Seismic Wave Propagation and Inversion with Neural Operators

Yan Yang,Zachary E Ross,Angela F Gao,Kamyar Azizzadenesheli,Robert W Clayton,Jorge C Castellanos

doi:10.1785/0320210026

Abstract

AbstractSeismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exacerbated by the fact that new simulations must be performed whenever the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called neural operator. A trained neural operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme to train neural operators on an ensemble of simulations performed with random velocity models and source locations. As neural operators are grid free, it is possible to evaluate solutions on higher resolution velocity models than trained on, providing additional computational efficiency. We illustrate the method with the 2D acoustic wave equation and demonstrate the method’s applicability to seismic tomography, using reverse-mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. The developed procedure is nearly an order of magnitude faster than using conventional numerical methods for full waveform inversion.

Highlights

Generalization to arbitrary velocity models The Fourier neural operator (FNO) was trained only on velocity models drawn from Gaussian random fields; and, this family of functions is broad, it does not include some types of functions that exist in the Earth, such as discontinuous functions
This study presents a prototype framework for applying neural operators to the 2D acoustic wave equation
The FNO method was applied successfully to the Navier–Stokes equations (Li et al, 2021), which can be more challenging to solve than the elastic-wave equation

Summary

Introduction

The simulation of seismic wave propagation through Earth’s interior underlies most aspects of seismological research, from the simulation of strong ground shaking due to large earthquakes (Graves and Pitarka, 2016; Rodgers et al, 2019), to imaging the subsurface velocity structure (Fichtner et al, 2009; Tape et al, 2009; Virieux and Operto, 2009; Lee et al, 2014; Gebraad et al, 2020), to derivation of earthquake source properties (Duputel et al, 2015; Ye et al, 2016; Wang and Zhan, 2020). Beyond the goal of accelerating compute capabilities, such physics-informed neural networks may offer other advantages such as grid independence, lowmemory overhead, differentiability, and on-demand solutions These properties facilitate deep learning being used to solve geophysical inverse problems (Zhu et al, 2020; Smith et al, 2021; Xiao et al, 2021; Zhang and Gao, 2021), as a wider. One of the major challenges associated with wave propagation is that a new simulation must be performed whenever the properties of the source or velocity structure are perturbed in some way This alone substantially increases the necessary compute costs, making some problems prohibitively expensive even if they are mathematically or physically tractable. Neural operators can be viewed as generalized Green’s functions

Methods

Experiments

Discussion