Full waveform inversion based on deep learning and the phase-preserving symplectic partitioned Runge-Kutta method

To obtain more accurate full waveform inversion results, we present a forward modeling method with minimal phase error, low numerical dispersion, and high computational efficiency. To solve the 2D acoustic wave equation, we utilize a finite-difference (FD) scheme with optimized coefficients for spatial discretization, combined with a phase-preserving symplectic partitioned Runge-Kutta method for temporal discretization. This results in the development of the optimized symplectic partitioned Runge-Kutta (OSPRK) forward modeling method. We further apply the OSPRK method in conjunction with a recurrent neural network (RNN) for full waveform inversion (FWI). Our study explores the impact of various loss functions, Nadam optimizer parameters, and the incorporation of physical information operators on inversion performance. Numerical experiments demonstrate that the OSPRK method significantly reduces numerical dispersion compared to traditional FD methods. The Log-Cosh loss function offers superior stability across different learning rates, while the Nesterov-accelerated Adaptive Moment Estimation (Nadam) optimizer with optimized parameters greatly enhances convergence speed and inversion accuracy. Furthermore, the inclusion of physical information operators markedly improves inversion outcomes.