Simultaneous estimation of Fractured Reservoir Properties and Lithofacies using Azimuthal AVO Probabilistic Nonlinear Inversion Based on Generalized Gaussian Mixture Model

Seismic amplitude variation with offset/angle and azimuth (AVOZ/AVAZ) inversion driven by rock physics is an important tool for the estimation of fractured reservoir properties. Generally, the azimuthal AVO reflection coefficients and fractured reservoir properties are nonlinearly coupled, resulting in strong ill-posedness in azimuthal AVO inversion. We propose an azimuthal AVO probabilistic nonlinear inversion methodology based on a generalized Gaussian mixture model and an improved adaptive-particle-swarm Metropolis-Hastings (APS-MH) algorithm to estimate fractured reservoir properties and lithofacies for fractured reservoirs with a group of vertical fractures. We first derive a novel nonlinear azimuthal AVO reflection coefficient related to the rock-matrix shear modulus, porosity, fracture density and water saturation. The approximation accuracy and inversion feasibility of the derived formulation are verified by a series of theoretical numerical analyses of the stiffness coefficient matrix and azimuthal AVO reflection coefficients. With a generalized Gaussian mixture probability model (GGMM) and the hierarchical Bayesian inference, we establish a nonlinear azimuth-AVO objective function coupling the irregular shape a priori of fractured reservoir properties and the lithology a priori. Combining the global search capability of the adaptive-particle-swarm optimization and the local sampling characteristics of Metropolis-Hastings, a probabilistic azimuthal AVO nonlinear inversion algorithm is developed, which improves the convergence speed and inversion accuracy of reservoir properties. Besides, the methodology simulates the a posteriori probability distribution of rock matrix shear modulus, porosity, fracture density, saturation and lithofacies effectively, which also evaluates the inversion uncertainty of reservoir properties simultaneously. The stability and applicability of the methodology is illustrated by theoretical numerical tests and real seismic data application.