A Computationally Efficient Deep Learning Approach to Approximate the 3D-Elastic Wave Equation

Accurate numerical simulation of seismic wave propagation is fundamental to applications such as full waveform inversion (FWI), earthquake analysis, and non-destructive testing. These simulations often require fine spatial and temporal discretizations to avoid numerical dispersion, particularly in near-surface environments where low velocities and high frequencies demand dense grids. As a result, the computational cost of wave modelling remains a significant challenge. Recent advances in machine learning offer promising alternatives, particularly through neural networks that can approximate the forward operator of the wave equation. In this study, we present a neural operator designed to efficiently approximate 3-D elastic wave propagation in near-surface settings, with a focus on S-wave-dominated surface wavefields. Our approach leverages the discrete cosine transform (DCT) to reduce the dimensionality of the input velocity models, improving training efficiency and generalization. Wavefields are represented in the Fourier domain, substantially reducing dataset size and memory requirements. Preliminary results show that the proposed neural operator achieves low prediction errors and strong generalization from limited training data. This approach offers a scalable and computationally efficient alternative to traditional numerical solvers, with potential applications in real-time modelling, inversion, and large-scale geophysical problems.