A regularization method for landslide thickness estimation

Accurately estimating landslides’ failure surface depth is essential for hazard prediction. However, most of the classical methods rely on overly simplistic assumptions [1]. In this work, we will present the landslide thickness estimation problem as an inverse problem Aw = b, obtained from discretization of the thickness equation [2]: ∂(hf vx)/∂x + ∂(hf vy)/∂y = − ∂ζ/∂t , (1) where the forward operator A contains information on the surface velocity (v_x, v_y), the right-hand side b corresponds to the surface elevation change ∂ζ/∂t, and w is the thickness hf . By employing a regularization approach, the inverse problem is reformulated as an optimization problem. In real-world scenarios, often no information on neither the noise type nor the noise level affecting data is available. In this context, the correct choice of the regularization parameter becomes a pressing issue. We propose a method to determine this parameter in a fully automatic way for the thickness inversion problem. Results obtained on both synthetic data generated by landslide simulation software and data measured from real-world landslides will be shown. [1] Jaboyedoff M., Carrea D., Derron M.H., Oppikofer T., Penna I.M., Rudaz B. (2020): A review of methods used to estimate initial landslide failure surface depths and volumes. Engineering Geology, 267, 105478 [2] Booth A. M. ; Lamb M. P. ; Avouac J.P. ; Delacourt C. (2013): Landslide velocity, thickness, and rheology from remote sensing: La Clapière landslide, France. Geophysical Research Letters, Vol. 40, 4299 - 4304.