Seismic Wave Simulation in Viscoelastic Two-phase Anisotropic Media

The reservoir parameters are partly predictable by BISQ poroelasticity theory, in which porosity, permeability and fluid viscous coefficient are taken into account. However, the solid matrix in traditional BISQ poroelasticity theory is assumed to be isotropic and elastic, which may not be a practical description of the real medium in respect of velocity dispersion and energy losses. We combine viscoelasticity mechanism with BISQ theory of poroelasticity and consider the solid skeleton to be anisotropic at the same time. We substitute anisotropic matrix parameters and viscoelastic terms for the original BISQ constitutive equations, and discretize them by staggered-grid finite-difference method. The resulting wave field shows that three kinds of wave are coupled with each other, the wavefront of traditional P-wave and SV-wave shows anisotropic feature while the slow P-wavefront is a perfect circle same as the one in isotropic cases. Compared with the wave field of the traditional BISQ model, the dissipation are much stronger when we choose a small quality factor, which mainly contributes to the attenuation of the fast P-wave and SV-wave. However, the attenuation of the slow P-wave are less sensitive to the Q factor than dissipation coefficients. The combination of the two dissipation mechanism may offer us a more precise measurement of the reservoir parameters.