How volcanic stratigraphy constrains headscarp collapse scenarios : the Samperre Cliff case study (Martinique Island, Lesser Antilles)

. Gravitational instabilities can be significant threats to populations and infrastructures. For hazard assessment, it is of prior importance to estimate the geometry and volume of potential unstable masses. This characterization can be particularly difficult in volcanic context due to the succession of deposition and erosion phases. Indeed, it results in complex layering geometries where the interfaces between geological layers may be neither parallel nor planar. Geometry characterization is all the more complex when unstable masses are located in steep and hardly accessible landscapes, which limits data acquisition. 5 In this work, we show how remote observations can be used to estimate the surface envelope of an unstable mass on a volcanic cliff. We use ortho-photographs, aerial views and topographic surveys to (i) describe the different geological units of the cliff, (ii) characterize the stability of geological units, (iii) infer the paleo-morphology of the site and (iv) estimate potential unstable volumes. We investigate the Samperre cliff in Martinique (Lesser Antilles, French West Indies) as a study site, where recurrent destabilizations since at least 1988 have produced debris flows that threaten populations and infrastructures. Our 10 analysis suggests that the destabilizations occurring on the cliff may be associated to the re-opening of a paleo-valley filled by pyroclastic materials. We estimate that between 3 . 5 × 10 6 m 3 and 8 . 3 × 10 6 m 3 could still be mobilized by future destabilizations in the coming decades.

Since the dramatic flank collapse of Mount St Helens in 1980 (Voight et al., 1983), massive debris avalanches (more than 30 10 7 m 3 ) have been widely studied (e.g. Siebert et al., 1987;Voight, 2000;Boudon et al., 2007). Siebert (1984) estimates a worldwide occurrence frequency of about 4 such events per century, but site specific occurrence frequencies are variable. For instance, the Soufrière de Guadeloupe volcano has produced at least 8 flank collapses in the past 9,150 years (Komorowski et al., 2005;Legendre, 2012). With one event per 1,100 yr on average, flank collapse events appear rather frequent on a geological time scale. However, from a human perspective this represents only one event in 45 generations. 35 In comparison, smaller mass wasting events (from 10 6 to 10 7 m 3 ) are more frequent. Landslide occurrence rate f is indeed related to landslide volume V through a power law f ∝ V −β , withβ a positive parameter. For instance, Brunetti et al. (2009) estimate β = 1.3 for a global dataset of landslides ranging from 10 −4 to 10 13 m 3 (including among others rockfalls, rock avalanches and debris avalanches). When considering landslides in volcanic context only, Brunetti et al. (2009) compute β = 1.1 (see their dataset R). Thus, although mass wasting events involving 10 6 to 10 7 m 3 affect smaller areas in comparison to 40 larger volcanic flank collapse (>10 8 m 3 ), their higher occurrence rate may result in similar risk levels.
In volcanic context, events involving 10 6 to 10 7 m 3 span a wide variety of landslide type, including slow moving landslides  (Jaboyedoff et al., 2019(Jaboyedoff et al., , 2020. However, as already said, the sub-surface is often not homogeneous in volcanic environment. It is thus necessary to identify the different geological units composing the unstable slope. This requires 60 field work and/or geophysical surveys (Rosas-Carbajal et al., 2016. The nature and geometry of geological units can then be processed in a expert way to identify preferential rupture surfaces. Rupture surfaces can also be inferred from limit equilibrium analysis, provided geotechnical data is available (Apuani et al., 2005;Verrucci et al., 2019;Heap et al., 2021).
However, in many cases, researchers and/or practitioners can only rely on remote observations and/or topographic models to estimate the surface envelope of the unstable mass. This happens when field work is difficult or dangerous (e.g. in remote 65 and steep areas), and when advanced remote sensing methods are not applicable (e.g. InSAR acquisition for displacement measurements does not yield conclusive results in densely vegetated areas). In these conditions where relatively few data are available but stakes require a quantified hazard assessment, how can we estimate the surface envelope of an unstable mass, from which the unstable volume can be quantified?
In this work, we show how the combined use of historical ortho-photographs and aerial photographs, Digital Elevation 70 Models (DEMs) and 3D point clouds can help estimate the surface envelope of an unstable mass. We investigate the Samperre cliff in Martinique (Lesser Antilles, French West Indies) as a case study. Located on the western flank of the Montagne Pelée volcano, it has undergone several episodes of destabilizations since at least 1980least or even 1950least (Aubaud et al., 2013Clouard et al., 2013). Although the resulting rock avalanches do not threaten directly populated areas, subsequent debris flows do propagate several kilometers downstream and impact populations, buildings and infrastructures. The quantification 75 of potentially unstable volumes is thus important to assess the volume of the resulting loose debris reservoir that could feed debris flows.
The geological context of the study site is given in Section 2. In Section 3 we present the topographic surveys and orthophotographs used in this work, along with the methods used to (i) characterize the geometry of geological units and (ii) compute the volume of the unstable mass. Then, in Section 4, we describe the different geological layers forming the Samperre cliff 80 and differentiate between stable and unstable layers (given the current morphology of the cliff). This allows to infer the paleomorphology of the site and identify the paleo-surface of a valley progressively filled by volcanic deposits. We extrapolate the geometry of this paleo-surface to construct a stable basal surface above which materials could be remobilized. The associated volume is computed and discussed in Section 5, along with the other results of our work.

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The first building stage of Montagne Pelée Volcanic Complex is a succession of andesitic breccias, lava domes and lava flows dated between 550 and 127 kyrs by Germa et al. (2011). The end of the first stage is marked by the Prêcheur flank collapse (Prêcheur collapse structure in Figure 1, Le Friant et al., 2003;Boudon and Balcone-Boissard, 2021). This 25×10 9 m 3 collapse (Brunet et al., 2016) entailed a lithostatic decompression of the lava chamber feeding this primitive Montagne Pelée edifice (Germa et al., 2011). It may have triggered the formation of the Piton Marcel lava dome near the boundary of the horse-shoe shaped collapse structure (Figure 1c).
The Prêcheur flank collapse marks the the beginning of the second phase of the Montagne Pelée Volcanic Complex. Lava dome-forming eruptions and associated concentrated pyroclastic density currents were the dominant activity. The edifice that grew in the Prêcheur collapse scar was destroyed by another flank collapse about 36 kyrs ago (Rivière Sèche collapse, Solaro et al., 2020). During the third building stage of the Montagne Pelée Volcanic Complex, the first 10 kyrs years were characterized 100 by abundant explosive activities with low-silica andesitic magma. Over the past 25 kyr, Boudon and Balcone-Boissard (2021) have recorded at least 55 magmatic eruptions, two third of which are dome forming eruptions, and the rest being plinian eruptions.
The volumes of flank collapses can be estimated from the on-land and submarine topography. However, before the new interpretation of Solaro et al. (2020), previous studies suggested the Prêcheur flank collapse 127 kyrs ago was constituted of 105 two separate collapses, 127 kyrs and 32 kyrs ago (Le Friant et al., 2003;Germa et al., 2015;Brunet et al., 2016). Their volumes were estimated to 25×10 9 m 3 and 13×10 9 m 3 by Brunet et al. (2016). Smaller volumes were computed by Germa et al. (2015) using a geomorphological analysis: 14.7 × 10 9 m 3 and 8.8 × 10 9 m 3 . Thus, the total volume for the Prêcheur collapse can be estimated between 27.5 × 10 9 m 3 and 38 × 10 9 m 3 . However, these volumes were likely destabilized by successive smaller debris avalanches less than 5×10 9 m 3 , as suggested by numerical simulations (Brunet et al., 2017). Such volumes are coherent 110 with the volume estimated for the Rivière Sèche flank collapse, between 2 × 10 9 m 3 (Brunet et al., 2016) and 3.5 × 10 9 m 3 (Germa et al., 2015). Even so, the magnitude of such events is about 100 to 1,000 times larger than that of the rock avalanches we focus on (less than 10 7 m 3 ).
Rock avalanches involving up to 10 7 m 3 occur in the Prêcheur river catchment that drains part of the western flank of Montagne Pelée. The Prêcheur river's major affluent is the Samperre river that skirts Piton Marcel to the south and has its in June 2010, a major debris flow inundated part the Prêcheur village at the river mouth and severely damaged the bridge crossing the river (Aubaud et al., 2013;Peruzzetto et al., 2022). A new and higher bridge has since been constructed, but major lahars could still destroy it. As a result, about 420 people would be isolated from the rest of the island (INSEE, 2015). For local risk management, it is thus important to assess the volumes of future rock avalanches from the Samperre cliff in order to estimate the magnitude of the associated debris flows and to quantify the resulting risks.

Material and methods
Our objective is to quantify the volume that could still collapse from the Samperre cliff in the coming decades. To that end, we need to analyze the geology of the cliff and infer the geometry of geological units. As field work is too dangerous and because no geophysical data are available, we must rely on remote observations and topographic surveys only.

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Over the past decades, and in particular since the first documented collapse sequence in 1980, numerous oblique aerial pictures taken during helicopter surveillance flights have documented the evolution of the cliff. We use them along with georeferenced ortho-photographs. The oldest available ortho-photographs date back to 1951 (IGN, 2021a, b). 6 other ortho-photographs are then available for the 1988 -2018 period. The date and details of acquisitions are given in Table 1. The comparison between successive photographs document the plan-view recession of the cliff and its geology ( Figure 2). We analyze in details the 140 08/2018 ortho-photograph to identify visually the different geological units composing the Samperre cliff from color or texture variations.
Several DEMs and 3D point clouds are also available, derived from LiDAR or photogrammetric acquisitions between March 2010 and August 2018 (see Table 1). They are used to characterize the geometry of identified geological units by means of the CloudCompare software (CloudCompare, 2020). We characterize (i) deposition horizons identified by sharp color contrasts,

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(ii) interfaces between units inferred from slope breaks and (iii) the surface of outcrops.

Geometric characterization of geological layers
We do not use the 08/2018 ortho-photograph to characterize deposition horizons because the Samperre cliff displays steep and even over-hanging topographic features. Instead, we work directly on textured 3-D point clouds that allow a better characterization of geometric features (e.g. Pavlis and Mason, 2017;Buckley et al., 2019). The horizons are thus identified on the 150 07/2010 photogrammetric 3D point cloud ( Figure 3). This point cloud has the best resolution compared to other point clouds of the area (on average, 32 pts/m 2 on the cliff). Horizons are picked in CloudCompare (CloudCompare, 2020) with the Compass plug-in (Thiele et al., 2017). This plug-in automatically interpolates paths between manually picked points, with a least-costpath solver, provided a cost function. As deposition horizons are identified by color change, we choose a cost function that depends on RGB (Red Green Blue) color gradient: the resulting path is chosen such that it follows strong RGB gradients. We    pick horizons that are first identified by visual inspection of the point cloud ( Figure 3a). Compass is also used to pick interfaces marked by a slope break: in this case, the cost function depends on the point cloud local curvature.
To assess the dip and dip direction of the deposition horizons and interfaces, we sample points along the picked polylines (10 pts/m). The resulting point cloud is then fitted by a plane. The quality of the fit is given by the Root Mean Square (RMS) of the distances from the points to the best-fit plane. Following Fernández (2005), we also compute two indicators, M and K 160 (see Appendix A for computation details). Fernández (2005) suggest that M > 4 indicates a good fit between the plane and the point cloud, and that K < 0.8 indicates a correct estimation of the plane orientation. Sampling bias results in an estimation uncertainty on dip and dip direction. We quantify this uncertainty by computing the 100-times bootstrapped standard deviation of dip and dip direction (see Appendix A for details).
The same methodology is used to estimate the dip and dip orientation of outcrop surfaces extracted from point clouds.

Unstable volume quantification
The identification of the different geological units, the characterization of their geometry, and their evolution since 1950 documents the progressive unearthing of interfaces limiting the basal and lateral surface of successive destabilization epsiodes.
Thus, we can differentiate between geological units affected by destabilisations and geological units that have remained stable.
These observations are used to reconstruct the paleo-morphology of the site and infer a basal stable surface above which 170 materials are unstable.
This basal surface is composed of (i) outcrop surfaces of geological units considered stable (approximated by planes, as described in the previous section) and (ii) planes fitted manually in CloudCompare to topographic features that have remained stable since 1951. The potentially unstable volume is then defined as the rock mass contained between this basal surface, and the topography (08/2018 DEM for the cliff, 03/2010 DEM elsewhere). Given the 1 m horizontal accuracy of the DEM, we 175 consider only height difference superior to 1 m, in an area above the contact between the stable and unstable geological units.
The computed rock mass volume is dependant upon the different modelled planar units. To estimate volume variations caused by sampling bias, we randomly resample 100 times the outcrop surfaces of stable geological units and derive the associated best-fit planes and resulting basal surface. Then, we compute the bootstrapped standard deviation of the potential unstable volume.

Results
In this section (i) we describe geological units composing the Samperre cliff, (ii) we characterize the relative stability of each unit, (iii) we reconstruct the paleo-morphology of the site, and (iv) we use these results to reconstruct the possible surface envelope of an unstable mass and compute the corresponding volume.

Geological description of the cliff 185
The different geological units composing the Samperre cliff ( Figure 4) have been progressively exposed by successive destabilization episodes. In the following we describe the successive layers from top to bottom.
The top most layer of the cliff is composed by brown to light brown, probably weathered materials (unit Pu, yellow patch in Figure 4c). It was exposed in 2010 as a 20 to 30 meter thick layer (Figure 5a), as mentioned by Mathon and Barras (2010) and Below unit Pu, a massive, light gray to light brown, 50 m thick layer was exposed in 2018 to the East and South of the cliff (unit La, orange patch in Figure 4c). This layer displays clear vertical prismatic patterns (Figures 5b and 5c). We associate these patterns to columnar jointing of tuffs (Lim et al., 2015;Hamada and Toramaru, 2020) rather than to a lava flow, because no recent lava flow has been identified in this sector in previous studies (Boudon and Balcone-Boissard, 2021).

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Most of the cliff below units Pu and La is formed by a 100 to 200 m succession of greyish materials (unit UPd, pink patch in Figure 4c). The interface between successive deposits can be clearly identified by color changes, from light to dark gray ( Figure 3a). The deposits show significant variability in thickness and grain size distribution, with blocks several meters wide.
We interpret unit Upd as pyroclastic deposits. On the 07/2010 photogrammetric model, we approximate the deposition horizons by planes (Figure 3b), with mean dip 16 • and dip direction N254 • (see Table A1). This is, to within 15 • , the opposite direction 200 of cliff retreat since 1950 (N062 • , black dashed line in Figure 3b).
The bottom part of the cliff is composed, in its North-West side, by a characteristic ocher unit (unit Co in Figure  UPd would then correspond to the eruptive phase characterized by scoriaceous, low silica, andesitic products and associated 230 to pyroclastic density currents (36-25 kyrs), and/or to the subsequent eruptive phase (25 kyrs -present) where dome-forming and plinian eruptions predominated (Boudon and Balcone-Boissard, 2021). The tuff unit La cannot be dated but was probably emplaced by the fallout of one of the 17 plinian to sub-plinian eruptions reported by Boudon and Balcone-Boissard (2021) between 25 kyrs and present time. Mathon and Barras (2010) and Clouard et al. (2013) interpret unit Pu as pumices of the most recent plinian eruption, P1, that occurred in 1348 ±50 CE (Boudon and Balcone-Boissard, 2021 From successive ortho-photographs and topographic surveys (Figure 2), as well as aerial photographs (e.g. Figure 5a and 5b), it is clear that the upper geological units Pu, La and UPd are involved in the main destabilization episodes. Thus, we conclude they are unstable. Following NGU (2012), the presence of water seapge at the base of unit UPd also favors its instability.
Units Co and LPd were previously covered by unit UPd. Successive destabilizations have increased the surface of the outcrops. These outcrops do not display any clear collapse scar. They have remained relatively intact since they were exposed 245 (e.g. compare outcrop of unit Co in Figures 5a and 5c). This suggests units Co and LPd are more resistant than unit UPd. This stability is further confirmed by water resurgences at the base of unit UPd, which indicates that the stability of units Co and LPd is less affected by increased pore pressures.
Thus, we make the hypothesis that units Co and LPd are more stable than unit UPd, given the current morphology of the cliff. From this assumption we deduce that the outcrop surfaces S1 and S2 correspond to the formerly hidden interface between 250 units Co and UPd (see Figures 6 and 7). Similarly, we deduce that the outcrop surface S3 corresponds to the formerly hidden interface between units LPd and UPd.

Paleo-morphology
From the geological and geometric observations described above we propose a scenario of the evolution of the catchment geomorphology, with successive construction and dismantling phases ( Figure 6).

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Following the interpretation of Solaro et al. (2020), the Prêcheur flank collapse that occurred 127 kyrs ago is the oldest event that can be related to the current morphology of the Samperre cliff. This major dismantling event was followed by a construction phase, when the accommodation space left by the collapse was progressively filled with new pyroclastic deposits (unit LPd, Figure 6a). Its surface may be given by the current interface between units LPd and UPd (surface S0).
A new dismantling phase then started (Figure 6b). It may have been initiated by the Rivière Sèche flank collapse 36 kyrs 260 ago: this collapse did not affect the Samperre cliff area but the resulting scar concentrated newly emitted volcanic materials.
Thus, unit LPd was progressively eroded. We suggest erosion was mainly caused by preferential flow path along the Prêcheur collapse structure, and thus along unit Co. It led to the formation of a valley in a West-South-West/East-North-East direction Hatched areas identify some of the surfaces used to construct a potential unstable volume (see Section 4.4). The contact between LPd and UPd units, inferred from slope breaks, is given in (b) and (c) by the black dashed lines. Ravines and rivers are also displayed, as in Figure 1. (N062 • , Figure 6b). The North-West flank of the paleo-valley is given by surfaces S1 and S2 of unit Co, and the South-East flank by surface S3 of unit LPd. As of 2022, this erosion phase is still an ongoing process. Thus, we suggest that the volumes that could be involved in future rock avalanches are constrained by the volume of materials filling the paleo-valley. To quantify this volume, we reconstruct the 280 surface of the paleo-valley that we believe is more stable.

Assessment of unstable volume
The geometry of the paleo-valley is reconstructed by extrapolating outcropping surfaces of stable units and surfaces fitted to stable topographic features (see Section 3.3 for methodological details). These surfaces are displayed in Figure 7a, and their characteristics are given in Table 2.

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The North-West (respectively South-East) side of the paelo-valley,is constrained by the surfaces S1 and S2 (respectively S3) of unit Co (respectively unit LPd). We also fit manually a planar surface S4 to the North-West wall of ravine B, in the continuation of which we identified another outcrop of unit Co (see Figure 4c). Similarly, we fit a planar surface S5 following the southern ridge of Samperre cliff, that has remained stable since at least 1988. Finally, we assume that the bottom of the paleo valley matches the current bed of the Samperre river (surface S6).

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The resulting basal surface envelope is represented in Figure 7b. The height difference between the basal surface and the 2018 topography is displayed Figure 8. The corresponding volume is about 8.3 × 10 6 m 6 . The uncertainty associated with least square plane fitting (but not to manual plane fitting) amounts to less than 1% of the estimated volume, and is thus negligible (see Table 3).   Table 2). (b) Basal surface (red planes), constructed by extending and combining planes fitted to S1, S2, S3 and S4, and planes S5 and S6. The Piton Marcel is highlighted by the purple patch. The black dashed line is the Prêcheur destabilization structure.  Table 3).

Stability of unit Co and Lpd
We inferred from visual observations over more than a decade that units Co and LPd are more stable than unit UPd. In order to further investigate this hypothesis, we would need to characterize the geotechnical properties of these units. Geotechnical properties can be measured with in-situ tests (e.g. penetration tests) or with laboratory analysis of rock samples (e.g. tri-axial tests). However, both methods require field work that would be very dangerous near the Samperre cliff for safety reasons.

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Samples could also be collected on outcrops of the same geological units located in more accessible areas. For the UPd unit, these outcrops could be identified by comparing their mineralogy, and age if possible, to that of lahars deposits in the Prêcheur river. Indeed, these deposits mainly correspond to screes remobilized at the Samperre cliff toe, and thus to collapsed materials from the UPd unit.
Until complementary field work and geotechnical characterization are carried out, remote observations must be used. For 305 instance, the stability of units Co and LPd in coming years could be assessed by monitoring their evolution, with yearly visual observations or topographic surveys. In the mean time, limit equilibrium numerical models can help characterize the stability of the cliff by performing a sensitivity analysis on key parameters, including the geometry of the interfaces between geological units, the geotechnical properties of materials, and the presence and level of aquifers. In a first approach, simple 2D limit equilibrium models such as SSAP (Brunetti et al., 2014;Borselli, 2022) or FLAC/Slope (Itasca, 2022) could be tested.

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The stability of units Co may be questioned. Indeed its ochre colour suggests it has been extremely hydrothermal altered (e.g. Salaün et al., 2011), and many studies (e.g. Heap et al., 2021) have linked hydrothermal alteration to reduced rock stability.
However, after the 127 kyrs flank collapse, alteration may have affected unit Co only at its surface. It is indeed a preferential flow path, as evidenced by water seepage at the interface between units Co and UPd. Besides, even if the unit is altered at greater depth, these water seepages suggest hydrothermal fluids no longer circulate within unit Co. Thus, we argue that the 315 alteration of unit Co is old and has been compensated by (i) hydrothermal sealing, (ii) diagenetical cementation and (iii) lithostatic compaction (e.g. del Potro and Hürlimann, 2008). These three processes reduce connected porosity. For volcanic rocks, lower porosity is associated to increased cohesion and friction coefficient (Villeneuve and Heap, 2021). Thus, stability is increased, and the alteration of unit Co is compensated for. In turn, the surface of unit Co becomes a preferential sliding surface as observed for instance for old collapse scars on the Soufrière de Guadeloupe volcano (Salaün et al., 2011).

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There is no clear sign of hydrothermal circulation within unit LPd, which limits possibility of both alteration and hydrothermal sealing. However, the proximity of the Montagne Pelée eruptive center suggests pyroclastic deposits of unit LPd may have been emplaced at relative high temperature, which favours welding (Quane and Russell, 2005). Then, as for unit Co, unit LPd was likely further strengthened by diagenetical cementing and lithostatic compaction. Furthermore, Boudon and Balcone-Boissard (2021) describe most of the pyroclastic deposits produced during this second stage as indured materials forming a 325 succession of ridges particularly visible on the more eroded western flank of Montange Pelée edifice.

Structural control of a valley paleo-surface on cliff destabilizations
The correlation between paleo-morphology and volcanic flank collapse has been investigated in several studies. For instance, Branca and Ferrara (2013) (Salvany et al., 2012;Chaput, 2013). Besides, Rault et al. (2022) suggest that most mass wasting events occurring in the Cirque of Salazie depression (associated to the dismantling of Piton des neiges volcano) are associated 345 to the remobilization of old debris avalanches and epiclastic deposits (see also Chaput, 2013). As a result, destabilization mechanisms may differ from the Samperre cliff that is mainly composed of pyroclastic deposits.
Without any documented similar case studies, further data are needed to confirm or invalidate the hypothese that the destabilizations of the Samperre cliff are structurally controlled by the surface of a paleo-valley. In this perspective, it will be important to analyze future destabilization episodes, should they occur. In the mean time, the geometry of the paleo-valley could be con-350 strained by geophysical surveys. Indeed, given observed water seepages, the contact between units Co and UPd, and LPd and UPd, is certainly associated to a permeability contrast, and thus a resistivity contrast (e.g. Romano et al., 2018;Huntley et al., 2019). Older volcanic formations often tend to have lower permeabilities as a result of filling of cavities and fractures (Singhal and Gupta, 2010), hydrothermal sealing (Polak et al., 2003) and compaction (Farquharson et al., 2017).
Given the difficulty to carry out terrestrial surveys in the Samperre cliff area, airborne electromagnetic surveys (AEM) are more feasible. They have already proven to provide valuable information to constrain landslides geometry (Nakazato and Konishi, 2005). Most of Martinique island was covered in 2013 by AEM surveys (Deparis et al., 2014;Coppo et al., 2015), and the resulting data were used to investigate hydrogeological systems (Vittecoq et al., 2015(Vittecoq et al., , 2019 and active landslides (Thiery et al., 2017(Thiery et al., , 2021. This highlights the great potential of this method, but unfortunately the Samperre cliff could not be flown over in 2013. The current development of AEM drone-based survey could help acquiring AEM data on this zone. We expect the 360 contrast between Co and UPd to be particularly clear, as these units clearly have different lithologies or degree of weathering (as evidenced by color variations). However, unit LPd and UPd are both pyroclastic deposits, hence the contrast may be less marked.

Volume estimation and implication for hazard assessment
The main surfaces controlling the extent of the reconstructed paleo-valley behind the cliff are S2 and S5. The river bed (surface 365 S6) has a very limited influence, because it lies below other surfaces, and in particular below S1, S2 and S3. This is why it does not appear in Figure 7b). Similarly, surfaces S3 and S4 do not influence the final computed volume, provided we consider only unstable materials in the Samperre cliff.
Our estimation of the uncertainty on the unstable volume is only related to the uncertainty on best-fit plane derivation. A more robust procedure should also take into account (i) the uncertainty on manual plane fitting for surfaces S4 and S5 and (ii) 370 possible variations in structural orientations below the 08/2018 topography. In particular, we may expect the surface of unit Co to curve itself to the East, following the same trend as the Prêcheur destabilization structure, instead of keeping the orientation of surface S2 (Figure 7b). This would be coherent with observations, as the dip direction of surfaces associated to unit Co gradually increases from the West to the East: N137 • for S4, N169 • for S1 and N206 • for S2 (see Figure 7 and Table 2).
Despite the lack of quantitative information, this possible bending of the interface between units Co and UPd can be taken 375 into account, in a first approximation, if we simply delimit vertical surfaces constrained by topographic features. In a first case scenario, we assume that the paleo-valley did not extend further than the destabilization structure of the Prêcheur flank collapse. We thus use a North-East limit defined by ravine A (that follows the Prêcheur structure), continued along the ridge of the Prêcheur structure (green dashed line in Figure 8). The corresponding volume, 7.9 × 10 6 m 3 , is of the same order than our first estimation (8.3 × 10 6 m 3 ) to within 5% difference. In a second more conservative scenario, we use ravine B (that runs 380 behind Falaise Samperre) as North-East limit. The associated volume is 3.5 × 10 6 m 3 .
The upper volume value 8 × 10 6 m 3 gives an estimation of the total rock mass volume that could be involved in future destabilization episodes, until the catchment reaches a long-term stability state. Given the collapsed volume between 2010 and 2018 (about 5 × 10 6 m 3 ), this equilibrium state may well be reached in the coming decades. However, this does not entail that hazard associated to lahars will be then reduced in the Prêcheur river. Indeed, solid materials remobilized by lahars could also 385 come from multiple other sources, including lateral erosion from the banks of the Samperre river and fresh eruptive materials in the event of a new phreatic or magmatic eruption. Besides, although units Co and LPd are more stable than unit UPd, they may still be subjected to retrogressive erosion or gravitational instabilities. Finally, gravitational instabilities could also occur in adjacent gullies, in particular in ravine D where superficial instabilities were witnessed in 2019 (figure 2 in Peruzzetto, 2021a).
In comparison, the smaller volume value 3.5 × 10 6 m 3 is consistent with volumes destabilized in recent times (e.g., 2.1 × 390 10 6 m 3 in 2010 and 4.9 × 10 6 m 3 between 2010 and 2018) and could correspond to the volume of the next destabilization episode. A more detailed estimation would require limit equilibrium 3D numerical modeling (Apuani et al., 2005;Reid et al., 2015;Verrucci et al., 2019;Heap et al., 2021), but more geotechnical data are needed to contrain simulations. The next destabilization episode could occur in a single event or, more likely, in a succession of smaller rock avalanches. In both cases, a significant scree reservoir will be formed at the toe of the Samperre cliff. The processes controlling its remobilization by 395 water depend on factors that are hard to constrain in real-time monitoring, including precipitation intensities and pore-pressure within the reservoir. The resulting lahars may occur as a few major high-discharge events with the potential to flood the Prêcheur village downstream, as in 2010; or as multiple smaller but still dangerous events during a longer time period, which is highly disruptive for inhabitants, as in 2018. Our study suggests either of these crisis situations could still occur in the coming years, as a result destabilizations from the Samperre cliff. In the worst case scenario, we can consider a 3.5 × 10 6 m 3 reservoir 400 created at the bottom of the cliff (neglecting bulking), and remobilized in a single lahar with solid fraction 75% (following classical solid fraction values as in Vallance and Iverson, 2015;Thouret et al., 2020). A rough estimation of the volume of the lahar is then 4.7 × 10 6 m 3 . The associated damages would be very important. Indeed, using numerical simulations, Peruzzetto et al. (2022) showed that a 2.0 × 10 6 m 3 lahar has already the potential to flood a large part of the Prêcheur village.
However, in the current state of knowledge, it is impossible to predict the date of the next collapse and of the subsequent 405 lahars: the physical processes controlling and triggering destabilizations on the Samperre cliff are difficult to constrain. Nevertheless, they are most likely associated with water circulations.

Destabilization mechanisms
As already suggested by Clouard et al. (2013) and Nachbaur et al. (2019) ground water circulations at the interface between units Co and UPd may be the main triggering factor for destabilizations. In the medium term (i.e. years), it could weaken the 410 base of unit UPd by washing out fine particles. This suffusion process is widely documented in the litterature (e.g. Moffat et al., 2011;Wan and Fell, 2008;Prasomsri and Takahashi, 2021). Precipitations (and associated increased pore pressure) could be a triggering factor in the short-term, but only after a time lag allowing ground water to reach the cliff. Indeed, the 2018 destabilizations episodes started only 2 days after the major rainfall of Dec., 31 2017 (almost 150 mm in one day in the Prêcheur village Quefféléan, 2018). We do not have access to precipitations records for previous events.  (Figure 2a). Thus, we suggest destabilizations espiodes start on the North-West side of the cliff, at the interface between units Co and UPd, and progress to the East and South-East by successive retrogressive failures.

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This yields an average volume of 0.9 × 10 6 m 3 yr −1 . This value certainly over-estimates the sediment production rate due to rock avalanches, because the 2018 collapse sequence was particularly large compared to previous episodes in 1998 or 2010.
Quefféléan (2018)  we assume a density of 3000 kg m 3 , we get a flux between 0.3 and 0.6 Mt yr −1 : it represents between 0.2% and 0.5% of the sediment flux from cliff retreat in Europe (over a distance of 127,000 km, see Regard et al., 2022).
In comparison, the total volume volumes involved in the Prêcheur and Rivière Sèche flank collapses is estimated between 27 × 10 9 m 3 (Germa et al., 2015) and 40 × 10 9 m 3 (Brunet et al., 2016). The associated long-time annual averages are 0.21 × Of course, the Samperre cliff has been particularly active since (at least) 1950 and our results suggest it could reach an equilibrium state in the coming decades. Thus, the associated sediment production rate may over-estimate the actual sediment 440 production rate linked to 10 6 -10 7 m 3 landslides on the Pelée edifice over a long time period. In particular, its specific location near the head-scarp of the Prêcheur collapse structure could enhance instabilities in comparison to other escarpments: as suggested by Germa et al. (2015), it is important to differentiate erosion rates inside and outside collapse calderas. However, the pyroclastic materials composing most of the cliff are, presumably, not specific to this site. Other outcrops are thus likely to be also eroded in the long-run by landslides or runoff. This is particularly true in tropical islands where intense rainfalls favour 445 superficial instabilities and erosion (e.g., more than 200 landslides cataloged in Martinique island between 2000 and 2020, Thiery et al., 2021). Besides, our results are coherent with the conclusions of Brunetti et al. (2009). Indeed, using a global database of landslides, they find that landslide occurrence probability is proportional to V −β , with V the landslide volume and β = 1.1 in volcanic context. Thus, the return period T V is proportional to V β . In turn, the sediment production rate V /T V is proportional to V (1−β) = V −0.1 . That is, the sediment production rate associated to landslides slightly decreases with landslide 450 volume, or at least does not depend significantly on the landslide volume (given the uncertainties associated to the estimation of β).
Thus, following Clouard et al. (2013), Germa et al. (2015) and Quartau et al. (2015), we suggest that the contribution of large edifice collapse to volcanic island dismantling is significant, but not necessarily dominant in comparison to other erosive processes, and in particular smaller landslides. Of course, this may depend on the geological context, and the disctinction 455 between processes is not easy as they can follow each other (e.g. surface water remobilizing landslide deposits). This question is still discussed in the literature. For instance, Salvany et al. (2012) argue that the the formation of volcanic cirques in the Réunion island (Indian Ocean) was mainly the result of regressive erosion by small landslides and runoff. On the contrary, Chaput (2013) suggests that the excavation of the cirques was first initiated by major gravitational instabilities, whose resulting breccias were then remobilized by smaller landslides and surface water. More recently, Rault et al. (2022)

Conclusions
The quantification of unstable volumes in rocky cliffs in volcanic context is difficult because of the complex geometry of successive geological layers, especially when no geophysical, geotechnical or displacement data are available. In this study, we used historic aerial oblique photographs, ortho-rectified photographs, Digital Elevation Models and 3D point clouds to: Our interpretation that destabilizations are linked to the presence of a paleo-valley could be verified or contradicted by airborne electro-magnetism surveys. They would identify, if it exists, the interface between the paleo-valley and materials filling it. A regular monitoring of the cliff morphology during future destabilization episodes will also help better constrain long-term evolution scenarios. Further field work should also be done in the future to identity and sample accessible outcrops of the geological units composing the Samperre cliff. This would allow to estimate the geotechnical properties of the materials 490 that compose the cliff, and carry out limit equilibrium simulations.
Data availability. The orthophotographs, DEMs, and photographs used to construct the photogrammetric models are not the property of the BRGM. Thus, they can't be made freely available. Aerial pictures of the cliff, taken during helicopter flights, are provided in supplementary materials.
Appendix A: Geometric analysis of points cloud 495 Provided a set of N points with coordinates ((X 1 , Y 1 , Z 1 ), ..., (X N , Y N , Z N )), we fit a plane of equation aX +bY +cZ +d = 0 to the corresponding cloud points through an ordinary least square regression, minimizing the distance between the points and the plane. The associated minimal Root Mean Square (RM S) is: To characterize the robustness of the fit, we introduce the (N × 3) matrix M : where E(X), E(Y ) and E(Z) are respectively the mean X, Y and Z coordinates of the point cloud. The (3 × 3) covariance matrix C is then given by: The three positive eigen-values λ 1 , λ 2 and λ 3 , and associated eigen-vectors e 1 , e 2 , and e 3 help describe the geometry of the 505 point cloud. Assuming λ 1 ≥ λ 2 ≥ λ 3 , e 1 points in the direction of the cloud main axis, e 2 in the second main axis direction and e 3 in the third axis direction, all three axes being orthogonal to one another. The distribution of the points along these three axes is quantified by the eigen-values. For instance, if the points are aligned along a line, λ 2 = λ 3 = 0. If the points are homogeneously distributed on a disk, λ 1 = λ 2 and λ 3 = 0. In this perspective, √ λ 1 can be seen as a characteristic length of the point cloud and √ λ 2 as a characteristic width (see corresponding columns in Tables 2 and A1). More precisely, λ 1 and λ 2 510 are the variance of points projection on the first and second axes. λ 3 describes the points dispersion around the plane given by eigen-vectors e 1 and e 2 : we have λ 3 = RM S.
For the plane fit to be robust, the RM S, i.e. λ 3 , needs to be small in comparison to the length of the cloud. Following Fernández (2005), we use the indicator: The higher M is, the better the fit. To estimate the reliability of the plane orientation, we must assess the linearity of the point cloud, as multiple planes can fit a linear distribution of points, with similar RM S. Fernández (2005) suggest the indicator K: K = ln(λ 1 /λ 2 ) ln(λ 2 /λ 3 ) The lower K is, the better the reliability of the fit. Low values of K are obtained if λ 3 << λ 2 (i.e. if the point cloud has a good degree of planarity) and/or if λ 1 /λ 2 is close to 1 (by construction, λ 1 /λ 2 ≥ 1). Fernández (2005) run multiple numerical tests 520 to estimate threshold values for M and K corresponding to good fit and reliability. They suggest we must have M ≥ 4 and K ≤ 0.8. In order to have a direct estimation of the uncertainty on dip and dip direction of the fitted plane, we use a bootstrap method. This is done by drawing randomly, with replacement, N points among the initial N points of the point cloud, and fitting a plane to the new point cloud. This procedure is repeated 100 times. The standard deviations of the resulting dip and dip directions are given in Table 2 and Table A1. Competing interests. The authors declare that they have no conflict of interest.