P-SV ELASTIC WAVEFIELD SIMULATION METHOD BASED ON FOURIER FEATURE PHYSICS-INFORMED NEURAL NETWORKS

Numerical seismic wavefield simulation is an important branch of computational solid-Earth geophysics. Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations. However, when applied to strongly oscillatory, multicomponent coupled elastic wavefields, PINNs still face difficulties associated with the spectral bias of neural networks and the loss-gradient imbalance caused by softly imposed initial conditions. Based on the two-dimensional isotropic P-SV elastic wave equations, this study develops a Fourier-feature-embedded physics-informed neural network (FF-PINN) method for elastic-wave forward modeling. A Gaussian Fourier feature mapping is introduced at the network input to project the spatiotemporal coordinates into a high-dimensional feature space. This mapping mitigates the spectral bias of multilayer perceptrons and enhances their ability to represent oscillatory wavefields. In addition, two parallel subnetworks are employed to approximate the horizontal and vertical displacement components separately, enabling the joint modeling of coupled P- and SV-wave propagation. An approximate distance function is used to transform the network outputs, ensuring that the zero-displacement and zero-velocity initial conditions are strictly satisfied by construction. Systematic ablation experiments are conducted using a homogeneous model to investigate the effects of the Fourier scale parameter, activation function, and soft and hard enforcement of the initial conditions. The method is then comprehensively evaluated using a three-layer curved-interface model, a dipping-fault model containing a weakened zone, and a mixed-Gaussian random heterogeneous model. The selected cases cover curved interfaces, localized velocity weakening, random heterogeneity, and multi-source interference. These models represent increasingly complex medium structures and source conditions and are used to examine the applicability of the method to coupled elastic-wave propagation. The results show that FF-PINN can clearly capture the propagation behavior of P-SV waves at complex interfaces and reproduce the principal spatial patterns of both horizontal and vertical displacement fields. The numerical experiments demonstrate the effectiveness of the developed method for two-dimensional elastic-wave forward modeling and its applicability to different complex media and source configurations.