State of activity classification of deep-seated gravitational slope deformation at regional scale based on Sentinel-1 data

Deep-seated gravitational slope deformations (DsGSDs) are very slow slope instabilities that can have a long-term impact on anthropic structures and infrastructures. The characterization of their state of activity is, therefore, essential to evaluate it. By employing Differential Interferometry Synthetic Aperture Radar (DInSAR) techniques, a dedicated procedure, to explore the behavior and define the state of activity of 279 DsGSDs, inventoried in the regional landslide inventory of the Aosta Valley Region (Western Italian Alps), has been implemented. The proposed methodology consists of several steps. Firstly, Sentinel-1 data have been processed through a two-step, advanced, DInSAR processing scheme to detect and identify Persistent Scatterers (PSs). The velocity values measured along the radar Line of Sight (LOS) have been projected along the steepest slope. Subsequently, an analysis of PSs within DsGSD polygons, devoted to the assessment of Sentinel-1 data coverage, has been carried out; in particular, considering the PS abundance, computing voids in point distributions and assessing PS clustering to identify cases with adequate point number and distribution for a suitable definition of the state of activity. Finally, a spatial analysis based on cluster and outlier identification has been carried out to characterize the moving phenomena and their degree of variability in deformation rates. Overall, the implemented methodology provides a valid instrument to remotely define the state of activity of these huge phenomena, often wrongly underestimated or neglected in risk management, useful for a better definition of DsGSD impacts on anthropic elements for a proper land use planning.


Introduction
Deep-seated gravitational slope deformations (DsGSDs) are large slow-moving phenomena highly widespread in the alpine territory (Mortara and Sorzana 1987;Ambrosi and Crosta 2006;Crosta et al. 2013).These phenomena usually affect extent areas, ranging from some kilometers in length to hundreds of meters in depth, up to involving entire valley flanks.Commonly, DsGSD evolution lasts over extremely long periods (i.e., Late Glacial Period) (Agliardi et al. 2012;Pánek and Klimeš 2016), with a progressive failure, comparable to a slow creep, that may locally evolve in a catastrophic collapse (Břežný and Pánek 2017).The long-lasting evolution of these gravitational phenomena is related to different controlling factors and their variable interaction, e.g., lithology and geological structures setting, tectonic and topographic stresses, glaciation and deglaciation, seismicity, climate weathering, rock dissolution, and human activities (Crosta et al. 2013).A typical geomorphological imprint can be recognized for DsGSDs.Usually, linear and persistent morpho-structural features (i.e., trenches, scarps and counter scarps, double ridges, elongated depression) characterize the upper-slope sectors of these phenomena, indicating a predominantly extensional regime.Instead, compressional features (i.e., toe bulging, variably fractured rock masses) and minor secondary landslides are often associated to the lower sectors of DsGSDs.All these features reflect the complex activity style of these huge phenomena, characterized by variable kinematics and heterogeneity in the displacement pattern (Giordan et al. 2017;Frattini et al. 2018;Crippa et al. 2020).The very slow movements, the long-lasting evolution, and the uneven behavior of DsGSDs can variably affect the anthropic elements, causing damage to buildings, roads, penstocks, and other strategic infrastructures (Frattini et al. 2013;Cignetti et al. 2020).
In mountain territories, the spatio-temporal evolution of DsGSDs and their impacts on anthropic elements remain difficult to characterize and, often, a classification of the state of activity of these phenomena is missing.In situ monitoring networks are often localized only along strategic infrastructures, not providing a full assessment of the whole DsGSD deformation pattern and evolution.All these factors still make it difficult to frame this phenomenon, hardly treatable as the other landslides, in the hazard assessment and risk management frameworks.As a result, the characterization of the state of activity of these huge phenomena, which is mandatory to evaluate their impact on artificial features, remains an open issue.
Differential Interferometry Synthetic Aperture Radar (DInSAR) techniques (Ferretti et al. 2001;Berardino et al. 2002;Hooper et al. 2004;Pepe and Calò 2017) proved to be a valid complementary tool to detect and monitor slow-moving phenomena (Herrera et al. 2013;Calò et al. 2014;Cignetti et al. 2016;Mantovani et al. 2019;Solari et al. 2019), providing measurements of ground deformation over extended areas, with high spatial coverage.In this work, DsGSD deformation analysis has been carried out by exploiting the Sentinel-1 dataset processed by the two-step SBAS technique, a two-step multitemporal SAR data processing strategy (Noviello et al. 2020).Likewise, the classical PSInSAR™ approach (Ferretti et al. 2001), two-step A-DInSAR, allows measuring only the component of the ground deformation along the sensor Line of Sight (LOS).Moreover, due to the appearance of shading and the intrinsic imaging distortions that lead to resolution losses for slopes facing the satellite orbits, high topography gradient and complex orography may cause reductions of the PS coverage.

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Finally, vegetation and long periods characterized by snow cover can heavily impair the temporal correlation properties of the backscattered SAR signal.
Despite the above-mentioned difficulties in applying A-DInSAR approaches in mountain territories, these techniques can often be the only means of characterizing the behavior of DsGSDs and their style of activities.Focusing on the Aosta Valley, north-western Italy, we implemented a procedure to preliminary classify the DsGSDs on the entire regional territory.In this alpine region, DsGSDs occupy the 13.5% of the regional territory, variably affecting inhabited areas and infrastructures (Martinotti et al. 2011;Cignetti et al. 2020), and pose a major concern to local and regional authorities.The classification of the state of activity of these huge phenomena in this alpine region is therefore a relevant issue to be addressed.To this aim, by exploiting the A-DInSAR derived displacements, we developed a rapid methodology to assess in an expeditious way the DsGSD activity at the regional scale.Operating in a GIS environment, a post-processing and a further investigation of Line of Sight (LOS) velocities have been carried out through dedicated algorithms (Notti et al. 2014).Subsequently, a multi-criteria procedure was employed to comprehensively evaluate the Persistent Scatterers' (PSs) number, data coverage, and distribution using R (R Development Core Team 2022).The objective was to identify cases with adequate SAR measurement point coverage, enabling accurate analysis of velocity values, which is crucial for characterizing deformation in DsGSDs and classifying their state of activity.
A spatial statistic analysis has been performed to evaluate the range of movement and the degree of spatial variability of the DsGSDs.
The implemented methodology allows remote defining of the state of activity of these huge phenomena, which are often wrongly underestimated or neglected in terms of associated risk, enabling to rapidly recognize the most critical phenomena that may be then investigated with further in-depth analysis at the local scale, representing a valid support for regional authorities to impove mitigation strategies and land use planning in mountain areas.

Deep-seated gravitational slope deformation of the Aosta Valley-study area
This study focuses on the DsGSD of the Aosta Valley Region (AVR), a mountainous territory located in the Western Italian Alps (Fig. 1).This small alpine region (about 3200 km 2 ) reveals a notable exposure to landslide phenomena, mainly related to its complex geostructural setting and geomorphological history.According to the Italian Landslide Inventory, i.e., "Inventario Fenomeni Franosi in Italia" (IFFI, Trigila et al. 2008), about three thousand landslide processes, varying in size and type, from punctual rock falls to large deep landslides, are catalogued over the entire AVR territory and available online in the regional web-portal named "Catasto Dissesti" (Centro Funzionale Regione Autonoma Valle d'Aosta 2020).Specifically, 279 polygons pertaining to DsGSD phenomena are inventoried in IFFI, covering an area of 460 km 2 (about 25% of all catalogued DsGSDs in the Italian Alps).The DsGSDs distributed on the AVR territory present a great variability, for spatial extent, causal factors, and, above all, for the spatially varying deformation mechanisms, state of activity, and patterns.Among the inventoried phenomena, the most extensive cases with a remarkable relief also affecting entire valley flanks are mainly distributed along the middle portion of the main Aosta Valley, as the Becca d'Aver DsGSD of about 30 km 2 , the Pointe Leysser of about 16 km 2 , and the Croix de Fana, Emarese, and the Punta de Chaligne of about 13 km 2 (Fig. 1).These huge DsGSDs show a gentle mean slope gradient of about 20°-24° (Fig. 2a) and a mean elevation ranging from 1000 to 1700 m a.s.l.(Fig. 2b).Other important DsGSDs are distributed in correspondence with the numerous secondary valleys north-south oriented, as the Hône DsGSD (Champorcher Valley), Motta de Pleté, and Torgnon DsGSDs (Valtournenche) of about 10 km 2 , and the Beauregard DsGSDs (Valgrisenche) of 5 km 2 (Fig. 1), with a mean slope gradient higher than those phenomena of the principal valley, varying between 20° and 35°.Moving to higher elevations, little extensive DsGSDs are more frequent and often affect only a small part of the slope or ridge, exhibiting higher mean slope values of about 30°-35°.
Lithologically, most of the DsGSDs are set in anisotropic rocks with moderate strength, such as calcschists, serpentinoschists, micaschists, and paragneiss, pertaining to the tectonometamorphic units constituting the entire axial zone of the Alpine chain, represented by an imbricate stack of continental crust and oceanic units (Dal Piaz 1992).This complex pile of nappes presents a post-collisional tectonic activity and important neotectonics fault systems, including the Aosta-Ranzola fault (Bistacchi et al. 2001) that influence the mountain slope dynamics and the DsGSD setting and evolution (Giardino and Polino 1997;CARG ISPRA 2015).Subsequent reactivations in a brittle regime, with local involvement of quaternary deposits, can be observed for example in the downslope sector of the Croix de Fana DsGSD (Giardino et al. 2000), testifying the prolonged deformation of these huge phenomena.Overall, the intense brittle tectonic, the complex morpho-structural setting, and the high relief energy, subsequent to the glacial retreat phase, favored and controlled the development of these huge phenomena in this alpine region.The most extensive DsGSDs are characterized by distinct morphological evidence, e.g., bulging, cone shape, like the Thoules DsGSD, the more active portion of the Pointe Leysser DsGSD, and extended surfaces of detachment derived from a progressive evolution through step-like profile.Characteristic linear morpho-structural features that testify the long-lasting slow deformation of these huge phenomena, widely described in literature (Crosta et al. 2013;Pánek and Klimeš 2016), are diffusely observable in the Aosta Valley DsGSD phenomena (Fig. 3).These typical gravitational surface features include, for instance, extended scarps associated with counter scarps, as in the case of Croix de Fana DsGSD, where an extended main scarp, visible along the western portion of the DsGSD, is associated with extended debris cover material and a counterscarp forming a graben structure (Fig. 3a), changes in valley cross-profile, as in the case of Motta de Pleté DsGSDs, where a large rotated block of bedrock, delimited by a counterscarp, is observable along the slope (Fig. 3b).Other typical morpho-structural elements may be lengthy elongated depressions (Fig. 3c), trenches (Fig. 3d), and double ridges (Fig. 3f and g).Furthermore, depending on the degree of evolution, distinct degree of rock mass fracturing, as in the case of Motta de Pleté DsGSD, showing rock masses outcrops variably fractured from very blocky rocks poorly interlocked up to heavily broken rocks collapsed onto themselves (Fig. 3e).Locally, deposits and glacial forms, when present, may be involved in DsGSD evolution, as observed in the Croix de Fana case with shear zones developed along the tectonic contact between the calcschists involved in DsGSD placed on top of glacial deposits (Fig. 3h).All these morpho-structural elements attest to the complex and variable local stress distribution recognizable within a single DsGSD phenomenon, indicative of extensive, compressive or mixed deformation style, mainly reflecting the tectonic or lithological settings.
Due to the high variability in terms of geological, geomorphological, and structural settings of this alpine territory, multiple factors control the evolution of the DsGSD phenomena, as well reported in the literature.In Martinotti et al. (2011), an indepth analysis of the main controlling factors of these phenomena, including litho-structural aspect, tectonic setting, postglacial debuttressing, and rock dissolution, has been carried out for the Aosta Valley territory.Multiple causal factors often concur, reflecting the complex long-lasting evolution of DsGSDs, as in the case of the Croix de Fana DsGSD, where the regional neo-tectonic activity, represented by the Aosta-Ranzola shear zone, plays an important role in slope deformation, associated to collapsed zones due a

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progressive subsidence of substratum for deep dissolution (Alberto et al. 2008) and a further propagation of deformation due to the progressive erosional down-cutting of the Aosta Valley related to glacial erosion, deglaciation and fluvial deepening of the valley.
Due to the gentle morphology and huge extension of these phenomena, DsGSDs in this alpine area are commonly characterized by the presence of sparse villages and numerous hamlets distributed along the slope; in addition, infrastructures like road network, railways, and penstocks of hydroelectric plants often intersect the DsGSDs both on the surface or underground paths.As an effect of the long-lasting and complex evolution of these phenomena, damage of various degrees to inhabited areas and artificial structures and infrastructures can occur.Several cases of DsGSDs in the Aosta Valley showed damage, from slight effects without significant cracks up to notable fracturing of buildings (Fig. 4a-c) as in the case of the Cielo Alto hamlet located over the Motta de Pleté DsGSD (Cignetti et al. 2022), or of engineered structures, as for the penstock of the Quart hydroelectric plant (Fig. 4d).This strategic infrastructure has been monitored since 1950 (Chiesa et al. 1991(Chiesa et al. , 1995) ) and constantly needs maintenance and remedial works.A similar case arises for the penstock of Perrères that interferes with the Motta de Pleté DsGSD (Fig. 4e).The long-term evolution of DsGSDs is exemplified by the intriguing case of the necropolis of Vollein archeological site, which is situated at the Croix de Fana DsGSD.Giardino et al. (2000) have meticulously documented the deformation evolution at this site, dating back from the Upper Pliocene to recent times.Furthermore, extreme cases of DsGSDs' impact on anthropic elements have even led to the redesigning of the infrastructures, as in the case of Villeneuve penstock (Martinotti et al. 2011) of the namesake DsGSD, or the partial dismantling and reduction of strategic infrastructures, as in the case of the Beauregard dam (Barla 2018) (Fig. 4f), affected by the namesake DsGSD.3. PS data coverage evaluation (Multi-criteria Exclusion Procedure-MEP); 4. Spatial statistic analysis of mean velocity.
Figure 5 shows the flowchart of the proposed methodology, described in detail in the following sections.

Two-step A-DInSAR processing
In this work, we have used a two-step A-DInSAR processing strategy based on the joint use of SBAS and DTomoSAR (Reale et al. 2011;Fornaro et al. 2014;Noviello et al. 2020).The method, applied to the 2014-2021 Sentinel-1 SAR dataset, is based on a sequence of a low-(small scale) and high-resolution (large scale) processing of interferometric SAR data acquired over repeated passes (Fig. 6).The low-resolution processing exploits the SBAS method described in Fornaro et al. (2009) and estimates the atmospheric disturbance and small-scale non-linear deformation.The subsequent fullresolution analysis is performed by applying DTomoSAR to the calibrated stack to detect and estimate the parameters of interest (topography and residual deformation rate) of PS at full resolution.Small-and large-scale deformation components are then combined to provide the final large-scale deformation measurements.The accuracy of the measurements depends not only on the coherency properties of the scatterers, but also on the processing accuracy and particularly on a critical step related to the phase unwrapping.A quantitative evaluation of the accuracy of the measurements is difficult, typically it is possible to reach the limit of 5 mm, and 1-2 mm/ year on the deformation rates, depending on the temporal span and number of acquisitions (Wasowski and Bovenga 2014).

Post-processing A-DInSAR derived measurements
Notoriously, A-DInSAR techniques allow the detection of deformations along the satellite LOS.Therefore, by using SAR images, only a component of actual ground displacement is measurable, depending on both the morphological setting (i.e., slope and aspect) and the acquisition geometries of the satellite.According to Colesanti and Wasowski (2006) 2017), a post-processing procedure has been performed by projecting the LOS deformation velocity (V LOS ) along the steepest slope to compare ground deformation velocity with different slope aspect.The velocity projected along the slope (V SLOPE ) has been computed for both ascending and descending SAR datasets for each measurement point, through the application of the C-index proposed by Notti et al. (2014), derived from Cascini et al. (2010), and specified as: where N, E, and H are the directional cosines of the radar LOS, precisely: where α is the LOS incident angle, and γ is the LOS azimuth.Instead, the parameters s and a correspond respectively to the slope and the aspect values derived from a digital terrain model (DTM).
The C coefficient represents the percentage of movement registered by the sensor (Notti et al. 2014).Hence, computing the C value for each PS, the V SLOPE was computed: However, it is worth noting that the high variability in the slope direction, where terrain shows hummocky geomorphology (e.g., counter slope, trench), can affect the post-processing projection procedure.In this way, the assumption that the prevailing movement occurs along the steepest slope is made, inducing a potential bias.Despite projecting V LOS on the slope, an underestimation related to the 3D direction of movement occurred.To limit this bias, we restricted the projection for PSs with slope gradient more than 5° and C values higher than 0.2 and less (1) Original Paper than − 0.2 to avoid the exaggeration of the projection, according to Notti et al. (2014).In fact, a value of C equal to 0.2 indicated a V SLOPE five times greater than the V LOS , with an amplification of the error.A threshold in V SLOPE values was imposed, excluding values with V SLOPE > + 2 mm/year, since a positive value is not reliable from a geomorphological point of view (i.e., a landslide moving upslope) (Ren et al. 2022).Using these thresholds, from 10 to 20% of PS for each dataset are discarded.Moreover, to limit the effect in the mean velocity projection related to the variability of topography, we used a 10 m DTM.It is recommended to use a coarser DTM to project velocity along the slope, reducing the local variation of slope morphology to avoid misinterpretation of velocity deformation data for large slope deformation.

PS data coverage evaluation (Multi-criteria Exclusion Procedure-MEP)
In mountainous areas, SAR-based deformation analyses still pose a challenge, primarily concerning unsuitable valley flanks orientation, high topographic gradients due to the complex orography, and abundant vegetation cover (Colesanti and Wasowski 2006;Cigna et al. 2013;Mondini et al. 2021).These factors affect the number, distribution, and density of PSs, impacting on the proper assessment of the kinematic behavior and of the state of activity of the phenomena.In literature, it is often pointed out that an inadequate number of measured points can limit the statistical robustness of the measured velocity values (Notti et al. 2011;Cigna et al. 2013), leading to an ambiguous definition of the evolution of the investigated phenomenon.In addition to the PS number, some studies (Bovenga et al. 2012;Bonì et al. 2020;Barra et al. 2022) highlight the importance of proper distribution and density of the SAR measure points for a correct definition of the state of activity of a certain phenomenon.The uneven distribution of points, i.e., with PS concentrated in restricted areas or distributed along a limited portion of the phenomenon, can constitute a limit in the definition of slope instability kinematic.Moreover, a suitable PS distribution and density allow delineating potential anomalous areas and heterogeneities in the slope movements.This aspect is very important for DsGSDs, affecting entire valley flanks, showing complex behaviors with high displacement pattern variability and sometimes with secondary associated active landslides (Giordan et al. 2017;Crippa et al. 2020).
The Multi-criteria Exclusion Procedure (MEP) presented in this work is designed to take into account all the aspects mentioned.Starting from the PSs filtered in the post-processing phase, based on the joint analysis of three different indexes: • Skewness of the first-order nearest neighbor distance.
The first index considers the number of PSs within each DsGSD collected in the inventory of the AVR.Considering the commonly large extent of these phenomena, an empirical threshold has been set, considering as a limiting condition a number equal to or greater than 20 PSs, useful to identify cases with few PSs surely unsuitable to analyze the degree of activity of the whole phenomenon.
Subsequently, to establish an index able to describe the distribution of PSs within each DsGSD polygon, a grid of 10 × 10 cells is set for computing the percentage of voids in points distribution.This helps to define the degree of PS distribution.The third index is considered to assess the PS clustering through the computation of the first-order nearest neighbor distance and then the skewness of their value.The last two indexes were normalized in a − 1 ÷ + 1 range and, for each one, an exclusion threshold was established, i.e. voids % norm ≥ 0.5 and skewness norm ≥ 0.3.All the values were then attributed to each DsGSD polygon and then reclassified as 0 or 1 whether they meet or not the established criteria.This allowed a primary exclusion of those polygons satisfying less than one criterion.On the contrary, the rest of the dataset, i.e., polygons fulfilling two or three criteria, was labeled as "suitable' for further analysis and processing.
Overall, these intermediate outcomes pose the basis for a proper assessment of the behavior of DsGSDs exploiting V SLOPE values and a fruitful evaluation of the state of activity of the observed phenomena.

Spatial statistic analysis of mean velocity
In this step, a semi-automated methodology through a stepwise sequence of analysis of SAR measurements has been implemented to evaluate the DsGSD activity.To this aim, the mean along-slope projected velocities computed in the previous step ("Post-processing A-DInSAR derived measurements") have been considered.It is worth noting that the state of activity has to be defined concerning the observation period.Accordingly, in our work, a phenomenon classified as active refers to the time interval of the used Sentinel-1 acquisitions, i.e., late 2014-June 2021.Moreover, considering the high complexity and heterogeneity of DsGSD behavior and their long-lasting evolution (> 10 2 years), we have operated outside the standard categories of state of activity defined for landslides (WP/ WLI 1993) by using the denominations "predominantly inactive" (PI) and "predominantly active" (PA).Initially, we carried out a preliminary distinction of DsGSD phenomena "predominantly inactive" (PI-DsGSDs) from those "predominantly active" (PA-DsGSDs).Operating in a GIS environment, we operated through a rasterization of the V SLOPE values by applying the "Point Statistics" tool, calculating the mean velocity on the points in a neighborhood around each output cell.The PI-DsGSD corresponds to those DsGSDs showing more than 60% of the raster cells with values of mean V SLOPE between − 2.5 and + 2 mm/year, while the other cases are considered PA-DsGSD.Subsequently, for the latter group, we implemented a semi-automated methodology to characterize both the movements and the degree of variability of these vast phenomena.The identification of areas affected by surface deformations and higher movements has been carried out by exploiting spatial statistic analysis.We applied the "Cluster and Outlier Analysis" GIS tool based on Anselin Local Moran's Index (Anselin 1995), a correlation coefficient that measures the overall spatial autocorrelation of a dataset.This clustering algorithm defines how a point is similar to the surrounding ones, allowing us to identify similarities in behavior, and distinguishing homogeneous groups (i.e., clustering of data with tendentially "high" or "low" values statistically significant) among spatially close data.Given a point dataset, this index highlights areas where high or low values are clustered and the outlier features, with high or low values that are very different from the surrounding values.The tool also provides a z-score and pseudop-values that indicate whether the apparent similarity (a spatial clustering of either high or low values) or dissimilarity (outliers) is more pronounced than one would expect in a random distribution, measuring the statistical significance.A high positive z-score indicates that the surrounding points have similar values ("low" and "high" values), returning "HH" for the statistically significant cluster of high values and "LL'" for the statistically significant cluster of low values.Starting from DInSAR-based measurements, we set V SLOPE values as the weighting value to calculate the spatial cluster, computing the density of points in a neighborhood around those points.Low clusters correspond to areas moving away from the satellite, while the high clusters to the areas moving towards the satellite.The cluster and outlier analysis led to the identification of three main patterns (Fig. 7): (i) homogeneous pattern, with a homogeneous distribution of background points, sometimes associated with one or more small and localized clusters with distinct velocity; (ii) heterogeneous pattern, with diverse low and high clusters variably distributed along the slope; (iii) bimodal pattern, with two main clusters sharply recognizable from upstream to downstream.
An average velocity datum was also assigned to each pattern to indicate the velocity range of those most moving sectors within a PA-DsGSD.In particular, three sub-classes have been established, corresponding to specific ranges of velocity: low velocity (from − 2.5 to − 5 mm/year); medium velocity (from − 5 to − 10 mm/ year); high velocity (greater than − 10 mm/year).For heterogeneous and bimodal cases, the assigned velocity corresponds to the mean velocity of the group with the highest velocity among the identified clusters.

DsGSD deformation map
In this work, C-Band SAR images acquired by the Copernicus Sentinel-1 mission along descending (track 139D) and ascending (track 88A) orbits over the AVR territory have been used.Datasets are composed, respectively, of a total number of 278 images covering a period from October 2014 to June 2021 and 336 images from November 2014 to June 2021.For both datasets, the A-DInSAR analysis described in "Two-step A-DInSAR processing," has been carried out, allowing the production of mean deformation velocity maps with a total number of 5,054,113 measure points (ascending dataset) and 2,033,608 measure points (descending orbits).Despite the challenges posed by the alpine territory characterized by high topography gradients and complex orography, extensive forested areas, and prolonged snow cover periods, the outstanding PS coverage enabled to carry out an extended and deep analysis of DsGSD phenomena at the regional scale (Reale et al. 2022).
The post-processing operations described in "Methodology" have been applied to the PSs distributed within the DsGSDs, considering the polygons inventoried in the regional catalogue.A buffer of 50 m around each polygon was imposed to consider an appropriate analysis environment.To examine the DsGSD ground deformation, the V SLOPE was computed applying the post-processing procedure based on the C-index computation (Eq.1).This index is influenced by the resolution of the DEM exploited to extract slope and aspect values.High-resolution DEMs accurately describe the terrain profile, presenting high variability in slope direction, affecting the C-index computation and consequently the V SLOPE calculation (Notti et al. 2014).For this reason, we used a DEM with a medium-low resolution, in particular the 10 m DEM of the AVR (courtesy of the regional authorities).The applied post-processing procedure allowed us to extract 199,847 points with mean deformation velocity values ranging from − 45 and 2 mm/year, with a highly variable PS distribution within the DsGSD polygons.Slightly less than 10% of cases have no points within the DsGSD boundaries.The derived map of the V SLOPE of the DsGSDs for the whole region is reported in Fig. 8.
By computing a preliminary analysis of the velocity values for each polygon, we observed that most of the phenomena record V SLOPE values above the − 2.5 mm/year, exceeding the stability threshold, and ranging between more the − 2.5 and − 10 mm/ year, as in the cases of Emarese, Becca d'Aver, and Pointe Leysser DsGSDs.In some cases, DsGSDs reach higher values with mean V SLOPE from − 10 up to − 24 mm/year, e.g., Valtournenche, Torgnon, Beauregard DsGSDs.Only about 20% of these huge phenomena display rather small values of mean V SLOPE from − 2.5 and 2 mm/ year.The results allow us to obtain a regional synoptic view of the ground displacement rates characterizing the DsGSDs.Overall, of

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the 279 DsGSD polygons of the AVR, 253 are covered by A-DInSAR measurement points.However, the information on the presence of PSs within a polygon is not sufficient for an appropriate characterization of the DsGSD state of activity and needs to be integrated with a comprehensive analysis of the measurement points coverage.

Assessment of the PS coverage suitability
The analysis of PS coverage performed through the MEP allowed us to define the suitability of the SAR measurements for the proper assessment of the DsGSD state of activity over the entire AVR (Fig. 9).
The MEP was applied to the V LOS data derived from the ascending and descending SAR datasets, projected along the steep slope through the post-processing procedure.The results show that only 73 DsGSD phenomena present a total absence or few PSs (no criteria met), with a very low density and a predominantly clustered distribution (Fig. 10a, b).
These cases mainly correspond to poorly extended DsGSDs (on average about 75 ha), predominantly located at high elevations in correspondence with densely forested or seminatural areas, often away from urban areas, and potentially with snow cover for a long period.One hundred three DsGSDs have more than 20 PSs within their boundary, satisfying only one of the three imposed thresholds, in particular the PS abundance one, but showing an unfavorable distribution with PSs predominantly concentrated only in reduced sectors of the DsGSDs (Fig. 10b).Also in this case, the DsGSD phenomena are poorly extended, with an average of about 96 ha and mainly distributed at high elevations, occupied by forest and seminatural areas.These two case histories present DsGSDs with common features mainly represented by small-size phenomena located in high mountain areas, often along with the watershed of the lateral valleys, generally characterized by an inadequate number of SAR points.Such features make these comparable phenomena unsuitable for a correct definition of their state of activity.
Instead, 67 DsGSDs variably satisfy at least two thresholds.In that case, DsGSD phenomena always exhibit a suitable number of PSs (≥ 20 PSs), with an average of 883 measured points per polygon, showing, in general, a good PS density and a proper spatial distribution within the DsGSD boundary (Fig. 10c).These cases correspond to quite extensive DsGSDs, with an average of 206 ha, variably distributed at medium-high elevations such as the Beauregard, Motta de Pleté, and Hône DsGSDs.For these phenomena, PSs are mainly distributed along the infrastructures or in correspondence with urban areas but maintain a good distribution along the slope without a local distribution in restricted areas or along limited portions of the investigated phenomenon.Lastly, 36 phenomena simultaneously satisfy all the three imposed thresholds.In these cases, DsGSDs correspond to the most extensive phenomena of the AVR, e.g., Emarese, Becca d'Aver, Torgnon, Croix de Fana, Saint Nicolas, Pointe de Chaligne, and Valtournenche DsGSDs, located along the main valley and site of the major urban centers of the region.The latter two cases generally present a great abundance of PSs with high spatial density and a homogeneous distribution within the DsGSD boundary (Fig. 10d).These features are considered representative of an adequate characterization of the DsGSD behavior and the classification of the state of activity.
Overall, the MEP-based results have pointed out that about the 37% of the investigated phenomena show an ideal spatial coverage and a high number of PSs, representing the cases suitable for subsequent analysis and proper classification of the state of activity.The other DsGSD phenomena, instead, show a total lack or a poor coverage of data (26%), or a suitable number of measured points (37%), but with an uneven and poorly representative distribution, resulting not suitable for the analysis of DsGSD behavior and the state of activity classification.

Regional DsGSD state of activity classification
By applying the stepwise procedure, we obtained the regional map of the DsGSD state of activity (Fig. 11), subdivided into five classes, including the not-classifiable cases characterized by absence, insufficient number, and/or poor distribution of PSs.A limited number of cases corresponds to phenomena predominantly inactive (25 PI-DsGSDs).Instead, forty-four DsGSDs correspond to moving phenomena, showing distinct patterns and velocity ranges.
Figure 11 shows the obtained DsGSD classification at the regional scale, including the unclassified phenomena, the predominantly inactive and predominantly active ones.Specifically, the PA-DsGSDs are represented on the basis of the cluster analysis categorization, distinguishing the homogeneous, the bimodal, and the heterogeneous patterns, associating to each the range of mean velocity.
In particular, among the PA-DsGSDs, most exhibits a subdivision in distinct domains with different mean velocity, characterized by a mixed and heterogeneous pattern, sometimes associated to the presence of secondary landslides, but also to shallow movements not strictly related to DsGSD movement, such as rock glaciers.The Becca d'Aver DsGSD (30 km 2 ) displays a good example of a heterogeneous pattern, showing numerous scattered clusters with medium velocity (mean velocity − 9 mm/year), and alternating clusters with lower mean velocity variably distributed across the slope.Similarly, Beauregard DsGSD displays a heterogeneous pattern, as already evidenced by the sub-polygon subdivision proposed in IFFI, with an upstream portion characterized by a medium range of velocity (about − 7 mm/year), diverse extended clusters with high velocity (more than − 13 mm/year), and a downstream portion with slower velocity just below − 5 mm/year.Twenty-five cases display a bimodal distribution, e.g., the Croix de Fana DsGSD showing an upstream moving portion with high velocity (more than − 11 mm/year), three central portions with medium velocity (from − 8 to − 10 mm/year), up to the downstream portion with a low velocity close to the stability threshold, in which the secondary landslide of Vollein is inserted.The reversed case is the Motta de Pleté DsGSD which shows a downstream portion more active (about − 14 mm/year) and an upstream portion with a minor strain rate (about − 4 mm/year).Nineteen PA-DsGSDs are classifiable instead as homogeneous, displaying the same background with consistent V SLOPE within the polygon boundary, e.g., Pointe Leysser DsGSD with a mean velocity of − 9 mm/year.

Discussion
The characterization of spatial and temporal deep deformation of DsGSD phenomena may be particularly arduous for their intrinsic compound behavior and long-term evolution (even thousands of years).These phenomena frequently display a highly spatially variable behavior, with distinct kinematic domains and heterogeneity Original Paper in deformation style (Pánek and Klimeš 2016;Giordan et al. 2017;Frattini et al. 2018;Crippa et al. 2020), also showing embedded minor landslides, thus requiring a thorough geomorphological analysis (Tolomei et al. 2013;Bossi et al. 2016).These specificities make the characterization of DsGSDs and the definition of their state of activities a challenging issue.
DInSAR techniques have been extensively used in slope movement studies, providing their capability for surface deformation detection and monitoring (Cascini et al. 2009;Herrera et al. 2013;Di Martire et al. 2016).Furthermore, despite several recent studies dealing with the impact of DsGSDs on anthropic structures and infrastructures (Frattini et al. 2013;Reyes-Carmona et al. 2020;Cignetti et al. 2020), there is still an underestimation of the effect of the movement and its spatial variability, as well as of the longterm evolution of DsGSDs, in terms of hazard assessment and land use planning regulation.Moreover, in alpine regions, high topography gradient associated to complex orography, land cover mainly represented by extended forests, or snow accumulation for long periods of the year, may represent a remarkable limitation for SAR measure points detection (Colesanti and Wasowski 2004;Mondini et al. 2021), although the latter, due to climate forcings, is becoming highly variable and in reduction trend (Colombo et al. 2022).As a result, data coverage may be limited, with SAR points concentrated only in small and extremely localized portions of the entire phenomenon, in correspondence with anthropic structures showing high SAR coherence (e.g., buildings, wall, penstock, electric line) or of areas covered by dense debris coverage.Diverse authors outline this issue, focusing on analyzing the PS distribution, through specific indexed (Bonì et al. 2018), or by imposing limiting conditions on their number (Crippa et al. 2021).
The two-step A-DInSAR approach applied in the proposed methodology allowed the detection of a highly populated dataset of SAR measure points over the entire mountainous regional territory of AVR (De Maio et al. 2009;Fornaro et al. 2014).The so-identified PSs have been further investigated through the Multicriteria Exclusion Procedure, aimed at analyzing their coverage and distribution, in order to discard cases poorly representative of the entire phenomenon, avoiding consequent minisinterpretation of the state of activity of DsGSDs.Via the MEP, indeed, we identified the unfavorable cases, for which the minimum conditions for a robust state of activity assessment are not met.Cases presenting a low number of PSs and an uneven distribution (e.g., measure points concentrated in restricted areas or distributed along a limited portion of the investigated phenomenon) as well as cases without SAR point coverage (about 25% of the regional phenomena) have been considered inadequate.These unfavorable cases, mainly represented by phenomena with small extent, located at high to very high elevations and/or covered by dense forest and woodlands, have been considered "not classifiable," i.e., related to an undefined activity state (Casagli et al. 2016;Bonì et al. 2018).Alongside, the MEP ensures distinguishing objectively if the PS data are adequate in terms of both abundance and distribution within the DsGSD.This step poses the basis for a proper assessment of DsGSD behavior and their state of activity, considering only those cases with a reliable PS spatial distribution represented by measure points uniformly distributed over the entire phenomenon or most of its extent.Only those cases that show an ideal spatial coverage and a high number of PSs (about 40% of cases), satisfying the imposed empirical thresholds (Fig. 11), were considered for the actual classification of the state of activity.The imposed conditions aim at ensuring a proper characterization of the DsGSD behavior, through an objective evaluation of the spatial variability of the A-DInSAR derived mean deformation velocity values in the next steps implemented in the proposed methodology.Through the spatially driven approach and the cluster analysis, a preliminary and rapid identification of phenomena characterized by higher strain rates and phenomena with strain localization at narrow sectors has been obtained.A suitable mapping of the state of activity of these huge slow-moving phenomena represents an essential data to identify the most critical areas that may pose a certain degree of risk for anthropic structures and infrastructure.The DsGSD classification so far obtained, combining the kinematic pattern with a range of velocity, allowed defining the deformation style and the eventual spatial variability of these vast phenomena.It should be noted that this subdivision in different sectors, as already present in some of the cases inventoried in the regional catalogue, is mainly related to previous local-scale analysis (Broccolato and Paganone 2012), which emphasized the heterogeneity of the behavior of such phenomena.
Undoubtedly, greater availability of damage information and/ or in situ ground deformation measurements (Del Soldato et al. 2019;Nappo et al. 2019) would strengthen the analysis performed at the regional scale by hardening the achieved results, especially for those cases with indications of high velocity associated with heterogeneous and bimodal patterns.However, leveraging on previous literature and unpublished technical reports, several comparisons between the proposed methodology outcomes and renowned and documented damage to structures and infrastructures have been made.A representative case is the Croix the Fana DsGSD, a south-facing extended phenomenon located in the middle portion of the main valley of the AVR.Our methodology pointed out a bimodal pattern with higher velocity in the upper part of this DsGSD, falling into the high-velocity range (> − 10 mm/year), including the impressive graben structures bordering the western sector of the DsGSD.It is worth noting that the state of activity of this phenomenon is confirmed by damage

Original Paper
to the concrete lining of the main tunnel of the Quart plant monitored by localized on-site instruments, as described by Chiesa et al. 1995.Based on such evidence, an important improvement for future studies could be provided by increasing the spatial resolution and resolving the velocity components for the detailed analysis of the slope deformation and the kinematic variability at the local scale, particularly for heterogeneous and bimodal cases.

Conclusion
In this work, we present a user-friendly methodology aimed at characterizing the state of activity of DsGSDs at the regional scale, by exploiting A-DInSAR techniques.The methodology allowed us to select the DsGSDs with an adequate PS density and spatial distribution over the entire AVR territory, and then to investigate the magnitude and spatial distribution of deformation velocities.To achieve this, we used the Multi-criteria Exclusion Procedure (MEP) based on three different indexes: (i) PS abundance; (ii) the number of voids; (iii) skewness of the firstorder nearest neighbor distance.On the selected deformation, we applied the "Cluster and Outlier Analysis" based on Anselin Local Moran's Index to identify similarities in behavior and distinguish homogeneous groups of PSs.The analysis led to recognizing three main patterns: (i) homogeneous, (ii) heterogeneous, (iii) bimodal.The combination of the state of activity and velocity patterns allowed us to classify the DsGSD style of activity.
The results show that about 37% of the 279 DsGSDs of the AVR are suitable for PS analysis, of which 63% predominantly active.The majority (57%) of DsGSDs show a heterogenous and bimodal displacement distribution, most of them with high (> 10 mm/ year) or moderate (5-10 mm/year) velocity.The results also point out that many PA-DsGSDs are very extensive phenomena, mainly located at medium and medium-high elevations.Several of them interact with strategic infrastructures such as hydroelectric plants and their penstock (e.g., Croix de Fana, Hône DsGSDs), dams (e.g., Beauregard DsGSD), and with the inhabited centers widespread along the slope (e.g., Valtournenche, Motta de Pléte DsGSDs).The analysis of the spatial distribution of velocity suggests the complex kinematics of these gravitational processes that, in many cases, show several sub-sectors and/or secondary landslides with complex and mostly unknown interactions, which will be the objective of future studies.
The presented methodology confirms the relevant role that DIn-SAR technologies play in slope movements investigations, and may represent a supporting tool for regional administrators to expeditiously assess the state of activity of these huge long-lasting phenomena, highly widespread in mountain regions and often cause significant socio-economic damage for the local communities.

Funding
Open access funding provided by IRPI -TORINO within the CRUI-CARE Agreement.This research was funded and carried out in the ASI contract n. 2021-10-U.0CUP F65F21000630005 MEFISTO, within which COSMO-SkyMed and SAOCOM data have been provided by ASI under license to use agreements.

Declarations
Competing interests The authors declare no competing interests.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.To view a copy of this licence, visit http:// creat iveco mmons.org/ licen ses/ by/4.0/.

Fig. 2
Fig. 2 Mean slope gradient (a) and mean elevation (b) of the DsGSDs inventoried in AVR

Fig. 3
Fig. 3 Main gravitational surface features characterizing DsGSDs: a Croix de Fana DsGSD, Quart municipality, graben structure formed by the main scarp of the western limit and a counter scarp, associated to extended talus material; b Motta de Pleté DsGSD, Breuil-Cervinia municipality, Valtournenche, zoom on the rotated block of bedrock delimited by a counter scarp (dashed line), and associated trenches; c elongated depression, Hône DsGSD, Champorcher Valley; d highly evolved trench, Croix de Fana DsGSD and e variably fractured rock masses outcrops close to the Cielo Alto hamlet, Motta de Pleté DsGSD, going from very blocky rocks poorly interlocked (Vr.Bl.), to heavily broken rocks collapsed onto themselves (Hv.Bk.); f highly extended scarps, counter scarps, elongated depression, and lineaments clearly visible from the orthoimages in the upper part of a DsGSD located in Val Ferret; g visible double ridge, Croix de Fana DsGSD (photo from Elter et al. 2007); h glacial deposits involved in DsGSD evolution (photo modified from Giardino 1995 PhD Thesis)

Fig. 4
Fig. 4 Several examples of the impact of the long-lasting evolution of the DsGSDs on artificial structures and infrastructures in the AVR: severe damage observed in correspondence with a the top and b exterior walls of the buildings in Cielo Alto hamlet, and c of a building of the Valtournenche town (photo from Google Street View); d underground portion of the penstock of the strategic hydroelectric plant of Quart affected by the namesake DsGSD, as reported in Martinotti et al. (2011) (photos from CVA gallery, available on: https:// www.cvaspa.it/); e the Perrères penstock variably interfering with the Motta de Pleté DsGSD; f Beauregard dam affected by the namesake DsGSD during the dismantled of this infrastructure (photo by Erik Kuschel, IAEG Summer School 2022)

Fig. 6
Fig. 6 The adopted two-step A-DInSAR processing strategy based on the joint use of SBAS and DTomoSAR: red lines highlight the main data flow during the processing

Fig. 7
Fig. 7 Examples of the three main patterns recognized applying the Anselin Local Moran's Index tool: a homogeneous pattern with clustering data with low values distributed along the slope, with a localized high values cluster at the lower limit of the DsGSD; b heterogeneous pattern with diverse low and high clusters widespread along the slope; c bimodal pattern with two separate low and high clusters

Fig. 8 V
Fig. 8 V SLOPE map of DsGSD phenomena in AVR derived from A-DInSAR processing of Sentinel-1 data acquired along ascending and descending orbits between late 2014 and June 2021

Fig. 9
Fig. 9 Map of DsGSDs classified on the basis of the number of met thresholds imposed in the MEP analysis

Fig. 10
Fig. 10 Examples of the cases observed by the MEP analysis: a DsGSD with no PSs within the phenomenon boundary, none of the imposed thresholds are met; b DsGSD (red polygon) with a low number of points (< 20 PSs) with lack of thresholds satisfaction as in the previous case, and DsGSD (orange polygon) with a good number of point (1 criterion met) but an unfavorable distribution, satisfying the PS abundance limit; c DsGSD that satisfies at least two of the imposed thresholds, showing a suitable PS abundance and distribution along the slope; d DsGSD that simultaneously satisfies all the imposed thresholds, showing high abundance of PSs, good spatial density, and a consistent distribution of the measured points along the slope

Fig. 11
Fig. 11 Regional map of DsGSDs classified on the basis of their state of activity, associated to a range of velocity based on the mean alongslope projected velocities, where low velocity corresponds to the range − 2.5-− 5 mm/year, medium velocity to − 5-− 10 mm/year, and high velocity to values > − 10 mm/year