P-Wave Amplitude Versus Offset and Azimuth and Low-Frequency Anisotropic Poro-Acoustoelasticity

Extending the well-established theory of anisotropic poro-elasticity, we introduce a novel framework for low-frequency anisotropic poro-acoustoelastic behavior. It incorporates the paradigm of acousto-elasticity and the low-frequency anisotropic Gassmann equation to quantify how stress influences the elastic and fluid properties, along with seismic reflection coefficients, in fractured porous media under stress. We present a model-based Bayesian inversion methodology to extract key properties from wide-azimuth seismic data acquired in stressed, fluid-saturated fractured media with aligned fractures. These properties include fluid content, the influence of fractures (represented by normal and shear weaknesses), and stress (represented by two stress-dependent parameters). Our approach leverages the theory of anisotropic poro-acoustoelasticity and perturbation theory. We first derive a linearized approximation for the relationship between seismic amplitude versus offset and azimuth (AVOAz) using the stationary phase method. This approximation separates the influence of various parameters, allowing us to estimate the fluid/porosity term, fracture weaknesses, and stress-dependent parameters associated with third-order elastic constants (3oECs). Next, we integrate a convolution model with a Bayesian framework to propose a practical approach for model-regularized AVOAz inversion. This inversion employs an iteratively reweighted least-squares (IRLS) algorithm. Finally, the effectiveness of both the derived approximation and the proposed inversion method is validated using synthetic and real data from stressed, gas-saturated reservoirs with aligned fractures.