Abstract:
Three-dimensional (3D) deformation monitoring of landslides is a key indicator for understanding their kinematic mechanisms and potential hazard risk. Taking the Malan landslide in Tianshui, China, as a case study, this paper employs InSAR-based 3D decomposition combined with rainfall−deformation coupling analysis to reveal the 3D deformation characteristics of the slope and its response to rainfall. Time-series Sentinel-1A ascending and descending SAR images acquired from July 2022 to July 2025 were processed using the SBAS-InSAR method to derive surface deformation series. A slope-aspect-constrained 3D decomposition model was then applied to retrieve deformation rates and cumulative displacements in the vertical, east−west and north−south directions. Based on this, typical profiles and representative points were extracted; the evolution stages of the landslide were characterized using the tangent angle of displacement−time curves, and wavelet coherence analysis with regional rainfall records was conducted to quantitatively assess the influence of rainfall on 3D deformation. (1) The 3D deformation field reveals an asymmetric composite sliding mode dominated by vertical subsidence with superimposed east−west horizontal motion. The maximum cumulative horizontal and vertical displacements reach 52 mm and 14 mm, respectively. The deforming area exhibits stage-wise intensification and marked spatial heterogeneity. (2) Wavelet coherence analysis between 3D point-wise displacement and rainfall indicates that vertical deformation exhibits strong coherence with rainfall at periods of 1−4 months , with coherence coefficients generally greater than 0.8. The phase relationship indicates that rainfall leads deformation by approximately 1−2 months. The east−west component shows scale-dependent coupling with rainfall, whereas the north−south component exhibits relatively weak coherence. Combined analysis of displacement−rainfall time series and tangent-angle evolution further demonstrates that intense summer rainfall events in 2023 and 2024 temporally coincide with multiple acceleration phases of the landslide. Seasonal heavy rainfall is the primary external factor influencing the enhancement of vertical subsidence and east−west sliding of the Malan landslide, which displays distinct stage-wise evolution during the monitoring period. The proposed methodology provides technical support and a methodological reference for refined 3D deformation characterization and early warning of rainfall-affected landslides.