiguous waveforms, we checked the seismic signal at nearby seismic stations from the regional network Sismalp to help distinguishing earthquakes from rockfalls. The small number of sensors and the large distance between sensors do not allow an accurate source location. Signals are emergent, therefore manual picking is difficult, and uncertainty can be as large as 1 second, leading to large location errors. The large distances (several hundred meters) between sensors make inter-sensor correlation very weak and does not allow the use of beam-forming methods [START_REF] Lacroix | Location of seismic signals associated with microearthquakes and rockfalls on the Séchilienne landslide, French Alps[END_REF]Dietze et al., 2017a). Nonetheless, we can obtain some information about the source location from manual picks of the seismic signals and from amplitude ratios (corrected from site effects). The rockfall is likely located closest to the station with the strongest amplitude. This information is only used to select rockfalls that are likely located within the study area.

Characterization of rockfalls from seismic signals

In order to compare characteristics of the seismic signals and rockfalls dynamics, we use five metrics extracted from either the seismograms or the DEMs: seismic energy of the detachment phase EsD, seismic energy of the impact phase EsI, free-fall duration Dff, rockfall volume measured VDEM and free-fall height HDEM measured on the DEMs. Figure 2 presents an overview of the different metrics.

To calculate the seismic energy Es, we assume a point-source [START_REF] Kanamori | Analysis of long-period seismic waves excited by the May 18, 1980, eruption of Mount St. Helens -A terrestrial monopole[END_REF][START_REF] Eissler | A single-force model for the 1975 kalapana, hawaii, earthquake[END_REF] and we consider the medium as isotropic and homogeneous. We also consider that surface waves dominate the seismic signal [START_REF] Dammeier | Characterization of alpine rockslides using statistical analysis of seismic signals[END_REF][START_REF] Levy | Friction weakening in granular flows deduced from seismic records at the Soufrière Hills Volcano, Montserrat[END_REF][START_REF] Levy | Real-time detection, location, and characterization of rockslides using broadband regional seismic networks[END_REF]. Signals were band-pass filtered between 2 and 50 Hz for the entire analysis.

The following relations were used:

𝐸 " = 2𝜋𝑟𝑝ℎ𝑐 ∫ + , + - 𝑢 /01 (𝑡) 5 𝑒 78 𝜀 𝑑𝑡 (2)
𝑢 /01 (𝑡) = ;𝑢(𝑡) 5 + 𝐻(𝑢(𝑡) 5 )

(3)

𝑢(𝑡) = ;𝑢 > 5 (𝑡) + 𝑢 ? 5 (𝑡) + 𝑢 @ 5 (𝑡) (4)
where t0 and t1 are the manually picked onset and end times of the seismic signal, r is the distance between the event and the recording station, h is the thickness of the layer through which surface waves propagate, p is the ground density, c is the phase velocity of the seismic waves, uenv(t) is the envelope of the ground velocity u(t) obtained using the Hilbert transform (H), 𝛼 is a damping factor that accounts for inelastic attenuation of the waves [START_REF] Aki | Quantitative Seismology[END_REF] and ε a coefficient accounting for site effects. Uncertainties on the distance, frequency, ground density, attenuation factor and wave velocity are taken into account in the calculation of seismic energy.

The distance between the detachment zone and the stations is well constrained by DEM data. For free-fall events, the distance between the impact area and each station is determined as the distance between the station and the intersection of the vertical projection of the compartment gravity center and the cliff face. We considered that this distance was prone to a maximal error of 20 m for Mount Saint-Eynard and 30 m for Mount Granier, due to the size of the block and to the slope angle in the impact zone (see Figures 2b and3c).

We have estimated the seismic wave velocity from the location of rockfalls estimated form the TLS surveys and from the manual picking of the first impact for all stations and all rockfalls detected at Mount Saint Eynard. We search for the velocity V that minimizes the residuals on the differential travel times. For each rockfall and each couple of stations i,j, we estimate the difference in arrival times tj-ti. The theoretical travel time delay is (ri-rj)/V. Minimizing the differences between the observed and theoretical time delays allows us to estimate V=1810 ±100 m.s -1 (Figure 4a).

We assume a density of 2500 ±100 kg.m -3 . The frequency centroid of the impact seismic signals averages at 10 ± 2 Hz. Therefore the thickness was taken as one wavelength of Rayleigh waves, h=181 ± 20 m for a frequency of 10 Hz.

We have estimated the site effect coefficient ε using a catalog of 200 earthquakes recorded by the Mount Saint-Eynard network and located by the regional seismic network Sismalp. We have computed the ratio of amplitude at stations MOL, GAR and RES over the reference station FOR located at the cliff head. This way we were able to correct the amplification at each station (Borcherdt, R.D, 1970). Site effect of Mount Granier was computed using 4 earthquakes recorded by the reference station FOR and by station GRA.

In order to estimate the attenuation factor, we used the relationship derived by [START_REF] Kanai | Study of the attenuation of seismic waves[END_REF]:

C D E D F G 8 E 8 F H 0 I = G ɛ E ɛ F H -𝛼M𝑟 N -𝑟 O P (5)
with ai and aj the maximum amplitudes at two stations filtered around the frequency centroid, between 9 and 11 Hz, n = 0.5 for surface waves, ri and rj the corresponding epicentral distances, and ɛi and ɛj constants depending on the ground and installation conditions of each sensor. This method has also been used in previous studies of rockfalls [START_REF] Levy | Friction weakening in granular flows deduced from seismic records at the Soufrière Hills Volcano, Montserrat[END_REF][START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF].

Since we have estimated the site effects term ɛ for each station, we can normalize each signal by this factor and rewrite (5) as

C D E ɛ F ɛ E D F G 8 E 8 F H 0 I = -𝛼M𝑟 N -𝑟 O P (6)
We can thus estimate α from a linear regression using Equation ( 6). We have selected seismic records of the rockfalls detected at Mount Saint Eynard (listed in Table 1) at all stations.

Using the location derived from the topographic analysis, we have estimated 𝛼 =8.8 x10 -4 m-1 (Figure 4b) with a regression uncertainty of ± 0.9 x10 -4 (confidence interval 68%). This factor is sensitive to the choice of the frequency band. Thus, as the centroid frequency of the impact phase has been determined as 10 ± 2 Hz, the lower bound of 𝛼 has been set to 6.9 x10 -4 m -1 (frequency 8 Hz) and the upper bound to 10.3 x10 -4 m -1 (frequency 12 Hz). There is only one station at Mount Granier, therefore we cannot estimate seismic wave velocity or the damping factor. We thus assume that material parameters (V, h, p, c and α) are the same as for the Mount Saint-Eynard's, since the geological context is similar in both cases.

Seismic energy can also be derived from the Gutenberg-Richter magnitude-energy relation with m the magnitude [START_REF] Kanamori | Theoretical basis of some empirical relations in seismology[END_REF].

Log Es = 1.5m +4.8

(7)

This relation was used for the Yosemite rockfalls and for the dataset of controlled block releases (Bibert et al., 2017).

When the fallen compartment undergoes a free-fall immediately after its detachment, the seismic signal of the detachment phase can be isolated from the blocks propagation. In our dataset, when the seismic signal of the detachment and first impact are not overlapping, it is possible to calculate the free-fall height Hs by measuring the free-fall duration Dff:

𝐻 " = v ww ² . y 5 (8)
where g is the gravity constant (9.81 m/s²). The impact time is determined on the seismograms at the maximum amplitude of the impact phase. To determine the detachment time, we chose to calculate it by averaging the initial time of the detachment phase t0 and the time of maximum amplitude tm (see Figure 2c).

Rockfall databases

We have constructed a database of rockfalls at Mount Saint Eynard and Mount Granier by coupling topographic surveys and seismic monitoring. We tried to associate each rockfall detected using DEMs with a rockfall seismic signal. We also analyze two other datasets, Yosemite rockfalls and controlled releases of blocks, in order to extend the range of rockfall volumes.

Rockfall catalogs obtained by topographic data

The south of the Mount Saint-Eynard has been yearly surveyed by TLS along a 750 m zone of interest. This survey allowed the detection of events with volumes as small as 0.01 m 3 . Overall, D'Amato et al. ( 2016) have detected 508 events by TLS comparison between November 2013 and April 2015.

There was no regular monitoring of Mount Granier using TLS or photogrammetric surveys. Rockfalls were first detected by the seismic station GRA. After these events, we reconstructed DEMs of the cliff based on existing photographs taken before the rockfalls and we performed photographic surveys after the rockfalls.

Rockfall catalogs obtained by seismic monitoring

Mount Saint Eynard

At Mount Saint-Eynard, we have detected several thousand events between November 2013 and December 2015, Most of these events have been classified as noise (electronic noise, road traffic, helicopters, storms…). Most of the remaining events (740) are likely seismic signals. Most of these events have also been detected by the regional seismic network Sismalp. We found only 87 events that could be identified as rockfalls. Among these events, 46 events were ruled because the seismic signal had a stronger amplitude at station RES and GAR compared to station MOL, indicating that they were likely located outside of the area monitored by the photographic time lapse survey. This spatial distribution of event (about 50% of events located between stations MOL and RES) is consistent with the data provided by photogrammetric surveys, which cover the area located between stations MOL and GAR (40% of the events detected by photogrammetry occured between stations MOL and RES.). We also discarded all events detected by only one seismic station (7 events).

Mount Granier

At Mount Granier, thousands of events were also detected between June 2016 and June 2017. Most of these events likely originate from the cliff just under station GRA, where a large rockfall occurred on May 2016 (Hobléa et al., 2018). Most events were indeed very short and high frequency. On the night of January 17 th -18 th 2017, we detected two events with amplitudes and duration much larger than all preceding events. Between these two large events, we also detected two smaller events, with similar waveforms but smaller amplitudes. Another seismic signal with similar properties was detected on February 1 st 2017.

Association of topographic and seismic data

Mount Saint-Eynard rockfalls

In order to associate events detected by TLS to those seismologically detected, we used the dating periods determined using the time-lapse photographic survey. This information allows us to associate events detected by TLS to those seismologically detected. In several cases, especially during winter when nights are longer and weather conditions unfavorable, several events can be distinguished within a pair of photographs. In this case, it is impossible to associate unambiguously events detected by TLS and by the seismic network. In order to avoid any mismatch, if several events had occurred within a pair of photographs, these events were ruled out.

One event detected by photogrammetry at the Mount-Saint-Eynard was added to this catalog (25.11.2015-03:54:39). This event, located outside of the area monitored by the photographic time lapse survey, could not be accurately dated making the association with seismically detected events ambiguous. During the time interval between two photogrammetric surveys (27 days), three rockfalls have been detected by the seismic network. Among these events, two events likely occurred near station MOL, because the amplitude at station MOL was much larger than at station GAR. The last event had similar amplitudes at stations MOL and GAR, in agreement with the rockfall location determined by photographic survey in between MOL and GAR. This allowed us to associate the event detected by photogrammetry to its seismic signal.

Association of photogrammetric and seismic data of Mount Granier rockfalls

Field observations on January 20, 2017 revealed the occurrence of a recent rockfall on the north face of Mount Granier. It was clearly visible as the rock deposits were not covered by snow. Since the last snow fall occurred on January 14, it provides a strong constraint on the date of occurrence, and allows us to associate this rockfall with the seismic signals recorded at station GRA on January 17 th -18 th 2017 (events A1, A2, A3, A4 in Table 1). Another seismic signal with similar properties was detected on February 1 st (event B). It can be associated with another rockfall that occurred at the same location and that can be dated from photographs taken the 2 nd of February 2017.

By constructing DEMs using photogrammetry, we could locate and measure the volume of the event of February the 1 rst . However, due to the quick succession of the first sequence of rockfalls, we were only able to build a 3D model corresponding to the cumulated volume of the A1-4 sequence (Figure 3, Table 1). By coupling DEM and seismologic methods, we have compiled a catalog of 16 rockfalls that occurred at Mount Saint-Eynard between November 2013 and December 2015 with an accurate time, location, geometry and volume (Table 1). The volume of these events ranges from 1.4 m 3 to 1550 m 3 . Among these 16 events, it is possible to distinguish the detachment phase for 10 events. This catalog is completed by five rockfalls that occurred at Mount Granier.

Mount Saint Eynard is better instrumented than Mount Granier (regular TLS and time-lapse photographic surveys, more seismometers). Therefore, rockfall parameters (volume, free fall height, seismic energy,...) are better constrained. We thus use this site as a training dataset in order to build scaling laws between rockfalls properties (volume, free-fall height, potential energy) and seismic parameters (seismic energy, free-fall duration). Results are then tested on the other sites. Mount Granier has a similar geological setting than Mount Saint Eynard and allows us to extend the range of investigated volumes and free-fall heights.

Other datasets: controlled releases of blocks and Yosemite park rockfalls

We analyze three very large rockfalls that occured in Yosemite valley, with well constrained parameters, in order to test how seismic energy scales with rockfall volume. The rockfalls were detected by regional seismic sensors located several tens of kilometers away. The first two events, Happy Isles rockfalls, occurred on July the 10 th 1996 [START_REF] Morrissey | Air blasts generated by rockfall impacts: Analysis of the 1996 Happy Isles event in Yosemite National Park[END_REF][START_REF] Wieczorek | The unusual air blast and dense sandy cloud triggered by the July 10, 1996 rock fall at Happy Isles, Yosemite National Park, California[END_REF][START_REF] Stock | Historical rock falls in Yosemite National Park, California (1857-2011[END_REF]. Rockfall characteristics were reconstructed by [START_REF] Morrissey | Air blasts generated by rockfall impacts: Analysis of the 1996 Happy Isles event in Yosemite National Park[END_REF] and [START_REF] Wieczorek | The unusual air blast and dense sandy cloud triggered by the July 10, 1996 rock fall at Happy Isles, Yosemite National Park, California[END_REF] from eyewitness accounts, seismic records and field evidences. Four separate events occurred within a short time interval. The first two events, which mobilized between 23000 and 38000 m 3 of granite, experienced a 550 m free fall. The impact at the base of the cliff generated seismic waves with magnitudes of 1.55 for the first block (block A) and 2.12 for the second block B [START_REF] Morrissey | Air blasts generated by rockfall impacts: Analysis of the 1996 Happy Isles event in Yosemite National Park[END_REF]. Seismic energies (1.33x10 7 J and 9.5x10 7 J for respectively block A and B) were inferred from the magnitude using Equation ( 7). [START_REF] Stock | Historical rock falls in Yosemite National Park, California (1857-2011[END_REF] estimated that the volume of block A represented about 15 to 20% of the total volume. In this study, we thus assume a volume of 3450-7600 m 3 for block A and 15450-34500 m 3 for block B. These two blocks slid down a steeply inclined ramp or shelf and then fell on a ballistic trajectory about 500 m before hitting the northern part of a talus slope at the base of a cliff. In order to estimate the potential energy of these events, we use two extreme free fall heights: 665 m, which represents the total height from the point of origin of the blocks to the base of the cliff, and 500 m, which represents only the height for which the block fell with a ballistic trajectory. This way we estimate that the potential energy of block A was ranging between 4.5x10 10 and 1.3x10 11 J and for block B between 2.0 and 5.9x10 11 J.

The third event occurred in 2009 near the summit of Ahwiyah Point. The rockfall involved a block of volume 27 400 ± 1370 m 3 that slid off a ramp after its detachment and fell approximately 350 m down the northwest face of Ahwiyah Point. It then impacted a prominent ledge, which induced the dislodging of additional material. The combined debris then tumble down the cliff over an additional 300 m. The rockfall volume was estimated from airborne LiDAR surveys collected in 2006 and 2010 [START_REF] Zimmer | Rock fall dynamics and deposition: an integrated analysis of the 2009 Ahwiyah Point rock fall[END_REF]. This event was detected on seismic networks as far away as 350 km and was measured as a magnitude 2.4 (seismic energy 2.5x10 8 J). [START_REF] Zimmer | Rock fall dynamics and deposition: an integrated analysis of the 2009 Ahwiyah Point rock fall[END_REF] studied this event and its dynamics and trajectography. They determined that the primary seismic signal was induced by the impact, at a high velocity of the falling block (73±5 m/s), on a prominent ledge 300 m below the bottom of the source area. This way, the kinetic energy of the falling block before impact was estimated to 4.0±0.75 x10 11 J.

Finally, we compare our results with the controlled releases of single block performed by [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF]

Analysis of seismic signals

Rockfall seismic signals typology

Figure 5 presents three examples of rockfall seismic signals along with their runout topography and volume. The first example (a) corresponds to a rockfall experiencing a succession of rebounds before rolling on the scree. It may have fragmented during its impacts and have mobilized loose blocks in the debris slopes while other blocks may have stopped along the slope. The second example (b) is typical of rockfalls that experience a long free-fall after their detachment. After impacting the cliff foot, the fallen compartment undergoes an important fragmentation leading to a mass flow type propagation of the blocks. The third example (c) is a more complex event. Due to the irregular topography of the cliff, the blocks experienced different propagation modes: free-fall, rebounds, and mass flow.

The analysis of seismic signals highlights the complexity and variability of rockfalls. However, it is possible to identify the propagation mode through the analysis of seismic signals.

Combined movement of several particles leads to a smooth seismic signal as rebounds wave packets overlap. In the case of mass flow propagation, the simultaneous arrivals of the waves produced by a combined movement of numerous particles produce a rather smooth envelope with frequency concentrating around 5-20 Hz. In contrast, seismograms of events having suffered little or no fragmentation present irregular envelopes showing several energetic pulses. These pulses can be linked to rebounds of blocks along the cliff. As also observed by [START_REF] Vilajosana | Rockfall induced seismic signals: case study in Montserrat, Catalonia[END_REF] and [START_REF] Bottelin | Seismic and mechanical studies of the artificially triggered rockfall at Mount Néron (French Alps, December 2011)[END_REF], the most energetic phases are produced by impacts after a free-fall. These impacts generate impulsive signals with frequency contents up to 50 Hz, whereas successive block rebounds are less energetic with more emergent waveforms and frequencies up to 30 Hz.

Our goal is to link rockfall properties (failure mechanism, propagation mode, free-fall height, volume, propagation velocity, extension) with characteristics of the seismic signal (signal duration and energy, frequency content, envelope properties). The studied events display a wide variability of volume and propagation mode. Some events went through free-fall phases whereas others only rolled and tumbled down the slope. This variability of rockfall sources leads to very different rockfalls signals. Finding common relations between source properties and seismic signals is therefore very challenging. Therefore, in this study, we select only rockfalls with a freefall phase and with a detachment seismic signal that can be isolated from the propagation phase. In order to remove the influence of the propagation mode, we focus on the first parts of the seismic signals, the detachment phase and the first impact. We assume that the rockfall compartment detached in one piece and thus that the associated seismic signal corresponds to the entire compartment detected by TLS or photogrammetry.

Detachment and free-fall

The detachment phase has a smaller amplitude than the impact phase. For Mount Saint-Eynard rockfalls, the detachment phase was visible for all free-fall type events at station FOR, located on rock at the top of the cliff face. However, the detachment phase was visible only for events larger than 6 m 3 at the other stations located on the scree slope. Although most events are not located closer to station FOR than to the other stations, the detachment phase is more visible at station FOR. This station has a better signal to noise ratio because it is located on rock and because it is farther away from the anthropogenic noise generated in the valley.

For the Mount Granier rockfalls, the detachment phase was clearly visible on all five rockfalls detected at station GRA, located 650 m away. Event A4 was more complex, suggesting that the compartment fragmented during its detachment (A4a and A4b, Figure 8c). Two pulses separated by 2 seconds can be distinguished on the detachment phase. Event A4a, is very small in comparison to event A4b as the seismic energy of event A4b is about ten times higher than A4a. This separation is difficult to establish for the impact phase as the two events overlap.

The detachment phase is characterized by frequency contents around 20 Hz but in some cases up to 40 Hz (Figure 6). The duration of this phase varies between 0.5 second and 4 seconds (Figure 7a). The waveforms generally show a slowly rising and falling seismic signal. We investigated how properties of the detachment phase (duration and energy) scale with the rockfall volume determined by TLS VDEM. We first consider Mount Saint Eynard rockfalls as a training dataset. In a second step, we test our results using Mount Granier rockfalls.

We estimated the duration of the detachment phase DurD recorded at station FOR. We picked manually the initial and final times of the detachment phase, because the seismic signal of the detachment phase is slowly rising and falling and because in some cases the detachment phase is not well separated from the impact phase. The duration increases slowly with rockfall volume (Figure 7a) and can be fitted by:

Dur D = aVDEM b (9)
with a = 0.6±0.05 and b = 0.2±0.03 (regression uncertainty for a confidence interval 68%) and with a correlation coefficient R² of 0.76.

The seismic energy of the detachment phase EsD recorded at station FOR is better correlated with the rockfall volume V (R² =0.87, Figure 7b) and increases much faster with volume than the duration. A power-law fit EsD = aVDEM b (10) yields a = 7±3 x10 -3 and b = 2.2±0.2.

We calculated Mount Granier rockfall volumes VEsD using Equation ( 10). The total volume of the set of events A1-4 is estimated to 726-3414 m 3 . This represents about half of the global volume 4600±50 m 3 determined using the DEMs. The calculated volume of event B is, for its part, higher than the one obtained by the DEMs: VDEM=11-12 m 3 versus VEsD = 17 -48 m 3 . Some detachment signals are preceded by a low amplitude and low frequency (<30 Hz) phase. We interpret these signals as precursory rupture nucleation leading to the failure and detachment of the compartment. This part of the seismic signal can be isolated from the detachment signal itself by a change in amplitude and frequency content (Figure 8).

We compare the free fall height Hs estimated from the seismic signal using equation ( 8) with the value HDEM determined on the DEMs (Figure 7c). In some cases, there is a large uncertainty on the free-fall height due to the geometry of the event (Figures 2b,3c). For Mount Granier events, it can be observed by the marks left on the cliff, that the rockfalls have impacted two different areas: a cliff ledge or the scree slope at the base of the cliff (Figure 3c).

Uncertainties on the calculated free-fall height Hs are due to the spreading of the detachment seismic signals. However, we can see that the calculated free-fall heights are consistent with the ones measured on the DEMs with a value of R² of 0.98. This result first validates our identification and interpretation of the different phases of the seismic signal: detachment phase, sometimes preceded by a precursory signal, and first impact.

Impact

The seismic energy of the impact phase is strongly correlated with the potential energy. Our data for Mount Saint Eynard suggest the following relation:

EsI = a Ep b (11)
We used only Mount Saint Eynard rockfalls in order to fit a power law relation between EsI and Ep (Figure 9a). The estimated parameters are a = 1±0.5x10 -8 and b = 1.55±0.05 (confidence interval 68%) and the correlation coefficient is R 2 =0.98. This fit correctly explains Mount Granier data, although these events were not used in the fit. However, this relation overestimates the seismic energy for Yosemite rockfalls. The seismic energy estimated from ( 11) is larger than the measured value by 7 to 50 %.

Data consistent with Hibert et al EsI = a Ep b , a=4.5x10-8±? and b = 1.38 ±?

The volume of the blocks VEsI can be calculated using the following relation:

𝑉 >"| = >} ỹ } • ~= > ~€ • y } • ~ (12)
The computed rockfall volumes VEsI are in good agreement with those determined from the DEMs (Figure 9b) with a value of R² of 0.99. Uncertainties on the calculated volumes VEsI are related to the uncertainties on the parameters used to determine EsI (V, α, r, p, c, f, see supplementary material) and Hs. This relation established for Mount Saint Eynard rockfalls has been tested with Mount Granier events. The calculated volume of event B is in agreement with the measured one (VEsI: 4-19 m 3 , VDEM: 11-12 m 3 ). However, the total volume of the set of events A1-4 is slightly underestimated with a calculated volume of VESI=683-4178 m 3 for a measured volume of VDEM=4550-4650 m 3 . Figure 9. a) seismic energy of the impact phase as a function of potential energy calculated with DEM metrics, b) rockfall volume calculated using seismic metrics as a function of rockfall volume measured on the DEMs. Blue dots: Mount Saint-Eynard rockfalls; violet squares Mount Granier rockfalls A4 and B; green diamond Yosemite rockfall [START_REF] Morrissey | Air blasts generated by rockfall impacts: Analysis of the 1996 Happy Isles event in Yosemite National Park[END_REF][START_REF] Wieczorek | The unusual air blast and dense sandy cloud triggered by the July 10, 1996 rock fall at Happy Isles, Yosemite National Park, California[END_REF][START_REF] Stock | Historical rock falls in Yosemite National Park, California (1857-2011[END_REF]. Lines are linear fits using only the Mount Saint-Eynard rockfalls.

Discussion

Detachment phase

In order to distinguish the detachment phase from the impact phase, the free-fall duration must be longer than the duration of the detachment phase. By combining Equations ( 8) and (10), we can estimate the minimal free-fall height detectable as a function of rockfall volume. For instance, for a 1 m 3 event the minimal free-fall height detectable is about 2 m whereas for 100 m 3 the minimal free-fall height is about 11 m. This drawback prevents us from studying all free-fall or topple events (3 events over 16 in the Mount Saint-Eynard data set).

We found that both the duration and the seismic energy of the detachment phase increase with rockfall volume. However, this relation is not well constrained. The scatter of these data might be due to the complexity of the detachment phase and to its variety of processes. Several factors may influence the detachment seismic signal, such as the surface of the rupture area, the detachment mode (slide, free-fall or topple), its duration, fragmentation of the compartment during the detachment, etc. However, due to the limited number of studied events and due to the lack of information on the detachment mode of these events, the influence of these factors could not be studied.

Relation between potential and seismic energy of the impact phase

The relation (11) between potential energy and seismic energy is difficult to interpret physically. The fact that the exponent b is larger than 1 implies that the process is not scale invariant, the ratio of seismic to potential energy increases with rockfall size. This relation cannot be extrapolated to very large energies. Indeed, this relation predicts that the seismic energy Ep would exceed the potential energy Ep for Ep >3x10 12 J, which is of course impossible. This suggests that the relation between potential energy and seismic energy presents a change of slope for potential energies larger than 10 10 J.

The ratio between seismic energy and potential energy Rs/p= EsI/EpDE of our data ranges from 10 -6 to 10 -4 . This ratio Rs/p is in good agreement with values found by previous studies. [START_REF] Deparis | Analysis of rock-fall and rock-fall avalanche seismograms in the french Alps[END_REF] estimated a ratio Rs/p ranging from 10 -5 to 10 -4 for rockfalls with volumes ranging from 10 3 to 10 6 m 3 , [START_REF] Hibert | Slope instabilities in Dolomieu crater, Réunion Island: From seismic signals to rockfall characteristics[END_REF] found 10 -5 <Rs/p< 10 -3 for granular flows at the Piton de la Fournaise volcano with 1 < V < 10 3 m 3 , Lévy et al. ( 2015) estimated Rs/p =10 -5 for volume 10 3 < V < 10 6 m 3 and Saló et al. ( 2018) 10 -6 < Rs/p<10 -4 for volumes 0.5<V<5 m 3 . [START_REF] Farin | Characterization of rockfalls from seismic signal: Insights from laboratory experiments[END_REF] and [START_REF] Bachelet | Elastic wave generated by granular impact on rough and erodible surfaces[END_REF] observed through laboratories experiments, that variations of Rs/p could be associated with the size of the impactor and with properties of the impacted medium (e.g., roughness and bed thickness). [START_REF] Farin | Characterization of rockfalls from seismic signal: Insights from laboratory experiments[END_REF] estimated larger values of R between 0.001 and 1 in laboratory experiments with impactors masses ranging from 0.001 to 100 g. For smooth impacted plates, this ratio increases toward 1 as the mass of the impactor increases, in agreement with their theory assuming that impact energy is dissipated as elastic energy and viscous deformation. However, for impacts on rough surfaces and for natural rockfalls, [START_REF] Farin | Characterization of rockfalls from seismic signal: Insights from laboratory experiments[END_REF] suggest that viscous deformation becomes negligible, and that most energy is dissipated through other processes such as plastic deformation, adhesion, or rotational modes of the impactor owing to surface roughness. Thus the value of Rs/p can be influenced by site properties, and may be scaledependant as we observe in our dataset.

The parameters used for the calculation of the seismic energy slightly influence this ratio.

The exponent of the power law between Ep and E s decreases with the frequency from 1.56 for a frequency of 20 Hz to 1.50 for a frequency of 5 Hz. For lower frequencies (e.g. 5 Hz), this change in exponent provides a better agreement with Mount Granier and Yosemite's events (supplementary material,Figure A.3.b). The exponent of the power law between Ep and Es varies very little with the change of seismic wave velocity. Changing the velocity mainly affects the Rs/p ratio.

Estimation of rockfall volume from the seismic energy of the impact phase

We have shown in this study how potential energy and free fall height can be estimated from seismic signals, allowing an estimation of rockfall volumes. However, this methodology only allows for the characterization of rockfalls experiencing a free fall immediately after their detachment. This represents 80% of the Mount Saint-Eynard rockfalls. This limitation is balanced by the improved accuracy of the results. In order to characterize all event types, it may be appropriate to calibrate a different relation between rockfall volume and seismic energy for each rockfall type.

The free-fall duration is estimated by manual picking of the detachment and of the impact phase. This is a delicate task and leads to uncertainties on both the free fall duration and on the seismic energy. In some cases, the time of maximum amplitude of the impact phase can be significantly off the first onset of this phase. This delay might be related to several points. In a few cases, the fallen compartment may have scraped a ledge before impacting the slope (e.g. 01.02.2017 Mount Granier rockfall, Figure 6). In this case, the impact signal is preceded by a small amplitude and high-frequency wave packet. This part of the seismic signal was not taken into account in the seismic energy calculation. This delay can also be interpreted as the delay between the first contact between the slope and the compartment and the time for which the maximum energy was transferred to the slope. This explanation was assumed for most cases (e.g. 18.01.2015 Mount Saint-Eynard rockfall or 17.01.2017 Mount Granier rockfall, see Figure 8). In this case, this delay might vary depending on the volume of the compartment, on the impacted material (loose scree or cliff face) and on the slope angle. However, no clear relations appeared in our data.

The relation between seismic and potential energy has been derived for Mount Saint-Eynard dataset and then tested on the Mount Granier rockfalls. The underestimation of the Mount Granier rockfall volume (VESI=683-4178 m 3 , VDEM=4550-4650 m 3 ) may be due to the parameters used to calculate seismic energy of the impact phase. They might need to be adjusted for the Mount Granier setting to account for differences in the wave propagation medium. Another explanation can be the overestimation of the free fall height due to high uncertainties on Hs (±30 m) for events A1 and A4, leading to smaller volumes. The seismic energies determined for the Yosemite Park events are smaller than expected from the relation (11) obtained for the Mount Saint-Eynard rockfalls. This discrepancy may be due to the method used to estimate seismic energy from the local magnitude of the signals recorded at large distances (several tens of kilometers). This method (developed for earthquakes and assuming body waves) may produce different values from the estimation of seismic energy using Equation (2), using nearby stations (less than 2 km) and assuming surface waves. The Mount Saint-Eynard relations were determined using rockfall volumes ranging from 1 to 100 m 3 . As the Mount Granier events included volumes larger than 1000 m 3 , the relation (11) between Ep and Es might need to be adjusted in order to better fit bigger volumes.

Real-time characterization of rockfalls

Real time characterization of rockfalls from seismic signals would be useful for rockfall hazard mitigation. However, developing a fully automated method is very challenging. Automatic location of rockfalls from seismic monitoring has been studied in previous works [START_REF] Lacroix | Location of seismic signals associated with microearthquakes and rockfalls on the Séchilienne landslide, French Alps[END_REF]Hilbert et al., 2014;Manconi et al., 2016[START_REF] Fuchs | the AlpArray Working Group, Seismic detection of rockslides at regional scale: examples from the Eastern Alps and feasibility of kurtosis-based event location[END_REF]. However, in the case of Mount-Saint Eynard, the number of sensors is too small to obtain accurate locations, therefore we used rockfall locations determined from TLS or photogrammetric surveys. We have also manually checked all events detected by the seismic network to select rockfall signals, and manually picked the detachment and first impact phases. Using a fully automatic procedure may be possible using artificial intelligence methods [START_REF] Hibert | Automated identification, location, and volume estimation of rockfalls at Piton de la Fournaise volcano[END_REF][START_REF] Provost | Towards a standard typology of endogenous landslide seismic sources[END_REF]. Most automatic methods (artificial neural networks, random forest, hidden Markov models, support vector machines) require a training set. By coupling different methods of detection (TLS, photogrammetry, seismology), we can be confident that all events in our dataset have been correctly classified and located. Therefore, our dataset could be useful in order to develop or to test such an automatic method for rockfall detection, location and characterization. Moreover, there are very few studies that were able to distinguish the detachment phase of rockfalls, therefore our database would provide a useful dataset in order to develop an automatic classification method.

Comparison with other studies

Previous studies, such as [START_REF] Deparis | Analysis of rock-fall and rock-fall avalanche seismograms in the french Alps[END_REF], [START_REF] Dammeier | Characterization of alpine rockslides using statistical analysis of seismic signals[END_REF]), Manconi et al., (2016) or [START_REF] Fuchs | the AlpArray Working Group, Seismic detection of rockslides at regional scale: examples from the Eastern Alps and feasibility of kurtosis-based event location[END_REF], studied scaling relations between rockfall parameters and seismic signals properties using regional seismic networks. In these studies, the distance between rockfalls and stations is much larger than in our study, of the order of tens of kilometers for regional networks compared with several hundred meters up to 2 km in our study. The rockfall volumes are also much larger (between 10 3 and 10 7 m 3 ) than in our study. The seismic signals are thus very different. The signals recorded by regional networks are strongly affected and transformed by the distance between event and stations. The propagation phases (i.e. detachment, impacts, mass-flow) can hardly be identified in these records. Thus, in these studies, seismic parameters (seismic energy, duration, peak ground velocity, etc.) were defined over the entire seismic signal. [START_REF] Deparis | Analysis of rock-fall and rock-fall avalanche seismograms in the french Alps[END_REF] found no clear relation between rock-fall parameters (fall height, runout distance, volume, potential energy) and rockfall seismic magnitudes. However, they found that signal duration was roughly correlated with the potential energy and the runout distance. [START_REF] Dammeier | Characterization of alpine rockslides using statistical analysis of seismic signals[END_REF] used multivariate linear regressions combining duration, peak envelope velocity, and envelope area and found a good correlation with rockfalls volume and potential energy. Finally, Manconi et al., (2016) and [START_REF] Fuchs | the AlpArray Working Group, Seismic detection of rockslides at regional scale: examples from the Eastern Alps and feasibility of kurtosis-based event location[END_REF] proposed relationships between rockfall or rockslide volumes, and respectively duration and local magnitude. [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF] carried out controlled releases of single blocks in a marl gully. They analyzed the correlation between rockfall properties and the induced seismic signals. They found that seismic energy was well correlated to the blocks kinetic energy (R²=0.64) and poorly correlated to blocks mass (R²=0.39).

We have compared the scaling laws between magnitude and rockfall volume obtained in these previous studies with our results. We used Equation (7) in order to estimate magnitude from the seismic energy estimated by [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF] and in our study. For the Mount Saint Eynard and Mount Granier database, we tested two methods for estimating seismic energy. We first selected the 18 rockfalls listed in Table 1 with a known volume VDEM (excluding events A1-3) and used the whole signal to estimate seismic energy (blue dots in Figure 10). Secondly, we selected only free-fall events and computed the seismic energy using the impact seismic signals (red dots in Figure 10). Results are shown in Figure 10 and Table 2. et al., 2017) and (last model) free-fall height H. (1) whole data set, magnitude calculated over the entire seismic signal, (2) free-fall events, magnitude calculated over the entire seismic signal, (3) free-fall events, magnitude calculated over the impact seismic signal, (4) free-fall events, correlation between potential energy and impact seismic energy. Manconi et al. (2016) and [START_REF] Fuchs | the AlpArray Working Group, Seismic detection of rockslides at regional scale: examples from the Eastern Alps and feasibility of kurtosis-based event location[END_REF] mix different types of propagation (free-fall, sliding, rebounds), different geological settings and slope angles. This leads to a large scatter between the observed and modelled volumes. In our study, we obtain a smaller error between observed and modelled rockfall volumes, even when using all events, probably because all events come from the same site, and also because our volumes are more accurate. Selecting only free-fall events further decreases the error. This highlights the importance of selecting rockfalls from their propagation mode. In order to remove the influence of the propagation mode of the events, we focus on the first impact. Once again, this greatly improves the accuracy of the estimated volume. Our relation (3) in Table 2 between rockfall volume and magnitude is in good agreement with the results obtained by [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF] for much smaller rockfall volumes. However, Figure 10 suggests that the relation between magnitude and rockfall volume changes for volumes larger than 1000 m 3 . This could explain why our relation derived for Mount Saint Eynard rockfalls with V<100 m 3 underestimates the volumes for Mount Granier and Yosemite rockfalls with V>1000 m 3 . Finally, we use the scaling relation between seismic and potential energy (11) in order to account for variations of free-fall height. This produces the strongest improvement on the estimated rockfall volume (relation (4) in Table 2). Similar results are obtained for the dataset of [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF]. The seismic energy is better correlated with kinetic energy than with volume. This relation yields a very accurate estimation of rockfall volume (median error of XX%), but requires an estimation of impact velocity to derive rockfall volume from kinetic energy, which is of course difficult for natural rockfalls.

The methodology presented in this paper only allows t

Conclusions

Monitoring rockfalls using photographic time lapse surveys and 3D reconstructions provides information such as volume, geometry, location, detachment mode, etc. The use of seismology adds information on the time of occurrence and on the propagation mode and duration of individual stages of an event. Coupling these methods at Mount Granier and Mount Saint-Eynard yields numerous information on natural rockfalls onto complex topography.

Analysis of seismic signals allows identifying several phases: detachment, free fall followed by an impact, rebounds, and granular flow. As the propagation mode strongly differs among rockfalls in our dataset, we were not able to find seismic signal features allowing a satisfying estimation of rockfall dynamics (energy, volume, etc.) for our whole data set. We therefore chose to focus on free-fall type of rockfalls and we considered only the beginning of the seismic signal: the detachment and the first impact. At Mount Saint-Eynard and Mount Granier, we have detected 15 detachment seismic signals corresponding to rockfalls of volume ranging from 1 to more than 1000 m 3 .

We found a significant correlation between the seismic energy of the detachment phase and the rockfall volume. By measuring the time delay between the detachment phase and the impact phase we were able to infer the free fall heights, which are in good agreement with values estimated from the DEMs. This result supports our interpretation of the different phases of the seismic signals. We also found that the seismic energy of an impact was well correlated with the potential energy of the rockfall. Rockfall volumes can thus be calculated by using the estimated potential energy and free fall height.

The relations developed with the Mount Saint-Eynard rockfalls were then tested using the Mount Granier and Yosemite rockfalls. We found that the results were in good agreement with the measurements for the smallest Mount Granier rockfall, but slightly underestimate the largest Mount Granier rockfall (volume estimated from seismic energy is 15-89% of the volume determined using DEMs). For Yosemite rockfalls, the seismic energy recorded is significantly smaller than the seismic energy predicted by our correlation for all three events (7 to 50 %). This might be due to a site effect or to the range of volumes of Mount Granier and Yosemite rockfalls. Our results are also in good agreement with controlled block release experiments of [START_REF] Hibert | Single-block rockfall dynamics inferred from seismic signal analysis[END_REF], which involved much smaller volume (0.03-0.2 m 3 ) than in our study.

By segregating rockfalls experiencing a free-fall from those with sliding or bouncing transport modes, and by focusing on a specific part of the rockfall seismic signal, i.e., the detachment and first impact, we were able to obtain more accurate volume prediction than other studies considering mixed propagation modes [START_REF] Deparis | Analysis of rock-fall and rock-fall avalanche seismograms in the french Alps[END_REF][START_REF] Dammeier | Characterization of alpine rockslides using statistical analysis of seismic signals[END_REF], Manconi et al., 2016[START_REF] Fuchs | the AlpArray Working Group, Seismic detection of rockslides at regional scale: examples from the Eastern Alps and feasibility of kurtosis-based event location[END_REF].

  It is a long doubled cliff making up the western border of the Isère Valley and the eastern edge of the Chartreuse Massif. It peaks at 1308 m above sea level. Its general morphology consists of two 7 km long subvertical cliffs dipping southeast (Figure 1c). The lower cliff (240 m high) is separated from the 120 m high upper cliff by a forested ledge. The upper cliff consists of massive limestone of the Tithonian stage. The lower cliff consists of fractured thin-bedded limestone, of the Sequanian stage.

Figure 1 .

 1 Figure 1. a) DEM of the Chartreuse massif (France), with the location of the photographs shown as blue triangles. b) photograph of the north face of Mount Granier. c): photograph of Mount Saint-Eynard. Red diamonds indicate the location of seismic stations, green dot is the camera enabling a time lapse monitoring of the cliff. Dashed rectangle: area monitored by TLS survey and by a photographic time lapse survey. Yellow triangles: location of origin of rockfall detachment areas. Stage formations: Urg. Urgonian limestone, H. Hauterivian marls, Val. Valanginian limestone, Be.Berriasian marls, Ti. Tithonian limestone, Ki. Kimmeridgian marls, S. Sequanian limestone, O. Oxfordian marls.

Figure 2 .

 2 Figure 2. Definition of the metrics used in this study using (a., b.) DEM of the cliff and (c.) rockfalls seismic signals of the 01.18.2015 event. a) cliff profile of the 02.02.2015 event presenting a sliding failure mechanism, b) cliff profile of the 15.08.2014 event presenting a free-falling failure mechanism. The black arrow represents the weight vector w built from the gravity center.

Figure 4 .

 4 Figure 4. a) Estimation of the seismic wave velocity. For each rockfall detected at Mount Saint Eynard and each couple of stations, we plot the difference in source-station distance dr as a function of the time delay between the impact time detected on each seismogram. (b) Estimation of the attenuation factor 𝛼 using equation (6) with n=0.5.

Figure 3 .

 3 Figure 3. a) Illustration of the set of events A1-4 (January 17th-18 th 2017), photographs taken January 19 th , in grey: rockfall compartment, b) DEM of the event B (February 1 st 2017), photographs taken February the 2 nd , in red: rockfall compartment, c) cliff profile with the event location in red. Colored lines: calculated impact areas of events A and B obtained from the DEM.

Figure 5 .

 5 Figure 5. Left: seismic signal (vertical ground velocity, filtered between 2 and 50 Hz) and corresponding spectrogram. The peak amplitude of each trace, Am, is indicated in m/s. The spectrograms are computed using a simple fast Fourier transform, using a hanning taper, with a window of 128 points and an overlap between successive windows of 64 points. Right: Cliff profile for each event, the red dot indicates the starting point of the rockfall. a) 05.03.2015 Mount Saint

Figure 6 .

 6 Figure 6. Detachment seismic signal, enlargement of the seismic signal and corresponding spectrogram of the a) 15/08/2014, b) 18/02/2017 (A4) event and of the c) 01/02/2017 (B) event recorded at station GRA located at the top of Mount Granier. Red dot: initial time of the detachment phase, blue cross: maximal amplitude of the detachment and impact phases.

Figure 7 .

 7 Figure 7. a) Duration of detachment phase and b) seismic energy of the detachment phase as a function of rockfall volume determined with DEMs. In a) and b), we consider only events A4b and B for Mount Granier and assume a volume VDEM=2850±1800 m 3 for event A4b c) Free fall height calculated from the seismic signals as a function of the free fall height measured on the DEMs, Blue dots: Mount Saint-Eynard rockfalls; violet squares Mount Granier rockfalls. Straight lines are power-law fits obtained using only Mount Saint-Eynard rockfalls.

Figure 8 .

 8 Figure 8. Seismic signal for three free-fall type rockfalls a) the 18/01/2015 event recorded at station

Figure 10 :

 10 Figure 10: Magnitude of the events versus their volume. Straight lines are linear relations between magnitude and logarithm of volume.

Table 1 .

 1 . Rockfall characteristics. Failure mechanism is described in section 3.1. Dating interval is based on photographic surveys and field evidences. The detachment phase is not visible for 6 Mount Saint-Eynard rockfalls (empty cells).

	Controlled release blocks data set : number of events, range of volume and kinetic energy

Table 2 .

 2 Scaling laws between rockfall seismic magnitude M, volume V, kinetic energy Ec (Hibert

	Hibert et al. (2017)	ML=7.4+1.3log(V)	37	0.03-0.2	0.39 -
		ML = X + Y log (Ec) 37	0.03-0.2	-	-
	Manconi el al. (2016)	MD=1.4+0.23log(V)	33	10 3 -10 8	0.71 71%
	This study (1)	ML=-2.1+1.01log(V) 18	1-10 3	0.89 56%
	This study (2)	ML=-2.2+1.17log(V) 12	1-10 3	0.92 41%
	This study (3)	ML=-2.6+1.21log(V) 12	1-10 4	0.91 33%
	This study (4)	ML=-4.15+log(VH)	12	1-10 5	0.98 18%

Acknowledgments

This work was carried out with the support of Géolithe, National Association of Research and Technology (ANRT), the Labex -OSUG@2020, the national project C2ROP, the program of Joint laboratories between research organizations and SMEs or intermediate-sized enterprises (LabCom) and the OMIV observatory of landslides. Mickael Langlais and Gaël Jannex are thanked for the fieldwork and data acquisition. Seismic data used in this study are available through the observatory OMIV (https://doi.org/10.15778/RESIF.MT). DEMs data are available at https://doi.org/10.5281/zenodo.2789093. Comments and suggestions from F. Fuchs and two anonymous reviewers and from the associate editor substantially improved this manuscript.


Tri Cong Pham

Son Giang
email: tran-giang.son@usth.edu.vn

Tran

Thi Phuong Nghiem

Antoine Doucet
email: antoine.doucet@univ-lr.fr

Chi Mai Luong

Van-Dung Hoang

A comparative study for classification of skin cancer

Keywords: Skin Cancer, Classification, Feature Extraction, Melanoma

Skin cancer is one of the most common types of cancer all over the world. It is easily treatable when it is detected in its beginning stage. Melanoma is the most dangerous form of skin cancer. Early detection of melanoma is important in reducing the mortality rate of skin cancer. Recently, machine learning has become an efficient method in classifying skin lesions as melanoma or benign. Main features for this task include color, texture and shape. A comparative study about color, texture and shape features of melanoma is useful for future research of skin cancer classification. Inspired by this fact, our study compares the classification results of 6 classifiers in combination with 7 feature extraction methods and 4 data preprocessing steps on the two largest datasets of skin cancer. Our findings reveal that a system consisting of Linear Normalization of the input image as data preprocessing step, HSV as feature extraction method and Balanced Random Forest as classifier yields best prediction results on the HAM10000 dataset with 81.46% AUC, 74.75% accuracy, 90.09% sensitivity and 72.84% specificity.

I. INTRODUCTION

Melanoma is one of the most malignant, metastatic and dangerous types of skin cancer that causes a majority of deaths related to skin cancer. It was estimated that in 2018 there were about 91,270 new cases of skin cancer from melanoma with 9,320 deaths [START_REF] Segal | Cancer statistics, 2018[END_REF]. [START_REF] Geller | Screening, early detection, and trends for melanoma: current status (2000-2006) and future directions[END_REF] [START_REF] Geller | Screening, early detection, and trends for melanoma: current status (2000-2006) and future directions[END_REF] indicated that melanoma is a curable disease if it is diagnosed early and correctly. Due to this, it is necessary to examine and observe melanoma closely when it is still at the early stage.

In order to detect skin cancer from melanoma, besides clinical tests, dermatologists often use their eyes to examine characteristics of skin lesions such as color, texture and shape to diagnose if the lesion is a benign or malignant tumor. Nowadays, advances in technologies allow the widely use of dermoscopy images in examining and diagnosing melanoma skin cancer. To support this task, many computer aided diag-nosis (CAD) systems are designed to detect melanoma from dermoscopy images.

One important step of the CAD system for melanoma skin cancer is to classify if the melanoma skin lesion is benign or malignant. Due to this, many methods are proposed in the literature to detect malignant melanoma from skin lesions. Hamd et al., 2013 [3] proposed a method to predict skin cancer from symmetry and color matching for lesion pigments. In detail, the method detects and segments lesion edges to compute symmetrization for all images to isolate benign tumor. The suspicious images are then nominated into one of the three classes: Melanoma, Basal Cell Carcinoma (BCC), or Squamous Cell Carcinoma (SCC) tumor based on symmetrization and pigment-color matching score table. The experimental results of two matching procedures are compared to 40 pre-classified images where 80% of true classification is obtained for the first procedure and 92.5% is for second procedure.

Celebi at el. [START_REF] Celebi | A methodological approach to the classification of dermoscopy images[END_REF] presented a method to classify pigmented skin lesions from dermoscopy images using color, texture and shape features. For color and texture features, the image is divided into a set of regions presenting significant clinical properties of the lesions. The extracted feature data are fed into an optimization framework to rank the features for finding the optimal subset of features. For shape features, the method performs lesion border detection to separate lesion from background skin. The detected border is then used to extract shape features of the lesions. The method obtains a specificity of 92.34% and a sensitivity of 93.33% on a set of 564 tested images. Barata et al., 2014 [5] introduced two systems for melanoma detection in dermoscopy images. The first system uses global features to classify skin lesions while the second system uses local features and the bag-of-features classifier to categorize skin lesions. The experimental results showed that color features obtained better performance than texture features when used alone for the problem of skin lesion classification. Besides, both texture and color features achieve good classification results of 96% sensitivity and 80% specificity for global features and 100% sensitivity and 75% specificity for local features on 176 dermoscopy images.

Since there are many methods in the literature to perform melanoma classification of skin cancer, a comparative study of these methods will be helpful in summarizing and demonstrating the best methods of melanoma classification. In this paper, we perform a throughout experiment to classify melanoma using pattern recoginition techniques, including a set of 4 preprocessing methods, 7 feature extraction methods and 6 different classifiers on two largest public melanoma dataset and summarize our findings from this in-depth evaluation.

The rest of the paper is described as follows: we present the materials and methods we used in section II. An analysis of results and our discussion are explained in section III. Finally, the conclusion and future works are presented in section IV.

II. MATERIALS AND METHODS

In this section, we describe the dataset and the methodology that we used for our experiments.

A. Dataset

We perform evaluations on two different datasets, organized by two challenges: ISIC 2016 [START_REF] Gutman | Skin lesion analysis toward melanoma detection: A challenge at the international symposium on biomedical imaging (ISBI) 2016, hosted by the international skin imaging collaboration (ISIC)[END_REF] and HAM10000 [START_REF] Tschandl | The ham10000 dataset, a large collection of multi-source dermatoscopic images of common pigmented skin lesions[END_REF]. Both datasets contain photos of Melanoma cases, divided into two classes as Melanoma and Benign.

The ISIC 2016 challenge dataset contains 900 images with labels, including 172 Melanoma images -728 Benign images. The second dataset ISIC 2018 consists of 10,015 images in total, including 1,113 Melanoma images -8,902 Benign images. The images are in high resolutions, can be approximately up to 1, 800 × 1, 200 pixels. Figure 1 shows several examples of melanoma cases and benign cases provided by the two given datasets.

We perform our evaluations, including training and testing, on each dataset separately to determine the effectiveness of the dataset size. For each dataset, we use 90% of the images as training data and the remaining 10% as testing data.

B. Methodology

Our classification evaluation procedure is illustrated on figure 2, including 4 main steps:

• Data Preprocessing • Feature Extraction • Melanoma Classification • Result Analysis
In the upcoming sections, we will describe experiment methods in each step.

1) Data Preprocessing: Firstly, due to the variety of input image resolution, we perform proportional scale of each input image to the image with 600 pixels in width. We then propose to use three different preprocessing methods: Gaussian Blur, Normalization and combination of Gaussian Blur and Normalization.

Gaussian Blur (GB) is a common way to reduce noise since the dataset images are collected from several sources. We use standard 5 × 5 Gaussian blur filter with σ = 1.1.

Additionally, each dataset itself is collected from several sources, therefore its brightness and contrast should be normalized. We perform linear normalization (LN) to [0, 255] range for each pixel provided in each input image as follows:

n(x, y) = 255 × i(x, y) -min max -min , (1)
in which i(x, y) denotes the original input signal and n(x, y) denotes the corresponding normalized value.

In our experiments, we also use a combination of GB and LN to verify the effectiveness of this mixture toward Melanoma classification result.

2) Feature Extraction: Many machine learning tasks require a feature selection step, reducing the number of dimensions from the feature space. It is mainly done by removing redundant, noisy and unimportant features. This step brings several benefits: reducing feature extraction time, reducing complexity for the next classification step, improving prediction results, reducing training and testing time. Each extracted feature is a vector representing an input image. We propose to use below features for different aspects of an input image:

HSV (Hue-Saturation-Value) [START_REF] Ma | Content-based image retrieval with hsv color space and texture features[END_REF] represents the color features of the input image. We convert the input image (in RGB format) to HSV color space and calculate a 3D histogram for all channels (H, S, V), each divided into 8 bins. We then flatten this 3D histogram to achieve a color feature vector of 512 (= 8 × 8 × 8) dimensions.

LBP (Local Binary Pattern) [START_REF] Guo | A completed modeling of local binary pattern operator for texture classification[END_REF] is a visual descriptor, representing textures of the input image. The input image is divided into 8×8 cells, each pixel in this cell is compared with its neighbour, providing a number for each pixel. We calculate the histogram of each cell, combine all together and perform normalization. The result is a 242-dimensional feature vector, representing textures of the input image.

HOG (Histogram of Oriented Gradients) [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] is another visual descriptor of an input image by counting gradient orientations of localized regions. The output of HOG is a shape feature vector composed of 65,520 dimensions.

SIFT (Scale-Invariant Feature Transform) [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF] extracts keypoints of an input images, regardless of image transformation, scaling and rotation. The SIFT keypoints are then used for calculate the similarities of images.

Not only are the previous features assessed separately, we also evalute the effectiveness when using them in combination. Firstly we attempt to use the extracted features of HSV, LBP and HOG all together without transformation. Secondly, we evaluate their effectiveness of an additional linear normalization step after combination of them, e.g. HSV, LBP and HOG with normalization. Finally, an additional PCA (Principal Component Analysis) [START_REF] Jolliffe | Principal component analysis[END_REF] is added after combining the 3 features, resulting in HSV, LBP and HOG with PCA, to evaluate the potency of dimension reduction.

To summarize, we use the following 7 feature extraction methods for evaluation of their effectiveness for Melanoma classification problem: HSV, LBP, HOG, SIFT, HSV+LBP+HOG, HSV+LBP+HOG with normalization, HSV+LBP+HOG with PCA.

3) Classification: The third step to solve the Melanoma classification problem is to perform classification, using the extracted features from previous step. This is a supervised learning task: for each image, its extracted features with their corresponding label (Melanoma or Benign) are fed to the classification model so that it can learn from the dataset. We evalute the following 6 models for the Melanoma classification problem due to their popularity in good performance on various datasets: SVM (Support Vector Machine) is a discriminative classifier defined by a separating hyperplane [START_REF] Schölkopf | Advances in kernel methods: support vector learning[END_REF]. The labelled training data are divided by an optimal hyperplane which could be used for categorizing new, untrained data.

LR (Logistic Regression) [START_REF] Hosmer | Applied logistic regression[END_REF] is a common technique for solving binary classification problem. It uses a logistic function to model a binary dependent variable, then use this trained function to classify untrained data.

RF (Random Forest) [START_REF] Breiman | Random forests[END_REF] is a classification technique that leverage usage of multiple decision trees, each contains leaves representing class labels and branches representing conjunctions of features that lead to those labels. The trained decision trees are then used in a randomized fashion (therefore called Random Forest, in an attempt to overcome overfitting nature of decision trees) to classify an untrained data.

AdaBoost (Adaptive Boosting) [START_REF] Rätsch | Soft margins for adaboost[END_REF] is used in our evaluation with Decision Trees in order to improve classification results. Adaboost gathers information at each stage of decision tree about the hardness of each training sample so that later trees can focus more on harder-to-classify examples.

BB (Balanced Bagging) [START_REF] Hido | Roughly balanced bagging for imbalanced data[END_REF] is another accuracy-improving algorithm that can be used with other classification methods. In our evaluation, we attempt to improve Decision Tree using BB method by constructing multiple decision trees and then combine their predictions to provide the final result.

BRF (Balanced Random Forest) [START_REF] Khoshgoftaar | An empirical study of learning from imbalanced data using random forest[END_REF] is an adaptive improvement of Random Forest to handle unbalanced datasets (i.e. the number of one class outweights the number of the other class). This approach tries to overcome the unbalanced number of samples for each class by attempting to train the samples equally (for both classes) in the bootstraping stage.

4) Comparison Metrics: After the training process is finished, the model is then used for untrained images (test data) to evaluate. To compare effectiveness of each combination (preprocessing, feature extraction and classification), we use the following metrics:

Accuracy is measured as the ability to differentiate the Melanoma and benign cases correctly, defined as:

Accuracy = T P + T N T P + T N + F P + F N (2)
Sensitivity is measured as the ability to determine the Melanoma cases correctly, defined as:

Sensitivity = T P T P + F N (3)
Specificity is measured as the ability to determine the benign cases correctly, defined as:

Specif icity = T N T N + F P (4)
In these formulas, TP (true positive) represents the number of cases correctly identified as Melanoma; FP (false positive) represents the number of cases incorrectly identified as Melanoma; TN (true negative) represents the number of cases correctly identified as benign; and FN (false negative) represents the number of cases incorrectly identified as benign.

AUC (Area Under Curve) is a higher level metrics, combining the true positive rate (T P R, same as sensitivity) and false positive rate (F P R = F P F P +T N , indicating how well a classification system distinguishes between the positive class and the negative class. When using only specificity and sensitivity separatedly, it is difficult to determine whether or not a classification method is overfit with positive samples (high Sensitivity) or overfit with negative samples (high specificity). Therefore, AUC is proposed in many classification system as the ultimate metric to measure their effectiveness, both for positive class and negative class. AUC is calculated as the area below a Receiver Operating Characteristic curve, composing of different combination of TPR and FPR when the classification threshold varies. Higher AUC value denotes the classification method is closer to a perfect prediction system.

Finally, we perform our experiments on a HP server, consisting of an Intel Xeon 2620 v3 (6 cores, 12 threads), 32GB of DDR4 memory and a NVIDIA GeForce GTX 1080.

III. RESULTS AND DISCUSSION

In this section, we summarize our evaluation results for the previously described steps (preprocessing: original, GB, LN, GB + LN; feature extraction: HSV, LBP, HOG, SIFT, HSV+LBP+HOG, HSV+LBP+HOG with LN, HSV+LBP+HOG with PCA; classifier: SVM, LR, RF, Ad-aBoost, BB, BRF). For each combination of a dataset, a preprocessing method, a feature extraction method and a classifier, our experiment consists of a training step (using 90% the provided dataset) and a prediction step (using the remaining 10% data) and a prediction result is provided, consists of accuracy, sensitivity, specificity and AUC values. In total, we have 1344 metric results (2 datasets × 4 preprocessing methods × 7 feature extraction methods × 6 classifiers × 4 metrics). We mainly focus on the AUC metrics as they represent the ability of the whole experiment both for positive class and the negative class.

A. Dataset

Firstly we compare the effectiveness of classification results with regard to dataset used for training and testing. Our thorough evaluation obtains best AUC values of 81.46% and 73.37% on HAM10000 and ISIC 2016, respectively. The former result (81.46%) is achieved on HAM10000 using linear normalization as preprocessing, HSV as feature extraction and Balanced Random Forest as classifier. The later result (73.37%) is with ISIC 2016 using original image (no preprocessing), LBP as feature extraction and also with Balanced Random Forest as classifier. With this result, it can be inferred that bigger dataset can provide better classification accuracy.

B. Preprocess

In this section, we evaluate the effectiveness of preprocessing methods for each given dataset. Particularly, we evaluate the best results achievable using the original image, gaussian blur (GB) filter, linear normalization (LN) and a combination of GB and LN. Figure 3 illustrates our results in this regard.

It can be seen that the best prediction results are given by Linear Normalization on HAM10000 dataset and by Gaussian blur with Linear Normalization on ISIC 2016 dataset. Our best AUC values of 81.46% is achieved with Linear Normalization as data preprocessing on HAM10000 dataset, in combination with HSV (as feature extraction method) and Balanced Random Forest (as classifier).

The upcoming result analysis sections only consider HAM10000 since most of the AUC results on ISIC 2016 are significantly inferior than the HAM10000 counterpart.

C. Features

In this section, we analyze the values of different features with regard to final prediction results. As previously discussed, the features being tested include HSV, LBP, HOG, SIFT, and combinations of HSV+LBP+HOG, HSV+LBP+HOG linearly normalized (HLH LN), HSV+LBP+HOG with principal component analysis (HLH PCA). Figure 4 summaries our findings in this regard.

An interesting result from this visualization is the superiority of HSV features (81.46% AUC) when compared with other feature extraction methods (65.99% -76.22% AUC), even better than the combination of HSV+LBP+HOG. HSV alone represents color feature of the input image and is faster than other methods to calculate. Therefore, it can be concluded that color plays a very important part in identifying and classifying Melanoma from a candidate image. When being combined with other methods, the prediction result is reduced.

HSV+LBP+HOG with principal component analysis (HLH PCA), unexpectedly, does not compete well with other methods. Its prediction results are among the worst (from 65.99% to 69.31%), when compared with other methods (HSV, LBP, HOG, SIFT, HSV+LBP+HOG (HLH) and HSV+LBP+HOG Insisting on the variance of prediction results for each classifier, table I shows its average AUC values and the corresponding standard deviations when used with our previously discussed feature extraction methods. Among these methods, SVM's, LR's and RF's performances are unstable. Although they can reach the average AUC up to 70.49%, their stability when used with different features is not as low as BRF (4.88% STD). On the other side, Adaboost, being the most steady classifier, predicts with lowest AUC values among these classifiers. Therefore, we can conclude that BRF is the best classifier for our experiments. Among all of our evaluations, the configuration providing best Melanoma prediction results in terms of AUC is as follows:

• Linear Normalization of the input image as data preprocessing step • HSV as feature extraction method • Balanced Random Forest as classifier The prediction results of such a configuration is 81.46% AUC, 74.75% accuracy, 90.09% sensitivity and 72.84% specificity.

IV. CONCLUSION AND PERSPECTIVES

In this paper, we perform an in-depth evaluation for Melanoma classification using machine learning. In particular, we proposed a classification system consisting of a preprocessing step, a feature extraction method and a classifier. We experimented with 4 different methods for data preprocessing steps, 7 feature extraction methods and 6 classifiers. Our experiment results show that: using the HAM10000 dataset is better than the ISIC 2016 counterpart; Linear Normalizaion on HAM1000 provides better prediction results that other preprocessing techniques; HSV is the best model for feature extraction; and Balanced Random Forest is the best classifier.

This Melanoma classification work can be continued by applying more modern preprocessing step (such as data augmentation), feature extraction and classifier (such as convolutional neural network). We believe that using neural network can furtherly improve classification results.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Examples of images from the two datasets. First row: Melanoma cases. Second row: benign cases.

Fig. 3 .

 3 Fig. 3. Best AUC results of preprocessing methods on two datasets.