  Wave propagation in real media is affected by various non-trivial physical
phenomena, e.g., anisotropy, an-elasticity and dissipation. Assumptions on the
stress-strain relationship are an integral part of seismic modeling and
determine the deformation and relaxation of the medium. Stress-strain
relationships based on simplified rheologies will incorrectly predict seismic
amplitudes, which are used for quantitative reservoir characterization.
Constitutive equations for the rheological model include the generalized
Hooke's law and Boltzmann's superposition principal with dissipation models
based on standard linear solids or a Zener approximation.
  In this work, we introduce a high-order discontinuous Galerkin finite element
method for wave equation in inhomogeneous and anisotropic dissipative medium.
This method is based on a new symmetric treatment of the anisotropic
viscoelastic terms, as well as an appropriate memory variable treatment of the
stress-strain convolution terms. Together, these result in a symmetric system
of first order linear hyperbolic partial differential equations. The accuracy
of the proposed numerical scheme is proven and verified using convergence
studies against analytical plane wave solutions and analytical solutions of
viscoelastic wave equation. Computational experiments are shown for various
combinations of homogeneous and heterogeneous viscoelastic media in two and
three dimensions.
