Parallel Numerical Simulation of 3D Anisotropic Elastic Wave Equations with Sparse Matrix Based on Compact Staggered Finite Difference

Numerical simulation of elastic waves in anisotropic media is a fundamental technique for seismic exploration and the characterization of subsurface geological structures. Compared with the conventional finite-difference method, the compact finite-difference method offers higher numerical accuracy and more effective suppression of numerical dispersion, making it well suited for high-precision elastic-wavefield simulations. However, its reliance on derivative-matrix operations imposes significant computational limitations. As the size of the computational domain increases, the derivative matrices grow rapidly in dimension, leading to substantial memory consumption and computational costs, which hinder the efficient simulation of large-scale three-dimensional (3D) anisotropic elastic-wave propagation. To address this limitation, we develop a high-precision discretization scheme for the 3D anisotropic elastic-wave equations based on compact finite-difference theory, while retaining its favorable characteristics of low numerical dispersion and high computational accuracy. To overcome the high memory requirements and low computational efficiency associated with dense derivative matrices, the derivative matrices are sparsified and implemented using sparse matrix storage and operations to eliminate redundant computations. Furthermore, the algorithm is optimized within a parallel computing framework to enable efficient and high-precision numerical simulation of large-scale 3D anisotropic elastic-wave equations. Numerical experiments on representative anisotropic models demonstrate that the proposed sparsified compact finite-difference algorithm preserves the low numerical dispersion and high wavefield accuracy of the conventional compact finite-difference method while substantially reducing memory consumption and computational costs for large-scale models, with significant parallel acceleration. The proposed method accurately and efficiently captures elastic-wave propagation in complex anisotropic media. This study overcomes the limitations of the compact finite-difference method in large-scale numerical simulations and provides an effective computational approach for high-precision, large-scale seismic-wave forward modeling under complex geological conditions.