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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.

The study of thin-bed seismic phenomena is important in crustal, exploration and engineering seismology. Presently, seismic reflectivity theories based on single-interface assumption are widely used though they are only suitable for thick deposits. Thin-bed reflectivity theories are established on complex propagator matrices and are difficult to be applied to reveal thin-bed properties directly. Therefore, an approximation of thin-bed PP-wave reflection coefficients (RPP) is derived in this paper. First, the relationship between thin-bed RPP and incidence angles is analyzed through series expansion method. For PP-wave, its reflection coefficients are even power series functions of sine incidence angles. Then, for small incidence, RPP of the thin bed is further simplified into a second-order series approximation with respect to the sine incidence angles. Simulations and accuracy analyses of the approximate formula show that approximation errors are smaller than 5% as the incidence angles smaller than 20 degrees. Based on this approximate formula, an approach is given for estimating thin-bed properties including P-wave impedance ratios and thickness. The estimation approach is applied in properties estimation of a thin bed model. Perfect performances of the model example show the future potentiality of the approximate formula in thin-bed Amplitude-Versus-Offset (AVO) analysis and inversion.

Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS data. This method assumes that the parameters satisfy a normal distribution and introduces the covariance matrix to describe the degree of correlation between the parameters and thus to improve the inversion stability. Then, we suppose that the parameter sequence is subject to the Cauchy distribution and employs another matrix Q to describe the parameter sequence sparseness to improve the inversion result resolution. Tests on both synthetic and real multi-component data prove that this method is valid, efficient, more stable, and more accurate compared to methods using PP data only.