Estimating landslide thickness through domain-based regularization

This paper introduces a novel domain-based regularization approach for estimating landslide thickness from surface velocity data. Such quantity is crucial for accurately assessing landslides behavior, potential impact, and associated risks. Here, we formulate the problem as an ill-posed inverse problem and propose, for its solution, a multipenalty regularization approach based on the decomposition of the landslide domain in several regions with uniform magnitude of the horizontal velocity. We extend the Balancing Principle to accommodate non-constant balancing parameters across decomposed regions. Our Domain-based Majorization-Minimization algorithm converges to solutions that satisfy this extended principle, demonstrating superior performance compared to traditional methods. Through rigorous testing on both synthetic and real-world landslide data, we show that strategic domain decomposition based on velocity field homogeneity enhances estimation accuracy. Our findings reveal that while excessive subdivision is counterproductive, identifying appropriate velocity-based macro-regions yields optimal results. This methodology provides more reliable thickness estimates crucial for landslide risk assessment and monitoring.