Numerical modeling of elastic wave propagation in the subsurface requires applicability to heterogeneous, anisotropic and discontinuous media, as well as support of free surface boundary conditions. Here we study the cell-centered finite volume method Multi-Point Stress Approximation with weak symmetry (MPSA-W) for solving the elastic wave equation. Finite volume methods are geometrically flexible, locally conserving and they are suitable for handling material discontinuities and anisotropies. For discretization in time we have utilized the Newmark method, thereby developing an MPSA-Newmark discretization for the elastic wave equation. An important aspect of this work is the integration of absorbing boundary conditions into the MPSA-Newmark method to limit possible boundary reflections. Verification of the MPSA-Newmark discretization is achieved through numerical convergence analyses in 3D relative to a known solution, demonstrating the expected convergence rates of order two in time and up to order two in space. With the inclusion of absorbing boundary conditions, the resulting discretization is verified by considering convergence in a quasi-1d setting, as well as through energy decay analyses for waves with various wave incidence angles. Lastly, the versatility of the MPSA-Newmark discretization is demonstrated through simulation examples of wave propagation in fractured, heterogeneous and transversely isotropic media.

翻译：地下弹性波传播的数值模拟需要适用于非均匀、各向异性及不连续介质，并支持自由表面边界条件。本文研究了采用弱对称多节点应力近似（MPSA-W）的单元中心有限体积法来求解弹性波方程。有限体积法具有几何灵活性、局部守恒性，且适合处理材料不连续性和各向异性。在时间离散化方面，我们采用了Newmark方法，从而发展出弹性波方程的MPSA-Newmark离散格式。本工作的一个重要方面是将吸收边界条件整合到MPSA-Newmark方法中，以限制可能的边界反射。通过对已知解进行三维数值收敛分析，验证了MPSA-Newmark离散格式，证明了其在时间上具有二阶、空间上最高二阶的预期收敛阶。通过纳入吸收边界条件，该离散格式在准一维设定中的收敛性分析以及针对不同波入射角的能量衰减分析得到了验证。最后，通过波在裂隙介质、非均匀介质和横向各向同性介质中传播的模拟算例，展示了MPSA-Newmark离散格式的广泛适用性。