Azimuthally anisotropic elastic impedance parameterisation and inversion for anisotropy in weakly orthorhombic media

Abstract

ABSTRACTA single set of vertically aligned fractures embedded in a horizontal fine layering may be considered a long-wavelength effective orthorhombic medium. Estimation of Thomsen anisotropic parameters and fracture weaknesses is of vital importance to characterise the orthorhombic anisotropy in orthorhombic media. Our goal is to demonstrate an azimuthally anisotropic elastic impedance parameterisation and Bayesian inversion approach to estimate orthorhombic anisotropy in a fractured reservoir. Previously derived reflection coefficient equations are limited to the assumption of a horizontally layered medium, which may be not suitable for orthorhombic media. Based on elastic inverse scattering theory, we first derive a linearised PP-wave reflection coefficient equation in terms of orthorhombic anisotropic parameters containing Thomsen anisotropic parameters and fracture weaknesses in a weakly orthorhombic medium. Using a new parameterisation for these orthorhombic anisotropic parameters, we derive an anisotropic elastic impedance equation variation with angles of incidence and azimuth. We perform anisotropic inversion in a Bayesian framework with the regularisation of Cauchy-sparse constraint and smoothing-model constraint. Using the nonlinear iteratively reweighted least squares algorithm, we iteratively estimate the orthorhombic anisotropy characterised by Thomsen anisotropic parameters and fracture weaknesses. Tests on both synthetic and real data validate the proposed approach.