Physics-Informed Deep Learning Approach for Modeling Crustal Deformation

Abstract

The movement and deformation of the Earth's crust and upper mantle provide critical insights into the evolution of earthquake processes and future earthquake hazards. Crustal deformation can be modeled by dislocation models that represent an earthquake fault in the crust as a defect in a continuum medium. Forward and inverse modeling have been performed using various analytical methods based on Green's function for linear responses and numerical methods that discretize model regions or boundaries. In this study, we propose a novel physics-informed deep learning approach to model crustal deformation due to earthquakes. This approach obtains continuous solutions using neural networks by representing the governing equations and boundary conditions as a loss function. We use the polar coordinate system to accurately model the displacement discontinuity on a fault as a boundary condition. Neural network modeling enables flexible representation of arbitrary geometrical structures and mechanical properties of rocks, which cannot be achieved via existing methods in practice. We illustrate the validity and usefulness of this approach through example problems such as curved strike-slip faults in heterogeneous elastic media with surface topographies. Furthermore, this approach can be extended to high-dimensional, anelastic, and nonlinear problems in a straightforward manner. We anticipate that the proposed approach will be a starting point for progress in the quantitative assessment of future seismic hazards.