Distributed acoustic sensing (DAS) has emerged as a transformative technology for high-resolution seismic exploration. However, compared to conventional geophysics, the vertical seismic profile (VSP) data obtained by DAS has a relatively low signal-to-noise ratio (SNR). This limitation stems primarily from the transient fiber deployment in casing operations, which leads to suboptimal fiber-ground coupling and creates characteristic zigzag noise patterns that degrade signal fidelity. This study presents a feature picking principal component analysis (FPPCA) framework for adaptive zigzag noise suppression. The method includes four stages: power spectral density estimation with multilevel spectral smoothing to preserve critical mid-low frequency components, design of frequency-adaptive hanning windows targeting harmonic sidelobe suppression, bandwidth parameter optimization guided by dominant frequency localization to prevent spectral aliasing during feature extraction, and PCA based noise separation using cumulative variance thresholds derived from localized zigzag features. Validation dataset comprising one synthetic and one field DAS-VSP datasets demonstrates the framework’s ability to maintain broadband signal integrity while achieving spectrally consistent noise attenuation.

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.

pre-stack seismic inversion technique serves as a critical method for obtaining elastic parameters of subsurface sediments, as it further guides the lithologic prediction of reservoirs. As exploration targets become more complex, identifying sandstones with different porosity and permeability characteristics (i.e., different types of effective reservoirs) based on accurate predictions of reservoir lithology distribution has become a new research focus. However, the fact that different types of effective reservoirs are distributed in sandstones and tend to have different sensitive elastic parameters with respect to lithology prevents traditional direct inversion strategies from making direct predictions of targets. To address this limitation, we propose a rock-physics-constrained pre-stack inversion method integrating fuzzy c-means (FCM) clustering strategy to achieve simultaneous inversion of sensitive elastic parameters and direct identification of effective reservoir types. First, sensitive elastic parameters for lithology discrimination and effective reservoir characterization were determined through rock-physics analysis. The results revealed that P-wave to S-wave velocity ratio (Vp/Vs) effectively discriminates lithology, while P-wave impedance (Ip) can indicate different types of effective reservoirs. Second, we derived approximate reflection coefficient equations for Vp/Vs, Ip and density characterization using generalized elastic impedance equation, which reduces conversion errors of elastic parameters and enhances computational efficiency. Finally, accurate estimation of elastic parameters coupled with direct reservoir characterization was achieved through the developed rock-physics-constrained pre-stack inversion method incorporating FCM clustering strategy. Both synthetic model validation and field case studies demonstrate the method's effectiveness, providing a feasible solution for predicting of different types of effective reservoirs.

Seismic reflection coefficient equation for the fluid-saturated porous reservoirs under the effect of in situ stress is of great importance to broad fields such as geofluid discrimination, in situ stress prediction, and safe production. However, the stress effect on seismic reflection coefficient in porous reservoirs is poorly understood. To fill this knowledge gap, an approximate seismic reflection coefficient equation for fluid-saturated porous reservoirs under horizontal stress was proposed to model the natural effect of horizontal stress on seismic reflection response. We first revisited the acoustoelasticity (AE) theory and used it to characterize the impact of horizontal stress on skeleton anisotropy. Then, the effective elastic stiffness tensor and the corresponding spatial perturbation in the stressed fluid-saturated porous reservoirs were established under the assumption of fluid incompressibility, which were further employed to derive the approximate seismic reflection coefficient equation based on the elastic inverse scattering theory. By comparing our equation to the exact one, we confirmed its validity within the moderate incidence angles and stresses. The effects of horizontal stress on the P-wave amplitude variation with angle and azimuth (AVAZ) characteristics and seismic response were thoroughly investigated. It was shown that the horizontal stress significantly influenced the amplitude magnitude and seismic phases. Furthermore, the derived reflection coefficient equation was inserted into the Bayesian inversion scheme to estimate the geofluid indicator and other elastic parameters. Synthetic test and filed application showed a reasonable agreement between the inverted result and drilling data, which illustrated the feasibility and stability of our inversion method.

Identifying geofluids is vital for advancing geophysical exploration and enhancing reservoir forecasting. However, the accuracy and resolution of current methods are often compromised due to their dependence on linear amplitude variation with incident angle (AVO) approximation inversions. These inversions generate fluid indicators that are susceptible to influences from various factors, such as porosity and rock modulus. To overcome these challenges, we recognize that the pore fluid bulk modulus encapsulates the fundamental characteristics of pore fluids, effectively mitigating interference caused by the mixing effect and enabling highly precise fluid identification. Incorporating L0 and L1 norms as sparse regularization terms is crucial for enhancing inversion resolution. On this basis, we formulate a novel nonlinear elastic impedance (EI) equation specifically for pore fluid bulk modulus, utilizing the exact Zoeppritz equation. Additionally, we developed a new nonlinear EI inversion method, which incorporates L0 and L1 norms constraints and is grounded in a nonstationary convolution model. This innovative method not only circumvents the limitations of linear approximation but also significantly enhances the resolution and delineation capabilities for identifying reservoir fluids. The efficacy of this method is corroborated by precision analysis of the equation and field data inversions, underscoring its potential for practical application in geophysical exploration and reservoir prediction.

The vertically transverse isotropic (VTI) reservoirs subjected to horizontal in situ stress are frequently encountered in the subsurface, which can be approximately treated as an orthorhombic medium in the framework of acoustoelasticity. However, the seismic estimation for anisotropy parameters in such stress-induced reservoirs is still poorly studied. To address this issue, we derive a linearized reflection coefficient equation in stress-induced orthorhombic media by means of the theories of acoustoelasticity and elastic inverse scattering. The acoustoelasticity theory is utilized to characterize the effective elastic stiffness tensor in a stress-induced orthorhombic medium. The introduction of two dimensionless stress-induced anisotropy (SIA) parameters eliminates the need for third-order elastic constants (3oECs). Then, the stiffness perturbation is presented under the weak-anisotropy hypothesis and is substituted into the scattering function to derive the linearized reflection coefficient equation in stress-induced orthorhombic media. The feasibility of our reflection coefficient equation within the range of moderate stress (or moderate SIA) is confirmed by comparing it to the exact solution. Incorporating the wavelet effect, our reflection coefficient equation as a forward operator is utilized to establish a step-wise Bayesian inversion approach to estimate the anisotropy parameters. Specifically, the SIA parameters are inverted from the amplitude differences in seismic data at different azimuths in the first step. Next, the obtained parameters as the prior dataset are input into the second-step procedure to predict the VTI parameters with partial angle-stacked seismic data. Synthetic and field tests illustrate the robustness and effectiveness of our approach.

In hydrocarbon exploration and development, fluid indicators that can directly identify reservoir hydrocarbons from seismic data are of great significance for seismic interpretation in the fracture-induced horizontal transversely isotropic (HTI) reservoirs. In this paper, based on the unified elastic wave theory of the medium, a new anisotropic fluid indicator is constructed incorporating squirt flow effect between the cracks of rocks. The novel anisotropic fluid indicator can better reflect the influence of pore fluid within the rock on wave propagation. Compared with conventional elastic parameters, the new established anisotropic fluid indicator is more sensitive to oil/gas. Subsequently, by combining the perturbation of the elastic stiffness component in fluid-saturated fractured porous media and the inverse scattering function, an anisotropic PP-wave reflection coefficient is derived in terms of an anisotropic fluid indicator incorporating squirt flow effect and fracture weaknesses. The comparison of Rüger’s equation and the new reflection coefficient equation confirms the validity of our equation for parameter estimation. Further our reflection coefficient equation is used to establish an anisotropic frequency-dependent azimuthal amplitude variation with offset (AVO) inversion method to estimate the anisotropic fluid indicator and fracture weaknesses. The feasibility of the inversion method is verified by the field data application in eastern China, which demonstrates that the anisotropic fluid indicator with the squirt flow effect is certainly sensitive to the gas-bearing fractured reservoirs, and can provide a more effective method for fluid identification in gas-fractured reservoirs.

Incorporating geological background information into pre-stack seismic inversion methodologies is a pressing concern within the field of seismic exploration. The current approaches to pre-stack seismic inversion often overlook crucial geological contexts and lack constraints derived from geological data. This deficiency motivates our comprehensive investigation into the utilization of various types of facies information to augment pre-stack seismic inversion methodologies. The classification of facies, encompassing seismic facies, lithofacies, and fluid facies, provides valuable geological insights that serve as a priori knowledge. These classifications, delineated by distinct facies boundaries, exhibit correlations with sedimentary structures, stratigraphic layers, and fluid distributions, thereby enhancing the lateral resolution of inversion results. By harnessing multiple type facies classification results capable of encapsulating the geological characteristics of subsurface media, we develop a probabilistic a priori model that integrates multiple type facies information. Subsequently, we formulate a probabilistic seismic inversion method underpinned by multitype facies constraints, specifically tailored for pre-stack seismic inversion. This methodological advancement provides a robust framework for improving the reliability of seismic inversion outcomes. Through rigorous validation procedures involving both model testing and field data analyses, we verify the efficacy and stability of the pre-stack seismic fluid prediction methodology driven by multiple type facies. This validation underscores the credibility of our approach and highlights its potential to enhance the accuracy and reliability of pre-stack seismic inversion results.

With the continuous development of oil and gas exploration, anisotropic medium has become an important target of oil and gas exploration. Both anisotropy and wave-induced fluid flow have significant influence on fluid identification, but the existing fluid identification methods cannot concurrently consider the impacts of medium anisotropy and wave-induced fluid flow. Therefore, to improve the fluid detection accuracy in anisotropic medium, an anisotropic media solid-liquid decoupling fluid factor with squirt flow effect suitable for the transversely isotropic media with a horizontal symmetry axis (HTI) is constructed based on the theory of rock physics. The fluid sensitivity analysis indicates that the new fluid factor exhibits the highest sensitivity for fluid indication. By introducing the nearly constant Q model to account for viscoelasticity, a reflectivity equation in terms of the new anisotropic media solid-liquid decoupling fluid factor incorporating the squirt flow is derived. Subsequently, a prestack seismic frequency-dependent amplitude variation with angle and azimuth (AVAZ) inversion method is developed. The inversion method takes advantage of the information of offset, azimuth, and frequency contained in seismic data. Synthetic and field examples illustrate the reliability and stability of the proposed prestack seismic frequency-dependent AVAZ inversion method in estimating the new anisotropic media solid-liquid decoupling fluid factor. Our method can serve as a complementary approach to enhance the accuracy of fluid detection in anisotropic reservoirs.

Accurate prediction for formation pressure is crucial for many practical scenarios in the field of oil and gas exploration, such as evaluating reservoir sweet spots. As formation depth gradually increases, the influence of diagenesis on formation pressure becomes more dominant. However, the diagenesis effect is still not well considered in the existing formation pressure methods. To address this issue, a seismic formation pressure prediction method incorporating the diagenesis effect is developed based on the depth-dependent diagenetic function. The proposed method concurrently incorporates the information of normal compaction trend, bulk modulus, and clay content. A diagenetic function is introduced into the classic effective stress theory to describe the diagenesis effect on depth dependency of formation pressure. The normal compaction trend is established using the rock physics model. The bulk modulus and clay content that are included in the prediction method are estimated from the pre-stack seismic data, respectively, with the linear Gray reflection coefficient equation and the proposed nonlinear reflection coefficient equation, where the Markov chain Monte Carlo (MCMC) method is used to obtain the optimal inversion results. Finally, the estimated normal compaction trend, bulk modulus, and clay content are employed to calculate the formation pressure. The proposed method has been applied in Xinjiang work area.

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.

The synchroextracting transform (SET) is a postprocessing algorithm for the result of short-time Fourier transform (STFT). It removes most of the divergent energy and only extracts the time–frequency (TF) coefficients on the instantaneous frequency trajectory, such that the TF resolution is significantly improved. However, the quality of seismic TF analysis (TFA) result of SET is largely affected by the STFT. If the window length is inappropriate, some distortion will occur when processing signals with fast frequency changes, indicating that neither the STFT or SET can flexibly handle nonstationary signals. Therefore, a recently proposed W transform (WT) is adopted to overcome the shortcoming of STFT. WT has a flexible window function and shows high time resolution at low frequencies. In consideration of the superiority of WT and the working principle of SET, a novel method called the synchroextracting WT (SEWT) is proposed in this letter to generate clearer and more reliable TFA results. Synthetic and field examples are utilized to validate the effectiveness of the proposed SEWT method.

Matching pursuit (MP) is an algorithm which can reconstruct signal accurately, and is widely used in signal processing. However, MP algorithm has efficiency problem in processing large amount of data like five-dimensional (5D) seismic data. Generalized orthogonal matching pursuit with singular value decomposition (SVD_GOMP) is an algorithm which can improve the calculation efficiency a lot, and keeps the advantage of high accuracy. In this study, a redundant atom dictionary includes incident angles and azimuth is built. Then the five-dimensional seismic data is reconstructed efficiently and accurately by the generalize orthogonal matching pursuit with singular value decomposition algorithm. Compared with traditional matching pursuit method, the proposed method decomposes the five-dimensional seismic data at the same time and recovers the angle information efficiently. The reconstructed results of synthetic and field data examples are utilized to demonstrate the feasibility, computational efficiency and precision of the proposed method.

Viscoelastic theory-based frequency-dependent amplitude variation with offset (AVO) inversions are a useful tool for identifying fluids based on their dispersion properties. When used to identify reservoir oil and gas qualities, the quality factors ($Q$-factors) derived from the inversion have produced good results. But currently, the majority of$Q$-factor inversions are linear inversions based on linear approximations, whereas nonlinear inversions based on exact equations with higher precision and fewer assumptions are only occasionally carried out. Meanwhile, in broadband seismic inversion, the low-frequency model estimated by complex frequency inversion can fully utilize seismic data’s low-frequency information and provide improved robustness and rationality for inversion. Therefore, we derive a frequency-dependent reflection coefficient equation that varies with angle by replacing the nearly constant$Q$model suggested by Aki and Richards into the exact Zoeppritz equation and simplifying. Additionally, using the Bayesian framework as a foundation, we created a novel two-stage broadband frequency-dependent nonlinear inversion approach for$Q$-factors that can estimate$Q$-factors, produce accurate fluid identification results, and serve as a solid foundation for oil and gas exploration and reservoir identification. Utilizing examples from both synthetic and real-world data, we verify the applicability of oil and gas indicators.

Young’s modulus and the Poisson ratio are critical for shale reservoir identification, and oil and natural gas detection since they are elastic parameters that can reflect the fracturing properties of subsurface rocks. The broadband inversion approach can make full use of the seismic ultralow-frequency information by combining it with the inversion results in the complex frequency domain. This plays an important role in the stability and reliability of the inversion, improving its resolution. Nevertheless, at present, the amplitude variation with offset (AVO) inversions of these parameters is mostly in the form of linear approximations, and there are few inversion methods of exact nonlinear equations or broadband. Considering that the nonlinear equation of reflection coefficient compared with the linear approximation has higher precision and fewer assumption conditions, and the low-frequency information of the complex frequency-domain inversion can improve the reliability of the inversion results, we derive an exact reflection coefficient equation for Young’s modulus, the Poisson ratio coefficient, and the density based on the exact Zoeppritz equation and apply it to the broadband complex domain nonlinear prestack inversion. Young’s modulus and the Poisson ratio coefficients estimated by the new inversion method provide a theoretical basis for evaluating the reservoir brittleness and compressibility, as well as a new approach for shale gas reservoir prediction and sweet spot identification. We tested the accuracy and rationality of this method with both synthetic and field data examples.

In the absence of a well-log-based low-frequency model, a broadband inversion strategy with a low-frequency model calculated in complicated frequency-domain inversion can successfully mine low-frequency seismic information and decrease the inversion results’ reliance on the starting model to some extent. Furthermore, from the standpoint of the equation, prestack nonlinear inversion based on the nonlinear reflection coefficient equation may meet the needs of greater precision inversion. Nonetheless, most prestack inversion approaches to subsurface elastic parameters have been based on linear time-domain approximations, which cannot meet the needs of high-precision underground reservoir prediction and fluid identification in the increasingly complex geological backgrounds of exploration areas. Given the aforementioned issues, we execute broadband prestack nonlinear elastic impedance (EI) inversion using a more accurate nonlinear reflection coefficient equation in conjunction with the Lévy flight Markov chain Monte Carlo (LFMCMC) stochastic inversion approach. Throughout this process, we also consider the reduction in seismic wave amplitude caused by transmission loss in the nonlinear forward operator, and we develop a modified convolution model to mitigate the impact of transmission loss in layered media on seismic amplitude. In comparison to the traditional linear elastic impedance inversion method, the new method not only improves inversion precision and adaptability to strong impedance changes but it also reduces the transmission loss in the case of sand and mudstone interbedding and protects the underlying strata’s weak amplitude changes, resulting in more reasonable inversion results for real changes in underground impedance. Using synthetic and field data samples, we assess the approach’s reliability and applicability.

In an anisotropic reservoir, it is crucial to determine the anisotropic media fluid factor that corresponds to the reservoir’s anisotropic properties. To address the lack of research on accurate hydrocarbon identification and fluid factors in anisotropic reservoirs, relevant research work has been carried out. First, the relationship between the anisotropic parameters and the physical parameters of the fluid-bearing reservoir is discussed based on petrophysical mechanisms. Subsequently, a new anisotropic media fluid factor is developed that exhibits higher fluid sensitivity. According to some studies, the dispersion and attenuation of seismic waves will significantly affect the reservoir’s amplitude variation with offset and azimuth (AVAZ) response. Consequently, an anisotropic frequency-dependent reflection coefficient is constructed using the frequency-dependent anisotropic media fluid factor to better utilize the frequency information in seismic data. The pre-stack seismic frequency-dependent inversion method is employed to extract the abundant azimuthal anisotropy information and frequency information from the wide-azimuth seismic data. Synthetic and field data examples provide evidence of the high reliability and stability of the pre-stack seismic frequency-dependent anisotropic inversion method. The development of pre-stack seismic frequency-dependent inversion, based on AVAZ response and frequency response, offers a novel theoretical method for hydrocarbon identification in anisotropic reservoirs.

The hydrocarbon-bearing shale reservoirs can be approximately modeled as the transversely isotropic media with the vertical symmetry axis (VTI), usually exhibiting strong anisotropy and significant contrast among the reservoirs. Therefore, the effects of strong anisotropy should be considered when conducting the seismic interpretation for this type of reservoir through the AVO (amplitude variation with offset) technique. However, the existing approximately linear PP-wave reflection coefficient equations derived based on the assumption of weak anisotropy and weak contrast in elastic parameters will create considerable errors in the case of strong anisotropy and contrast. Quadratic approximation has also been proposed in the case of strong contrast in elastic parameters. To overcome the problem of strong anisotropy and contrast in AVO inversion, we propose a novel PP-wave reflection coefficient equation (expressed by Lamé constants) in terms of five reflectivity parameters (i.e., the ratio of the difference to the mean value between the parameters of two half-spaces) based on the quasi-Zoeppritz equation for the VTI media. Combining the novel reflection coefficient equation and Bayesian inversion framework, we constructed the nonlinear inversion objective function. We chose the multivariate Gaussian distribution as the prior function to reduce the inversion multiplicity. The MCMC sampling algorithm was adopted to estimate the five reflectivity parameters for the nonlinear inversion problem.

AVO inversion is an important method for estimating elastic parameters in geosciences. The inversion results are highly affected by the initial low-frequency model. Deep learning, as a data mining algorithm, has the potential to capture more reliable low-frequency components from seismic data and well logs. In order to fully utilize limited seismic data and recover more reliable low-frequency components of elastic parameters, a data-driven complex frequency domain AVO inversion is proposed by combining convolutional neural network (CNN) with a complex frequency forward solver. The proposed method makes full use of the advantages of deep learning algorithms and the low-frequency components of the attenuation wave field in the complex frequency domain. To better fit the characteristics of complex frequency domain seismic data, we designed a dual-channel U-shaped CNN (DC-UCNN) as an inversion network to extract the low-frequency components contained in the real and imaginary parts of the attenuated wave field, respectively. Furthermore, data-driven complex frequency forward modeling operator is used to constrain the training of the inversion network to improve its reliability. The experiment on the Marmousi2 model shows that the proposed DC-UCNN-based complex frequency domain inversion has better accuracy than traditional complex frequency domain AVO inversion and UCNN (U-shaped CNN)-based time domain inversion. Finally, the application of field data has proven the feasibility of proposed method, which can recover richer and more reliable low-frequency components far from the well location.

Wave attenuation and velocity dispersion are of great significance to fluid evaluation in fluid-saturated rocks. Inspired by the double-porosity and cracked porous elastic wave theory, we develop a multiscale heterogeneities elastic wave theory to better describe the attenuation characteristics caused by wave-induced fluid flow at various scales in saturated rocks. First, we introduce penny-shaped and narrow-shaped coupled cracks into double-porosity model. The potential energy function is given by the stress–strain relationship. The kinetic energy function and dissipation function are derived based on the generalized Biot’s theory. Next, we derive the multiscale wave equations through the Lagrange equation and obtain three compressional waves and one shear wave. According to the novel wave equations, we work out the phase velocity and inverse quality factor in double-porosity and cracked media based on plane-wave analysis. The numerical simulation results show that there are four attenuation peaks in the whole frequency band, corresponding to mesoscopic fluid flow, and two kinds of squirt flow and Biot flow, respectively. Then, we investigate the effect of poroelastic parameters on wave propagation. It is found that porosity, inclusion size, crack aspect ratio, and other parameters significantly affect the dispersion and attenuation. Finally, we compare experimental data and theoretical prediction. Moreover, the new elastic wave theory can degenerate into classical Biot’s theory, double-porosity theory, and pore-crack theory under certain conditions, which demonstrates the consistency of this method. The proposed theory can better predict and simulate the wave propagation by incorporating the effects of microscopic, mesoscopic, and macroscopic heterogeneities.

Fracture detection and characterization remains challenging for azimuthal seismic inversion for effective elastic anisotropic media, especially for the more complex orthorhombic (ORT) anisotropic media formed by two orthogonal sets of vertical, aligned fractures in a homogenously isotropic background rock. We first review multiple modes of rock-physics characterization for orthorhombic anisotropy. We also review the inversion methods or strategies in seismic characterization for the complicated naturally fractured reservoirs. Next, we derive the effective elastic stiffness matrix in such a weak ORT anisotropic medium, and also obtain the linearized PP-wave reflection coefficient based on scattering theory and perturbated stiffness tensor. Then, we propose a method of Bayesian azimuthal seismic inversion for the effective elastic ORT anisotropic media based on the anisotropic perturbations in PP-wave reflection coefficient and the iteratively reweighted least-squares algorithm. Finally, the applications of synthetic and real data sets acquired from a gas-bearing fractured reservoir with orthorhombic symmetry demonstrate the effectiveness of the proposed inversion approach, and our method may provide an alternative way to describe the effective elastic orthorhombic anisotropic media formed by two orthogonal sets of vertical fractures.

Matching pursuit (MP) is an algorithm that can represent signal sparsely, and this advantage makes MP popular in signal processing. However, MP algorithm is a greedy algorithm which means it cannot deal with a large family of signals like seismic data which becomes larger and larger with development of data acquisition technologies. Generalized orthogonal MP (GOMP) is an improved algorithm which helps to reduce the cost of the calculation greatly. Fast MP algorithm is a method that can build dynamic dictionary by making full use of the characteristics of the original signal. In this study, singular value decomposition (SVD) is involved into the GOMP algorithm with dynamic dictionary to improve its efficiency. Compared with conventional MP, the proposed method picks multiatoms at each iteration. It has advantage in calculation speed and can reconstruct the original signal more exactly. Synthetic and field data examples are utilized to demonstrate the feasibility, computational efficiency, and precision of the proposed method.

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.

Time-frequency analysis method is an effective tool to describe the relationship between the time and frequency of seismic signal. Accurate time-frequency results help to better delineate subsurface geological structures. S-transform (ST), due to its high resolution, is known as a kind of pragmatic time-frequency analysis tool in seismic signal processing. However, the center of the energy group estimated by the ST is shifted to the higher frequency. A recently proposed W-transform (WT), which brings in the dominant frequency, solves this problem to some extent. However, the dominant frequency calculated by the temporal average of the instantaneous frequency is unstable, which shows negative value sometimes. Therefore, an improved WT incorporating fast matching pursuit (WT-FMP) decomposition method is proposed to estimate the well-concentrated time-frequency distribution. It decomposes the seismic signal into a series of matched wavelets selected from an over-complete dictionary initially. Furthermore, the whole time-frequency distribution of the signal is generated by superposition of each wavelet’s WT coefficients. The proposed method helps to avoid the dependence on the instantaneous frequency and it owns higher resolution because the time-frequency map for signal is well localized using fast matching pursuit (FMP). Synthetic and field examples are utilized to validate the effectiveness of the proposed WT-FMP method. The results demonstrate its priority in providing more concentrated spectrum and revealing abundant stratigraphic and geological information.

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.