The possibility of using accurate numerical methods to simulate seismic wavefields on unstructured meshes for complex rheologies is explored. In particular, the Discontinuous Galerkin (DG) finite element method for seismic wave propagation is extended to the rheological types of viscoelasticity, anisotropy and poroelasticity. First is presented the DG method for the elastic isotropic case on tetrahedral unstructured meshes. Then an extension to viscoelastic wave propagation based upon a Generalized Maxwell Body formulation is introduced which allows for quasi-constant attenuation through the whole frequency range. In the following anisotropy is incorporated in the scheme for the most general triclinic case, including an approach to couple its effects with those of viscoelasticity. Finally, poroelasticity is incorporated for both the propagatory high-frequency range and for the diffusive low-frequency range.

For all rheology types, high-order convergence is achieved simultaneously in space and time for three-dimensional setups. Applications and convergence tests verify the proper accuracy of the approach. Due to the local character of the DG method and the use of tetrahedral meshes, the presented schemes are ready to be applied for large scale problems of forward wave propagation modeling of seismic waves in setups highly complex both geometrically and physically.