Wave propagation modeling using machine learning-based finite difference scheme

Abstract

The staggered-grid finite-difference (SGFD) method is essential in wave forward modeling, waveform inversion, and seismic imaging. However, the numerical dispersion that can lead to reduced accuracy in simulations may arise from either coarse spatial discretization or a suboptimal SGFD scheme. Given the high computational cost associated with finer spatial steps, employing the optimal SGFD scheme offers a feasible and effective approach for dispersion suppression. However, the commonly used SGFD schemes are limited by a narrow maximum wavenumber range, reducing their dispersion suppression efficacy. To address this issue, a machine learning-based SGFD scheme is presented in this study. A composite objective function that combines the sum of the absolute error and the maximum absolute error is proposed, aiming to broaden the maximum wavenumber range while minimizing the cumulative error. A physics-consistent neural network is constructed by specifying weights, biases, activation functions, layer connections, and loss function, enabling the back-propagation of the proposed objective function within the machine learning framework to yield globally optimal SGFD coefficients.