Physics-guided deep learning using Fourier neural operators for solving the acoustic VTI wave equation

Abstract

Summary Many real-world seismic modeling and imaging applications require computing frequency-domain numerical solutions of acoustic wave equation (AWE). However, obtaining such solutions in media characterized by strong parameter contrasts and anisotropy poses significant practical challenges to existing numerical solvers, especially for 3D scenarios. Physics-informed neural networks (PINN) provide a computationally efficient alternative approach for AWE solutions. However, PINNs solve only a single instance of AWE and need to be re-trained for each different subsurface models and frequencies. Fourier neural operators, on the other hand, can solve AWE for a wide range of models and frequencies with a single set of network configuration and parameters. This method, though, requires a tremendous amount of data, which can be difficult and expensive to obtain. Here, we propose a methodology that combines PINNs with Fourier neural operators to learn AWE solution operators that are valid for a wide range of frequencies without requiring any training data. We present two numerical examples that demonstrate the capabilities of the proposed method in modeling the acoustic wavefield accurately and efficiently in the frequency domain.