Non-uniform grid finite-difference seismic wave simulation using multiblock grids by adding positive and negative singularity pairs

SUMMARY The finite-difference method (FDM), limited by uniform grids, often encounters severe oversampling in high-velocity regions when applied to multiscale subsurface structures, leading to reduced computational efficiency. A feasible solution to this issue is the use of non-uniform grids. However, previous discontinuous grid approaches required careful consideration of interpolation operations in transition regions, while single-block continuous grids lacked flexibility. This paper proposes a novel approach using multiblock stretched grids with positive and negative singularities to achieve non-uniform grids, the numerical simulation of seismic waves is realized by combining it with the curvilinear grid FDM (CGFDM). Our method facilitates seamless information exchange between coarse and fine grids without additional interpolation or data processing and allows for flexible grid configurations by adjusting singularity pairs. The effectiveness of our approach is verified through comparisons with the generalized reflection/transmission method and the finite-element method. Numerical experiments demonstrate the method's reliable accuracy and significant reduction in grid points compared to uniform grids. Although the stability of our method has not been rigorously mathematically proven, we demonstrate that the algorithm remains applicable for sufficiently long simulations to address realistic scenarios.