Deep learning techniques have seen widespread application in seismic inversion, yet they face significant challenges when applied to fracture property inversion. The limited availability of labeled data and the lack of robust geophysical constraints can severely impact the accuracy of predictions. To address these challenges, we propose a model-data dual-driven network system. To mitigate data scarcity, we introduce a semi-supervised learning framework enhanced by data augmentation techniques. This framework leverages unlabeled data to enhance the diversity of the training dataset, thereby improving the robustness of the learning process. Additionally, we embed initial model constraints into our inversion network, ensuring that the inversion process is guided by geophysically plausible starting points. Drawing on the principles of a horizontally transversely isotropic (HTI) medium, we develop a forward model that establishes a clear relationship between fracture properties and azimuth-dependent seismic data. This model is implemented through convolutional operations between the azimuthal PP-wave reflection coefficient equation and seismic wavelets, effectively linking fracture attributes to observable seismic responses. The integration of these components results in a model-data dual-driven network capable of performing fracture property inversion with high accuracy. To validate the effectiveness and superiority of our proposed method, we apply it to both synthetic overthrust model and real datasets, and the results demonstrate that the predicted fracture weaknesses values achieve high correlation coefficients of 0.97 and 0.84 with the ground truth, respectively. Furthermore, the training time is significantly reduced compared to conventional data-driven methods, effectively improving both inversion accuracy and computational efficiency.

Fracture weaknesses represent two critical elastic parameters utilized for characterizing fracture properties in naturally fractured reservoirs. Given the intricate seismic attributes associated with amplitude variation with angles of incidence and azimuth (AVAZ) in fractured reservoir, accurately delineating the mapping relationships between azimuthal seismic data and fracture weaknesses in analytic form poses a significant challenge. Leveraging neural networks offers a nonlinear mechanism to bridge this gap. Initially, we establish a forward model by employing convolution operations between the azimuthal PP-wave (incident and reflected P-wave) reflection coefficient equation in transversely isotropic (HTI) media with a horizontal axis of symmetry and seismic statistical wavelets. This foundation enables the synthesis of azimuth-dependent seismic data. Subsequently, a convolution neural network (CNN) is constructed to predict subsurface rock fracture properties from azimuthal pre-stack seismic data. To quantify the uncertainty associated with neural network estimation, we employ the approximate Bayesian computation (ABC) method to determine the posterior distribution of model parameters. Finally, we present the application of both synthetic and filed data. Our results indicate a correlation of 90% and 86.8% between the synthetic model and the blind well, respectively. Furthermore, the estimated posterior distribution serves to validate the constraint capability of the proposed method, thereby furnishing comprehensive evidence supporting the feasibility and robustness of our approach.

Seismic impedance inversion is an effective technique for estimating subsurface rock attributes from poststack data. The inversion efficacy, however, can be compromised by factors such as data noise, initial model, and regularization constraints. Traditional single trace inversion usually exhibits obvious spatial discontinuities due to the absence of geometric constraints on the reconstructed impedances, especially in datasets with high noise levels, while the inversion may easily get trapped in local minima because of a poor initial model. To improve the imaging quality, we develop a structure-guided modified total variation (SGMTV) regularization scheme. This introduces seismic features extracted from seismic data into the modified total variation (MTV) regularization scheme, aiming to simultaneously reconstruct multitrace impedances with enhanced structures and suppressed model noise. Moreover, the SGMTV inversion is integrated with a time-domain multiscale strategy to alleviate its dependence on initial model. Both synthetic and field examples demonstrate the superiority of the multiscale SGMTV inversion compared with the conventional methods. The robust performance establishes it as a reliable tool for seismic imaging and interpretations.

Seismic inversion is an effective way to investigate the lithology and fluid in hydrocarbon-bearing reservoirs. In addition to obtaining inversion results, probabilistic seismic prediction can be used for uncertainty evaluation. Its prior probability is usually assumed to follow a specific distribution, which limits the prediction accuracy. By considering both the p-norm and total variation (TV) constraints, an improved prior is proposed. The p-norm constraint is first introduced into the probabilistic seismic prediction, which can be reduced to other probability distribution forms. With the p-norm constraint, the probability density function is updated. Then, the posterior probability with both the p-norm and TV constraints is re-derived. By analysis, the proposed approach helps to preserve the boundary and highlight the sparsity. Compared with a specific prior distribution, the proposed prior is more flexible and can effectively improve the prediction accuracy. The proposed approach is discussed in detail in terms of probabilistic prediction by using synthetic data. Both synthetic data and field data tests demonstrate the superiority of the proposed prior. The construction of the prior with p-norm and TV constraints is of great help to improve probabilistic prediction.

Fracture weakness is one of the most important anisotropic parameters used to characterize the fractures and identify the fluids. The model of horizontal transversely isotropic (HTI) medium is usually utilized in seismic azimuthal inversion for the fracture weaknesses. Low-frequency component of fracture weaknesses plays a significant role in seismic fracture characterization and fluid identification due to the deficiency of low-frequency component in acquired seismic azimuthal data. The commonly used approaches to estimate low-frequency component include the smoothing model constraints and the damped wave field in complex-frequency domain. Following the Bayesian framework, we propose a novel approach used for compensating the low-frequency component of fracture weaknesses in Laplace-Fourier domain. Firstly, we reconstruct the seismic forward solver in Laplace-Fourier domain to obtain the low-frequency component of fracture weaknesses. Then, we propose a method of seismic azimuth-difference inversion for fracture weaknesses in Laplace-Fourier domain in a Bayesian framework. Finally, both synthetic and field data examples are used to demonstrate the superiority and stability of the proposed inversion approach. Compared with the conventional inversion approach, the proposed approach can reduce the dependence on the initial model of model parameters and weaken the effect of missing low-frequency components of fracture weaknesses in azimuthal seismic data, and it may help to improve the inversion accuracy of fracture weaknesses and reduce the uncertainty of inversion results.

The probabilistic prediction approach can be used not only for obtaining the maximum posterior probability solution but also for uncertainty evaluation. Its prior distribution has a significant impact on the prediction result. An improper prior assumption may lead to prediction deviation. To improve the prediction accuracy of elastic parameters, a Laplace prior with total variation (TV) constraint is introduced in the probabilistic prediction. First, the effect of TV constraint on the probability distribution of elastic parameters is analyzed in detail. Then, two approaches are proposed to handle the cases where the elastic parameters have blocky boundaries and no blocky boundaries: probabilistic prediction scheme for elastic parameters with blocky boundaries and probabilistic prediction scheme with blocky lithology prior constraint. The former imposes a sparse constraint on the elastic parameters, while the latter imposes a sparse constraint on the TV processing lithology. Their posterior probabilities are re-derived. Considering that the discrete lithology is more likely to be blocky compared with the continuous elastic parameters, the sparse lithology constraint can handle more general cases. In addition, this approach allows for lithology prediction. The applications of numerical examples and field seismic data verify the feasibility of the proposed approaches.

Due to the special petrophysical properties of tight reservoirs, such as poor connectivity and low porosity, conventional rock physics models show limitations. Based on an inclusion-based method, a new formula containing fluid pressure is derived without an equilibration assumption of fluid pressures in the inclusions. Then, the formula is simplified with an equivalent pore structure to yield a new fluid identification parameter, the inclusion-based effective fluid modulus (IEFM). By analysis, this fluid identification factor is quite sensitive to water saturation for different pore connectivity. A well-logging data test shows the superiority of the proposed model in identifying tight gas-bearing zones. Seismic data application also demonstrates the validity of the proposed model and the predicted results match well with the well-logging data. In fluid identification, two probabilistic estimation methods are used: Bayes posterior prediction framework is a combination of Bayes’ theory and a deterministic rock physics model; Bayes discriminant method is a statistical rock physics method. The proposed IEFM is a novel identification parameter for tight gas-bearing reservoirs, which can have many applications in the exploration of tight reservoirs.

Prestack amplitude variation with offset (AVO) inversion can provide abundant reservoir information underground, which is always implemented trace-by-trace. However, it cannot guarantee the lateral accuracy of the inversion results. To utilize the lateral difference of the angle gathers and improve the lateral resolution, the difference angle gathers are introduced. Based on the Bayes inversion framework, the objective function considering the difference angle gathers is first constructed. Then, the effect of difference angle gathers on inversion results is analyzed, which is essential to improve the accuracy of the inversion results. To further figure out the applicable conditions of difference angle gathers, different forward operators are analyzed including a nonlinear operator and a linear operator. The used nonlinear operator is the exact Zoeppritz’s equation. The linear operator is a linear perturbation equation based on the elastic inverse-scattering theory. Due to the difference of angle gathers in adjacent traces, the linear forward operator may cause a deviation of the updated parameters. By comparison, the exact Zoeppritz’s equation as the nonlinear forward operator has better applicability and precision. Based on the proposed method, the elastic parameters are obtained from seismic data. Numerical examples show that the inverted elastic parameters of the proposed method have a higher horizontal resolution, and the details in the inversion profile can be better highlighted.

The time–frequency analysis is very useful for attenuation compensation, quality factor Q estimation, anomaly detection, and so on. Among plenty of time–frequency analysis methods, the S transform (ST) and its extensions are widely used because of their self-adjustable flexibility, compared with the short-time Fourier transform and Gabor transform. However, the traditional ST has a poor amplitude-preserving property near the boundary while being implemented in the time domain, because the partition of unity cannot be guaranteed. Besides, the frequency distribution biases the actual Fourier spectrum because of the linear-frequency-dependent term in the analytical window, which can decrease the accuracy of attenuation estimation. To preserve the amplitude and frequency, a new analytical window is designed, and the corresponding comprehensive window is derived in the time domain. The frequency-domain formulae are derived in detail for an efficient implementation, in which the time-domain convolution is achieved through multiplication. Numerical examples on the synthetic layered model and pseudorandom time series demonstrate the validity of the proposed method in amplitude- and frequency-preserving quantitatively. Examples at a well location of field data further demonstrate its frequency-preserving property qualitatively. Furthermore, the proposed method can have wide applications in exploration geophysics, seismology, or signal analysis fields, combining with the synchrosqueezing transform.