Linearized AVOA and Anisotropic Poroelasticity

Our goal is to demonstrate an AVOA inversion approach to utilize the observable azimuthal seismic reflection data to extract the fluid and fracture properties in a gas-saturated fractured reservoir. Starting from Gassmann’s anisotropic poroelasticity theory, we first derive a linearized AVOA approximation in terms of fluid and dry-rock fracture parameters using the scattering function and perturbations in dry-rock stiffness matrix of a horizontal transversely isotropic (HTI) medium formed by a system of aligned vertical fractures embedded in an isotropic background, which avoids the complicated nonlinear relationship between the characteristics of fluid and fracture and the seismic response of azimuthal amplitudes. Incorporating convolution model and Bayes formula, a feasible Bayesian AVOA inversion method is then presented to estimate the fluid and fracture parameters directly. Cauchy and Gaussian probability distribution are used for the a priori information of model parameters and the likelihood function, respectively, and the nonlinear iteratively reweighted least squares (IRLS) strategy is finally utilized to solve the maximum a posteriori solutions of model parameters. The synthetic examples containing a moderate noise demonstrate the feasibility of AVOA inversion, and the real data illustrates the inversion stabilities of fluid and fracture parameters in a gas-saturated fractured reservoir.