Azimuthal amplitude inversion in stress-induced anisotropic media based on stress-dependence of microcrack compliance

The elastic properties of subsurface rocks are almost always stress-dependent, which is usually attributed to stress-sensitive microcracks. Incorporating the effect of stress on microcrack compliance, we use a novel PP-wave reflection coefficient to implement azimuthal amplitude inversion in an anisotropic media induced by horizontal uniaxial stress. Firstly, we assume the initial unstressed media is elastic and isotropic, and possesses a dual-porosity system with stress-insensitive background and randomly distributed and randomly orientated microcracks. When such the media is subjected to horizontal uniaxial stress, normal and tangential compliances of microcracks decrease depending on their orientation with respect to the applied stress. A corresponding stress-induced anisotropy model is proposed, and then utilized to construct the effective elastic stiffness tensor of the uniaxial-stress-induced anisotropic media under the assumption of weak anisotropy. Two stress-induced anisotropy parameters (SIAPs), defined as the combination of elastic modulus, microcrack normal/tangential compliance and horizontal uniaxial stress, are introduced to quantify the magnitude of stress-induced normal and tangential anisotropy, respectively. Existing laboratory data of an uniaxially stressed rock sample illustrate that the effective elastic stiffness tensor possesses satisfactory accuracy. Subsequently, combining the perturbation of the stiffness tensor and the scattering theory, a linearized PP-wave reflection coefficient is established in terms of P-wave modulus, shear modulus, density and SIAPs. The effect of stress on seismic response characteristics is thoroughly analyzed. Finally, based on the azimuthal amplitude difference inversion method with the Cauchy-sparse and low-frequency prior regularization, the SIAPs are estimated form azimuthal seismic data. The inverted SIAPs are then used as inputs to estimate the remaining isotropic parameters. Numerical experiments and field data are used to illustrate the feasibility of the inversion method.