Elastic Impedance Parameterization and Inversion for Anisotropy in HTI Media

Abstract

A single set of vertically aligned fractures embedded in a purely isotropic background medium may be considered to be long-wavelength effective transversely isotropy with a horizontal symmetry axis (HTI). The estimation of fracture weaknesses is significant to characterize the anisotropy in HTI media. The elastic inverse scattering theory can be utilized for the inversion for elastic and anisotropic parameters in weakly anisotropic and heterogeneous HTI media. Based on the seismic scattering theory, we first derive a linearized PP- wave reflection coefficient in terms of P- and S-wave moduli, density as well as the fracture weaknesses in weakly anisotropic and heterogeneous media. A novel parameterization method of elastic impedance variation with angles of incidence and azimuth (EIVAZ) in terms of the fracture weakness reflectivity is then proposed. To refine the stability and lateral continuity, we develop the EIVAZ inversion method in Bayesian framework incorporating Cauchy-sparse regularization and low-frequency information regularization, and the nonlinear iteratively reweighted least squares (IRLS) strategy is used to estimate the fracture weaknesses in the end. A test on a real data shows that the estimated results agree well with the well log interpretation, and our method appears to be a stable approach to characterize the fracture-developed zones.