Incorporating the Nearly Constant Q Models Into 3-D Poro-Viscoelastic Anisotropic Wave Modeling

The Earth is often characterized by viscoelastic rocks, porous sediments, and anisotropic structures. Poroelasticity with Biot's theory is considered fundamental to describe the interaction between the deformation of the elastic porous solid and the flow of fluid in the porous structure. The quality factor (Q) in the theory of viscoelasticity relates seismic wave attenuation and dispersion to physical properties of the Earth's interior, e.g., temperature, stress, and composition. However, the constant Q wave equation in its time-domain differential form remains difficult to solve when describing the attenuation in an explicitly specified Q parameter. Here, we introduce the first-and second-order nearly constant Q models capable of describing the attenuation of the solid skeleton, thereby extending the Biot and Biot-squirt (BISQ) models to poro-viscoelastic media. The bulk and shear moduli of the solid frame are represented by the modified relaxation function. By presenting examples with finite-difference time-domain (FDTD) numerical modeling for seismic wavefields in anisotropic, viscoelastic porous media including transversely isotropic media with a vertical symmetry axis [vertical transverse isotropy (VTI)] and orthorhombic media, we demonstrate that the extended Biot and BISQ models provide good descriptions of the wave propagation in poro-viscoelastic anisotropic media and can thus help better understand the Earth's interior.