A Finite Volume Method for Elastic Waves in Heterogeneous, Anisotropic and Fractured Media

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.