Pressure Effects on Plane Wave Reflection and Transmission in Fluid-Saturated Porous Media

Abstract

The wave reflection and transmission (R/T) coefficients in fluid-saturated porous media with the effect of effective pressure are rarely studied, despite the ubiquitous presence of in situ pressure in the subsurface Earth. To fill this knowledge gap, we derive exact R/T coefficient equations for a plane wave incident obliquely at the interface between the dissimilar pressured fluid-saturated porous half-spaces described by the theory of poro-acoustoelasticity (PAE). The central result of the classic PAE theory is first reviewed, and then a dual-porosity model is employed to generalize this theory by incorporating the impact of nonlinear crack deformation. The new velocity equations of generalized PAE theory can describe the nonlinear pressure dependence of fast P-, S- and slow P-wave velocities and have a reasonable agreement with the laboratory measurements. The general boundary conditions associated with membrane stiffness are used to yield the exact pressure-dependent wave R/T coefficient equations. We then model the impacts of effective pressure on the angle and frequency dependence of wave R/T coefficients and synthetic seismic responses in detail and compare our equations to the previously reported equations in zero-pressure case. It is inferred that the existing R/T coefficient equations for porous media may be misleading, since they lack consideration for inevitable in situ pressure effects. Modeling results also indicate that effective pressure and membrane stiffness significantly affect the amplitude variation with offset characteristics of reflected seismic signatures, which emphasizes the significance of considering the effects of both in practical applications related to the observed seismic data. By comparing the modeled R/T coefficients to the results computed with laboratory measured velocities, we preliminarily confirm the validity of our equations. Our equations and results are relevant to hydrocarbon exploration, in situ pressure detection and geofluid discrimination in high-pressure fields.