Seismic Wave Simulation for Complex Rheologies on Unstructured Meshes

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.