Azimuthal P-wave AVA Inversion for Fracture Orientation and Density



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This thesis studies the numerical seismic modeling of a simulated fractured medium to analyze variations of seismic reflection amplitudes with incident and azimuthal angles (AVAZ). The intent is to extract the information about the fracture orientation and intensity of a fractured medium. The effective compliance tensor for a fractured medium can be written as the sum of the compliance tensor of the unfractured background rock and the compliance tensor for the set of aligned fractures. Based on the assumption of rotationally invariant fracture sets, two fracture compliances—the normal and tangential compliance—are required to specify the fracture compliance tensor. The stiffness tensor can be attained by inverting the compliance tensor. The P-wave reflection coefficients for arbitrary anisotropic media are obtained by two methods (Chattopadhyay, 2004; Schoenberg and Protazio, 1992). Rüger’s linear approximation can accurately estimate the exact reflection coefficients and hence it is widely used in the linear inversion. Analysis is applied in the decision to choose between the incident angle and the average angle for Rüger’s linear approximation. Linear AVAZ inversions, based on singular value decomposition (SVD), and non-linear AVAZ inversion, based on generalized linear inversion (GLI), for fracture orientation and HTI anisotropy parameters, were applied on P-wave reflection coefficients with variable incident angle and azimuth. However, 90˚ ambiguity in the estimation of the fracture orientation always exists. Sensitivity analysis of the inversion results, including S/N ratio, maximum incident angle used, and error propagation, confirms the accuracy of the amplitude analysis.



AVAZ, Fracture behavior, Fracture Density, Effective medium theory, Singular value decomposition (SVD), GLI, Error Analysis