KOSMIK: A Kernel-Based Two-Orbit InSAR Constitutive Framework for Landslide Kinematic Field Reconstruction

Conventional interpretations of InSAR observations primarily regard line-of-sight (LOS) measurements as projections of surface displacement that require predefined geometrical assumptions for kinematic reconstruction. In this work, we propose a different perspective, in which multi-orbit LOS observations are interpreted as diagnostic variables whose differential information can be exploited to constrain landslide kinematics. Building upon this concept, we present KOSMIK (Kinematic-Oriented Framework for Slope Motion Analysis from PS-InSAR Data via Kernel Processing). The framework introduces the Differential Observation-Oriented (DOO) model, a constitutive geometrical approach that provides internally self-consistent closed-form kinematic solutions, while explicitly retaining the non-univocal character of the reconstruction. Opposite-sign LOS configurations define constrained kinematic families, whereas same-sign configurations preserve a larger geometrical ambiguity. In both cases, affinity with the local Aspect or Anti-Aspect morphometric direction is used as a proximity-based tiebreaker among the admissible DOO azimuthal solutions. The DOO model is integrated with two adaptive Kernel operators for PS-data continuization. Within this framework, the diagnostic information embedded in non-collinear LOS observations is exploited to reconstruct coherent landslide kinematics while reducing reliance on externally prescribed motion directions. Consequently, KOSMIK derives three-dimensional kinematic fields within an internally self-consistent constitutive framework rather than through a prior observational 3-D inversion. The framework was applied to multiple 2 benchmark cases and validated against independent GPS and inclinometric measurements, and was also compared with conventional ENU and slope-parallel reconstructions. In the present methodological preprint, one representative benchmark case is reported as a demonstrative application.