  We introduce a high-order weight-adjusted discontinuous Galerkin (WADG)
scheme for the numerical solution of three-dimensional (3D) wave propagation
problems in anisotropic porous media. We use a coupled first-order symmetric
stress-velocity formulation. Careful attention is directed at (a) the
derivation of an energy-stable penalty-based numerical flux, which offers
high-order accuracy in presence of material discontinuities, and (b) proper
treatment of micro-heterogeneities (sub-element variations) in the numerical
scheme. The use of a penalty-based numerical flux avoids the diagonalization of
Jacobian matrices into polarized wave constituents necessary when solving
element-wise Riemann problems. Micro-heterogeneities are accurately and stably
incorporated in the numerical scheme using easily-invertible weight-adjusted
mass matrices. The convergence of the proposed numerical scheme is proven and
verified by using convergence studies against analytical plane wave solutions.
The proposed method is also compared against an existing implementation using
the spectral element method to solve the poroelastic wave equation.
