Fault Geometry Invariance and Differentiable Ensemble Solutions for Simultaneous Fault and Slip Inversion in Heterogeneous Crustal Structures

Fault slip inversions based on geodetic observations deepen our understanding of earthquake source processes. Previous attempts to simultaneously estimate the fault geometry and slip distribution have typically assumed homogeneous half-space owing to the prohibitively high computational costs of conventional numerical approaches. Here, we develop a simultaneous inversion method considering heterogeneous crustal structures. First, an infinite-dimensional problem of fault geometries is reduced to finite dimensions by introducing a dislocation potential based on fault geometry invariance. Second, physics-informed deep learning is used to provide differentiable solutions for the dislocation potential, allowing for efficient Bayesian inversions. Numerical investigations on 2-D inplane problems show that incorporating suitable heterogeneous structures substantially improves the stability and accuracy of fault and slip estimations compared with biased results obtained under homogeneous assumptions. This represents a significant advance in finite fault inversion, as it addresses heterogeneous crustal structure and uncertain fault geometries by overcoming a computational constraint.