Rocks containing inclined fractures can be approximated as tilted transversely isotropic media with a tilted symmetry axis (TTI). Azimuthal differences in seismic data enable quantitative estimation of fracture-related parameters in TTI media. However, the inversion accuracy is limited by weak azimuthal differences in seismic amplitudes and the empirical selection of regularization parameters and constraint forms. In this study, an approximate PP-wave reflection coefficient for TTI media is derived in a form that is directly parameterized by P-wave velocity, S-wave velocity, density, and fracture weaknesses. The elastic and seismic responses are analyzed to examine the effects of fracture, fracture fluid, fracture dip angle, and background medium parameters. An adaptive AVAZ inversion method is then developed. A stepwise inversion strategy for TTI media is adopted to alleviate the ill-posedness of multiparameter inversion, in which background elastic parameters are first estimated, and fracture parameters are then inverted from azimuthal difference data. To improve inversion accuracy, a kurtosis-based adaptive Lp-norm constraint is proposed for the objective function, with the sparsity level adaptively adjusted based on the statistical characteristics of the model parameters. The resulting non-L2 inversion problem is solved using the Iteratively Reweighted Least Squares method. The generalized cross-validation (GCV) approach is introduced to determine the optimal regularization parameter. Synthetic tests indicate that AVAZ inversion accuracy is affected by the regularization parameter selection, the regularization constraint, and the input fracture dip angle. The tests also show that the proposed method improves the inversion accuracy of fracture-related parameters and remains robust to noise. Application of the method to field seismic data further demonstrates its effectiveness.

The exploration of petroleum resources is currently extended to unconventional oil/gas reservoirs, such as tight sandstones. These reservoirs require theoretical and experimental studies on the wave response. This study conducts ultrasonic measurements on three tight sandstone samples under varying confining pressures and fluid conditions. To estimate the inverse quality factors of P-waves and S-waves, the spectral ratio theory is employed. With increasing pressure, the P- and S-waves velocities rise, while the attenuation declines. The pressure has the greatest influence on the anelastic properties. At the same pressure, the unloading process exhibits lower attenuation and higher velocities compared with the loading process. This is due to the fact that the cracks do not completely return to their pre-loading state after unloading. A rock-physics model is developed through the Voigt-Reuss-Hill average, the differential effective medium theory, and the squirt-flow model. The model results agree with the experiments. The modeling also shows that with increasing pressure, the attenuation peak in the water-saturated and oil-saturated state gradually shifts to higher frequencies, while the peak in the gas-saturated state shifts to lower frequencies. Water-saturated rocks are less pressure-dependent than oil-saturated rocks, while fully gas-saturated rocks undergo the greatest deformation. This study supports seismic exploration in tight oil and gas reservoirs.

Multiscale pore systems, dominated by intergranular pores, dissolution pores, and microcracks, form in tight-rock reservoirs through diagenesis, tectonics, and dissolution processes. These heterogeneities cause significant seismic wave dispersion and attenuation, which conventional rock physics models do not adequately describe. To address this limitation, we propose a novel scattering model to obtain the wave response based on a statistical description of fractal cracks, parameterised by crack density, aspect ratio, radius distribution, and fractal dimension. The results show that these properties, along with the pore fluid, dominate velocity dispersion and attenuation. Specifically, decreasing fluid modulus or increasing crack density and thickness reduces P-wave velocity while enhancing scattering attenuation. Resonance scattering occurs when the crack scale is comparable to the wavelength. Velocity-attenuation templates derived for tight sandstones agree with ultrasonic data and well-log measurements from the Yanchang Formation in the Ordos Basin, China. Discrepancies in water-saturated attenuation are attributed to unaccounted factors such as crack geometry, crack interactions, and coda wave-induced fluid flow. The sonic templates enable the prediction of porosity and crack density from well logs, providing a robust foundation for sweet spot identification in tight-rock reservoirs.

Quantitative prediction of petrophysical parameters, such as porosity, is crucial for the evaluation and development of coalbed methane (CBM) reservoirs. However, conventional methods based on linear assumptions and empirical formulas often fall short due to the strong heterogeneity of coal seams, complex lithologies and structures, and the highly non-linear relationship between seismic elastic parameters and reservoir properties under deep-buried conditions. While machine learning techniques have shown promise in petrophysical prediction, many existing approaches struggle to effectively capture long-range dependencies within sequential log data. This study proposes a deep learning-based method that integrates comprehensive input feature selection with a bidirectional long short-term memory (Bi-LSTM) network incorporating dropout regularization for enhanced petrophysical parameter prediction. The proposed method is designed to fully exploit the non-linear mapping between seismic elastic parameters (e.g., P-wave velocity, S-wave velocity, density, elastic impedance) and petrophysical parameter (porosity). By combining the bidirectional contextual learning capability of Bi-LSTM, the model effectively captures feature relationships within depth sequences. Comparative analysis against a fully connected neural network and a standard LSTM network demonstrates the superiority of the proposed method. The analysis also reveals the optimal feature combination and network parameter setting (sequential length, sampling interval, etc.). Results indicate that the Bi-LSTM model achieves a significant improvement in prediction accuracy, outperforming other models, and demonstrating better generalization capability in blind well tests. The method provides a reliable and effective tool for quantitative reservoir characterization, offering substantial potential for application in deep CBM exploration.

Shale oil has been considered an important resource for the global oil and gas industry in recent years. The Yanchang formations in the Ordos Basin, China, are characterized by rich oil reserves, complex structural features, low porosity, and low permeability, with developed microcracks and indistinct oil-water contacts. A rock-physics model (RPM) developed to interpret these features considers ten rock samples from the Chang-7 member to measure ultrasonic velocity, density, porosity, and permeability, and X-ray diffraction to obtain mineral composition and micropore structures. The Chang-7 member consists of interbedded thin layers of two lithologies (sandstone and shale). The proposed model is based on the Voigt-Reuss-Hill average (VRH), self-consistent approximation (SCA), differential effective medium (DEM) theory, and the squirt-flow and Gassmann equations, and analyzes the acoustic response in terms of various pore structures and mineral components. The model is tested with the measured P-wave (VP) and S-wave (VS) velocities, and multiscale 3D rock-physics templates of the sandstone and shale layers are built, and calibrated with ultrasonic, sonic (log) and seismic data. The spectral-ratio, centroid frequency-shift and its improved version are used to estimate the attenuation. Then, the templates are used to predict the properties of the two lithologies, showing good agreement with the log data and the production report..

Seismic petrophysical inversion extracts petrophysical properties from seismic reflections, but conventional methods typically assume uniform pore structures, which limits their effective application in complex-pore reservoirs. Conventional inversion methods using either elastic or seismic data suffer from cumulative errors or low resolution with poor robustness to noise. To address these issues, we develop a coupled inversion method to simultaneously estimate porosity, fluid saturation, mineral content, and the equivalent pore aspect ratio using elastic (P-/S-wave velocities and density) and seismic (amplitudes of different angle gathers) data. The method adopts a Bayesian linear inversion approach with a seismic-petrophysical linearized forward model that represents pore complexities by including the pore aspect ratio as one of the objective parameters to be estimated. The inversion is conditioned on coupled elastic and seismic data. We conduct a comparison between our coupled inversion and con-ventional petrophysical inversion techniques, and we determine that our method improves the inversion accuracy and robustness with respect to noise. Moreover, we also define the initial model of petrophysical parameters required for the linearized inversion. This work provides an efficient and stable petrophysical inversion method for reservoirs with complex-pore structures. The inver-sion output is a model of the petrophysical properties of rock, fluid, and fracture properties.

Source rocks (shales) exhibit different geometric pore types and considerable anisotropy caused by the preferential orientation of the clay and kerogen layers, which is not accounted for in classical rock-physics models. Pore geometry can be effectively studied through the aspect ratio, and in this study, we use the aspect ratio to characterize different pore geometries. Then, we consider a pore connectivity index as well as a lamination index associated with these orientations. An inclusion-based theory (differential effective medium and self-consistent approximation) and the Brown-Korringa equations are used in the modeling approach. The results show that the indices as well as the aspect ratio of the connected pores significantly affect the elastic properties. We propose an inversion method to invert these three parameters simultaneously from experimental vertical P- and S-wave velocities using a global optimization algorithm. The method is applied to well log and seismic data from the Longmaxi shale reservoir in southwest China to verify its predictive ability.

The time-fractional Cattaneo (TFC) equation is a practical tool for simulating anomalous dynamics in physical diffusive processes. The existing numerical solutions to the TFC equation generally deal with the Dirichlet boundary conditions. In this paper, we incorporate the absorbing boundary condition as a complex-frequency-shifted (CFS) perfectly matched layer (PML) into the TFC equation. Then, we develop an adaptive-coefficient (AC) finite-difference frequency-domain (FDFD) method for solving the TFC with CFS PML. The corresponding analytical solution for homogeneous TFC equation with a point source is proposed for validation. The effectiveness of the developed AC FDFD method is verified by the numerical examples of four typical TFC models, including the different orders of time-fractional derivatives for both the homogeneous model and the layered model. The numerical examples show that the developed AC FDFD method is more accurate than the traditional second-order FDFD method for solving the TFC equation with the CFS PML absorbing boundary condition, while requiring similar computational costs.

Carbonate reservoirs are an important aspect for improving the revealed reserves and productions of oil/gas resources in China. However, such sort of reservoirs usually develops complex pore structures, which may influence the accuracy of seismic prediction for petrophysical parameters. This work proposes a seismic rock-physics simultaneous inversion method for petrophysical and pore parameters with the Gaussian mixture model. Based on the differential effective medium model and the Gassmann equation, a linearized forward operator is derived to quantitatively relate porosity, fluid saturation, and pore aspect ratio to the elastic parameters. To characterize the statistical variations within lithofacies, the Gaussian mixture model is introduced to describe the joint prior probability distribution of petrophysical and pore parameters. The analytical expression for the posterior distribution of the objective parameters is obtained with the linearized model based on the Bayesian inverse theory. Pore aspect ratio is inverted at a well location so as to provide reliable prior constraints of the pore parameter, and an iterative Bayesian inversion algorithm is adopted to improve the forward modeling accuracy. The proposed method treats pore aspect ratio as an objective parameter to account for the spatial variations of pore structures in carbonates, and employs the Bayesian linear inversion to improve the accuracy and efficiency of seismic prediction for petrophysical parameters. Numerical tests indicate that the accuracy of inverted petrophysical parameters by the proposed method is significantly improved, and the method is less affected by the initial models and elastic parameters to some extent, compared to those by the conventional method. The application to the 3D data validates the method, wherein the porosity result well indicates the spatial distribution of potential reservoirs.

Carbonate reservoirs are important targets for promoting the oil and gas reserve exploration and production in China. However, such reservoirs usually contain developed complex pore structures, which heavily affect the precision in seismic prediction of petrophysical parameters. As one of the most important parameters to characterize reservoir rock, pore-related parameters can not only describe the pore structure, but also be used to evaluate the oil/gas-bearing capabilities of potential reservoirs. The conventional rock-physics models (e.g. Gassmann's model) are formulated assuming fully connected pores, which is unable to accurately capture the geometrical complexity in real rocks. To characterize the influences of multiple pores on the elastic properties, this work presents a rock-physics modeling method for carbonates, wherein the percentage composition of connected pores is equivalently quantified as the pore-connectivity factor. The method treats the pore-connectivity factor as an objective variable to characterize the spatial variations of pore structure. Specifically, the method combines the differential equivalent medium theory and Gassmann's model, and derives a linearized forward operator to quantitatively link porosity, water saturation, and pore-connectivity factor to seismic elastic parameters. According to the Bayesian linear inverse theory, the simultaneous estimation of petrophysical and pore-connectivity parameters is achieved. To characterize the statistical variations with multiple lithofacies, the Gaussian mixture model is employed to quantify the prior distribution of the objective variables. The posterior distribution of the objective variables is analytically expressed with the linearized forward operator. Numerical experiments show that the accuracy of the proposed method in predicting elastic parameters is improved. Compared with the conventional Xu-White model and the varying pore aspect-ratio method, the accuracy of predicted P-wave velocity increases by 10.29% and 1.33%, respectively, and the predicted S-wave velocity increases by 6.44% and 0.03%, in terms of correlation coefficient. The application to the field data validates the effectiveness of the method, wherein the porosity and water saturation results help indicating the spatial distribution of potential reservoirs.

Petrophysical inversion quantitatively extracts reservoir properties from seismic data/attributes, which has gained increasing attention in assisting hydrocarbon reservoir exploration and evaluation. However, given complex reservoirs, its application is limited either due to the adopted rock-physics model or due to the computational demand. We have developed a semianalytic seismic petrophysical inversion method intended for complex reservoirs. The method incorporates the double-porosity Biot-Rayleigh (BR) model into the petrophysical forward operator, to take into account the heterogeneities within reservoir rocks. The inversion process combines statistical rock-physics modeling and Bayesian Gaussian mixture estimation, by which the analytical expression of the results can be achieved with limited computational cost. To better describe pore structure complexities, the inclusion content that constitutes a double-porosity medium of the BR model is considered an unknown variable, which favors the spatial variation of pore structures under complex lithofacies conditions. In addition, the method uses simulated annealing to estimate the inclusion content at a well location to obtain its prior information and takes advantage of the Monte Carlo simulation in rock-physics modeling to stabilize the inversion results. The method is tested and applied to the field data from a carbonate reservoir in southern China, the results of which show that the accuracy of the petrophysical parameters in terms of root-mean-square error are increased by as much as 12% compared with the method based on the Gassmann model.

Tight gas sandstone reservoirs play an important role in the field of exploration and development of unconventional oil/gas resources. However, these reservoirs typically exhibit low-porosity and poor-permeability, with pore structures of strong heterogeneity comprising connected and isolated pores. The traditional rock physics models (such as the Gassmann model) are established under the assumption of fully connected pores, which cannot reasonably describe the complexity in tight reservoirs. In this regard, this work proposes a rock physics modeling approach aimed at tight sandstone reservoirs based on a reformulated Xu–White model. Specifically, the differential effective medium model and Xu–White model are combined to analyze the influences of isolated pores on the dry rock skeleton. To characterize the general effects due to the different pore types on rock elastic moduli, the volume content of connected pores is defined as a pore-connectivity parameter. The simulated annealing algorithm is applied to invert the parameter, which is treated as a weighting coefficient for correcting the wet rock elastic moduli, thereby improving the precision of rock physics modeling. The proposed approach is tested and verified by using the log data of the work area of Sichuan Basin, West China. The result shows that, compared with the conventional method, the P- and S-wave velocities predicted by the proposed method are consistent with the log data. In addition to the inversion results of the conventional petrophysical parameters, the inverted pore-connectivity parameter can be a good auxiliary attribute that assists locating potential targets for tight gas sandstone reservoirs.

As an important geophysical data processing technique, seismic inversion estimates subsurface rock properties with seismic observations. However, anisotropic inversion, intended for a vertical transverse isotropy (VTI) media that primarily describes shale gas/oil resources, suffers from high nonlinearity. Simulated annealing is a widely used global optimization algorithm for solving nonlinear seismic inverse problems, but it involves multiple optimization parameters (e.g., initial temperature, search limit, and perturbation range). The importance of such parameters has been proven whilst the relevant analysis is limited in seismic inversion studies. This work hereby proposes a sequential anisotropic inversion method for VTI media, wherein we combine Bayesian linear and simulated annealing nonlinear inversion schemes. The simulated annealing is featured by adaptive optimization parameters aided by the linear result. Rather than the conventional method, the adaptive setting can be implemented trace by trace for complex reservoirs, which endows the method with enhanced stability and extended applicability. Synthetic tests and practical application demonstrate the validity of the method, wherein the obtained stiffness parameters facilitate the characterization of potential shale reservoirs with an improved accuracy.

Rock-physics amplitude-variation-with-offset (AVO) inversion aims at directly predicting reservoir properties from prestack seismic data. However, carbonate reservoir rocks often develop complex pore structures, which limits the application of conventional inversion methods with fixed pore-geometry parameters. We derive a PP-wave reflectivity equation in terms of porosity, water saturation, and pore-aspect ratio and we develop a rock-physics AVO inversion method to jointly estimate the petrophysical and pore-geometry parameters in carbonates. The reflectivity equation is obtained by linearizing the rock-physics model based on the differential effective medium model and Gassmann’s equation using Taylor series approximation, and we combine the linearization with the Aki-Richards equation. Thanks to the linearized model, the analytical solution to the inverse problem is derived using Bayesian linear theory. Our solution combines simulated annealing to estimate the prior information of the pore geometry and the iterative Bayesian inversion to update the posterior model. The method is tested on a benchmark data set and compared with conventional methods with a fixed aspect ratio. The results show that our method improves the petrophysical results. The method is also compared with two-step and nonlinear inversion methods to demonstrate its advantages. The method is applied to a field seismic section from a carbonate reservoir with a complex pore structure to demonstrate its advantages in terms of prediction accuracy.

Fracture orientation and in particular the fracture strike play an important role in guiding the accurate estimation of the orientation of in situ stress fields. Fracture strike can be extracted based on the azimuthal seismic reflection responses. Thus, the characteristics of seismic reflection responses varying with fracture strike are critical for fracture strike estimation. In this work, a set of vertical fractures with different strikes is introduced into an isotropic host matrix based on the Schoenberg linear-slip theory, and the azimuthal seismic reflection response is modeled based on the reflection/transmission analysis at a plane interface. The effect of fracture parameters, i.e., fracture density, fracture aspect ratio, and fluid infill on the seismic reflection response, is analyzed. The influences of fracture strike on the stiffness matrix are simulated, and we further discuss the impacts on the P- and S-wave velocities. The influences of fracture strike on the reflection coefficient are depicted using the rose diagram method. The proposed workflow is applied to real seismic reflection data. The method is used to estimate the fracture strike with the seismic data in the Sichuan Basin work area by assuming that all fractures are vertically oriented, and the rose diagram is obtained close to the target layer. The results show that the fracture strike predicted by the method is in good agreement with the estimation based on the well-bore imaging data.

Carbonate reservoirs hold promising potential for hydrocarbon exploration, but they usually exhibit complex pore structures, which lead to difficulties in the seismic/elastic prediction via conventional rock physics modeling, and in turn, hinder an accurate estimation of reservoir properties from seismic observations. This work presents a seismic rock-physics inversion method to jointly estimating reservoir-property (porosity and fluid saturation) and pore-type (pore aspect ratio) parameters in carbonates from seismic/elastic data. The method considers the aspect ratio as a pending parameter, which favors the pore-type variation so as to describe the structure complexity. To achieve the joint estimation, we derive a linearized rock physics model based on the differential effective medium model and the Biot-Gassmann equation that relate porosity, water saturation, and aspect ratio to elastic parameters. Moreover, to realize the estimation with computational efficiency, we derive the analytical solution to the inversion with the linearized model based on the Bayesian inverse theory. We estimate the pore aspect ratio at a well location to provide prior information for the inversion and employ an iterative inversion strategy with piecewise linearization to improve the result. The proposed method is applied to two carbonate reservoirs including 2D and 3D field data sets. Compared with the conventional rock physics inversion scheme with a constant aspect ratio, the application demonstrates that the method achieves better accuracy for reservoir property estimation, which can be a good indicator for the potential target areas of complex reservoirs.

Reservoir parameters, such as porosity, saturation, and clay volume, are directly related to the hydrocarbon-bearing properties of potential reservoirs, of which estimation is one of the ultimate goals of data processing for seismic exploration. However, the complex pore structure of tight sandstone presents difficulty in evaluating reservoir properties. This study proposes a novel reservoir parameter inversion method intended for tight sandstone reservoirs. The method builds the forward operator by combining the rock physics model and the seismic reflectivity equation, enabling the direct inversion of reservoir parameters from observed seismic data. In particular, the (sand- and clay-related) pore aspect ratios of rock frame are treated as internal variables, which are iteratively updated during the inversion process. The varying aspect ratios address the complex pore structure, which facilitates the improved accuracy in rock physics modeling of tight sandstone reservoirs. Besides, the Bayesian inversion constrained by the prior Gaussian mixture model considers the complex prior distributions of reservoir parameters in different lithofacies, which stabilizes the inversion process and achieves the optimal solution. The method is tested by the synthetic data which exhibits less uncertainty. The application to the field data from tight sandstone gas reservoirs in southwestern China demonstrates the method has the good capability of indicating the gas-bearing areas.

The estimation of reservoir parameters from seismic observations is one of the main objectives in reservoir characterization. However, the forward model relating the petrophysical properties of rocks to observed seismic data is highly nonlinear. and solving the relevant inverse problem is a challenging task. We have developed a novel inversion method for jointly estimating the elastic and petrophysical parameters of rocks from prestack seismic data. We combine a full rock-physics model and the exact Zoeppritz equation as the forward model. To overcome the ill conditioning of the inverse problem and address the complex prior distribution of model parameters given lithofacies variations, we have developed a regularization term based on the prior Gaussian mixture model under a Bayesian framework. The objective function is optimized by the fast simulated annealing algorithm, during which the Gaussian mixture-based regularization terms are adaptively and iteratively adjusted by the maximum likelihood estimator, allowing the posterior distribution to be more consistent with the observed seismic data. The adaptive regularization method improves the accuracy of petrophysical parameters compared with sequential inversion and nonadaptive regularization methods, and the inversion result can be used for indicating gas-saturated areas when applied to field data.

Estimation of subsurface properties by using the scattering integral equation is a method that finds increasing use in near-surface and shallow oil/gas exploration, based on seismic, low-frequency electromagnetic, and surface-radar surveys. The method can accurately simulate physical realizations induced by small-scale perturbations, but its accuracy depends on a suitable low-frequency property model. We propose a 3-D geological-structure-guided model building to provide a reliable low-frequency model and combine it with the Born-Wentzel-Kramers-Brillouin-Jeffreys (WKBJ)-approximation-based inversion algorithm. Instead of the traditional approach based on artificially interpreted horizons, we use 3-D seismic-slope attributes as lateral constraints, which contain more geological information. Plane-wave destruction (PWD) in 3-D is exploited to extract the 2-D slopes along the inline and crossline directions, which are the key factors in computing 3-D slopes. Then, by introducing the shaping regularization, we build low-frequency models by solving the inverse problem. Numerical analysis indicates that an appropriate background model is essential for seismic modeling with the Born-WKBJ approximation. The methodology is applied to synthetic and 3-D field data, and the examples show that it provides reliable background models and improves the inversion performance.

叠前地震反演可以同步反演出纵横波速度和密度等弹性参数信息,在岩性分类和流体识别领域发挥重要作用.但是叠前多参数同步反演是一个不适定问题,难以获得较精确的结果.在反演优化算法方面,线性优化算法易于陷入局部极值,且强烈依赖初始模型,非线性优化算法可以避免这些问题.常规模拟退火算法在多参数同步反演过程中稳定性较差,难以获得理想的多参数结果.本文基于纵向高斯先验约束和横向马尔科夫随机场约束建立反演目标函数,能有效降低反演的不适定性和噪声的干扰.此外,提出基于多变量高斯分布的快速模拟退火算法,提高多参数同步反演的稳定性.最后,通过合成数据和工区数据测试,结果显示三参数反演剖面具有较好的横向连续性,反演结果与测井数据较吻合,表明本反演方法具有较高的分辨率和稳定性,具有一定的实际应用价值.