Mimetic Modeling of Anisotropic Elastic Waves

Abstract:

In the broad field of computational geophysics, one of the most challenging problems is the modeling of seismic data sets that corresponds to complex media with irregular geometry and non-homogeneous anisotropic features. In such scenarios, the corresponding elastic wave equation that emerges from the model must be accurately and efficiently solved by means of numerical methods. In particular, fluxes involved in this equation are represented on the model as a non-diagonal symmetric and positive definite tensor which can potentially have jump discontinuities over a material boundary that are not aligned with the coordinate axis. High order mimetic differential operators are discrete approximations of their continuous counterparts and have been broadly used with success in multiple fields of fluid and solid mechanics. We model anisotropic fluxes using a novel three-dimensional mimetic flux operator. In this talk, we examine the viability of employing an explicit approach to construct a high order mimetic scheme along with second and fourth order temporal discretization for solving a three-dimensional fully anisotropic elastic wave problem on a staggered mesh.