Velocity-adaptive vertically variable grid optimized elastic wave forward modeling

Abstract Seismic wave forward modeling in complex geological settings requires both high numerical accuracy and computational efficiency. However, the high computational cost of elastic forward modeling for large-scale seismic datasets limits its practical application in industry. To reduce the computational cost of elastic forward modeling and improve efficiency, we propose a velocity-adaptive vertically variable grid-optimized elastic forward modeling method. We obtain the velocity-adaptive grid spacing sequence using a search algorithm and derive an explicit depth-dependent expression for grid spacing via equation fitting. Different from the traditional vertically-variable grid technique, which assumes a linear increase in velocity with depth and may fail to provide adequate sampling in deep layers with velocity reversals, the proposed method dynamically adjusts the grid spacing to velocity variations. This adaptivity mitigates wavefield distortions in low-velocity regions while avoiding excessive computational costs in high-velocity zones. Moreover, by using P- and S- component formulations derived from the complete elastic velocity-stress system, adaptive grid spacings are assigned to different wave modes while the two components remain defined in the same elastic medium. This strategy effectively eliminates the computational redundancy caused by a unified grid spacing constrained by the lowest velocity. Numerical experiments demonstrate that, compared to linear vertically-variable and fine-uniform grid-based elastic forward modeling, the proposed velocity-adaptive vertically-variable grid approach achieves a favorable balance between modeling accuracy and computational efficiency.