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.

Seismic amplitude variation with offset (AVO) inversion is a cornerstone of oil and gas reservoir prediction, enabling the estimation of subsurface elastic parameters and characterization of stratigraphic interfaces. However, balancing inversion accuracy and computational efficiency remains a critical challenge. To address this, we propose a novel probabilistic AVO inversion framework integrating three key innovations. First, we derive a high-precision quadratic approximation for compressional (P-wave) reflectivity by retaining first- and second-order terms from the exact Zoeppritz equations through a perturbation strategy. This approach significantly enhances accuracy compared to conventional linear approximations, particularly in reflecting the true amplitude variation at large angles. Subsequently, to improve lateral continuity and stratigraphic resolution, we introduce an instantaneous phase constraint derived via the Hilbert transform. This constraint leverages phase sensitivity to seismic waveform coherence, ensuring geologically consistent interface characterization during stochastic inversion. Furthermore, we develop a hybrid Markov Chain Monte Carlo (MCMC) algorithm combining adaptive Gibbs sampling with the independent doubly adaptive rejection Metropolis sampling (IA2RMS) method. This framework efficiently samples high-dimensional posterior probability density functions (PDFs) of elastic parameters: Gibbs sampling generates adaptive proposal distributions, while IA2RMS accelerates Markov chain convergence through location- and scale-adjustable proposals. Numerical experiments and field seismic data demonstrate the robustness and feasibility of the proposed probabilistic AVO inversion method.

Accurate characterization of the fault system is crucial for the exploration and development of fractured reservoirs. The fault characterization technique based on multi-azimuth and multi-attribute fusion is a hotspot. In this way, the fault structures of different scales can be identified and the characterization details of complex fault systems can be enriched by analyzing and fusing the fault-induced responses in multi-azimuth and multi-type seismic attributes. However, the current fusion methods are still in the stage of violent information stacking in utilizing fault information of multi-azimuth and multi-type seismic attributes, and the fault or fracture semantics in multi-type attributes are not fully considered and utilized. In this work, we propose a physic-guided multi-azimuth multi-type seismic attributes intelligent fusion method, which can mine fracture semantics from multi-azimuth seismic data and realize the effective fusion of fault-induced abnormal responses in multi-azimuth seismic coherence and curvature with the cooperation of the deep learning model and physical knowledge. The fused result can be used for multi-azimuth comprehensive characterization for multi-scale faults. The proposed method is successfully applied to an ultra-deep carbonate field survey. The results indicate the proposed method is superior to self-supervised-based, principal-component-analysis-based, and weighted-average-based fusion methods in fault characterization accuracy, and some medium-scale and microscale fault illusions in multi-azimuth seismic coherence and curvature can be removed in the fused result.

Reservoirs with a group of vertical fractures in a vertical transversely isotropic (VTI) background are considered as orthorhombic (ORT) medium. However, fracture detection in ORT medium using seismic inversion methods remains challenging, as it requires the estimation of more than eight parameters. Assuming the reservoir to be a weakly anisotropic ORT medium with small contrasts in the background elastic parameters, a new azimuthal elastic impedance equation was first derived using parameter combinations and mathematical approximations. This equation exhibited almost the same accuracy as the original equation and contained only six model parameters: the compression modulus, anisotropic shear modulus, anisotropic compression modulus, density, normal fracture weakness, and tangential fracture weakness. Subsequently, a stepwise inversion method using second-order derivatives of the elastic impedance was developed to estimate these parameters. Moreover, the Thomsen anisotropy parameter, epsilon, was estimated from the inversion results using the ratio of the anisotropic compression modulus to the compression modulus. Synthetic examples with moderate noise and field data examples confirm the feasibility and effectiveness of the inversion method. The proposed method exhibited accuracy similar to that of previous inversion strategies and could predict richer vertical fracture information. Ultimately, the method was applied to a three-dimensional work area, and the predictions were consistent with logging and geological a priori information, confirming the effectiveness of this method. Summarily, the proposed stepwise inversion method can alleviate the uncertainty of multi-parameter inversion in ORT medium, thereby improving the reliability of fracture detection.

Seismic prediction of cracks is of great significance in many disciplines, for which the rock physics model is indispensable. However, up to now, multitudinous analytical models focus primarily on the cracked rock with the isotropic background, while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth. Hence, we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy, respectively, by forty groups of numerical experiments. Based on the conclusion from the experiments, the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background. Further, we comprehensively analyzed, according to the developed model, effects of the crack dip angle, background anisotropy, filling fluid and crack density on the effective elastic properties of the cracked rock. The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P- and SH-wave velocities, whereas they have relatively small effects on the SV-wave velocity anisotropy. Moreover, the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters, while its effects on shear coefficients depend on the crack dip angle. The increasing crack density reduces velocities of the dry rock, and decreasing rates of the velocities are affected by the crack dip angle. By comparing with exact numerical results and experimental data, it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients. Moreover, the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Classical multi-channel technology can significantly reduce the pre-stack seismic inversion uncertainty, especially for complex geology such as high dipping structures. However, due to the consideration of complex structure or reflection features, the existing multi-channel inversion methods have to adopt the highly time-consuming strategy of arranging seismic data trace-by-trace, limiting its wide application in pre-stack inversion. A fast pre-stack multi-channel inversion constrained by seismic reflection features has been proposed to address this issue. The key to our method is to re-characterize the reflection features to directly constrain the pre-stack inversion through a Hadamard product operator without rearranging the seismic data. The seismic reflection features can reflect the distribution of the stratum reflection interface, and we obtained them from the post-stack profile by searching the shortest local Euclidean distance between adjacent seismic traces. Instead of directly constructing a large-size reflection features constraint operator advocated by the conventional methods, through decomposing the reflection features along the vertical and horizontal direction at a particular sampling point, we have constructed a computationally well-behaved constraint operator represented by the vertical and horizontal partial derivatives. Based on the Alternating Direction Method of Multipliers (ADMM) optimization, we have derived a fast algorithm for solving the objective function, including Hadamard product operators. Compared with the conventional reflection features constrained inversion, the proposed method is more efficient and accurate, proved on the Overthrust model and a field data set.