To address the issues that deep learning inversion relies heavily on labeled data and tends to produce results inconsistent with geological principles, this paper proposes a semi-supervised closed-loop dual-network pre-stack seismic inversion method based on prior constraints. The method builds a closed-loop dual-network framework based on residual networks. By coupling the forward and inversion networks in an end-to-end manner and incorporating a cycle-consistency loss, hard physical constraints from forward modeling are imposed. Furthermore, a loss-function embedding fusion strategy is designed, where low-frequency data are treated as pseudo-labels for unlabeled samples to construct an independent loss term. This term is then combined through tunable weights with the supervised loss and the cycle-consistency loss, ultimately forming a multi-objective joint optimization paradigm that integrates “hard physical constraints” and “soft low-frequency constraints.” Validation on synthetic data and real field data demonstrates that the method can be efficiently trained with only a limited amount of well-log data. The inversion results exhibit high vertical resolution, clearly delineated formation boundaries, and a profile energy distribution that conforms to geological patterns, showing strong agreement with the true model and blind well data. This approach effectively mitigates the limitation of scarce labeled data, enhances the physical plausibility and interpretability of the inversion results, and provides reliable technical support for high-precision seismic interpretation and detailed reservoir characterization.

Five-dimensional seismic data encompasses seismic reflection wavefield information across three-dimensional space, offset, and observation azimuth. The interpretation of such data offers a novel approach for high-precision characterization of complex oil and gas reservoirs. This paper reviews key scientific issues and foundational research related to five-dimensional seismic data interpretation, with a particular emphasis on major advances in techniques involving rock physics theories, seismic attribute analysis, seismic inversion optimization, fracture prediction, in-situ stress estimation, and fluid identification, both domestically and internationally. It further explores the opportunities, challenges, and future directions in the development of theories and methods for interpreting five-dimensional seismic data. Theoretical research and real applications have shown that constructing a five-dimensional seismic rock physics model—incorporating temperature and pressure conditions, strong heterogeneity and anisotropy, and other microscopic rock physics mechanisms—provides the physical basis for seismically identifying different types of complex reservoirs. Additionally, the development of robust inversion and quantitative interpretation methods tailored to fractured reservoirs can address issues such as computational instability and low information utilization often associated with massive high-dimensional datasets. Innovations in fracture prediction technology, leveraging multi-dimensional information fusion attributes—including five-dimensional geometric attributes, azimuthal elastic modulus ellipse fitting, Fourier series decomposition, and azimuthal inversion attributes—have proven effective in enhancing fracture prediction accuracy. Moreover, the establishment of five-dimensional seismic prediction methods for engineering sweet spots (e.g., reservoir brittleness and in-situ stress) based on anisotropy theory enables effective evaluation of the fracturability of subsurface formations. The application of five-dimensional seismic interpretation theory and technology provides a new pathway for predicting complex reservoirs and oil-gas identification.

Multi-trace amplitude variation with angle inversion (MAVAI) is a vital tool for estimating the physical parameters of subsurface media, and it plays an important role in oil and gas exploration. However, the existing MAVAI method relies on the Kronecker product to construct an extremely large-scale inverse problem, and its computational inefficiency limits its widespread application. Furthermore, regarding regularization constraints, the existing MAVAI method only considers the smoothness of the inversion parameters, which leads to ambiguous formation boundaries and hinders accurate identification for complex reservoirs. To address these issues, a compressed MAVAI method with elastic half-norm regularization is proposed. Specifically, we first developed a compressed MAVAI (CMAVAI) framework that uses compressed measurements of seismic data and reference models in a sparse domain to construct the CMAVAI objective function, thereby reducing the scale of the inversion problem and improving inversion efficiency. Subsequently, the elastic half-norm is introduced into the CMAVAI framework as a regularization constraint for reservoir parameter estimation. Since the elastic half-norm can simultaneously characterize both the smoothness and blocky features of the subsurface medium, it effectively improves inversion accuracy compared to the MAVAI method. Finally, the performance of the proposed method is evaluated using a theoretical model and field data. The results demonstrate that, compared with the traditional MAVAI algorithm, the CMAVAI framework can effectively improve inversion efficiency while maintaining inversion accuracy. Moreover, the CMAVAI method regularized by the elastic half-norm can improve the accuracy of inversion parameters while retaining the high prediction efficiency of the CMAVAI framework.

Accurate density characterization of subsurface reservoirs is crucial for various applications, such as formation pressure prediction and hydrocarbon exploration. Conventionally, density reflectivity is first estimated via seismic AVO (amplitude versus offset) inversion, and trace integration is subsequently used to acquire absolute density. Nevertheless, high-precision estimation of density reflectivity remains a formidable challenge. To improve the estimation accuracy of density reflectivity, we derive a reflection coefficient equation in terms of reflectivities of P- and S-wave velocities and density using extended elastic impedance. Compared with the Zoeppritz equation, the new reflection coefficient equation amplifies the contribution of density reflectivity to reflection coefficients and improves its inversion accuracy, indirectly enhancing the inversion accuracy of density. Combining the wavelet effect, we construct a Bayesian inversion method incorporating the new reflection coefficient equation for multi-parameter inversion of P- and S-wave velocities and density. Synthetic tests demonstrate that the proposed method yields more stable and accurate density estimations with a relative error below 1.5% compared with the Aki-Richards-equation-based method, even in the presence of moderate noise. In field applications, the inverted density from this method shows better agreement with drilling data. Nevertheless, the P- and S-wave velocities estimated by both methods are closely comparable. Both synthetic and field tests indicate the superior practicability of the proposed method.

We propose a method for extracting reflection coefficients, which can transform the seismic data in the slowness domain obtained by the forward modeling of the composite matrix reflectivity method into the angular domain. By comparing it with existing methods, the feasibility of this method is verified. Moreover, through the processing of this method, the wavefield combination of any seismic wave can be obtained as required. At the same time, in order to improve the accuracy of prestack inversion based on the reflectivity method, we provide the constraint conditions for the variation ranges of P-wave and S-wave velocities and density. Under the constraints of these conditions, the Snell-based domain conversion method can be used for seismic angular domain transformation, which reduces the computational cost of AVO inversion based on the composite matrix reflectivity method.

In-situ stress is a critical parameter in the process of oil and gas exploration and development, playing an important role in controlling oil and gas transportation, maintaining wellbore safety and guiding fracturing. Due to the significant economic and efficiency advantages, seismic prediction methods for in-situ stress fields have received widespread attention. The existing seismic inversion methods can predict elastic properties of rocks, such as velocities and rock modulus. It is worth noting that these inversion results not only reflect the intrinsic elastic properties of rock, but also effect by the stress state in which the rock is located. Through rock mechanics analysis based on acoustoelastic theory, the intrinsic elastic characteristics and stress-induced elastic characteristics have been decoupled. Furthermore, the in-situ stress is decomposed into a combination of equivalent hydrostatic stress and deviatoric stress. By analyzing the effects of these two parts of stress on elasticity and anisotropy, reflection coefficient equations related to equivalent hydrostatic stress and deviatoric stress are established separately. On this basis, applying Fourier series and multi-parameter inversion techniques, a stepwise triaxial stress inversion method is proposed. The method is capable of providing reliable and meaningful in-situ stress results through azimuthal seismic data. Besides, the feasibility of this method has been demonstrated by synthetic model and actual data testing.

Poisson's ratio is a crucial parameter for reservoir identification and the evaluation of hydrocarbon-bearing characteristics. However, due to various assumptions that are hard to satisfy, the AVO approximation formula containing Poisson's ratio is inaccurate and struggles to meet the demand for higher accuracy of inversion results. To address this issue, the inversion method based on well-control AVO is proposed. Firstly, the well-control AVO operator is obtained through well-seismic data itself, not directly using the theoretical forward operator. Then, to ensure the feasibility and stability of obtaining the well-control AVO operator, the simplified forward framework is proposed based on the physical significance indicated by prestack seismic data. Furthermore, a comprehensive well-control AVO operator can be extracted by all well data, thereby ensuring its universality. Finally, the objective function of prestack three-parameter simultaneous inversion is constructed by the well-control AVO operator, and parameter decorrelation is introduced to eliminate mutual interference between parameters. Additionally, to obtain inversion results efficiently, the regularization factors in the objective function are optimized by orthogonal experiment. Numerical test results show that the well-control AVO can obtain more accurate forward record. Moreover, inversion using the method in this paper can yield more accurate Poisson's ratio and enable better identification of hydrocarbon-bearing reservoirs.

The simulation of seismic wave attenuation and dispersion in a fractured medium and the analysis of the influencing factors have an important guiding role for fracture detection and characterization. In this paper, for the fractured medium saturated with fluid, the finite element numerical simulation method of the Lamé–Navier and Navier–Stokes equations is investigated and compared with the numerical simulation method based on Biot’s equation. Biot’s method is more suitable for simulating fractured media at the mesoscopic scale, whereas for microscopic media, the Lamé–Navier and Navier–Stokes equations demonstrate distinct advantages. Meanwhile, the numerical simulation method is employed to analyze the influencing factors of connectivity of symmetrical fractures, effective compression length of seismic waves, and fluid viscosity. This analysis further elucidates the mechanisms and change characteristics of seismic wave attenuation and dispersion, providing theoretical guidance for the detection of fractures and fluids.

Initial stress exerts a crucial impact on the elastic properties and thus the wave reflection in the layered media. However, the stress effect on wave reflection characteristics in such media remain insufficiently understood. To address this issue, we develop a composite matrix reflectivity method incorporating initial overburden stress (CMRMS) by means of acoustoelasticity theory, enabling accurate modeling of seismic wave propagation in stressed layered media. The proposed method can better simulate multiple reflections, converted waves and transmission loss of seismic waves in layered media, compared to the classic stress-dependent reflection coefficient equation for a single interface. Moreover, our method can degenerate into the existing methods in the cases of no initial stress and single interface, which verifies its correctness. We further extended the CMRMS to elastic and viscoelastic non-welded interfaces using the linear-slip theory and standard linear solid model, respectively. The extended method is used to investigate the impacts of non-welded interface compliance, overburden stress, fluid viscosity and frequency on seismic reflection characteristics within layered model. It is shown that the stress effect magnitude on interface reflection significantly depends on the interface depth, due to cumulative transmission losses from overlying layers. Moreover, increasing either the compliance or the number of overlying non-welded interface significantly reduces the reflection amplitude at deeper interface. Our results show the potential of the proposed composite matrix reflectivity method to consider the joint effects of initial stress, multiple waves and transmission loss in both forward modelling and inverse applications.

The wave-induced fluid flow (WIFF) between the pores in fluid-saturated porous orthorhombic (FSPOR) media inevitably leads to the wave energy attenuation and seismic dispersion. Yet the WIFF effect is seldom considered in the prevailing seismic inversion methods for FSPOR media. We developed a rock physics model for FSPOR media that incorporates the squirt-flow effect, jointly caused by the background matrix and fractures. We then analyzed the impacts of incidence angle and azimuth on wave dispersion and attenuation behaviors. We further derived a linearized PP-wave reflection coefficient equation in terms of P- and S-wave moduli, density, squirt-flow fluid indicator, Thomson's anisotropic parameters and weaknesses using the elastic inverse scattering theory. The proposed equation exhibits excellent consistency with two classic equations within moderate incidence angles. Incorporating the seismic wavelet effect, our reflection coefficient equation is incorporated into the Bayesian inversion framework to estimate model parameters. Synthetic tests demonstrate the feasibility and robustness of our method even with moderate noise. Field application shows that the inverted results are consistent with the drilling data near the well location and exhibit consistent lateral continuity with the seismic profiles. In addition, the inverted fluid indicator profile obviously discriminates the three oil bearing reservoirs compared with the traditional fluid indicator, which demonstrates the potential of our method in hydrocarbon detection in fractured reservoirs.

Supervised deep learning methods currently used for prestack parameter prediction are suffered from the problem of limited training samples. The lack of clear physical meanings for deep learning models also makes prediction results unreliable. To address these issues, we proposed a geophysical prior knowledge guided semi-supervised (GPKGS) deep learning framework for amplitude-versus-angle (AVA) inversion. Based on prior physical knowledge, the prestack seismic data are decoupled into prestack seismic attribute data of the elastic parameters. Meanwhile, according to the prestack seismic attribute data, constructing the new forward models corresponding to each elastic parameter. The intelligent inversion framework is built based on the constructed forward models. This reduces the dependence of the framework on training data. This GPKGS framework preserves the physical procedure of AVA inversion, making intelligent inversion results reliable. The framework contains three branch networks for each elastic parameter. Each branch network contains an inversion neural network (INN) and a forward neural network (FNN). The INN can invert the prestack seismic attribute data into elastic parameters, which corresponding to inversion process. The FNN convert the obtained elastic parameters into synthetic prestack seismic attribute data, which corresponding to forward process. To ensure a reliable training process, the difference between the prestack seismic attribute data and the synthetic data are used to train the framework supervised by well log data. In addition, to obtain more stable results, at prediction stage, the prior information is introduced to help the FNN update the elastic parameters output by INN. The Marmousi2 model and a deep carbonate data are used to test the proposed framework. We find that the intelligent inversion results of the proposed network perform well at the situation of few training data.

Deep learning is prevalent in many fields and attempts have been made to use it in nonbidirectional mapping problems, such as seismic inversion. These nonbidirectional mapping problems have two special issues, that is, insufficient labels and uncertainty of solution. Therefore, current deep-learning structures are not suitable for handling this kind of problem. A distinctive knowledge-embedded close-looped (KECL) deep-learning framework is developed, tuned to the characteristics of the seismic inverse problem. The KECL deep-learning framework is composed of a reservoir parameter generator (RPG) and a reservoir parameter updater (RPU). The former half-loop is RPG, which takes the seismic data as input to generate the initial reservoir parameters. The latter loop is RPU, which takes the initial parameters as input to output synthetic seismic data. Through the training by well data, the difference between field seismic data and synthetic seismic data modeled by the RPU is used to optimize the RPG and RPU. In this deep-learning framework, knowledge of the Robinson convolutional model is embedded to address the problem of insufficient labels. Furthermore, semisupervised learning is used as prior information to reduce the uncertainty of solution. After the training, with the help of prior geologic information data, the RPU is used to update the initial reservoir parameters generated by RPG for final reservoir parameter inversion. Numerical models and field data are used to test the feasibility of our deep-learning framework. We find that intelligent inversion results using data from one well to train the KECL network are consistent with results using multiple well data. Experiments demonstrate that it is adaptable to situations in which insufficient well data are available and is able to achieve reliable intelligent inversion.

The mechanism of wave propagation in fluid-saturated porous media is influenced by pressure and frequency. Pressure dependence is mainly dominated by the opening and closing of compliant and stiff pores in rocks, as well as nonlinear deformation respect to high-order elastic constants. Frequency dependence is mainly reflected in the dispersion and attenuation caused by wave-induced fluid flow (WIFF). Therefore, the propagation characteristics of seismic waves in subsurface rocks when pressure and frequency are coupled have broad practical significance, such as geofluid discrimination and in situ stress detection. A new equivalent elastic modulus applicable to fluid-saturated porous media has been established, which simultaneously considers the effects of pressure and WIFF. First, the dual-porosity model is incorporated to account for the changes in rock porosity under pressure and corresponding linear and nonlinear deformations. Then, based on the heterogeneity of rock at the mesocale and microscale, a unified pressure- and frequency-dependent elastic modulus over a wide frequency band is established using the Zener model. The wave equation of fluid-saturated porous media is constructed using the new model, and the pressure- and frequency-dependent phase velocities are derived. Rock physics and digital simulation experiments are applied to analyze the variation of elastic parameters and velocity with pressure and frequency. Comparison with experimental measurement data shows that the new model has higher accuracy than traditional models, especially in the low effective pressure region and the frequency band respect to seismic exploration.

Based on the compressive sensing（CS）theory and the wavelet interference mechanism between strong and weak reflections,a dynamic dictionary strong reflection decomposition method by approximating arbitrary strong reflection waveforms and a strong reflection reduction method based on shielding function were proposed.The validity of the methods was verified using numerical models and physical models with large lateral variations of strongly reflected waveforms. The methods have been practically applied in the second member of Permian Maokou Formation in the central uplift tectonic zone of central Sichuan Basin. The results show that:（1）Compared with the conventional de-strong reflection method,the strong reflection reduction method based on shielding function has better lateral continuity of the seismic event,the strong reflection event is more thoroughly reduced,and the weak reflection of the blocky sand body shielded by the strong reflection is revealed. At the same time,the method has low dependence on the horizon and can process the strong reflection within the time window at one time without accurate strong reflection horizon data.（2）The strong reflection reduction method based on shielding function has a better elimination effect when the distance between the sand body and the strong reflection layer is less than λ（wavelength）and greater than λ/4. The strong reflection can be completely removed and the weak reflection is completely revealed. When the distance between the sand body and the strong reflection layer is less than λ/4,the elimination effect is poor. When the distance between the sand body and the strong reflection layer is less than λ/8,the elimination effect is worse.（3）This method is better applied in the second member of Permian Maokou Formation in the central uplift tectonic zone of central Sichuan Basin. The weak reflection of the reservoir is revealed when the distance between the reservoir and the strong reflection layer is less thanλ/4. The reservoir response is enhanced when the distance between the reservoir and the strong reflection layer is greater than λ/4.

With the development of oil and gas exploration targets towards deep water and deep layer, change of subsurface rock physical properties caused by in-situ stress can no longer be ignored. Hence, it is of great significance to study the acoustoelasticity characteristics of rocks under complex subsurface stress environment. Based on acoustoelasticity theory and anisotropic analysis of rock under triaxial stress state, equivalent stiffness matrix of acoustoelastic-orthotropic media is established. According to the equivalent stiffness matrix, exact solution of reflection coefficient for stress-induced orthotropic media is derived. Through model experiments, reflection coefficient varies with incident and azimuth angle is analyzed. Based on the azimuthal characteristics of acoustoelastic medium reflection coefficient and in-situ stress prediction models, two in-situ stress characteristic parameters are proposed to describe in-situ stress distribution. Then, by numerical simulation, the law between azimuthal characteristics of acoustoelastic medium reflection coefficient and in-situ stress characteristic parameters is summarized. And an effective way to predict in-situ stress field that wide azimuth seismic data dependent is established. Finally, through actual wide azimuth seismic data in a field, the practicability of this insitu stress prediction method rely on stress characteristic parameters is verified. The results illustrate that the prediction method of in-situ stress characteristic parameters can accurately describe the distribution of in-situ stress.

Seismic high resolution processing plays a crucial role in seismic interpretation and reservoir characterization. However, the low and high frequency of seismic signal are lost owing to the effects of earth filtering and diffraction. The missing of low-frequency increases the energy of wavelet side lobe, which not only enhances the interference with adjacent events, but also lead to side lobe artifacts. High frequency attenuation is more serious, which significantly reduces the seismic resolution. In addition, the current resolution enhancement methods are difficult to achieve desirable result in noise contaminated environment. A novel resolution enhancement method that extends high and low frequencies simultaneously and improves the signal-to-noise ratio (SNR) under the framework of sparse decomposition theory is proposed. Firstly, an over-complete dictionary is constructed using non-zero phase Ricker wavelet and then the effective seismic signal is extracted by sparse decomposition using the fast sparse Bayesian learning (FSBL) algorithm. Secondly, the effective frequency range of the seismic signal is determined through a series of atoms obtained by sparse decomposition. Then, a desired broadband spectrum can be identified depending on this range. By approximating the broadband spectrum of seismic data, the weak high-frequency information can be extended. Furthermore, a correction term is introduced in frequency domain to suppress the side lobes of atoms. The side lobes are well suppressed without distorting the main lobe, meanwhile, both the low and high frequencies are extended. Finally, the validity of this method is verified by synthetic and field data. The results show that this method has better performance than the ordinary deconvolution and spectral whitening methods in processing high resolution data.

Enhancing seismic resolution is a key component in seismic data processing, which plays a valuable role in raising the prospecting accuracy of oil reservoirs. However, in noisy situations, existing resolution enhancement methods are difficult to yield satisfactory processing outcomes for reservoir characterization. To solve this problem, we develop a new approach for simultaneous denoising and resolution enhancement of seismic data based on convolution dictionary learning. First, an elastic convolution dictionary learning algorithm is presented to efficiently learn a convolution dictionary with stronger representation capability from the noisy data to be processed. Specifically, the algorithm introduces the elastic L1/2 norm as a sparsity constraint and employs a steepest gradient descent strategy to efficiently solve the frequency-domain linear system with substantial computational cost in a half-quadratic splitting framework. Then, based on the learned convolution dictionary, a weighted convolutional sparse representation paradigm is designed to encode the noisy data to acquire an optimal sparse approximation of the effective signal. Subsequently, a high-resolution dictionary with a broadband spectrum is constructed by the proposed parameter scaling strategy and matched filtering technique on the basis of atomic spectrum modeling. Finally, the optimal sparse approximation of the effective signal and the constructed high-resolution dictionary are used for data reconstruction to obtain the seismic signal with high resolution and high signal-to-noise ratio. Synthetic and field dataset examples are executed to check the effectiveness and reliability of the developed method. The results indicate that this method has a more competitive performance in seismic applications compared with the conventional deconvolution and spectral whitening methods.

Deep hydrocarbon resources have become more and more important nowadays. However, owing to the affection of long-distance propagation and stratigraphic absorption, seismic data coming from deep beds generally suffer from weak energy, low resolution, and low signal-to-noise ratio (SNR), which seriously influence the reliability of seismic interpretation. Generally, inverse Q (quality factor) filtering (IQF) is used for absorption compensation, but it may amplify noise at the same time. Although compensation methods based on inversion overcomes the instability, it is still difficult to obtain high-SNR results. To address this issue, under the framework of sparse representation theory, we proposed a single-channel attenuation compensation method constrained by generalized minimax concave (GMC) penalty function. It takes the modified Kolsky model to describe seismic absorption and combines sparse representation theory to create objective function. Furthermore, a GMC penalty function is utilized to promote sparsity. It allows more accurate estimates of sparse coefficients from noise-contaminated seismic data. Although the GMC penalty itself is concave, the objective function remains strictly convex. Therefore, globally optimal sparse solutions can be obtained through an operator-splitting algorithm. Even in the presence of noise, this method can obtain stable and accurate compensation results through reconstruction. Synthetic data tests and field seismic data application showed that this method has high robustness to noise. It can stably and effectively compensate for the energy loss of seismic data, as well as maintain high SNR.

Exploration of potash resources under complex geological condition is particularly important. However, it is difficult to establish characteristic equations for direct prediction, since there is no direct relation between potash content (PC) and seismic response. To solve this problem, this paper proposed a potash reservoir prediction method by a specially designed convolution neural network (CNN) structure to train the special waveform and petrophysical characteristics of potash reservoirs. Considering that the potash reservoirs and petrophysical characteristics are not a one-to-one mapping, the prediction procedure is divided into two parts. First, a CNN is constructed for potash reservoir prediction, according to the spatial waveform characteristics of potash reservoirs. The mapping between potash reservoirs and waveform characteristics is used to obtain the potash reservoir probability data by the soft-max function. Then, another CNN for PC prediction is built based on the petrophysical characteristics of potash reservoirs. Meanwhile, according to the Hadamard criterion, the petrophysical characteristics of potash reservoir are constrained by the waveform characteristics. The two CNN models are used to directly predict the PC synergistically. Consequently, the bidirectional mapping problem can be alleviated and a loss function of the PC prediction CNN constrained with the waveform is obtained. Finally, by tuning the PC prediction CNN through the loss function, PC prediction is performed. The correlation between the predicted and true PC values can reach more than 80

Recently, multi-trace impedance inversion has attracted great interest in seismic exploration because it improves the horizontal continuity and fidelity of the inversion results by exploiting the lateral structure information of the strata. However, computational inefficiency affects its practical application. Furthermore, in terms of vertical constraints on the model parameters, it only considers smooth features while ignoring sharp discontinuity features. This leads to yielding an over-smooth solution that does not accurately reflect the distribution of underground rock. To deal with the above situations, we first develop a low-dimensional multi-trace impedance inversion (LMII) framework. Inspired by compressed sensing, this framework utilizes low-dimensional measurements in sparse space containing the maximum information of the signal to construct the objective function for multi-trace inversion, which can significantly reduce the size of the inversion problem and improve the inverse efficiency. Then, we introduce the elastic half (EH) norm as a vertical constraint on the model parameters in the LMII framework and formulate a novel constrained LMII model for impedance inversion. Because the introduced EH norm takes into account both the smoothness and blockiness of rock impedance, the constrained LMII model can effectively raise the inversion accuracy of complex strata. Finally, an efficient alternating multiplier iteration algorithm is derived based on the variable splitting technique to optimize the constrained LMII model. The performance of the developed approaches is tested using synthetic and practical data, and the results prove their feasibility and superiority.