Abstract
In the Earth’s subsurface, there is an extensive presence of porous, viscoelastic, and anisotropic structures, which profoundly influence the propagation of seismic waves. Poroelasticity, based on the Biot-squirt (BISQ) theory, can characterize the impact of fluid flow on seismic waves. However, an improved mechanistic understanding and mathematical representation of seismic wave propagation in porous formations requires the accounting of both velocity and attenuation anisotropy. Here, we derive the wave equations based on an efficient sum-of-exponentials (SOE) approximation, by combining the porous BISQ equations with the Kjartanssons constant-Q dissipative model to describe seismic wave propagation in poroviscoelastic vertical transversely isotropic (VTI) media. The approximation involves representing the fractional differential equations as a SOE, enabling a reduction in computational costs and storage compared to the traditional L2 scheme. Numerical examples prove that the extended BISQ model can describe the wave propagation characteristics in poroviscoelastic anisotropic media and effectively captures potentially strong, direction-dependent attenuation phenomena.
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