OkadaTorch: A Differentiable Programming of Okada Model to Calculate Displacements and Strains from Fault Parameters

TL;DR

OkadaTorch is a PyTorch implementation of the Okada model that enables automatic differentiation for efficient fault parameter inversion and seismic displacement analysis.

Contribution

We developed a differentiable PyTorch version of the Okada model, facilitating gradient-based inversion and integration with machine learning methods.

Findings

Enables efficient gradient and Hessian computations for fault parameters.

Facilitates Bayesian inference and optimization in seismic modeling.

Open-source implementation available for community use.

Abstract

The Okada model is a widely used analytical solution for displacements and strains caused by a point or rectangular dislocation source in a 3D elastic half-space. We present OkadaTorch, a PyTorch implementation of the Okada model, where the entire code is differentiable; gradients with respect to input can be easily computed using automatic differentiation (AD). Our work consists of two components: a direct translation of the original Okada model into PyTorch, and a convenient wrapper interface for efficiently computing gradients and Hessians with respect to either observation station coordinates or fault parameters. This differentiable framework is well suited for fault parameter inversion, including gradient-based optimization, Bayesian inference, and integration with scientific machine learning (SciML) models. Our code is available here: https://github.com/msomeya1/OkadaTorch