Amplitude variation with incidence angle inversion of fluid parameters in porous media using an accurate estimation of the Jacobian matrix

Abstract

Amplitude variation with incidence angle (AVA) or amplitude variation with offset (AVO) inversion provides remarkable information in discriminating lithology in hydrocarbon reservoirs. Fluid parameters (e.g., porosity, water, and oil saturations) are normally obtained through two steps and difficult to obtain from seismic data directly and accurately. Theoretically, the exact Zoeppritz equations and Biot-Gassmann equations can be combined together to invert fluid parameters using seismic data directly. We carry out AVA inversion to invert porosity, water, and oil saturations from seismic data using the exact Zoeppritz equations and accurate estimation of the Jacobian matrix. This matrix is composed of the partial derivatives of P- and S-wave reflection coefficients with respect to fluid parameters. Characteristics of these partial derivatives are analyzed. In addition, the iterative equations for AVA inversion are derived based on the Taylor series expansion. The numerical tests indicate that this algorithm can invert fluid parameters directly and accurately using seismic gathers. Unlike the conventional AVA using the approximations, the inversion using the exact Zoeppritz equations and accurate estimation of the Jacobian matrix is not limited by the selection of incidence angles and reflection interfaces. This method also is applicable to seismic data collected from formations with strong elastic contrast interfaces or large incidence angles.