Approximate equations of PP-, PS1- and PS2-wave reflection coefficients in fluid-filled monoclinic media

Abstract

SUMMARY Studying the seismic reflection characteristics of fractured strata can provide a theoretical basis for the exploration of unconventional oil and gas reservoirs. When several (more than 1) sets of oblique vertical fractures that are rotationally non-invariant are embedded in an isotropic or vertical transversely isotropic (VTI) background, the stratum exhibits equivalent monoclinic anisotropy. However, the exact algorithm of the reflection and transmission coefficients of monoclinic media is algebraically complicated and difficult to use in theoretical analysis and application. In this paper, under the assumption that fractures are filled with fluid, based on the linear-slip theory, we solve the phase velocities of monoclinic media from the Christoffel equations by using the first-order perturbation method and then derive the recursive equations of the PP-, PS1-, and PS2-wave reflection coefficients. The theoretical analysis results show that for an interface of monoclinic media, when setting a series of fracture densities for the lower medium, the relative error of the proposed approximate reflection coefficient of the PS2 wave is less than 5.7 per cent, and those of the PP and PS1 waves are generally less than 2.5 per cent for a wide range of anisotropy strength and impedance contrast; when setting a series of fracture densities for the upper medium, the relative error of the proposed approximate reflection coefficients of the PP, PS1 and PS2 waves are generally less than 6.4, 5.1 and 4.5 per cent, respectively. When degenerated to the horizontal transversely isotropic model, compared with Rüger's approximation, at incidence angles of 1–30°, the two results are almost coincident, but the proposed approximations are closer to the exact solutions.