Model Parameterization and PP-Wave Amplitude Versus Angle and Azimuth (AVAZ) Direct Inversion for Fracture Quasi-Weaknesses in Weakly Anisotropic Elastic Media
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Homogeneous isotropic or vertically transverse isotropic rocks containing a single set of aligned, vertical fractures exhibits an effective long-wavelength horizontally transverse isotropy (HTI) or orthorhombic anisotropy. The estimation for properties of subsurface fractures has significant application in characterization of naturally fractured rocks. The purpose of this work is to demonstrate an approach of amplitude versus angle and azimuth (AVAZ) direct inversion for fracture characterization utilizing the observable wide-azimuth seismic reflection data in weakly anisotropic elastic media. The simplest single fracture system is HTI model. Much attention has been devoted to the weak-contrast and weak-anisotropy HTI model due to its significance for reservoir characterization. Treating the fractures as linear-slip interfaces, we begin with the derivation for perturbations of stiffness matrix at a planar weak-contrast interface separating two weakly anisotropic HTI half-spaces that share the same fracture normal, as a function of background elastic moduli and fracture parameters. Using the perturbation matrix and scattering function, we then derive a linearized PP-wave reflection coefficient of a weakly HTI medium in terms of P- and S-wave moduli, density, and fracture weaknesses, which builds a linearized relationship between the fracture parameters and reflection coefficient with the priority calculation for the azimuth of fracture normal based on the least square ellipse fitting method. Finally, we reformulate the reflectivity caused by weakness differences to parameterize the weaknesses for the so-called quasi-weaknesses and propose a method of Bayesian AVAZ direct inversion in seismic detection of subsurface fractures. Cauchy and Gaussian probability distribution are used for the a priori information of model parameters and the likelihood function, and the maximum a posteriori estimate of quasi-weaknesses is reasonably estimated with the nonlinear iteratively reweighted least squares algorithm. Synthetic and real data illustrate the applicability of the proposed AVAZ inversion method in fracture characterization.
KeywordsBayesian AVAZ inversion Horizontally transverse isotropy and orthorhombic anisotropy Fracture quasi-weaknesses Maximum a posteriori estimate
We would like to express our gratitude to the sponsorship of National Natural Science Foundation of China (41674130, U1562215), and National Basic Research Program of China (2014CB239201), National Grand Project for Science and Technology (2016ZX05027004-001, 2016ZX05002005-09HZ), and the Fundamental Research Funds for the Central Universities for their funding in this research. We also thank Alexey Stovas and another anonymous reviewer for their constructive suggestions.
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