Linearized amplitude variation with offset and azimuth and anisotropic poroelasticity

The normal-to-shear weakness ratio is commonly used as a fracture fluid indicator, but it depends not only on the fluid types but also on the fracture intensity and internal architecture. Amplitude variation with offset and azimuth is commonly used to perform the fluid identification and fracture characterization in fractured porous rocks. We demonstrate a direct inversion approach to utilize the observable azimuthal data to estimate the decoupled fluid (fluid/porosity term) and fracture (normal and shear weaknesses) parameters instead of the calculation of normal-to-shear weakness ratio to help reduce the uncertainties in fracture characterization and fluid identification of a gas-saturated porous medium permeated by a single set of parallel vertical fractures. Based on the anisotropic poroelasticity and perturbation theory, we first derive a linearized amplitude versus offset and azimuth approximation using the scattering function to decouple the fluid indicator and fracture parameters. Incorporating Bayes formula and convolution theory, we propose a feasible direct inversion approach in a Bayesian framework to obtain the direct estimations of model parameters, in which Cauchy and Gaussian distribution are used for the a priori information of model parameters and the likelihood function, respectively. We finally use the non-linear iteratively reweighted least squares to solve the maximum a posteriori solutions of model parameters. The synthetic examples containing a moderate noise demonstrate the feasibility of the proposed approach, and the real data illustrates the stabilities of estimated fluid indicator and dry fracture parameters in gas-saturated fractured porous rocks.