Wave propagation in poroviscoelastic vertical transversely isotropic media: A sum-of-exponentials approximation for the simulation of fractional Biot-squirt equations

Abstract

The presence of porous, viscoelastic, and anisotropic structures profoundly influences 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 require the accounting of velocity and attenuation anisotropy. We derive the wave equations based on an efficient sum-of-exponentials (SOE) approximation by combining the porous BISQ equations with Kjartansson’s constant-Q dissipative model to describe seismic wave propagation in poroviscoelastic vertical transversely isotropic media. The approximation represents the fractional differential equations as an SOE, enabling a reduction in computational costs and storage compared with 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.