First-order approximate analytical expressions of oblique incident elastic wave at an interface of porous media saturated with a non-viscous fluid

Abstract

The analysis technology of Amplitude Variation with Offset (AVO) is one of the important methods for oil and gas reservoir prediction. Zoeppritz equation and its approximations are the theoretical basis of AVO analysis, which assumes that the upper and lower media of a horizontal interface are single-phase media. Limited by this assumption, AVO analysis has limited prediction and identification accuracy for complex porous reservoirs. In view of this, the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived. Firstly, the incident and scattering characteristics of various waves at the interface of porous media are analyzed, and the displacement vectors generated by these elastic waves are described by exponential function. Secondly, the kinematic and dynamic boundary conditions at the interface of porous media are discussed. Thirdly, by substituting the displacement vectors of incident and scattered waves into boundary conditions, the exact analytical equation is derived. Then, considering the symmetry of scattering matrix in the equation, the exact analytical expressions of each scattered wave are obtained. Furthermore, under the assumptions of small incident angle, weak elasticity at an interface of porous media, and ignoring the second- and higher-order terms, the first-order approximate analytical expressions are derived. Establishing a model of sandstone porous media with different porosity in upper and lower media, the correctness of the approximate analytical expressions is verified, and the elastic wave response characteristics of lithology and pore fluids are analyzed.