Second-order approximation of reflection coefficient based on decomposition of scattering matrix

The first-order approximation of the exact Zoeppritz equation is widely used in conventional AVO inversions, which is more suitable for the interface with weak medium variations and the problem of small angle or short offset. The assumptions will lead to calculation errors, which are not conducive to accurate inversion of density and prediction of complex reservoirs and medium-deep reservoirs. And seismic data near the critical angle cannot be fully used. The high-order approximation method based on the exact equation of reflection/transmission coefficients is too complicated. The physical meaning of the process of second-order Taylor expansion of the reflection/transmission coefficients based on the eigenvector matrices of up-and-down waves and matrix symmetry is not clear enough. And the second-order approximation is also not perfect enough. In this paper, a high-order approximation of the scattering matrix based on the incident/scattering matrix of P-SV plane wave is presented. The scattering matrix can be decomposed into the background matrix, the first- and second-order perturbation matrices, and the background term based on the theory of perturbations. The background term, first- and second-order perturbation terms can be derived respectively and the second-order approximation of P wave reflection coefficient can be further obtained. The model comparison analysis shows that the second-order approximation obtained in this paper has higher accuracy in the case of medium-high angle and even near-critical angle incidence and more sensitive to the density variations. It provides a basis for making full use of large-angle or long-offset seismic data and the accurate inversion of physical parameters. © 2019, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.