Deep Neural Helmholtz Operators for 3D Elastic Wave Propagation and Inversion

TL;DR

This paper introduces a memory-efficient neural operator for 3D elastic wave simulation in the frequency domain, enabling faster seismic inversion and modeling with high accuracy and generalization capabilities.

Contribution

The study presents a 3D Helmholtz neural operator that is 40 times more memory-efficient and 100 times faster than traditional methods, improving seismic wave simulation and inversion.

Findings

Achieves two orders of magnitude acceleration over spectral methods

Generalizes well to variable velocity structures

Reduces inversion computation time by a factor of 350

Abstract

Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is particularly problematic for full waveform inversion, which typically involves numerous runs of the forward process. In machine learning there has been considerable recent work in the area of operator learning, with a new class of models called neural operators allowing for data-driven solutions to partial differential equations. Recent works in seismology have shown that when neural operators are adequately trained, they can significantly shorten the compute time for wave propagation. However, the memory required for the 3D time domain equations may be prohibitive. In this study, we show that these limitations can be overcome by solving the wave equations in the frequency domain, also known as the Helmholtz equations, since the solutions for a set of frequencies can be determined in parallel. The 3D Helmholtz neural operator is 40 times more memory-efficient than an equivalent time-domain version. We employ a U-shaped neural operator for 2D and 3D elastic wave modeling, achieving two orders of magnitude acceleration compared to a baseline spectral element method. The neural operator accurately generalizes to variable velocity structures and can be evaluated on denser input meshes than used in the training simulations. We also show that when solving for wavefields strictly on the surface, the accuracy can be significantly improved via a graph neural operator layer. In leveraging automatic differentiation, the proposed method can serve as an alternative to the adjoint-state approach for 3D full-waveform inversion, reducing the computation time by a factor of 350.