Seismic amplitude variation with offset/angle and azimuth (AVOZ/AVAZ) inversion driven by rock physics is an important tool for the estimation of fractured reservoir properties. Generally, the azimuthal AVO reflection coefficients and fractured reservoir properties are nonlinearly coupled, resulting in strong ill-posedness in azimuthal AVO inversion. We propose an azimuthal AVO probabilistic nonlinear inversion methodology based on a generalized Gaussian mixture model and an improved adaptive-particle-swarm Metropolis-Hastings (APS-MH) algorithm to estimate fractured reservoir properties and lithofacies for fractured reservoirs with a group of vertical fractures. We first derive a novel nonlinear azimuthal AVO reflection coefficient related to the rock-matrix shear modulus, porosity, fracture density and water saturation. The approximation accuracy and inversion feasibility of the derived formulation are verified by a series of theoretical numerical analyses of the stiffness coefficient matrix and azimuthal AVO reflection coefficients. With a generalized Gaussian mixture probability model (GGMM) and the hierarchical Bayesian inference, we establish a nonlinear azimuth-AVO objective function coupling the irregular shape a priori of fractured reservoir properties and the lithology a priori. Combining the global search capability of the adaptive-particle-swarm optimization and the local sampling characteristics of Metropolis-Hastings, a probabilistic azimuthal AVO nonlinear inversion algorithm is developed, which improves the convergence speed and inversion accuracy of reservoir properties. Besides, the methodology simulates the a posteriori probability distribution of rock matrix shear modulus, porosity, fracture density, saturation and lithofacies effectively, which also evaluates the inversion uncertainty of reservoir properties simultaneously. The stability and applicability of the methodology is illustrated by theoretical numerical tests and real seismic data application.

Rocks with a set of vertical fractures embedded in a vertical transverse isotropic (VTI) background can be regarded as an effective long-wavelength orthorhombic (ORT) medium, common in fractured reservoirs. Seismic inversion using wide-azimuth data is an effective tool for fracture detection. However, azimuthal seismic inversion in ORT medium is inherently ill-posed and uncertain, largely due to the considerable number of parameters involved in the reflection coefficients and the relatively minor contribution of fracture parameters to the reflection coefficients. Therefore, in this article, a modified PP-wave reflection coefficient equation was derived through parameter combination, comprising only five model parameters and exhibiting near-equivalent accuracy to the existing equation. Furthermore, each parameter in the equation has a clear physical meaning. These include attribute A (P-wave impedance), attribute B (anisotropic shear modulus), attribute C (horizontal P-wave phase velocity), normal fracture weakness, and tangential fracture weakness. Subsequently, an azimuthal seismic inversion method was developed to estimate the above five model parameters based on Bayesian inference, combined with Cauchy prior information and low-frequency regularization constraints. The method was validated through synthetic tests, which demonstrated its efficacy and feasibility even with moderate noise. Field data also illustrated the stability and effectiveness of the method. Finally, based on field data, the interpretation capability of attribute parameters was discussed. The modified reflection coefficient equation and the inversion method proposed in this article serve to enhance the inversion robustness of the ORT medium, which in turn guides the prediction of the orthogonally fractured reservoir using azimuth seismic data.

In geological exploration, due to various factors, raw seismic data often corrupted by random noise, posing significant challenges to data fidelity, signal-to-noise ratio (SNR), and resolution. Traditional denoising techniques are limited by their inability to fully consider spatiotemporal correlations within seismic data, reliance on fixed filter parameters, and inadequate modeling of complex noise, and they have limited effectiveness and applicability when processing complex seismic signals. Therefore, this study proposes an innovative seismic data denoising model named seismic transformer generative adversarial network (STGAN). This model combines Transformer technology with generative adversarial networks (GANs) to effectively remove noise from seismic data. By incorporating the GAN, the model can effectively learn complex noise features in seismic data and generate cleaner, more realistic data. Meanwhile, the adoption of Transformers makes it possible to captures the temporal dependencies of seismic signals, thus significantly improving the accuracy and efficiency of data processing. The model employs serial and parallel structures in the generator to effectively extract multiscale features and achieve a balance between denoising effect and computational efficiency. Additionally, traditional batch normalization (BN) is replaced with batch renormalization (BRN) to further improve the stability of the model and optimize model performance. Comparative experiments on synthetic and field datasets demonstrate that the STGAN model has better denoising performance than classical methods such as bicubic interpolation, nonlocal means algorithm, and DnCNN, providing a more accurate basis for further interpretation and analysis of seismic data.

The transversely isotropic media with a vertical symmetry (VTI) has been widely used in shale reservoirs, and the reflection response and prestack seismic inversion have been of interest to geophysicists. Petrophysical experiments have shown that shale reservoirs may exhibit moderate or even stronger anisotropy, causing limitations in the weak anisotropy-based reflectivity approximation. Existing weak-contrast approximations are usually highly nonlinear equations characterized by the stiffness parameters and slowness, which is not conducive to AVO analysis and prestack seismic inversion of anisotropic parameters. We proposed a novel approach for weak-contrast PP-reflectivity based on the P- and S-elastic impedance matrices and applied it to prestack seismic inversion. First, by simplifying the phase velocities and polarization vectors, the elastic impedance matrices are linearly characterized in the weak-contrast half-spaces. Then, the perturbation theory is used to derive the weak-contrast PP-reflectivity, which consists of two terms, one directly resulting from the difference between the parameters of upper and lower media, and the other resulting from the first-order perturbation of the phase velocity and polarization. It has a clear physical meaning and can degenerate to the Aki-approximation in isotropic media. In particular, the isotropic second-order terms are introduced to significantly improve its accuracy at the interfaces with high-speed contrast. Furthermore, we designed a coefficient matrix to linearize the high-order reflectivity terms and developed an improved algorithm based on the alternating direction method of multipliers (ADMMs). Finally, the applications on logging curves and field seismic data for the shale prove the feasibility and effectiveness of the proposed method.

Shale is a critical hydrocarbon reservoir generally considered a typical transverse isotropy with a vertical axis of symmetry vertical transverse isotropic (VTI) media. Petrophysical experiments indicated that shales may exhibit moderate or strong anisotropy, exacerbating uncertainties in seismic reflection analysis and pre-stack seismic inversion. In addition, the significant difference in contribution between the elastic and anisotropic parameters to the reflection coefficients limits the stability of anisotropy predictions. A quadratic reflectivity-based joint PP and PS inversion for VTI media was proposed, which indirectly predicts the anisotropy using the stiffness matrix. First, based on the elastic impedance matrix, we derived the weak-contrast PP and PS reflectivities characterized by the stiffness matrix. The contribution analysis indicates that the PP wave is sensitive to the stiffness matrix C11, and the PS wave is sensitive to C13, which implies that the joint PP and PS reflection was more effective in analyzing the effects of anisotropic parameters. Then, to improve the accuracy of the reflectivity at the interface with high-contrast velocity, quadratic PP and PS reflectivities for isotropic media were derived. Tests on different typical models showed that the reflectivity with quadratic terms performed well in accuracy, even for strong anisotropy. Finally, a joint inversion constrained by the nonlinear relationship between the stiffness matrix and the anisotropic parameters was developed, which can overcome the ill-posedness of indirectly calculating the anisotropic parameters using the stiffness matrix. The model and field seismic data applications prove the feasibility and effectiveness of the proposed method.

Fracture discrimination and reservoir fluid identification guide the characterization of the spatial distribution of reservoir oil and gas and the comprehensive evaluation of sweet spots, which are crucial for the exploration and development of unconventional hydrocarbons. However, the reflection coefficient equation derived under the anisotropic medium assumption contains numerous parameters, thereby augmenting the uncertainty of amplitude variation with offset and azimuth (AVOAz) inversion. In this study, an anisotropic reflection coefficient equation, including Gassmann fluid term and fracture parameters, is rewritten based on the horizontal transversely isotropic (HTI) medium assumption, which reduces the equation’s dimension and ill-posedness. In addition, the traditional Markov Chain Monte Carlo (MCMC) algorithm is complicated to stably sample from the high-dimensional posterior probability distribution function due to the large number of inversion parameters. To overcome the problem and evaluate the uncertainty of AVOAz inversion, the adaptive independent sticky MCMC (AISM) strategy combined with the Gibbs algorithm is introduced. Under the Bayesian framework, the enhanced algorithm constructs a proposal distribution from a non-parametric distribution and employs support points for adaptive updating of the proposal distribution. The method of equation rewriting, coupled with the refined AISM algorithm, significantly improves the accuracy and robustness of inversion. The proposed method is validated through model testing and application to real data from a shale exploration area in Southwest China. The inversion results demonstrate a high concordance with well data, affirming the reliability and applicability of the inversion method.

Periodic horizontal thin interlayers, or formations developing horizontally layered fractures in a homogeneous background, are commonly studied as a transverse isotropy with a vertical axis of symmetry (VTI) media. Anisotropy needs to be considered in predicting such special reservoirs, and can be inferred from the amplitude variation with offset (AVO) by the exact or linear reflectivity equations. However, the linear approximation is usually derived based on the assumptions of weak anisotropy and weak contrast, the accuracy suffers when the anisotropy or the contrast of two adjacent media increases. In addition, due to the high nonlinearity of the Graebner equation, the stability and efficiency of the exact inversion are limited. To address these issues, we propose a robust pre-stack seismic inversion for VTI media using quadratic PP-reflectivity approximation. Firstly, by deriving quadratic approximations for phase velocity and polarization, we analyze the advantage of the second-order terms at a higher-contrast interface. Then, based on perturbation theory, we derive a quadratic PP-reflectivity approximation from the exact equation. It consists of first- and second-order terms with isotropic and anisotropic components, and the accuracy is significantly improved even with enhanced anisotropy. Finally, we introduce the Hadamard product operator to linearly characterize the objective function, and develop an improved Alternating Direction Method of Multipliers (ADMM) algorithm to handle the nonlinearity of the quadratic equations. The feasibility and stability of the proposed method are tested on two datasets, that is, the logging curves used as numerical experiments and a field dataset from a shale reservoir.

From the observed seismic data, the estimation of elastic parameters and lithofacies of subsurface layers with seismic amplitude variation with offset (AVO) inversion plays an important role in reservoir characterization. The sequential estimation of elastic parameters and lithofacies in AVO inversion usually affect the prediction accuracies of model parameters without considering the prior information related to lithofacies. We propose a novel probabilistic AVO inversion approach in hierarchical Bayesian framework that combines a hierarchical iterative strategy with Gibbs-IA2RMS sampling, to estimate elastic parameters and lithofacies simultaneously. From the exact PP-wave reflection coefficient, we first derive the posterior distribution of model parameters involving a Bayesian hyper-parameter of lithofacies through the hierarchical prior probability distributions and the likelihood distribution of observed data. Based on Monte Carlo Markov chain approximation, we then introduce an iterative Gibbs-IA2RMS sampling to achieve the high sampling stability of the high-dimensional posterior PDF in AVO inversion. The algorithm realizes the adaptive construction of proposal distribution, and has a higher acceptance rate than the generic Metropolis-Hastings algorithm. The numerical results show that the approach effectively simulates the posterior distributions and inversion uncertainties of model parameters, and improves the computational efficiency of probabilistic AVO inversion. The applicability and validity of the proposed approach are also demonstrated with a field data application.

The rock with a vertical group of aligned fractures in the tilted transverse isotropy (TTI) background medium is regarded as an effective monoclinic medium. Thomsen parameters and fracture weaknesses can reflect the development degree of TTI background anisotropy and vertical fractures, respectively. Thus, this paper first establishes the approximate stiffness matrix of the monocline medium through the Bond transformation from Thomsen weak anisotropy theory and effective medium theory. Moreover, considering the Born scattering theory, a linearized approximate formula of PP wave reflection coefficient is further deduced. This approximate formula contains the parameters of incident angle, azimuth, tilted angle, compressional and shear moduli, density, fracture weaknesses, and Thomsen parameters. Then, the contribution of each parameter on the reflection coefficient by numerical simulation is analyzed respectively. Finally, from the perspective of Bayesian inference, an azimuthal seismic amplitude difference inversion approach incorporating Cauchy prior information and low-frequency regularization of model parameters is proposed to realize the simultaneous estimation of fracture weaknesses and Thomsen parameters. The synthetic test demonstrates that the inversion approach proposed in this article can obtain information on vertical fractures and TTI background medium and can be applied to azimuthal seismic data with moderate noise well. Furthermore, the inversion results of the synthetic test and field data illustrate the stability and feasibility of the inversion approach and also confirm the fracture weaknesses and Thomsen parameters of the monoclinic medium can be reasonably estimated by the inversion equation derived in this paper.

Time-frequency analysis of the nonstationary signals is one of the hot researches in geophysics, environmental science, geology, and other fields. Matching pursuit (MP) has been widely used to reveal the characteristics in time-frequency domain, which helps to study the changes and differences of subtle geological structures. Compared with traditional time-frequency analysis methods, MP has higher time-frequency resolution. The synchrosqueezing transforms (SSTs) have been proven to be an effective methodology to improve the time-frequency resolution by squeezing and redistributing the time-frequency coefficients in the frequency direction. Considering the superiority of the SSTs, this letter proposes a novel time-frequency analysis method called synchrosqueezing MP to enhance the energy aggregation of the time-frequency plane. The proposed method can squeeze the time-frequency distribution into near the center time and frequency of the selected wavelet by a 2-D Gaussian function. We used synthetic and field seismic data to demonstrate the feasibility of our method. The results prove the superiority of our method in describing reservoir boundaries.

Seismic inversion is an important approach in parameters estimation in the fields of geosciences. The low-frequency component of the model parameter plays an important role in seismic inversion. The emergence of broadband seismic data acquisition and processing technologies is pushing the attention of the low frequency to a new level. With the review of the research status of the estimation of the low-frequency models in history and the low-frequency component contained in the complex frequency domain, a novel broadband seismic Bayesian inversion approach in the complex frequency domain is proposed to implement the estimation of the low-frequency component of the model parameter. The proposed approach makes full use of the advantage of broadband seismic data and the low-frequency component of the damped wave fields in the complex frequency domain. The kernel function of the proposed inversion approach is built with Bayesian inference. Synthetic examples demonstrate the feasibility and robustness of the proposed inversion approach in the estimation of the low-frequency component of the model parameter. A field data example verifies the feasibility and reasonability of the proposed inversion approach in application. Finally, the estimated low-frequency component of the model parameter is utilized as the initial model for the suggested seismic Bayesian inversion method in time domain. Model and field data examples further verify the effectiveness and superiority of the proposed inversion method in the final estimation of the model parameter by comparing with the conventional inversion approach.