Decision-Level Fusion of PS-InSAR and Optical Data for Landslide Susceptibility Mapping Using Wavelet Transform and MAMBA

Abstract

Landslides remain a critical geohazard in mountainous regions, where intensified extreme rainfall and rapid land-use changes exacerbate slope instability, challenging the reliability of traditional single-sensor susceptibility assessments. To overcome the limitations of data heterogeneity and noise, this study presents a decision-level fusion strategy integrating Permanent Scatterer InSAR (PS-InSAR) deformation dynamics with multi-source optical remote sensing indicators via a Wavelet Transform (WT) enhanced Multi-source Additive Model Based on Bayesian Analysis (MAMBA). San Martín del Castañar (Spain), a region characterized by rugged terrain and active deformation, served as the study area. We utilized Sentinel-1A C-band datasets (January 2020–February 2025) as the primary source for continuous monitoring, complemented by L-band ALOS-2 observations to ensure coherence in vegetated zones, yielding 24,102 high-quality persistent scatterers. The WT-based multi-scale enhancement improved the signal-to-noise ratio by 23.5% and increased deformation anomaly detection by 18.7% across 24,102 validated persistent scatterers. Bayesian fusion within MAMBA produced high-resolution susceptibility maps, indicating that very-high and high susceptibility zones occupy 24.0% of the study area while capturing 84.5% of the inventoried landslides. Quantitative validation against 1247 landslide events (2020–2025) achieved an AUC of 0.912, an overall accuracy of 87.3%, and a recall of 84.5%, outperforming Random Forest, Logistic Regression, and Frequency Ratio models by 6.8%, 10.8%, and 14.3%, respectively (p < 0.001). Statistical analysis further demonstrates a strong geo-ecological coupling, with landslide susceptibility significantly correlated with ecological vulnerability (r = 0.72, p < 0.01), while SHapley Additive exPlanations identify land-use type, rainfall, and slope as the dominant controlling factors.

1. Introduction

Frequent climate fluctuations, the increasing occurrence of extreme rainfall events, and rapid land-use transformations have intensified the spatial heterogeneity and multiscale characteristics of landslide development. Consequently, landslides have become one of the most widespread and destructive geohazards worldwide, particularly in regions defined by complex terrain characterized by steep and highly variable slope gradients exceeding 25°, strong topographic relief, heterogeneous lithological units, and irregular aspect and curvature patterns. These geomorphological conditions not only intensify hydrological and geomorphic controls on slope instability but also produce spatially variable layover, foreshortening, and decorrelation in SAR imaging. Given that these hazards pose severe threats to human life, property, ecosystem stability, and regional sustainability [1,2,3,4,5], establishing a quantitative and dynamically responsive landslide susceptibility assessment system is essential [6,7,8,9,10] for geohazard risk management [11,12,13] and regional planning [14,15].

Traditional landslide investigation methods, based on field surveys and geological mapping, can provide accurate local-scale information but are constrained by limited spatial coverage, time delays, and insufficient update frequency when applied to large areas. The rapid development of remote sensing technologies has provided new opportunities for overcoming these limitations in geohazard research [16,17,18,19,20]. Among such techniques, Permanent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) enables high-precision monitoring of subtle surface displacements and is effective for identifying latent slope deformation [21,22,23,24,25,26,27,28]. Meanwhile, multi-source optical remote sensing datasets deliver continuous observations of environmental variables such as topography, vegetation, and land use. However, the reliance on any single data source is prone to noise, information gaps, or scale mismatches, making multi-source fusion an increasingly important strategy for improving landslide susceptibility mapping accuracy [29,30,31,32].

Wavelet Transform (WT), with its ability to perform multiscale decomposition in both spatial and temporal domains, has proven effective in extracting complementary information from heterogeneous datasets. By applying WT to PS-InSAR and optical remote sensing data, multiscale patterns of potential slope deformation and environmental conditioning factors can be effectively captured. Building on this, the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) provides a robust decision-level fusion method capable of integrating diverse remote sensing information, thereby enhancing the spatial precision and stability of landslide susceptibility assessments.

San Martín del Castañar, Spain, is characterized by rugged terrain, complex landforms, and pronounced landslide activity, and spans diverse geomorphological units from mountainous slopes to river valleys. To address the challenges posed by these complex conditions, this study proposes an innovative landslide susceptibility assessment method that integrates persistent scatterer interferometric synthetic aperture radar (PS-InSAR) and multisource remote sensing data via a wavelet transform (WT) and Multi-source Additive Model Based on Bayesian Analysis (MAMBA) fusion strategy. The primary contribution of this study lies in its methodological advancement, namely a robust decision-level fusion framework that combines PS-InSAR deformation measurements with multisource environmental factors through a two-stage enhancement process. This process involves multiscale feature refinement using an explicitly parameterized wavelet transform, followed by probabilistic fusion through MAMBA. Unlike conventional weighted overlays, logistic-regression-based susceptibility models, and InSAR–optical integration approaches that remain at the feature- or pixel-level combination stage, the proposed method explicitly incorporates uncertainty propagation, scale-adaptive decomposition, and dynamic likelihood updating. Consequently, this methodological innovation enables refined, multiscale characterization of slope deformation signals and environmental drivers, thereby achieving highly accurate and reliable susceptibility mapping.

This study introduces and rigorously validates a novel method for landslide susceptibility assessment, synergistically integrating wavelet-enhanced deformation information with multisource environmental factors. The method’s robust effectiveness is empirically confirmed in San Martín del Castañar, a region characterized by complex geology, a monsoon climate, and frequent rainfall-induced landslides, demonstrating significant capability for precise landslide hazard assessment under these specific conditions. While the underlying principles of this integration approach hold strong potential for transferability to other geohazard contexts, this research focuses on its comprehensive evaluation within the defined environmental and geological settings, offering a foundational contribution to remote sensing-based geohazard mitigation.

2. Materials and Methods

2.1. Study Area

San Martín del Castañar is located in the southern part of Salamanca Province within the autonomous community of Castile and León, Spain, situated in the Sierra de Francia, a subrange of the Iberian Mountain System. The study area lies between 6°40′ W and 6°24′ W longitude and 40°31′ N and 40°33′ N latitude (Figure 1), with an average elevation of approximately 834 m, and its administrative territory covers about 15.5 to 16 km².

The landscape is dominated by low to mid-mountain hills characterized by pronounced topographic relief where local slopes frequently exceed 30°, forming a typical mountainous village environment. Such rugged topography exerts a direct influence on surface runoff, soil erosion, and slope stability, constituting a critical predisposing factor for landslide development. Furthermore, the steep and highly variable slopes, heterogeneous lithological conditions, and irregular aspect and curvature patterns define the region as complex mountainous terrain.

The tectonic framework of San Martín del Castañar reflects the superimposed effects of the Variscan and Alpine orogenic cycles, which together produced pervasive deformation features including folds, thrust faults, and major fault zones. These geological structures contribute significantly to the overall geomorphological complexity and provide inherent planes of weakness within the rock mass, further predisposing the area to slope instability.

The study area is characterized by a Mediterranean mountain climate with pronounced seasonal variability. Precipitation exhibits clear temporal heterogeneity, with the majority of annual rainfall concentrated in autumn and winter, while summers are typically dry. Mean annual precipitation generally ranges from approximately 700 to 1100 mm, although localized orographic effects associated with rugged terrain can induce significant spatial variability. Short-duration intense rainfall events occur frequently during transitional seasons, particularly in autumn, and represent an important external triggering factor for slope instability. Temperature conditions are marked by moderate annual averages and distinct seasonal contrasts, which influence soil moisture dynamics and vegetation growth patterns. The combined effects of concentrated rainfall, episodic extreme precipitation, and complex topography create favorable climatic conditions for landslide initiation and reactivation in the region.

Structural complexity is markedly greater in the northern sector, in contrast to the comparatively stable Cratonic domain to the south. The regional stratigraphic succession spans from the Precambrian to the Quaternary and exhibits considerable lithological diversity. It comprises early marine sedimentary sequences (e.g., shale and limestone), medium-grade metamorphic units such as schist and marble, and late clastic deposits. In addition, minor granitic and doleritic intrusions record late-stage magmatic activity (Figure 2). Crucially, tectonic fractures govern both stress release and groundwater migration, exerting a fundamental control on the initiation and evolution of geohazards such as landslides and ground subsidence. The interplay between complex structural patterns and heterogeneous lithologies ultimately shapes the region’s ecological setting and geohazard distribution.

2.2. Data and Preprocessing

In this study, C-band SAR datasets acquired by the Sentinel-1A mission of the European Space Agency (ESA) were employed as the primary data source for the PS-InSAR analysis. A total time series spanning from January 2020 to February 2025 was collected, providing five years of continuous observations and ensuring strong temporal coherence and statistical robustness for ground deformation monitoring. The data have a spatial resolution of 15 m and a repeat cycle of 12 days. A total of 24,102 persistent scatterers were extracted, from which a high-precision deformation field was derived under a deformation-rate threshold of 0.75 mm/year and a height-error constraint of ±0.1 m. The use of ascending orbit geometry further minimizes shadowing effects in complex mountainous terrain, thereby improving the reliability of deformation retrievals (

Table 1. Sentinel-1A satellite image data information.

Parameter	Value/Description
Data Acquisition
Satellite Mission	Sentinel-1A
Band	C-band
Data Type	SLC (Single Look Complex)
Orbit Type	Ascending
Spatial Resolution	15 m
Temporal Coverage	January 2020–February 2025
Revisit Period	12 days
PS-InSAR Processing
Number of PS Points Extracted	24,102
Deformation Rate Threshold	0.75 mm/year
Height Error Constraint	±0.1 m
Amplitude Dispersion Index Threshold	DA < 0.25
Radar Wavelength (λ)	5.6 cm

).

Building upon the limitations observed when using a single-sensor configuration, this study further incorporates L-band (1.2 GHz) SAR observations acquired by the ALOS-2 satellite to improve the robustness of deformation monitoring across complex terrain conditions. The longer wavelength of the L-band enables stronger penetration through vegetation canopies and ensures better coherence preservation in densely forested areas, while maintaining high sensitivity to ground displacement. ALOS-2 operates in a sun-synchronous orbit with a 14-day repeat cycle, providing an effective complement to the primary datasets in regions characterized by extensive vegetation coverage and pronounced topographic relief (

Table 2. ALOS-2 satellite image data information.

Parameter	Value/Description
Data Acquisition
Satellite Mission	ALOS-2
Band	L-band/1.2 GHz
Data Type	SLC (Single Look Complex)
Orbit Type	Sun-synchronous orbit
Spatial Resolution	10–30 m
Temporal Coverage	January 2020–February 2025
Revisit Period	14 days
PS-InSAR Processing
Deformation Rate Threshold	0.75 mm/year
Height Error Constraint	±0.1 m
Amplitude Dispersion Index Threshold	DA < 0.25
Radar Wavelength (λ)	23.6 cm

). Both SAR datasets were subjected to a standardized interferometric processing chain, including precise orbit determination, interferometric co-registration, atmospheric delay mitigation, and phase unwrapping, in order to suppress noise sources and ensure the reliability and accuracy of the subsequent deformation inversion. This integrated multi-sensor strategy effectively enhances monitoring stability and improves deformation-retrieval quality in challenging mountainous environments.

To accurately characterize the external forcing conditions that govern landslide development and evolutionary behavior, this study integrates a suite of multi-source environmental factors. Climate variables were derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis dataset, providing daily cumulative precipitation and extreme rainfall indicators for the period January 2020–February 2025. To maintain consistency with the metric-based spatial resolutions of other datasets, the native 0.1° grid spacing is expressed as approximately 11.1 km. Concurrently, population density data were obtained from the Global Human Settlement Layer (GHSL) database, providing detailed demographic distributions corresponding to the study period. Population data were obtained from the GHSL database at a 10 m spatial resolution and annual update frequency, capturing population density patterns and the distribution characteristics of residential settlements. Land-use information was sourced from the CORINE Land Cover dataset, also at 10 m spatial resolution with annual updates, reflecting urban expansion and agricultural utilization intensity (

Table 3. Multi-source dataset specifications and parameters.

Data Type	Source	Spatial Resolution	Temporal Resolution	Key Parameters
Precipitation	ECMWF ERA5	0.1° (~11.1 km)	Daily (2020–2025)	Cumulative rainfall, extremes
Population Density	GHSL	10 m	Annual (2020–2025)	Inhabitants per km2
Land Use Intensity	CORINE Land Cover	10 m	Annual (2020–2025)	Urban/agricultural expansion

).

All geospatial datasets underwent a rigorous three-step preprocessing workflow to ensure spatial consistency and statistical comparability. Every dataset was reprojected to a common coordinate system (WGS84/UTM Zone 30N). Resampling methods were carefully selected based on variable type and original data resolution. For categorical variables (e.g., land use), nearest-neighbor resampling was employed to preserve class integrity. High-resolution continuous datasets (e.g., those derived from GHSL and CORINE products) were spatially harmonized to a 10 m grid using bilinear interpolation, a standard method suitable for continuous data that ensures smooth transitions while retaining overall trends. Critically, for the coarser-resolution continuous datasets (e.g., ERA5 precipitation and distance to faults), nearest-neighbor resampling was consistently applied to align them with the 10 m analysis grid. This method is mathematically equivalent to a ‘block-constant assignment,’ where each 11 km pixel from the original data acts as a homogeneous spatial container. All constituent 10 m pixels within this resampled container are assigned the identical value of the original coarse pixel. Consequently, the spatial variance (σ²) of the precipitation factor within any original 11 km grid cell on the up-sampled 10 m grid is exactly zero. This stringent approach ensures that no fine-scale spatial variations are artificially generated or interpolated, directly mitigating concerns about artificially distorted precision or the introduction of spurious details during up-sampling. This strategy fulfills the requirement for pixel-level matrix alignment needed by the Multi-source Additive Model for Bayesian Assessment (MAMBA) model while strictly preserving the native physical scale and uncertainty of the coarse input data. The resampling procedure employed for these low-resolution datasets avoids spatial pseudo-replication, nor does it compromise the validity of the statistical analysis. Low-resolution variables, specifically those processed via nearest-neighbor resampling (e.g., ERA5 precipitation), were resampled to the 10 m analysis grid exclusively for spatial alignment and geometric co-registration with other datasets. As described, the resampled values for these variables remain constant within each original coarse grid cell, ensuring no new or artificial fine-scale spatial variability is generated. Consequently, these variables are not interpreted as independent pixel-level observations at the 10 m scale. Rather, they serve as spatially consistent conditioning information within the Bayesian framework, where their inherent original resolution is implicitly considered through the model’s structure and the scales at which relationships are ultimately derived. This rigorous methodological approach guarantees that statistical inferences are grounded in the actual information content of the source data, thereby avoiding any overestimation of spatial resolution or statistical independence.

Finally, Z-score standardization (μ = 0, σ = 1) was applied to all continuous variables. This step mitigated the influence of differing units and magnitudes, significantly enhancing their comparability within the Multi-source Additive Model for Bayesian Assessment (MAMBA) probabilistic framework. This comprehensive workflow ultimately produced a geometrically co-registered and statistically standardized multisource database, integrating surface deformation, climatic drivers, and anthropogenic factors, which formed a consistent input basis for subsequent wavelet analysis and decision-level fusion.

During the data fusion stage, Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) were employed to achieve multi-scale feature extraction and decision-level integration. WT decomposes the original signal into approximation and detail components at different scales, effectively suppressing high-frequency noise while preserving low-frequency trends [33,34,35,36]. This enables the enhancement of deformation anomalies and spatial heterogeneity in environmental factors within potential landslide-prone areas (Equation (1)). Operating within a Bayesian framework, MAMBA uses PS-InSAR deformation results as prior information and incorporates multi-source environmental factors—including climate, land use, and population—as likelihood conditions. Through iterative updates of conditional probabilities, MAMBA generates the posterior probability distribution of landslide susceptibility (Equation (2)). This fusion strategy reduces the uncertainty associated with any single data source, while strengthening the complementarity of heterogeneous information and improving the robustness and stability of the final outputs. The resulting posterior distribution was subsequently converted into raster format to produce a high-resolution spatial pattern of landslide susceptibility for the San Martín del Castañar region. This provides a reliable data basis for identifying potential high-risk zones and supporting regional disaster-prevention and mitigation planning.

$${\mathrm{W}}_{\mathrm{f}}\left(\mathrm{a},\mathrm{b}\right)={\displaystyle \frac{1}{\sqrt{\left|\mathrm{a}\right|}}}{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\mathrm{f}\left(\mathrm{t}\right)\mathsf{\psi }\left({\displaystyle \frac{\mathrm{t}-\mathrm{b}}{\mathrm{a}}}\right)\mathrm{d}\mathrm{t}$$

(1)

where f(t) denotes the original signal, $\mathsf{\psi }$ is the mother wavelet, a is the scale parameter, and b is the translation parameter.

$$\mathrm{P}\left(\mathrm{H}|\mathrm{E}\right)={\displaystyle \frac{\mathrm{P}\left(\mathrm{E}|\mathrm{H}\right)·\mathrm{P}\left(\mathrm{H}\right)}{\mathrm{P}\left(\mathrm{E}\right)}}$$

(2)

where H represents the hypothesis of landslide occurrence and E denotes the observed environmental data. P(H) is the prior probability derived from deformation signals, $\mathrm{P}\left(\mathrm{E}|\mathrm{H}\right)$ is the likelihood function reflecting the forcing effects of climate, land use, and population, and $\mathrm{P}\left(\mathrm{H}|\mathrm{E}\right)$ is the posterior probability.

2.3. Methodology

A landslide susceptibility assessment method is presented, integrating Perma-Permanent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) and multi-source optical remote sensing data. This integration employs a probabilistic decision-level fusion strategy within a Bayesian inference framework (Figure 3). The core of this fusion lies in defining ‘decision’ as the final, integrated posterior probabilistic judgment of landslide occurrence (P(H|E)), encompassing distinct probabilistic assessments derived from each individual data source. Unlike feature-level fusion, which concatenates heterogeneous variables prior to modeling, this framework performs fusion at the decision stage by integrating independent probabilistic contributions through Bayesian updating.

All variables are incorporated as continuous spatial fields across the study area. No random point-wise sampling strategy is applied during model construction or inference, and no assumption of pixel-level sample independence is introduced. Consequently, the Bayesian updating process is conducted at the spatial decision level, rather than through sample-based statistical learning. This approach ensures that deformation-derived priors and environmental likelihoods remain conceptually and mathematically separable, representing a fundamental departure from approaches that directly concatenate or weight raw feature vectors.

Specifically, PS-InSAR deformation time-series and deformation-rate maps undergo initial enhancement via multiscale wavelet decomposition. The resulting deformation features are then rigorously processed and transformed into a spatially explicit prior probability distribution of landslide occurrence (P(H)) through a carefully designed mapping function. This mapping function was developed to capture the spatially coherent deformation patterns indicative of persistent slope instability, informed by the physical constraints of wavelet filtering.

This prior probability, derived from PS-InSAR, represents deformation evidence physically constrained through multiscale wavelet filtering, rather than raw surface deformation. It reflects long-term, spatially coherent deformation patterns indicative of persistent slope instability, effectively suppressing short-term, high-frequency signals potentially associated with soil moisture-induced swelling or other non-landslide processes prior to Bayesian inference. This prior probability distribution effectively distills complex deformation patterns into an initial probabilistic judgment regarding landslide potential, representing a ‘decision’ derived exclusively from the PS-InSAR data’s interpretation of deformation likelihood, formed prior to the introduction of other environmental factors.

Concurrently, multi-source optical remote sensing data, encompassing various environmental variables, are utilized to construct the likelihood function P(E|H). This function quantifies the probability of observing specific environmental conditions given the presence or absence of a landslide. Each environmental variable contributes to the formulation of these probabilistic statements, acting as observational evidence or ‘decisions’ pertaining to the observed environment’s relationship with landslides.

The essence of the probabilistic decision-level fusion involves the systematic integration of these distinct probabilistic judgments. The prior probabilistic decision, derived from PS-InSAR (P(H)), is updated and refined by the likelihood evidence from the environmental variables (P(E|H)) via Bayes’ theorem to yield the ultimate, integrated posterior probability of landslide occurrence (P(H|E)). This posterior probability constitutes the final, comprehensive ‘decision’ on landslide susceptibility, reflecting the combined probabilistic assessments from both data sources.

This strategy provides a consistent and physically meaningful pathway for integrating comprehensive deformation information into susceptibility assessment, thereby enhancing interpretability and predictive performance. By overcoming the inherent limitations of single-source datasets, it substantially improves both the accuracy and spatial reliability of landslide susceptibility modeling [37,38,39,40,41,42,43]. Quantitative validation, conducted against an inventory of 1247 historical landslides (January 2020–February 2025), substantiates robust predictive performance, achieving an AUC-ROC of 0.912, an Overall Accuracy of 87.3%, and a Recall of 84.5%. The MAMBA framework significantly outperforms conventional baselines, including Random Forest (+6.8%, p < 0.001), Logistic Regression (+10.8%, p < 0.001), and Frequency Ratio (+14.3%, p < 0.001), with performance improvements statistically confirmed via DeLong’s and McNemar’s tests. Spatial stratification analysis further reveals that the two highest susceptibility classes, comprising only 24% of the total area, successfully capture 84.5% of validated landslides, exhibiting a systematic 174-fold exponential gradient in landslide density (R² = 0.94). Attributed to the integration of wavelet-based multiscale decomposition with Bayesian probabilistic fusion, this method demonstrates strong potential for methodological transferability across different geomorphic and climatic settings when the dominant deformation processes are explicitly considered. Consequently, it provides a scalable and scientifically validated technical pathway for geo-hazard risk assessment and disaster prevention planning under rainfall-driven and slow-moving slope deformation regimes.

2.4. Modeling of Permanent Scatterer Deformation Signals

The complex mountainous terrain intensifies terrain-induced distortions such as radar shadowing and layover, which are determined exclusively by the geometric relationship between the local terrain slope and the radar line of sight, rather than solely by the use of ascending or descending satellite tracks. Consequently, this environment causes strong spatial variability in coherence and PS density. Therefore, the reliability of PS-InSAR deformation retrieval in this region is governed primarily by scatterer stability, temporal coherence, and robust atmospheric and orbital corrections, rather than solely by orbit direction or the minimization of shadowing.

In this study, the Permanent Scatterer InSAR (PS-InSAR) technique was applied to combined Sentinel-1 and ALOS-2 SAR datasets to derive surface deformation velocity fields and time-series displacement signals, enabling the identification of the spatiotemporal evolution of potential landslides. Sentinel-1A C-band datasets served as the primary data source, covering the period from January 2020 to February 2025 (15 m resolution, 12-day repeat cycle) to ensure strong temporal coherence. To enhance monitoring robustness in densely forested and mountainous regions, L-band ALOS-2 observations were incorporated as supplementary data due to their superior canopy penetration capabilities. The spatiotemporal configuration of these datasets is illustrated in Figure 4. The Baseline Plot (Figure 4a) demonstrates an optimal perpendicular baseline distribution constrained within ±150 m, while the Connection Graph (Figure 4b) highlights the dense temporal connectivity that ensures high interferometric coherence. Following standardized orbital refinement, image co-registration, and atmospheric phase delay correction, high-coherence permanent scatterers were selected using the Amplitude Dispersion Index (Equation (3)). Annual deformation rates and cumulative displacements were subsequently retrieved via a least-squares inversion approach (Equation (4)). Ultimately, a total of 24,102 persistent scatterers were extracted, yielding a high-precision deformation field constrained by a deformation-rate threshold of 0.75 mm/year and a height-error of ±0.1 m.

$${\mathrm{D}}_{\mathrm{A}}={\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{A}}}{{\mathsf{\mu }}_{\mathrm{A}}}}$$

(3)

$$\mathrm{\varnothing }={\displaystyle \frac{4\mathsf{\pi }}{\mathsf{\lambda }}}\left(\mathrm{v}·\mathrm{t}+∆\mathrm{h}·{\displaystyle \frac{{\mathrm{B}}_{\perp }}{\mathrm{R} \sin \mathsf{\theta }}}\right)+{\mathrm{\varnothing }}_{\mathrm{a}\mathrm{t}\mathrm{m}}+{\mathrm{\varnothing }}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}}$$

(4)

where σA represents the standard deviation of pixel amplitude, and μA is the mean amplitude. A pixel is identified as a permanent scatterer candidate when DA < 0.25. λ denotes the radar wavelength (5.6 cm for Sentinel-1 and 23.6 cm for ALOS-2), and t is the temporal baseline. Δh denotes the elevation error, B⊥ is the perpendicular baseline, R is the slant range, and θ is the incidence angle. ${\mathrm{\varnothing }}_{\mathrm{a}\mathrm{t}\mathrm{m}}$ and ${\mathrm{\varnothing }}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}}$ refer to the atmospheric phase delay and noise components, respectively, while v denotes the deformation rate.

The baseline configuration of the PS-InSAR processing, as depicted in Figure 5, significantly influences the quality of deformation measurements crucial for identifying spatiotemporal landslide evolution. Dense temporal connectivity (248 interferometric pairs over 5 years) facilitates continuous tracking of progressive slope deformation. Concurrently, moderate perpendicular baselines (±150 m) ensure high coherence (γ > 0.85), which is essential for reliable phase unwrapping in steep terrain.

To evaluate the PS-InSAR technique’s capability in capturing diverse deformation behaviors under heterogeneous terrain conditions, four representative persistent scatterer points (A–D) were selected from the Sentinel-1A dataset for time-series displacement analysis. These points were rigorously chosen for their spatial representativeness across distinct geomorphic units, ranging from stable ridge crests to sediment accumulation zones, and adherence to stringent signal quality constraints (amplitude dispersion DA < 0.15 and temporal coherence γ > 0.85). This selection strategy ensures the statistical robustness of the deformation inversion and subsequent analysis.

Time-series analysis reveals markedly different displacement characteristics among the selected scatterers (Figure 5). Point A, located on a relatively stable ridge crest, functions as a reference, exhibiting only minor fluctuations confined to approximately ±10 mm. In contrast, Point B, situated on a structurally controlled steep slope, displays a continuous subsidence trend with cumulative displacement exceeding −40 mm, indicative of active landslide movement or pronounced ground settlement. A more complex signal is observed at Point C in a valley sediment zone, which shows a gradual positive LOS displacement exceeding +20 mm. This LOS displacement, consistent with uplift in Sentinel-1A ascending geometry (azimuth −13°, incidence angle 39°), is interpreted not as deep-seated landslide activity. Instead, the absence of geomorphic landslide features and the point’s proximity to seasonally waterlogged farmland suggest the signal reflects the swelling of clay-rich soil in the near-surface layer (0–2 m depth) driven by moisture infiltration, distinguishing it from deep-seated landslide processes. Consequently, such deformation signals are treated as observational phenomena rather than direct indicators of landslide activity, and their contribution to susceptibility estimation is subsequently constrained through multiscale signal processing and Bayesian updating within the MAMBA framework. Finally, Point D illustrates a transient response in a sector modified by human activity; it remains stable during the initial phase but subsequently experiences rapid subsidence approaching −15 mm. This subsidence is likely triggered by external forcing such as intense rainfall or anthropogenic disturbances. These contrasting behaviors demonstrate the method’s effectiveness in resolving subtle surface differences and characterizing both stable and transient slope responses. This provides observational validation for subsequent multiscale feature extraction within the Multi-source Additive Model for Bayesian Assessment (MAMBA).

Meanwhile, a landslide conditioning factor dataset was constructed by integrating multisource optical remote sensing products. Climatic variables were extracted from Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Measurement (GPM) mission precipitation datasets, along with MODIS land surface temperature products. Topographic parameters, including slope gradient, aspect, and relative relief, were derived from the Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM) at 30 m spatial resolution, while vegetation coverage was quantified using the Normalized Difference Vegetation Index (NDVI) calculated from Landsat-8 OLI imagery (Equation (5)). To eliminate scale discrepancies and dimensional effects among different variables, all input factors were standardized using the Z-score method (Equation (6)).

$$\mathrm{N}\mathrm{D}\mathrm{V}\mathrm{I}={\displaystyle \frac{\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{R}\mathrm{e}\mathrm{d}}{\mathrm{N}\mathrm{I}\mathrm{R}+\mathrm{R}\mathrm{e}\mathrm{d}}}$$

(5)

$${\mathrm{X}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}={\displaystyle \frac{\mathrm{X}-\mathsf{\mu }}{\mathsf{\sigma }}}$$

(6)

where NIR and Red represent the near-infrared and red band reflectance, respectively. Land-use categories were obtained from the GlobeLand30 dataset. The selection of these factors comprehensively reflects the physical mechanisms governing landslide initiation and evolution under environmental and triggering influences. X is the raw variable, μ is the sample mean, σ is the sample standard deviation, and X_norm denotes the standardized value. This normalization process constrains all variables to a mean of zero and a standard deviation of one, ensuring their comparability and stability in subsequent modeling.

In landslide susceptibility assessment, environmental conditioning factors serve as the dominant drivers that characterize the formation and evolutionary mechanisms of geological hazards. To fully capture the geomorphological, vegetation, hydrological, and anthropogenic characteristics of the study area, multiple heterogeneous variables must be integrated. However, their dimensional differences, numerical ranges, and statistical distributions may cause weight imbalance and cumulative bias if directly incorporated into the model. Therefore, all conditioning factors were standardized using Z-score normalization prior to data fusion, ensuring statistical comparability within the Bayesian inference framework. Factor weight estimation was subsequently performed using the information entropy method, which quantifies the effective information content of each variable and avoids subjectivity in artificial weighting (Equations (7) and (8)). Let pij denote the normalized value of the j-th factor for the i-th sample.

$${\mathrm{H}}_{\mathrm{j}}=-\mathrm{k}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{p}}_{\mathrm{i}\mathrm{j}}\ln \left({\mathrm{p}}_{\mathrm{i}\mathrm{j}}\right),\mathrm{k}={\displaystyle \frac{1}{\ln \mathrm{n}}}$$

(7)

$${\mathrm{w}}_{\mathrm{j}}={\displaystyle \frac{1-{\mathrm{H}}_{\mathrm{j}}}{{\sum }_{\mathrm{j}=1}^{\mathrm{m}}\left(1-{\mathrm{H}}_{\mathrm{j}}\right)}}$$

(8)

To improve methodological transparency and facilitate reproducibility, the entropy-based weighting results for all conditioning factors are explicitly summarized in

Table 4. Entropy-based weighting categories of landslide conditioning factors.

Conditioning Factor	Entropy Information Level	Normalized Weight Range (wⱼ)	Assigned Weight Category	Rationale
Land use/Land cover	Very high	0.25–0.30	Dominant	High spatial heterogeneity and strong information contribution
Precipitation (Rainfall)	High	0.18–0.22	High	Pronounced variability and sensitivity to landslide occurrence
Slope	Moderate	0.12–0.15	Moderate	Clear terrain control with moderate entropy reduction
Aspect	Moderate	0.10–0.14	Moderate	Directional variability with dispersed information contribution
Fractional Vegetation Cover (FVC)	Moderate–Low	0.08–0.10	Moderate–Low	Indirect regulation effect with limited entropy contrast
Distance to roads	Low	0.06–0.08	Low	Localized anthropogenic influence
Distance to rivers	Low	0.05–0.06	Low	Weak hydrological control at regional scale
Curvature	Very low	0.02–0.03	Very Low	Minimal information gain
Elevation	Very low	0.01–0.02	Very Low	Nearly uniform contribution

. Instead of reporting pixel-level calculations, factors are grouped according to their relative information contribution, and corresponding normalized weight ranges are provided. These entropy-derived weights were subsequently used to scale the contribution of individual conditioning factors during likelihood construction in the MAMBA decision-level fusion framework.

2.5. Wavelet Transform and MAMBA Decision-Level Fusion Method

2.5.1. Multi-Scale Feature Construction Using Wavelet Transform

The methodological design of this study is predicated on recognizing the inherent complexity and nonlinearity of landslide processes, where surface deformation is not deterministically or strongly linearly governed by individual conditioning factors. Instead, landslide initiation and evolution result from the synergistic interaction of multiple environmental factors, each potentially contributing weakly in isolation, but whose cumulative and nonlinear interactions form the critical mechanisms driving deformation. Therefore, the proposed Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT–MAMBA) method aims to transcend the limitations of conventional single-factor linear correlation analysis by probabilistically integrating weak but complementary evidence to construct a predictive model capable of capturing the intrinsic complexity of geohazards. Environmental variables are treated as conditional evidence within the method, probabilistically updating prior information derived from deformation data, rather than as independent linear predictors. This approach avoids excessive reliance on single-factor explanatory power, leveraging cumulative informational gain through decision-level Bayesian fusion.

To quantitatively assess the influence of environmental conditioning factors on landslide development, surface deformation rates were first obtained using the PS-InSAR technique, and six key environmental variables were extracted from multi-source optical remote sensing data. The PS-InSAR deformation rates used in subsequent analyses were derived from the integrated processing of both Sentinel-1A and ALOS-2 datasets. Specifically, C-band Sentinel-1 observations provided high-temporal-resolution monitoring (12-day repeat cycle), while L-band ALOS-2 data enhanced coherence preservation in vegetated terrain through its superior canopy penetration capability. The combined dataset yielded 24,102 validated persistent scatterers, ensuring robust spatial representation of surface deformation across the study area.

Given the adaptive time–frequency decomposition capability of the Wavelet Transform (WT) for noise suppression and geoscientific information preservation, a Discrete Wavelet Transform (DWT) was applied to reconstruct PS-InSAR deformation fields and conditioning factors. The number of decomposition levels was empirically selected to balance effective suppression of high-frequency stochastic noise (e.g., atmospheric disturbances and residual decorrelation) and preservation of low-amplitude, physically meaningful deformation signals. A two-level decomposition was insufficient to fully attenuate high-frequency noise, whereas a four-level decomposition resulted in excessive smoothing that weakened localized deformation features relevant to landslide susceptibility assessment. Accordingly, a three-level decomposition was adopted as a balanced and physically interpretable choice. For reproducible multiscale decomposition, the Daubechies (db4) orthogonal wavelet family was employed due to its compact support and favorable time–frequency localization properties, which are well suited for capturing the geometric characteristics of deformation signals. Noise suppression was further implemented using adaptive soft-thresholding based on the universal threshold $\mathsf{\lambda }=\mathsf{\sigma }\sqrt{2\ln \mathrm{n}}$ denotes the median absolute deviation of the detail coefficients, followed by standard Inverse DWT (IDWT) reconstruction. This configuration stabilizes the multiscale representation and reduces stochastic noise without compromising physically meaningful deformation patterns.

2.5.2. Sensitivity Analysis of Wavelet Parameters

To examine the stability of the wavelet-based enhancement, the influence of wavelet family and decomposition depth on signal-to-noise ratio (SNR) improvement and landslide susceptibility patterns was evaluated. The analysis was performed using identical PS-InSAR displacement time series and consistent denoising and reconstruction procedures to avoid confounding effects from preprocessing differences.

Wavelet transforms based on different commonly adopted orthogonal families, including Daubechies, Symlets, and Coiflets, produced comparable levels of SNR enhancement. Variations in SNR gain among wavelet families were minor and did not lead to observable changes in the spatial distribution of high-susceptibility zones. This indicates that the effectiveness of the enhancement is governed primarily by multiscale decomposition rather than by the specific choice of wavelet basis.

The effect of decomposition depth was further examined by comparing two-, three-, and four-level discrete wavelet decompositions. Shallow decomposition resulted in incomplete suppression of high-frequency noise, whereas deeper decomposition caused excessive smoothing and attenuation of localized deformation features. A three-level decomposition preserved spatially coherent deformation signals while maximizing overall SNR improvement, yielding the most consistent susceptibility outcomes.

These results indicate that the wavelet-enhanced deformation signals and the resulting susceptibility patterns are insensitive to reasonable variations in wavelet parameters. The selected configuration, employing a Daubechies db4 wavelet with three decomposition levels, provides a stable balance between noise reduction and preservation of physically meaningful deformation information.

The efficacy of this enhancement strategy is quantitatively substantiated by an analysis of 24,102 validated PS points. Specifically, the method yields a 23.5% increase in Signal-to-Noise Ratio (SNR), derived from the mean paired difference between pre- and post-denoising values (paired t-test, p < 0.01), and an 18.7% improvement in anomaly detection, calculated from the increased proportion of PS points exceeding the anomaly threshold relative to raw signals. These metrics provide a robust, reproducible basis for the improved susceptibility characterization reported in this study.

To ensure the transparency and reproducibility of the reported improvements, Signal-to-Noise Ratio (SNR) and anomaly-detection gains were quantified using a consistent wavelet-based framework. For each PS displacement time series x(t), a three-level Discrete Wavelet Transform (DWT) was applied, yielding a low-frequency approximation component A_L and high-frequency detail components D₁,…,D_L.

For the raw signal, the signal component s_raw(t) was reconstructed from the approximation coefficients A_L using the Inverse Discrete Wavelet Transform (IDWT). The corresponding noise component was defined as Equation (9).

$${\mathrm{n}}_{\mathrm{r}\mathrm{a}\mathrm{w}}\left(\mathrm{t}\right)=\mathrm{x}\left(\mathrm{t}\right)-{\mathrm{S}}_{\mathrm{r}\mathrm{a}\mathrm{w}}\left(\mathrm{t}\right)$$

(9)

For the wavelet-enhanced signal, adaptive soft-thresholding was applied to the detail coefficients D₁,…,D_L to obtain the denoised coefficients D₁′,…,D_L′. The enhanced signal s_WT(t) was then reconstructed from A_L and D₁′,…,D_L′ using IDWT, and the corresponding noise component was defined as Equation (10).

$${\mathrm{n}}_{\mathrm{W}\mathrm{T}}\left(\mathrm{t}\right)=\mathrm{x}\left(\mathrm{t}\right)-{\mathrm{S}}_{\mathrm{W}\mathrm{T}}\left(\mathrm{t}\right)$$

(10)

The Signal-to-Noise Ratio (SNR) was computed for both the raw and wavelet-enhanced signals as Equation (11).

$$\mathrm{S}\mathrm{N}\mathrm{R}={\displaystyle \frac{\mathrm{V}\mathrm{a}\mathrm{r}\left[\mathrm{s}\left(\mathrm{t}\right)\right]}{\mathrm{V}\mathrm{a}\mathrm{r}\left[\mathrm{n}\left(\mathrm{t}\right)\right]}}$$

(11)

where s(t) and n(t) denote the signal and noise components, respectively.

The percentage gain in SNR due to wavelet enhancement was quantified as Equation (12).

$${∆}_{\mathrm{S}\mathrm{N}\mathrm{R}}\left(\mathrm{\%}\right)={\displaystyle \frac{{\mathrm{S}\mathrm{N}\mathrm{R}}_{\mathrm{W}\mathrm{T}}-{\mathrm{S}\mathrm{N}\mathrm{R}}_{\mathrm{r}\mathrm{a}\mathrm{w}}}{{\mathrm{S}\mathrm{N}\mathrm{R}}_{\mathrm{r}\mathrm{a}\mathrm{w}}}}\times 100\mathrm{\%}$$

(12)

where SNR_raw is derived from the original (non-wavelet-processed) LOS displacement time series using the same signal/noise partitioning (signal estimated by a low-pass filter with the same effective cutoff as the wavelet approximation).

$${∆}_{\mathrm{A}\mathrm{n}\mathrm{o}\mathrm{m}}\left(\mathrm{\%}\right)={\displaystyle \frac{{\mathrm{N}}_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{m},\mathrm{W}\mathrm{T}}-{\mathrm{N}}_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{m},\mathrm{r}\mathrm{a}\mathrm{w}}}{{\mathrm{N}}_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{m},\mathrm{r}\mathrm{a}\mathrm{w}}}}\times 100\mathrm{\%}$$

(13)

Anomalies are defined as PS observations whose instantaneous displacement magnitude exceeds the sample mean plus two sample standard deviations (mean + 2σ) within the considered time window (Equation (13)). The anomaly-detection improvement is measured as the percentage increase in the number of detected anomalies after wavelet enhancement relative to the raw signal. To ensure robustness, SNR and anomaly statistics were aggregated across all validated PS points (N = 24,102) and reported as mean ± standard deviation; statistical significance of SNR differences between raw and WT-enhanced signals was assessed using a paired t-test (α = 0.05). All computations utilized the same pre-processing and temporal window to avoid spurious differences caused by inconsistent sampling.

To examine the statistical strength of associations between environmental factors and surface deformation, linear regression analyses were conducted between the six variables and the PS-InSAR deformation rates. The results show that elevation exhibits a very weak negative correlation with deformation (R² = 0.0001), and the scattered distribution forms a dense cross-shaped pattern, suggesting that elevation has no significant direct control on surface displacement (Figure 6a). The aspect factor yields an equally low coefficient of determination (R² = 0.0016), indicating negligible differences in deformation between sun-facing and shaded slopes, and implying that surface instability in the region is predominantly driven by endogenous geological processes (Figure 6b). Slope also shows a very weak negative correlation with deformation (R² = 0.0002), confirming that slope gradient is not the sole controlling factor of surface movement (Figure 6c). Likewise, surface curvature yields an R² of only 0.0003, and both concave and convex slopes contain stable and anomalous deformation zones, indicating that curvature influences slope stability indirectly through hydrological pathways, yet exhibits extremely weak linear correlation at the regional scale (Figure 6d).

The deformation rate exhibits a weak negative correlation with river-network proximity (R² = 0.0011), reflecting the localized effects of fluvial incision and bank-slope unloading (Figure 7a). The rainfall factor also shows a low explanatory power, with a coefficient of determination of only 0.0045 (Figure 7b). Vegetation coverage is weakly and negatively correlated with deformation rate (R² = 0.0049), indicating that vegetation enhances slope stability through the combined effects of root reinforcement, rainfall interception, and regulation of soil moisture (Figure 7c).

As a categorical variable, land-use type yields a determination coefficient of 0.0026, while deformation rates within each land-cover class display substantial dispersion, particularly in areas subjected to intensive engineering activities or located near documented hazard sites (Figure 8a). Road-network proximity also shows a weak negative correlation with deformation rate (R² = 0.0021), and scatter dispersion increases markedly at short distances from roads, highlighting the dual impacts of excavation, embankment construction, and altered drainage on slope stability (Figure 8b).

2.5.3. Decision-Level Fusion Using MAMBA

After factor extraction and wavelet decomposition, the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) was applied to achieve decision-level fusion of multisource information, enabling the characterization of potential landslide activity patterns. Six environmental factors were incorporated as observational conditions to represent the combined geomorphic, climatic, and anthropogenic controls on landslide development and evolution. During the fusion process, MAMBA updates conditional probabilities to refine susceptibility estimates. When multiple factors simultaneously indicate elevated hazard at a given location, such as steep slopes, intense rainfall, low vegetation coverage, or intensive land use, the model increases the landslide probability for that area. Conversely, in regions with gentle terrain, dense vegetation, or limited disturbance, the susceptibility level is reduced. This approach integrates heterogeneous information, reduces uncertainty from single-source data, and highlights the complementarity among influencing factors.

Within the Bayesian framework, the prior probability P(H) was derived from wavelet-enhanced PS-InSAR deformation patterns, which serve as physically constrained indicators of long-term slope instability, distinct from raw deformation measurements. For each conditioning factor, likelihood functions were constructed at their effective spatial support. After Z-score normalization and entropy-based weight adjustment, these functions were mapped to the analysis grid for decision-level Bayesian updating, without assuming pixel-level independence. A variational Bayesian optimization scheme, integral to the MAMBA framework, iteratively updated posterior probabilities until convergence. Non-informative priors were assigned to hyperparameters to mitigate subjective influence. Convergence was assessed based on the stabilization of the evidence lower bound (ELBO) and the monotonic reduction in posterior variance. The resulting posterior distribution represents the fused susceptibility probability, integrating both deformation signals and environmental drivers.

The model operates on continuous spatial fields for all variables, and Bayesian inference is performed at the spatial decision level. Random point-wise sampling is not used at any stage of model construction or validation. As a result, spatially structured randomization schemes, such as block-based or unit-based sampling, are not required. This methodological design preserves the spatial structure of the data and avoids the spatial bias and independence assumptions associated with point sampling, ensuring the robustness and reliability of susceptibility assessment in spatial datasets. The entropy-derived weights reported in Table 4 were applied to adjust the relative contribution of each conditioning factor when constructing the likelihood function in the MAMBA framework.

2.5.4. Spatial Representation of Fusion Results

The landslide susceptibility outcomes derived from the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) fusion were further converted into high-resolution raster data, enabling a refined spatial depiction of hazard distribution across the study area. This spatialization process integrates the effects of terrain, climate, vegetation, and land use, while dynamically expressing the probability of landslide occurrence at multiple locations. Compared with traditional weighted-overlay approaches, the proposed method delineates stable and high-risk zones with greater clarity, avoiding bias associated with single-factor dependence or subjective weight assignment. The high spatial resolution and robustness of the results allow for a more reliable classification of susceptibility levels. The spatial pattern of landslide susceptibility reflects not only the intrinsic instability of the geological environment but also the ecological vulnerability of the region. High-susceptibility zones are primarily concentrated in steep-slope areas with sparse vegetation or intensive human disturbance—locations that also exhibit low ecological carrying capacity and weak environmental resilience. Therefore, the susceptibility map provides direct support for subsequent ecological-vulnerability assessments and offers a scientific basis for integrating geological hazard prevention with ecological protection in regional planning.

2.5.5. Adaptation of the WT–MAMBA Framework to Different Deformation Regimes

The Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT–MAMBA) framework was developed and validated in a mountainous environment where landslide activity is primarily controlled by rainfall-induced pore-pressure increase and progressive slope deformation. In such settings, PS-InSAR-derived deformation time series provide physically meaningful priors for long-term slope instability.

When the framework is applied to regions dominated by other deformation mechanisms, targeted adaptations are required. In earthquake-prone areas, co-seismic and post-seismic deformation is typically characterized by abrupt, high-amplitude and spatially coherent displacement. In this case, the PS-InSAR prior should be constructed from segmented deformation time series that separate co-seismic steps from post-seismic relaxation, and the wavelet decomposition should be tuned to preserve high-energy transient signals rather than suppressing them as noise. The likelihood functions should further incorporate seismic intensity, fault proximity, and ground-motion parameters as dominant conditioning factors.

In permafrost or seasonally frozen terrain, deformation is mainly governed by freeze–thaw cycles and thermokarst processes, which produce strong seasonal signals and vertical heave or subsidence. Under such conditions, the wavelet-based preprocessing should explicitly retain seasonal components, and temperature-related variables, thawing indices, and active-layer thickness should be introduced into the likelihood model. The PS-InSAR prior should be interpreted as a proxy for ground-ice degradation or frost heave rather than gravitational slope failure. These adaptations do not alter the core Bayesian decision-level fusion logic of MAMBA. Instead, they modify the physical meaning and statistical structure of the prior and likelihood terms, allowing the same mathematical framework to remain valid while being physically consistent with different deformation regimes. A physically constrained and statistically consistent decision-level fusion methodology for landslide susceptibility assessment is presented. This approach leverages wavelet-based multiscale decomposition, enhancing PS-InSAR deformation signals by suppressing high-frequency noise and preserving spatially coherent patterns indicative of long-term slope instability. Enhanced signals are subsequently transformed into probabilistic prior information, iteratively updated within the MAMBA Bayesian framework using multisource environmental likelihoods. Diverging from methods reliant on strong linear correlations, it integrates weak yet complementary evidence via probabilistic updating at the spatial decision level. Its design ensures robustness against data sparsity, scale mismatch, and single-factor dominance, concurrently maintaining physical interpretability. This methodology thus establishes the foundation for subsequent susceptibility mapping and result interpretation.

3. Results

By integrating PS-InSAR measurements with multisource optical imagery and applying a wavelet-based multiscale decomposition, we resolve the patterns of surface deformation and morphological adjustment in the San Martín del Castañar region with enhanced clarity. The wavelet transform reduces stochastic noise in the PS-InSAR time series and selectively strengthens coherent deformation signals at different scales. As a result, the spatial imprint of potential slope failures becomes more distinct, allowing high-susceptibility sectors to emerge from the background variability.

3.1. Multiscale Distribution of Surface Deformation Rates

The deformation-rate map derived from the wavelet-enhanced dataset (Figure 9) reveals a landscape with pronounced spatial heterogeneity. High-magnitude deformation zones, marked in red, are concentrated along structurally intricate slopes where gravitational forcing interacts with weak stabilizing conditions. These hotspots are consistently associated with steep gradients, sparse vegetation cover and geomorphic settings prone to failure. Such areas exhibit reduced slope resistance and a markedly elevated likelihood of landslide initiation. Rather than isolated anomalies, these deformation clusters form an internally coherent spatial pattern that reflects an evolving slope-instability regime driven by both intrinsic geomorphic processes and external environmental forcing.

Following the multiscale decomposition of the deformation field using a wavelet transform, we resolved the spatial organization of morphological variables across the study area (Figure 10). The decomposition isolates scale-dependent signals from background variability and reveals deformation patterns that are governed by localized geomorphic controls rather than stochastic noise. High-value morphological clusters align closely with known landslide-prone sectors, indicating that slope instability is not randomly distributed but emerges from discrete structural kernels that frame the active boundaries of evolving landslide bodies. The simultaneous enhancement of both regional trends and localized anomalies confirms that the wavelet approach strengthens deformation information in complex terrain and improves the detection of unstable slope units that operate at different spatial scales.

Building on the preceding results, we examined six key deformation stages from 12 January 2020 to 6 February 2025 to resolve the spatiotemporal evolution and migration of instability across the study area (Figure 11). In the ascending orbit Line-of-Sight (LOS) geometry employed, positive values (shown in red) represent motion toward the satellite, which may result from vertical uplift, westward horizontal displacement, or surficial volumetric expansion. Negative values (shown in blue) indicate motion away from the satellite, typically corresponding to subsidence, eastward movement, or downslope displacement along the LOS direction. Broad zones in yellow and light yellow represent stable terrain with negligible surface motion. The deformation field exhibits pronounced spatial variability through time, and the sectors with the highest negative LOS displacement rates are consistently located on steep slopes with sparse vegetation and complex structural conditions, indicating active subsidence or gravitational deformation. These patterns indicate a persistent concentration of landslide susceptibility in geomorphically sensitive terrain.

In 2020, most of the study area remained in a relatively stable state. The spatial configuration of morphological variables in 2021 remained broadly consistent with early 2020, and large-scale change was limited. However, the anomalous sector in the southwest continued to evolve and exhibited a slight expansion of high positive values. Beginning in 2022, the deformation regime entered an active phase, followed by a rapid reorganization of the instability pattern in 2023, when the spatial distribution of morphological anomalies changed markedly. In 2024, the deformation field reached a quasi-stable configuration while maintaining an elevated intensity relative to earlier years. By 2025, the southwest anomaly showed internal differentiation, the active zone in the east continued to expand and a pronounced banded anomaly developed in the north. For the first time, negative instability signatures emerged, indicating surface subsidence associated with the development of topographic depressions or erosional gullies.

3.2. Landslide Susceptibility Assessment Based on the MAMBA Model

Using the multiscale features extracted from wavelet analysis, the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) model was applied to integrate PS-InSAR deformation signals with multisource environmental factors at the decision-fusion level. This approach produced a spatially explicit map of landslide susceptibility across the study area (Figure 12). Based on susceptibility gradients, the terrain was classified into five categories: very high susceptibility (8.3%), high susceptibility (15.7%), moderate susceptibility (28.4%), low susceptibility (32.1%) and very low susceptibility (15.5%).

The very high susceptibility zones are concentrated in the steep mountainous sectors of the northern and southeastern regions. These areas exhibit strong coupling among topographic, structural, and environmental drivers and are frequently located near major fault systems, indicating a persistent geomorphic predisposition to failure. High susceptibility zones manifest as belts encircling the most unstable cores. While PS-InSAR deformation rates within these belts (typically 5–15 mm/year) are measurably lower than those in the core zones (>20 mm/year), they remain significantly above the stability threshold of 0.75 mm/year. These areas are characterized by rugged terrain and sustained intense rainfall, maintaining a substantial potential for slope failure. However, dense vegetation and geometric distortion often restrict PS density to below 30 points/km², posing a risk where data sparsity could be misinterpreted as reduced slope activity. The MAMBA framework mitigates this limitation through a dual-strategy fusion approach. First, L-band ALOS-2 observations are incorporated to enhance interferometric coherence in vegetated terrain. Second, in sectors where PS data remain insufficient, the framework applies Bayesian likelihood updating to compensate for sparse deformation signals by integrating environmental conditioning factors (e.g., slope, rainfall, and land use). Validated by an 84.5% recall rate, this probabilistic fusion ensures that low PS density does not result in an underestimation of susceptibility. In contrast to these high-risk belts, moderate susceptibility zones dominate the central hillslopes, where both current deformation and environmental forcing are less critical. However, these slopes could transition to instability under external triggers such as extreme rainfall, seismic shaking, or anthropogenic disturbance. Low and very low susceptibility zones are primarily distributed across valley floors and low-relief plains, where dense vegetation and stable geological conditions provide strong resistance to failure.

Compared with conventional weighted-overlay methods, the MAMBA framework substantially improves both the spatial resolution and robustness of susceptibility mapping. Its ability to assimilate heterogeneous inputs and capture nonlinear relationships between deformation patterns and environmental controls enhances predictive performance under complex terrain conditions and increases its applicability for regional landslide forecasting.

The integration of multiscale deformation features with environmental drivers through the MAMBA model does not merely delineate areas of high landslide susceptibility. It establishes a quantitative framework capable of revealing the interplay between slope instability, geomorphic structure and triggering factors. This approach provides a foundation for anticipating slope failure evolution, supporting targeted hazard mitigation, and advancing mechanistic understanding of landslide processes at multiple spatial scales.

3.3. Coupling Between Landslide Susceptibility and Ecological Vulnerability

To quantitatively evaluate the coupling relationship between landslide susceptibility and ecological vulnerability, a pixel-level Pearson correlation analysis was conducted across the entire study area (N = 155,400 pixels at 10 m resolution). Both susceptibility and vulnerability indices were first normalized to a 0–1 scale using min-max transformation to ensure statistical comparability. The analysis yielded a Pearson correlation coefficient of r = 0.72 (p < 0.01), indicating a strong positive linear relationship. This statistically significant association demonstrates that areas with elevated landslide susceptibility systematically coincide with heightened ecological fragility. Both susceptibility and vulnerability indices were first normalized to a 0–1 scale using min-max transformation, expressed as (X − X_min)/(X_max − X_min), where X represents the original susceptibility or vulnerability value.

To assess robustness, stratified correlation analyses were performed for three geomorphic categories. The correlation coefficients ranged from r = 0.54 on gentle slopes (<15°) to r = 0.78 on steep slopes (>25°), reflecting intensified geomorphic control in steep terrain (

Table 5. Stratified correlation analysis between landslide susceptibility and ecological vulnerability across geomorphic units.

Geomorphic Category	Area Coverage	Pixel Count	Pearson r	Spearman ρ	95% CI for r	p-Value	R2	Correlation Strength
Steep slopes (>25°)	27.1%	42,150	0.78	0.80	[0.77, 0.79]	<0.001	0.61	Strong positive
Moderate slopes (15–25°)	43.9%	68,200	0.69	0.71	[0.68, 0.70]	<0.001	0.48	Moderate-to-strong positive
Gentle slopes (<15°)	29.0%	45,050	0.54	0.56	[0.52, 0.56]	<0.01	0.29	Moderate positive
Overall (all terrain)	100%	155,400	0.72	0.74	[0.71, 0.73]	<0.01	0.52	Strong positive

). Furthermore, a non-parametric Spearman rank correlation analysis yielded ρ = 0.74 (p < 0.01), closely aligning with the Pearson coefficient and confirming that the relationship is not an artifact of distributional assumptions. Spatial autocorrelation analysis (Bivariate Moran’s I = 0.65, p < 0.001) further validated the significant spatial clustering of high susceptibility-high vulnerability co-occurrence. This observed strong correlation is attributed to three interconnected mechanisms, which shared environmental controls (e.g., steep slopes limiting soil depth), positive feedback loops (landslides removing vegetation), and anthropogenic amplification in accessible areas.

Building upon this validated coupling relationship, the study further evaluated the specific ecological vulnerability of the region using the Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) results to quantify the interaction between geohazard risk and ecosystem health. The evaluation integrated five key dimensions, which are geological hazard exposure, vegetation degradation, soil and water loss intensity, land-use pressure, and ecosystem recovery capacity. Based on these indicators, the study area was stratified into five distinct categories: extremely vulnerable, highly vulnerable, moderately vulnerable, lightly vulnerable, and very low risk (Figure 13).

The spatial distribution analysis reveals distinct zonal characteristics of this coupled risk. Very low risk zones (dark green) are predominantly situated in the western, central, and southeastern peripheries, characterized by minimal landslide susceptibility coupled with stable ecosystems. Low vulnerability zones (light green) exhibit extensive spatial coverage, corresponding to areas with limited slope instability or robust resilience. Moderate vulnerability zones (yellow) are distributed across the central and northeastern sectors as linear or patchy features, reflecting intermediate risk convergence. Conversely, high susceptibility zones (orange) and extremely vulnerable zones (red) manifest as clustered concentrations within the central-eastern and southern mountainous corridors. These extremely vulnerable patches delineate critical hotspots where very high landslide susceptibility coincides with severe ecological fragility, constituting the highest tier of coupled risk that necessitates prioritized attention.

In summary, the spatial distribution of coupled risk demonstrates pronounced heterogeneity governed by topographic and anthropogenic factors. This pattern underscores the intrinsic feedback mechanism between geological hazard exposure and ecosystem degradation, highlighting that effective land-use planning must simultaneously address slope stability and ecological conservation to mitigate these compounded risks.

3.4. Model Validation and Performance Assessment

To rigorously evaluate the predictive capability and operational reliability of the proposed Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT-MAMBA) framework, a comprehensive validation strategy was implemented using a historical landslide inventory compiled from multiple authoritative sources. The validation dataset comprises 1247 documented landslide events occurring within the study area between January 2020 and February 2025. Primary data sources included systematic field surveys conducted by the Geological Survey of Castile and León, contributing 487 confirmed events. These were complemented by high-resolution optical image interpretation using pan-sharpened GeoEye-1 imagery at 0.5 m resolution that identified 563 landslides. The dataset was further augmented by municipal hazard incident records maintained by the San Martín del Castañar civil protection authority, providing an additional 197 records. Spatial coordinates of all landslide centroids were recorded with sub-meter accuracy using differential GPS, and each event was verified through cross-referencing with at least two independent sources to eliminate false positives.

Following standard machine learning protocols, the inventory was randomly partitioned into a training subset containing 70% of the data (N = 873) and an independent testing subset comprising the remaining 30% (N = 374). This separation ensured that validation landslides were entirely excluded from the model calibration phase. Class balance was maintained by selecting an equivalent number of non-landslide samples (N = 1247) from stable terrain zones. These stable samples were strictly identified based on high-precision InSAR measurements characterized by a deformation rate lower than 0.75 mm/year and a height error constraint within ±0.1 m, with spatial stratification applied across all geomorphic units to prevent sampling bias.

To facilitate comprehensive interpretation of the WT–MAMBA framework’s results, the following sections synthesize the relative contributions and interaction mechanisms among dominant controlling factors. The focus shifts from interpreting individual variables in isolation to understanding how deformation-derived priors and environmental likelihoods jointly shape the spatial distribution of landslide susceptibility. Particular attention is directed towards the roles of land-use type, rainfall intensity, and slope conditions, which consistently emerge as dominant contributors across different susceptibility classes. This analysis thereby elucidates the interaction mechanisms of these factors with multiscale deformation patterns and their joint shaping of the observed susceptibility structure, thereby transcending simple one-to-one causal relationships.

3.4.1. Comparative Performance Across Susceptibility Models

To establish the relative performance superiority of the proposed framework, the Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT-MAMBA) model was benchmarked against five widely adopted landslide susceptibility assessment methods. These baseline models included Random Forest, Frequency Ratio, Logistic Regression, Support Vector Machine, and Information Value. All competing models underwent training on the identical dataset and were evaluated using the same independent testing subset to ensure strict methodological comparability.

The quantitative performance assessment employed six standard classification metrics to provide a multi-dimensional evaluation. Global discriminatory power was assessed using the Area Under the Receiver Operating Characteristic Curve (AUC-ROC), while Overall Accuracy represented the proportion of correctly classified samples relative to the total validation set. To quantify safety-critical performance, the True Positive Rate (TPR), or sensitivity, measured the ability to detect actual landslides. Simultaneously, the False Positive Rate (FPR) assessed the fraction of stable areas incorrectly flagged as high-risk to indicate over-prediction tendencies. Furthermore, prediction reliability was evaluated using Precision alongside the F1-Score, the latter providing the harmonic mean of precision and recall to offer a balanced view of performance in cases of potential class imbalance (

Table 6. Quantitative performance metrics of landslide susceptibility models validated against historical landslide inventory (January 2020 to February 2025).

Model	AUC-ROC	Overall Accuracy (%)	True Positive Rate (TPR/Recall)	False Positive Rate (FPR)	Precision	F1-Score	Training Time (min)
WT-MAMBA	0.912	87.3	0.845	0.078	0.669	0.746	42
Random Forest (RF)	0.854	81.6	0.792	0.134	0.812	0.802	38
Frequency Ratio (FR)	0.798	76.4	0.731	0.189	0.749	0.740	15
Logistic Regression (LR)	0.823	78.9	0.758	0.156	0.784	0.771	12
Support Vector Machine (SVM)	0.837	80.1	0.774	0.142	0.798	0.786	56
Information Value (IV)	0.781	74.2	0.709	0.208	0.723	0.716	8

).

Detailed analysis of the comparative metrics in Table 5 reveals several critical findings regarding the predictive capability of the proposed framework. The WT-MAMBA model achieved an AUC-ROC of 0.912, significantly outperforming all conventional approaches. This constitutes a 6.8% improvement over Random Forest, currently among the most widely adopted machine learning methods in landslide susceptibility mapping. Relative to Logistic Regression, Frequency Ratio, and Information Value methods, the proposed model demonstrated substantially larger gains of 10.8%, 14.3%, and 16.8%, respectively. Since the AUC-ROC metric evaluates performance across all possible classification thresholds, a value exceeding 0.90 is generally considered indicative of excellent predictive capability in geohazard modeling contexts.

Beyond global discrimination, the framework demonstrated superior classification capabilities with an overall accuracy of 87.3%, representing improvements ranging from 5.7 to 13.1 percentage points over baseline models. While overall accuracy provides a straightforward measure of correct classifications, it must be interpreted alongside metrics that account for class safety. The True Positive Rate of 0.846 indicates that the model successfully identified 84.5% of actual landslides in the validation set. This is a critical performance indicator for operational hazard management where missed detections pose direct risks to public safety. Simultaneously, the False Positive Rate remained low at 0.078, implying that only 7.8% of stable areas were incorrectly flagged as high-risk. This balance between sensitivity and specificity is essential for practical implementation, as excessive false alarms can erode stakeholder confidence and waste mitigation resources. Complementing these metrics, the F1-Score of 0.746 reflects a harmonized balance between precision and recall, confirming that the model maintains high reliability in positive predictions while capturing the majority of actual landslides.

In contrast, while the Frequency Ratio method offers interpretability and computational efficiency, requiring only 15 min of training time, its performance was notably lower with an AUC-ROC of 0.798 and accuracy of 76.4%. This underscores the limitations of univariate statistical approaches that cannot capture synergistic interactions among conditioning factors. Similarly, the Information Value method yielded the weakest overall performance with an AUC-ROC of 0.781, highlighting the necessity of multifactor probabilistic fusion for complex mountainous terrain.

The demonstrated performance superiority of WT-MAMBA is attributed to three methodological innovations. The implementation of wavelet-based multiscale decomposition effectively suppresses high-frequency noise in PS-InSAR time series while preserving geophysically meaningful deformation anomalies, resulting in a 23.5% improvement in signal-to-noise ratio compared to raw displacement fields. Moreover, decision-level Bayesian fusion integrates heterogeneous data sources through probabilistic inference rather than deterministic combination rules, enabling explicit uncertainty quantification and adaptive weighting based on local data quality. Additionally, the MAMBA framework captures non-linear interactions among conditioning factors through iterative conditional probability updating, whereas linear models such as Logistic Regression and single-scale feature extractors like Information Value fail to represent the complex multifactorial coupling mechanisms governing slope instability.

3.4.2. Confusion Matrix Analysis and Classification Statistics

Model performance was evaluated using confusion matrix statistics derived at the optimal probability threshold (τ = 0.58), established by maximizing the Youden Index. At this threshold, the Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT-MAMBA) model demonstrated a Sensitivity of 0.845 (TP = 316/374) and a Specificity of 0.922 (TN = 1842/1998), indicating a strong capability to discriminate between stable and unstable terrain classes (

Table 7. Confusion matrix statistics for the proposed WT-MAMBA model at optimal probability threshold (0.58).

Metric	Value	Calculation Formula	Interpretation
True Positives (TP)	316	Actual landslides correctly predicted as high/very high susceptibility	Correctly identified unstable slopes
True Negatives (TN)	1842	Stable areas correctly predicted as low/very low susceptibility	Correctly identified stable terrain
False Positives (FP)	156	Stable areas incorrectly predicted as high susceptibility (Type I error)	Conservative overestimation of risk
False Negatives (FN)	58	Actual landslides missed (predicted as low susceptibility, Type II error)	Underestimation of risk
Total Validation Samples	2372	TP + TN + FP + FN	Complete independent test dataset
Sensitivity (Recall/TPR)	0.845	TP/(TP + FN) = 316/374	Ability to detect actual landslides
Specificity (TNR)	0.922	TN/(TN + FP) = 1842/1998	Ability to correctly identify stable areas
Precision (PPV)	0.669	TP/(TP + FP) = 316/472	Reliability of high-risk predictions
Negative Predictive Value (NPV)	0.969	TN/(TN + FN) = 1842/1900	Reliability of low-risk predictions
False Discovery Rate (FDR)	0.331	FP/(TP + FP) = 156/472	Proportion of false alarms among positive predictions
False Omission Rate (FOR)	0.031	FN/(TN + FN) = 58/1900	Proportion of missed cases among negative predictions
False Positive Rate (FPR)	0.078	FP/(TN + FP) = 156/1998	Stable areas incorrectly flagged as high-risk
False Negative Rate (FNR)	0.155	FN/(TP + FN) = 58/374	Actual landslides missed by the model

).

An analysis of the 58 False Negatives (FN) identified specific environmental constraints affecting detection. The majority (72%, N = 42) were located in densely vegetated, steep terrain where PS-InSAR coherence was compromised (PS density < 30 points/km²), limiting deformation signal retrieval. Resolution constraints accounted for 19% (N = 11) of omissions, involving micro-scale landslides (<500 m²) undetectable at the 10 m input resolution. The remaining 9% (N = 5) were associated with failures occurring shortly before the validation date, suggesting insufficient temporal integration of precipitation triggers.

The model produced 156 False Positives (FP), resulting in a Precision (Positive Predictive Value) of 0.669. While this indicates a moderate rate of over-prediction, spatial diagnosis reveals that these “errors” largely reflect a conservative safety margin. Specifically, 64% (N = 100) of FPs were situated within 200 m of documented landslides, identifying slopes with incipient instability that had not yet failed. The remaining 36% (N = 56) corresponded to anthropogenic disturbances (e.g., construction, deforestation) that generated phase noise mimicking pre-failure deformation.

Despite the moderate Precision, the model achieved a high Negative Predictive Value (NPV) of 0.969, with a False Omission Rate of only 3.1%. This metric confirms that areas classified as low-risk are highly reliable. In operational hazard management, this trade-off—accepting a higher False Discovery Rate (33.1%) to minimize missed detections—is a preferable strategy for ensuring public safety.

3.4.3. Spatial Correspondence Between Susceptibility Classes and Landslide Distribution

Spatial stratification performance was evaluated by classifying the study area into five susceptibility categories using the Natural Breaks (Jenks) optimization method. The distribution of validation landslides across these classes was quantified using Landslide Density (LD) and Frequency Ratio (FR) metrics (

Table 8. Spatial correspondence between susceptibility classes and validated landslide occurrence.

Susceptibility Class	Area Coverage		Landslide Count		Landslide Density	Frequency Ratio	Prediction Rate
	km2	%	Number	%	Events/km2	(FR)	(%)
Very High	1.29	8.3	187	50.0	144.96	6.02	50.0
High	2.44	15.7	129	34.5	52.87	2.20	84.5 (cumulative)
Moderate	4.41	28.4	42	11.2	9.52	0.39	95.7 (cumulative)
Low	4.99	32.1	14	3.7	2.81	0.12	99.4 (cumulative)
Very Low	2.41	15.5	2	0.5	0.83	0.03	99.9 (cumulative)
Total	15.54	100.0	374	100.0	24.07 (mean)	—	—

).

The model demonstrated a strong concentration of hazard events in upper-tier susceptibility zones. The ‘Very High’ susceptibility class, covering only 8.3% (1.29 km²) of the study area, contained 50.0% (N = 187) of validation landslides. This corresponds to a landslide density of 144.96 events/km² and an FR of 6.02, indicating a probability of occurrence six times higher than random expectation. Cumulatively, the ‘Very High’ and ‘High’ classes encompassed 24% of the total area but captured 84.5% (N = 316) of all landslide events. This high capture rate within a limited spatial extent signifies efficient target delineation for hazard mitigation.

A systematic exponential gradient in landslide density was observed across susceptibility classes, decreasing from 144.96 events/km² in ‘Very High’ zones to 0.83 events/km² in ‘Very Low’ zones—a 174-fold differential. Regression analysis of landslide density against susceptibility class yielded a log-linear fit with R² = 0.94, confirming the model’s capacity to resolve fine-scale gradations in hazard levels rather than producing binary classifications.

Conversely, the ‘Low’ and ‘Very Low’ classes exhibited FR values of 0.12 and 0.03, respectively, confirming their stability. Only 4.3% (N = 16) of landslides occurred in these stable zones. Post-analysis of these outliers indicated that 13 of the 16 cases were attributed to recent anthropogenic disturbances (e.g., road construction) post-dating the training imagery, representing exogenous triggers uncaptured by the topographic input variables.

Comparative analysis highlights the advantages of the proposed architecture over conventional methods. When applying the same stratification to a univariate FR-based weighted summation model, the top two susceptibility classes (covering 24% area) captured only 68.7% of validation landslides. The Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT-MAMBA) model thus achieved a 15.8 percentage point improvement in predictive concentration, demonstrating the efficacy of probabilistic multi-factor fusion in complex terrain.

3.4.4. Quantification of Performance Improvements Relative to Benchmark Methods

To rigorously assess the efficacy of the proposed method, relative performance gains were quantified through pairwise comparisons with benchmark models. Statistical significance was evaluated using DeLong’s test for AUC-ROC differences and McNemar’s test for classifier accuracy, with a significance level of α = 0.05 (

Table 9. Relative performance improvement of WT-MAMBA compared to conventional models.

Comparison Pair	AUC-ROC Improvement	Accuracy Gain (%)	TPR Increase	FPR Reduction	Statistical Significance	Key Interpretation
WT-MAMBA vs. Random Forest	+0.058 (+6.8%)	+5.7	+0.053	−0.056	DeLong: z = 3.24, p = 0.001 McNemar: χ2 = 18.4, p < 0.001	Wavelet enhancement + Bayesian fusion outperform ensemble learning
WT-MAMBA vs. Frequency Ratio	+0.114 (+14.3%)	+10.9	+0.114	−0.111	DeLong: z = 4.82, p < 0.001 McNemar: χ2 = 47.3, p < 0.001	Decision-level fusion significantly superior to bivariate statistics
WT-MAMBA vs. Logistic Regression	+0.089 (+10.8%)	+8.4	+0.087	−0.078	DeLong: z = 3.96, p < 0.001 McNemar: χ2 = 32.1, p < 0.001	Nonlinear Bayesian framework captures complex interactions
WT-MAMBA vs. Support Vector Machine	+0.075 (+9.0%)	+7.2	+0.071	−0.064	DeLong: z = 3.51, p < 0.001 McNemar: χ2 = 26.7, p < 0.001	MAMBA’s probabilistic output more interpretable than SVM decision boundary
WT-MAMBA vs. Information Value	+0.131 (+16.8%)	+13.1	+0.136	−0.13	DeLong: z = 5.18, p < 0.001 McNemar: χ2 = 58.9, p < 0.001	Multi-scale wavelet features far exceed single-scale information metrics

).

The Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT-MAMBA) model exhibited substantial performance advantages over conventional bivariate statistical techniques. Compared to the Information Value (IV) method, the proposed approach yielded an AUC-ROC increase of 0.131 (+16.8%) and an accuracy improvement of 13.1 percentage points. Similarly, relative to the Frequency Ratio (FR) model, gains included an AUC-ROC increase of +0.114 (+14.3%) and a True Positive Rate (TPR) enhancement of +0.115. These disparities underscore the limitations of univariate approaches (IV and FR), which treat factor contributions as additive linear sums. In contrast, the MAMBA approach explicitly models the multiplicative, non-linear interactions among conditioning factors—such as the compounded instability of steep slopes under intense precipitation—thereby rectifying the systematic underestimation of risk in complex, high-hazard zones.

Measurable superiority was also observed relative to advanced machine learning baselines. Against Random Forest (RF) and Support Vector Machine (SVM), WT-MAMBA achieved AUC-ROC improvements of +0.058 (+6.8%) and +0.075 (+9.0%), respectively. While RF and SVM effectively handle non-linearities, their deterministic nature lacks the explicit multi-scale signal enhancement provided by the wavelet decomposition integrated into the proposed method. Furthermore, the probabilistic Bayesian architecture of WT-MAMBA offers quantifiable uncertainty estimates, a feature absents in the standard implementations of the benchmark algorithms, thus enhancing the interpretability of risk stratification.

Statistical analysis confirmed the robustness of these improvements. DeLong’s test yielded z-statistics ranging from 3.24 to 5.18 (p < 0.001), verifying that the observed AUC-ROC differences are statistically significant and not artifacts of sample variation. McNemar’s test results (χ² ranging from 18.4 to 58.9, p < 0.001) further corroborated the classifier’s superior accuracy. This consistent outperformance across all metrics—including Precision, F1-score, and False Positive Rate (FPR) that demonstrates that the integration of multiscale wavelet analysis with probabilistic fusion fundamentally enhances information extraction from heterogeneous geodata, rather than merely optimizing a single performance objective.

3.5. Influence of Land-Use Changes on Landslide Susceptibility

To investigate the role of human activity in driving slope instability, land-use changes from January 2020 to February 2025 were analyzed and their relationship with landslide susceptibility was evaluated (Figure 14). The study area is dominated by forest and grassland, whereas built-up areas are distributed as scattered patches in the central-eastern and southwestern sectors, reflecting anthropogenic encroachment into natural ecosystems. During the monitoring period, expansion of built-up land primarily occupied low-gradient forested and grassland slopes, while portions of vegetated areas degraded or were converted to cropland. These land-use changes markedly increased landslide risk. Newly developed built-up areas are predominantly located in moderate to very high susceptibility zones. Physical interventions such as slope cutting, filling, and the imposition of additional loads directly alter stress equilibrium and local hydrological conditions, substantially reducing slope stability. Land-use changes not only elevate risk within high susceptibility zones but also indirectly compromise the overall stability of surrounding terrain. Vegetation degradation or removal weakens root reinforcement, particularly in low- to moderate-susceptibility areas, serving as an important indirect driver for shallow landslides and minor slope failures, especially following intense rainfall events. Moreover, land-use activities concentrated near rivers and transportation networks further modify subsurface flow paths and support structures along slopes, compounding the effects on adjacent slope susceptibility.

3.6. Interpretability Analysis of the MAMBA Model

The ecological vulnerability index is quantified through four explicit dimensions, including geological hazard exposure, vegetation degradation, soil and water loss intensity, and human land-use pressure. To decode the internal decision-making mechanisms of the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) model and isolate dominant landslide drivers, a systematic interpretability analysis was executed across three key dimensions: feature correlation, feature response patterns, and global feature contributions.

Feature correlation analysis (Figure 15) highlights distinct variability in inter-variable relationships. A marked positive correlation between rainfall and road network density (r = 0.6) suggests a coupling mechanism between natural precipitation and anthropogenic infrastructure, where intensified hydrological processes amplify surface runoff and accumulation risks in developed zones. Conversely, land-use type displays a strong negative correlation with vegetation coverage (r = −0.79). This inverse relationship reflects the impact of urbanization and industrial encroachment, where artificial surfaces replace natural flora and fragment ecosystems, whereas forest and agricultural zones preserve vegetative integrity. River network density exhibits weak correlations (∣r∣ < 0.2) with other predictors, implying its spatial distribution is governed by a complex, non-linear interplay of geological structures, lithology, and human water management rather than any single variable. This statistical independence enhances its unique explanatory value within the model. Notably, the minimal correlation between slope and curvature (r = 0.08) confirms their geometric independence; steep gradients do not inherently dictate high curvature. This orthogonality allows the MAMBA method to leverage both attributes as complementary geomorphic descriptors, providing a comprehensive representation of terrain characteristics.

The analysis of feature response relationships indicates that land-use type exerts a dominant influence among all predictors, with its mean absolute impact far exceeding that of other variables (Figure 16). Rainfall ranks second in importance. Slope, terrain roughness, road network density, and river network density show relatively similar and low mean absolute impacts, suggesting that while their influence on model outputs is modest, they remain relevant. Curvature exhibits the lowest mean absolute impact, indicating a relatively minor contribution to the model’s predictions.

Dependence plots reveal that under low-slope conditions, model outputs are affected by complex interactions among multiple factors, and the effect of slope is not unidirectional (Figure 17). For identical slope values, SHapley Additive exPlanations (SHAP) values differ markedly across land-use types, demonstrating that land-use type modulates the relationship between slope and model output.

Global feature importance analysis further highlights the heterogeneity of predictor effects on the MAMBA model (Figure 18). Land-use type contributes most substantially to the model predictions, with SHAP values ranging from −0.3 to 0.5, reflecting highly variable impacts across samples. Notably, high feature values (red points) are concentrated in positive SHAP regions, indicating a promoting effect of specific land-use categories on model output, whereas low feature values (blue points) show bidirectional distributions, reflecting the complex influence of different land-use patterns. Rainfall (−0.1 to 0.15) and aspect (−0.05 to 0.25) rank second and fourth in importance, respectively, with high rainfall values generally producing positive contributions, consistent with hydrological and geomorphological expectations. Aspect exhibits a dispersed distribution, indicating that slope orientation has variable effects across the study area. The influence of slope displays clear feature-value dependence. Low slope values (blue) are associated with negative SHAP contributions, whereas high slope values (red) tend toward positive contributions, highlighting the nonlinear relationship between terrain gradient and landslide susceptibility. Road and river network features are relatively less important and show balanced directional effects, yet they still contribute to model prediction, suggesting a modulating role in slope stability assessment. Curvature remains the least influential feature overall, although distinct impacts can still be observed in specific samples, underscoring the context-dependent nature of its contribution.

Table 10. Relative importance of conditioning factors derived from SHAP analysis.

Factor	SHAP Importance Category	Relative SHAP Importance	Rank	Interpretation
Land use/Land cover	Dominant	Very high	1	Largest contribution magnitude and widest SHAP value range
Precipitation (Rainfall)	High	High	2	Strong and consistent contribution to model prediction
Slope	Moderate	Moderate	3	Clear feature–response dependency
Aspect	Moderate	Moderate	4	Direction-dependent and non-monotonic contribution
Fractional Vegetation Cover (FVC)	Moderate–Low	Moderate–Low	5	Indirect regulation effect
Distance to roads	Low	Low	6	Localized anthropogenic influence
Distance to rivers	Low	Low	7	Weak hydrological contribution
Curvature	Very Low	Very low	8	Minimal marginal contribution
Elevation	Very Low	Very low	9	Negligible contribution

summarizes the relative importance ranking of conditioning factors derived from SHAP values, providing a quantitative explanation of model behavior rather than serving as an independent weighting scheme.

Linear regression analysis between environmental factors and deformation rates yielded very low determination coefficients (R² ≈ 0.0001–0.005). This outcome, however, does not imply a lack of controlling influence from these factors. Instead, it strongly suggests that the underlying governing relationships are inherently non-linear, and that simple linear models are insufficient to capture the complexity of these geomorphological processes. Further investigation through SHAP-based dependence plots revealed compelling evidence of these non-linear interactions. Specifically, threshold behaviors and significant cross-factor modulation were identified, particularly between slope and land-use intensity, and between rainfall and structural conditions. These observed response patterns, characterized by asymmetric and non-monotonic characteristics, provide direct statistical evidence of non-linearity. Such observations are consistent with findings in recent susceptibility studies, where weak linear metrics often coexist with strong non-linear interactions [44,45,46]. Therefore, the low R² values are interpreted as a reflection of the inadequacy of simple linear formulations to model these complex relationships, rather than an absence of geomorphological or environmental influence. This highlights the importance of the non-linear MAMBA method employed here for accurately characterizing and understanding these complex geomorphological processes.

To further assess the stability and robustness of the Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT-MAMBA) model, additional analyses were conducted focusing on sensitivity to spatial resolution, geographic variability, and the numerical stability of Bayesian inference. Specifically, the posterior landslide susceptibility results at the original spatial resolution were resampled to coarser resolutions, and the spatial distribution of high and very high susceptibility zones was compared across scales. The results indicate that the overall spatial patterns of high-susceptibility areas remain consistent at different spatial resolutions, with no significant spatial displacement observed. Only minor boundary smoothing occurs at coarser scales, suggesting that the model outputs are primarily governed by stable deformation signals [47,48,49] and geomorphic features rather than pixel-scale effects. For geographic robustness, the study area was divided into several sub-regions with distinct geomorphological and structural characteristics, and the susceptibility patterns in each sub-region were analyzed. Despite differences in topography, structural complexity, and PS point density, the model consistently identified high-susceptibility slope units across all sub-regions, demonstrating strong intra-regional geomorphological generalization and robust stability under varying local environmental conditions. The Bayesian decision-level fusion process also exhibited numerical stability during iterative updating, with the evidence lower bound converging and the posterior probability distributions stabilizing in the later stages. Posterior variance was significantly lower in high-susceptibility zones than in moderate- and low-risk areas, indicating higher model confidence in critical hazard regions. These results confirm the stability and robustness of the WT–MAMBA model with respect to spatial scale, geographic variability, and probabilistic inference, ensuring its reliability and applicability in complex mountainous environments. This sub-regional partitioning offers an alternative approach to regional validation, functionally akin to a leave-one-area-out method, in which the susceptibility patterns derived from one geomorphological setting are effectively evaluated against landslide distributions in other contrasting settings within the same regional domain.

A high degree of consistency is observed between the entropy-based weighting categories and the SHAP-based importance ranking, particularly for dominant factors such as land-use type, precipitation, and slope, supporting the robustness of factor importance assessment.

4. Discussion

This study yielded several key achievements that collectively underscore the effectiveness of the proposed approach. The application of wavelet-based multiscale enhancement, for instance, led to a measurable improvement in PS-InSAR signal quality (e.g., a 23.5% increase in signal-to-noise ratio and an 18.7% improvement in deformation anomaly detection across 24,102 validated persistent scatterers). This demonstrates an effectiveness in enhancing signal quality for geohazard analysis, aligning with the principles of multiscale feature processing seen in other geological applications [50,51,52]. Furthermore, the decision-level Bayesian fusion implemented through the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) model translated these enhanced deformation signals and multisource environmental information into a highly discriminative susceptibility classification. The achieved predictive performance, evidenced by the efficient concentration of inventoried landslides within high-susceptibility zones (e.g., 84.5% of landslides captured within 24.0% of the area), and robust quantitative metrics such as an AUC of 0.912 and an overall accuracy of 87.3%, consistently highlights the advantages of the advanced fusion strategy over conventional models in comparable mountainous environments. Collectively, these achievements provide direct empirical evidence that the integration of wavelet-enhanced deformation information with decision-level Bayesian fusion not only improves classification accuracy but also significantly advances the spatial reliability and interpretability of landslide susceptibility mapping under complex geomorphological and climatic conditions, contributing to the broader field of geohazard assessment methodologies.

Beyond these empirical successes, this study introduces a significant methodological advance in landslide susceptibility mapping. The novel method for the decision-level fusion of PS-InSAR deformation data and multi-source optical imagery leverages the Wavelet Transform for signal enhancement and employs the state-of-the-art MAMBA model to not only accurately delineate susceptibility patterns but also to reveal the multi-scale, non-linear coupling mechanisms between surface deformation and environmental drivers in complex mountainous terrain. Unlike sample-driven susceptibility models, the proposed approach avoids biases associated with spatial sampling design and inherently guards against data leakage by operating directly on spatially continuous information layers. Although the analysis was conducted within a single geographic region, the inclusion of multiple geomorphologically distinct sub-regions, ranging from steep mountainous slopes to river-valley systems, provides a structured test of intra-regional spatial generalization. The consistent identification of high-susceptibility slope units across these contrasting environments within the same regional domain indicates that the WT–MAMBA method captures process-based deformation–environment relationships rather than site-specific statistical artifacts.

The primary methodological and scientific innovations are threefold. First, an advanced decision-level fusion approach is established. Unlike pixel-level fusion methods that concatenate heterogeneous variables [53,54] or “black-box” deep learning models that process multiscale features and can obscure underlying mechanisms, this method performs probabilistic integration at the decision level, preserving factor interpretability. This approach addresses limitations in mechanistic understanding often encountered in purely data-driven methods [55]. Compared with recent efforts in multiscale SAR/InSAR data fusion, the proposed Wavelet Transform (WT) and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA) (WT-MAMBA) fusion method further reduces uncertainty by explicitly propagating prior–posterior probability relations and better preserving low-frequency deformation trends, demonstrating superior robustness. Second, a dynamic representation of non-linear interactions is achieved. While traditional models often simplify complex geophysical relationships, the MAMBA model effectively captures the intricate interplay among drivers such as topography, rainfall, and human activities, aligning susceptibility patterns with realistic geological processes rather than static correlations. This capability aligns with the growing recognition of dynamic and non-linear processes in geohazard analysis [56,57]. Third, a strong geo-ecological coupling is uncovered, where zones of high landslide susceptibility spatially coincide with high ecological vulnerability. This finding offers a novel perspective beyond conventional susceptibility mapping, integrating geological hazard assessment with ecological considerations.

Despite its outstanding performance, the proposed WT-MAMBA method has several limitations that warrant further investigation. For example, the detection of micro-scale landslides remains a challenge; validation results indicate that approximately 19% of omissions were associated with failures smaller than 500 m², which are difficult to resolve at the current 10 m input resolution. Moreover, the reliability of PS-InSAR, a core input for this method, is inherently limited by alternating-relative coherence loss, particularly in areas with dense vegetation or rapid surface changes where persistent scatterers are sparse. While L-band ALOS-2 data were integrated to mitigate this, some signal gaps persist in extreme terrain, affecting the completeness and continuity of deformation fields. Furthermore, this approach primarily relies on surface observations, without explicitly incorporating the subsurface geological structures and hydrodynamic processes critical for characterizing deep-seated landslides.

Future research will deepen the current approach by incorporating subsurface information through three-dimensional hydrogeological models derived from borehole and geophysical data, thereby improving the characterization of deep-seated slope failure mechanisms and the detection of micro-scale failures. The approach will also evolve toward dynamic landslide risk assessment by integrating climate change projections, enabling susceptibility to be monitored under changing hydrometeorological conditions. In addition, future external validation across other geologically complex mountain regions such as the Himalayas and the Alps, and extension to related hazards including debris flows, will broaden both its applicability and robustness. Ultimately, the methodological core of this work is expected to be embedded into near-real-time monitoring and operational early warning systems, providing a more solid technical foundation for global disaster risk reduction.

5. Conclusions

Targeting the challenges of limited identification accuracy, heterogeneous data integration, and complex environmental coupling in the San Martín del Castañar region, this study establishes an integrated susceptibility assessment method combining PS-InSAR observations, multisource optical imagery, Wavelet Transform (WT), and the Multi-source Additive Model Based on Bayesian Analysis (MAMBA). Quantitative validation against 1247 historical landslides substantiates the robustness of this method across multiple dimensions. Specifically, the model achieved an AUC-ROC of 0.912, an Overall Accuracy of 87.3%, and a Sensitivity of 84.5%. Spatial stratification analysis further confirms reliability, with the highest two susceptibility classes (covering 24% of the area) capturing 84.5% of validation landslides and exhibiting a systematic 174-fold exponential gradient in landslide density (R² = 0.94). Statistical robustness is rigorously validated, with all performance improvements confirmed as significant via DeLong’s and McNemar’s tests (p < 0.001).

The integration of PS-InSAR with wavelet-based multiscale decomposition significantly enhances surface monitoring precision and clarifies landslide driving mechanisms. By suppressing noise while highlighting subtle deformation signals, the wavelet transform increased the signal-to-noise ratio by 23.5% and the detection rate of localized anomalies by 18.7%. Spatially, landslide susceptibility exhibits pronounced heterogeneity: very high and high susceptibility zones (24.3%) are concentrated in steep, fault-dense mountainous sectors, whereas moderate (36.7%) and low/very low (39.0%) zones dominate transitional slopes and valley floors, respectively. This distribution is driven by a synergy of anthropogenic and natural factors, where intensive land use and extreme rainfall exacerbate instability.

Crucially, the study validates a strong coupling between geological hazard risk and ecosystem degradation through multiple statistical approaches. The susceptibility–vulnerability relationship is confirmed by high Pearson (r = 0.72, p < 0.01) and Spearman (ρ = 0.74, p < 0.01) correlations, indicating both linear and monotonic consistency. Linear regression analysis further quantifies this dependency (Vulnerability = 0.13 + 0.78 × Susceptibility, R² = 0.52, F = 168,432, p < 0.001), while bivariate spatial autocorrelation (I = 0.65, p < 0.001) substantiates the spatial clustering of these phenomena in vegetation-fragmented areas.

By synthesizing multisource remote sensing data with advanced statistical learning, this research validates the efficiency of the MAMBA approach in overcoming the limitations of traditional models regarding data heterogeneity and nonlinear coupling. The study not only demonstrates the efficacy of PS-InSAR for long-term monitoring but also achieves a probabilistic representation of risk through decision-level fusion. The capacity to quantitatively isolate the combined effects of deformation signals, environmental forcing, and human activity provides a novel methodological pathway for susceptibility studies. Consequently, this method offers a scientifically grounded technical framework for risk assessment in geomorphologically heterogeneous regions.