Azimuthal Fourier coefficients inversion for effective stress parameter and fracture parameters

Abstract

Estimating sensitive parameters of fractured sweet spots such as effective stress parameters and fracture properties from azimuthal seismic amplitude data can be useful to optimize development of shale-gas fractured reservoirs. Based on anisotropic Gassmann's equation and the relationship between porosity and effective stress, we propose a simplified expression of the saturated stiffness tensor in terms of exponential effective stress and fracture weaknesses for an HTI model formed by a single rotationally symmetric set of vertical fractures. Using the perturbation in stiffness matrix, we derive a linearized reflection coefficient as a function of effective stress parameter and fracture parameters and corresponding Fourier series expression. Finally, we propose to estimate the effective stress parameter and fracture weaknesses using a three-step azimuthal Fourier-Coefficients (FCs) inversion involving 1) estimating the FCs using azimuthal seismic data, 2) estimating the effective stress parameter using the zeroth FC, and 3) estimating the normal and tangential fracture weaknesses using the second FC. A synthetic seismic data example reveals that the effective stress parameter and fracture parameters can be reliably estimated for the case of SNR ≥ 2. Test on a real data set implies that the proposed inversion method can generate meaningful results that are useful for identifying abnormal overpressure and fracture in reservoirs.