Wave propagation in the poro-viscoelastic orthorhombic two-phase media: plane-wave theory and wavefield simulation

Abstract

SUMMARY Most researches on the Biot-squirt (BISQ) model are limited to the poroelastic transverse isotropic (TI) media. Actually, the poro-viscoelasticity and the orthorhombic anisotropy are closer to the realistic properties of many reservoir media. Therefore, we expand the BISQ model theory to the poro-viscoelastic orthorhombic media and develop the corresponding constitutive relation and 3-D wave equations in the time domain. Here, the generalized Zener linear body model is introduced to describe the relaxation effect of the solid skeleton, and the pore fluid is assumed to be saturated. The expressions of the complex and phase velocities for two quasi-compressional waves qP fast (qP1) and qP slow (qP2), and two quasi-shear waves qS1 and qS2 are obtained from the homogeneous plane-wave analysis, respectively. While introducing the viscoelasticity to our model, the attenuation value predicted by the conventional quality factor is not accurate, and the group velocity representing the position of the wave front in the poroelastic model becomes meaningless. So we derive the novel quality factor and the energy velocity expression by invoking the energy balance equation and the Poynting theorem. Two examples are implemented. First, the 3-D multicomponent wavefield is simulated. The snapshots show the orthorhombic anisotropy and viscoelastic effects lead to significant changes in the wavefield. The comparison to the synthetic seismogram in the poroelastic model indicates that the relaxed skeleton can describe the strong attenuation of seismic waves in the seismic exploration band. Secondly, the variations in the velocities and the quality factor curves with propagation direction, frequency and porosity are analysed. Both examples present the characteristics of wave propagation in the poro-viscoelastic orthorhombic media and validate the correctness of the proposed theory and equations.