Methods for modeling crustal deformation related to earthquakes and plate motions have been developed to incorporate complex crustal structures and multi-fidelity observations. A machine learning approach called physics-informed neural networks (PINNs), which can solve both forward and inverse problems of physical systems, was proposed and applied to the forward simulations of antiplane deformation. Here, we aimed to extend the PINN approach to crustal deformation in two directions: (1) inplane deformation, which is typically used for modeling subduction zones, and (2) inversion analysis of fault slips from geodetic observations. We verified the performance of PINNs on these problems and suggested that formulations in Cartesian and polar coordinates are suitable for forward and inverse modeling, respectively. Furthermore, PINNs yielded stable inversion results without explicit regularization terms, implying that solving the governing equations with PINNs implicitly imposes regularization based on the physical requirements. This may elucidate the distinctive properties of PINNs and provide insights into inversion analyses in geophysics and other fields.

This study presents a new method of centroid moment tensor (CMT) data inversion to estimate time-dependent regional stress fields. A Gaussian process (GP) is applied to resolve a computational difficulty of the existing basis function expansion method in analyzing high-dimensional data including time dependence. A critical step in the formulation is an analytical derivation of the relationship of the covariance function, which is a key ingredient of GP, between CMT data and a model stress field based on an observation equation. Applications to CMT data in and around Japan after the 2011 Tohoku earthquake show the efficiency and validity of the method, which clarifies that the stress field has small-scale heterogeneity in space and long-term stability in time for most regions. Additionally, significant temporal variations are observed around the margin of the focal region of the 2011 event, the sense of which is opposite in the landward side and the oceanward side. GP would be particularly effective in geophysical inversions of high-dimensional data distributed in a broad region.