High-frequency wavefield extrapolation using the Fourier neural operator

Abstract

Abstract In seismic wave simulation, solving the wave equation in the frequency domain requires calculating the inverse of the impedance matrix. The total cost strictly depends on the number of frequency components that are considered, if using a finite-difference method. For the applications such as seismic imaging and inversion, high-frequency information is always required and thus the wave simulation is always a challenging task as it demands tremendous computational cost for obtaining dispersion-free high-frequency wavefields for large subsurface models. This paper demonstrates that a data-driven machine learning method, called the Fourier neural operator (FNO), is capable of predicting high-frequency wavefields, based on a limited number of low-frequency components. As the FNO method is for the first time applied to seismic wavefield extrapolation, the experiment reveals three attractive features with FNO: high efficiency, high accuracy and, importantly, the predicted high-frequency wavefields are dispersion free.