Elastic Mimetic Finite-differences in the Presence of Topography

Finite-differences (FD) are the most popular schemes for seismic modelling. For elastic problems, staggered-grid FD offers many advantages in terms of accuracy and efficiency. However, FD methods typically struggle at modelling seismic waves in the presence of a non-flat topography. This is due to two main issues: First of all, the free-surface boundary condition is badly represented with classical differentiating operators and, additionally, the topography is poorly represented by regular Cartesian grids. We introduce a new FD scheme which combines mimetic finite-difference operators with a deformed-grid approach to successfully model elastic waves in 3D scenarios including topography. Our results show that our scheme produces precise results with few points per wavelength, which translates in low computational requirements for large 3D simulations, and compares well with a discontinuous Galerkin method.