Seismic data are frequently contaminated by incoherent random noise and coherent surface waves; both severely degrade subsurface data quality. While random noise is statistically irregular and uncorrelated, surface waves exhibit structured regularity in both temporal and spatial domains. Their coherent low-frequency propagation makes them fundamentally distinct from random noise, posing significant challenges to simultaneous suppression. This letter presents a Deep Adaptive Signal Denoising network (DASDNet) designed for random and ground roll simultaneous suppression using weakly supervised training on synthetic clean-noisy pairs. The architecture incorporates short-time Fourier transform (STFT) and discrete wavelet transform (DWT) for multiscale time-frequency decomposition. A fuzzy logic-based encoder is employed to mitigate feature uncertainty, complemented by a time-frequency regularization module that preserves structural coherence. A unified loss function across time, frequency, and spatial domains guides robust training. DASDNet demonstrates remarkable generalization capability to both synthetic and field-recorded datasets, achieving robust performance without reliance on labeled field data or manual post-hoc parameter tuning. Experimental results show that DASDNet improves signal-to-noise ratio (SNR) by 6.86 dB, reduces mean squared error (MSE) by 4433, and increases structural similarity index (SSIM) by 0.22, outperforming other methods. Qualitative analysis further demonstrates its advantage in preserving primary fidelity while suppressing noises.

When seismic waves propagate through horizontal transversely isotropic (HTI) media, the variation of acoustic impedance with azimuth can effectively reflect the fracture density and direction information. The key to high-precision fracture parameter prediction lies in improving the accuracy of azimuthal impedance inversion and elliptical analysis. This study proposes an integrated solution: First, the total-variation multiplicative regularization multichannel impedance inversion technique is employed to obtain azimuthal impedance information. By incorporating formation dip constraints and an improved Polak-Ribière-Polyak-Hestenes-Stiefel (PRP-HS) hybrid conjugate gradient algorithm, the inversion accuracy and lateral resolution are significantly enhanced. Second, to address the small-sample problem in azimuthal impedance elliptical analysis, we developed a hybrid elliptical analysis method incorporating probability distribution and uncertainty estimation. The methodology involves: (1) applying the adaptive random sample consensus (RANSAC) algorithm to screen high-quality data points, (2) utilizing Bayesian regression for probabilistic modeling of the data, and (3) implementing Bayesian inference through Markov chain Monte Carlo (MCMC) methods. This combined strategy of random sampling and iterative optimization ensures the stability and reliability of fitting results. Furthermore, a planar transformation matrix is introduced to correct the rotation angle, thereby optimizing the prediction accuracy of fracture direction. Application results from actual well logging and seismic data demonstrate that this method exhibits superior performance in predicting both fracture direction and density, providing a reliable technical approach for fractured reservoir characterization.

Seismic acoustic impedance (AI) inversion is essential for reservoir prediction and characterization. In recent years, deep learning has shown immense potential as a data-driven approach in seismic data processing, inversion, and interpretation. As a data-driven method, deep learning-based seismic inversion results better when sufficient labeled data are provided. Overfitting and poor generalization often occur when labels are insufficient. Due to the lack of labeled data in seismic inversion problems, the difficulty of inversion increases, leading to unstable and poor generalization of prediction results. To partially address this issue, we propose a constrained seismic inversion strategy. Since seismic records are time series, we exploit the convolutional neural network (CNN) and bidirectional LSTM (Bi-LSTM) network structures that are more applicable to time series. We combine the physical model and the initial model as constraints to improve the network stability and generalization ability, and impose sparse constraints on the reflection coefficient to further improve the prediction accuracy. The network structure transformation improves the efficiency and stability of the training process. Through numerical experiments and real data tests, it is proved that the proposed method improves the vertical resolution and geological reliability, providing a more stable and efficient method for seismic inversion under conditions of limited labeled data. The overall performance improved by 2% through comparative analysis.

As an important elastic parameter, seismic acoustic impedance is usually obtained through poststack inversion. However, there are usually two problems that limit the quality of the inversion results. First, conventional inversion methods typically use regularization terms to enhance the stability of the inversion results, and effective regularization terms are particularly important for accurately inverting seismic impedance. Second, most inversion methods adopt a trace-by-trace inversion strategy, resulting in poor lateral continuity when connecting the inversion results of all traces into a 2-D profile, especially for processing noisy data. To address these two problems, we propose a structure-oriented minimum entropy stabilizer for acoustic impedance inversion that enhances the lateral continuity of the inversion results while restoring the blocky structures of the strata and improving the resolution of the inversion results. The stabilizer consists of a structure-oriented regularization (SOR) operator and the minimum entropy norm. The SOR operator is constructed using the local dip estimated from the seismic data by the plane-wave destruction (PWD) algorithm and constrains the inverted impedance along the structural trend, making it more consistent with geological features. The minimum entropy norm restores the blocky structures and enhances resolution by imposing sparse constraints on the temporal and spatial derivatives of the impedance. Based on synthetic and field seismic data, we compare the inversion results of the proposed method with those of conventional Tikhonov regularization and total variation (TV) regularization methods. The results show that the proposed method exhibits superior performance, especially in processing noisy data.

Multiple attenuation plays an important role in marine seismic data processing, and a slew of methods have been developed for multiple attenuation. However, due to acquisition limitation, the performance of such methods will degrade when it comes to incomplete seismic data. Here, we proposed a novel method to implement data reconstruction and multiple suppression simultaneously. Compared with the two-step methods (e.g., interpolation and multiple attenuation), the proposed method can restore and highlight primary reflections directly without data reconstruction in advance, which avoids introducing interpolation-related errors and simplifies the data processing routines. Based on the incomplete data, we first sort seismic data into common midpoint (CMP) gathers and use normal moveout (NMO) to flatten the primary reflections, and the multiples still retain parabolas. Then, we reassigned the seismic traces randomly to decrease the coherency of the multiples from near-offset to far-offset and applied the damped rank reduction (DRR) method to the disordered traces to reconstruct seismic data and remove the unexpected multiples simultaneously. Compared with conventional two-step methods, the proposed one-step method can suppress multiples and benefit useful signal preservation more effectively. Moreover, in addition to multiples, the proposed method can remove random ambient noise and provide superior results with an improved signal-to-noise ratio (SNR). Synthetic and field examples are used to validate the validity of the proposed method on data reconstruction and multiple attenuation for incomplete seismic data.

Quality factor Q is an important parameter that accounts for the amplitude dissipation and phase distortion of seismic waves propagating in the Earth’s interior. Q estimation with improved accuracy benefits nonstationary seismic inversion, seismic imaging, fluid identification, and so on. Usually, logarithmic spectral ratio (LSR) is widely used to estimate Q based on vertical seismic profile (VSP) and poststack data. However, LSR is very sensitive to noise, and the effect of normal moveout (NMO) distorts the spectrum of the stacked seismic data, leading to an inferior Q estimation result. To weaken the effect of NMO and enhance the accuracy of Q estimation, we expand an improved LSR method in the zero-offset traveltime-local slope (e.g.,$t_{0}-p$) domain and propose a robust prestack Q estimation method based on common midpoint (CMP) gathers. The proposed method incorporates warped mapping (WM) and shaping regularization to stabilize it during Q estimation in the case of low signal-to-noise ratio (SNR). Additionally, we incorporate nonzero-offset information for Q estimation, which weakens the strong dependence on zero-offset information during prestack Q estimation. Compared with the single-gather prestack Q estimation methods (SPQEM), we make the most of the spatial coherence between the adjacent CMP to eliminate the unexpected noise-related outliers during spectral division for improved robustness and accuracy. Numerical examples are used to validate the superior performance of the proposed method, even in the presence of strong ambient noise.

Prestack seismic inversion is one of the most commonly used methods to describe reservoirs. Deep learning (DL) has received wide attention because of its ability to handle complex nonlinear problems. The existing DL-based seismic inversion method adopts a single training dataset, which is prone to poor generalizability and geological artifact. In addition, field data are often difficult to transfer learning due to the lack of a training dataset. To partially overcome these problems, we improve the training dataset and network parameters, thus developing a new DL-based prestacked inversion framework. First, we generate a training dataset using a forward model and pretrain the network by adding labels to a portion of it as the training dataset. We use multitrace information for training and prediction to reduce the lateral geological artifact problem. For unlabeled or less-labeled datasets, we construct data residual loss terms and initial model constraints to achieve weakly supervised or even unsupervised learning, which solves the poor generalizability problem due to insufficient training datasets. Compared with previous data-driven approaches, the inverse framework in this article compensates for the lack of the training dataset, diminishes geological artifacts, and improves generalization and robustness. The effectiveness of the framework is verified by synthetic data from two different models and field data from S-fields, and good inversion results are obtained even with a low signal-to-noise ratio or lack of well data.

Based on the Bayesian framework, pre-stack inversion aims to find the solution with the maximum posterior probability under the prior constraint. The prior constraint is usually a mathematical expression of the inverted parameters, and guides the updating of the inversion results. To obtain a stable, high-resolution and high-fidelity inversion result, we introduce a new prior constraint named ‘amplitude entropy’ to help perform the pre-stack inversion. The amplitude entropy can make the chaos of the parameters to be inverted close to those of the known well-logging data. Compared with the traditional L2 prior constraint, amplitude entropy can improve the resolution of the inversion results, and compared with the conventional L1 prior constraint, it can obtain a solution that is more consistent with the geological characteristics. In addition, multi-component seismic data contains richer lithology and fluid information than single-component data. Therefore, in this paper, we directly develop the pre-stack inversion method based on the multi-component seismic data. Furthermore, due to the high nonlinearity of the objective function under the amplitude entropy constraint, the quantum annealing (QA) algorithm is employed to solve the objective function of the joint inversion and find the final solution. Synthetic and field data examples demonstrate that the pre-stack inversion method with the amplitude entropy constraint is effective and stable, especially for processing seismic data with a low signal-to-noise ratio.

Coherent and incoherent noise in seismic data inevitably reduces the quality of subsequent processing, e.g., migration and inversion. Different from random noise, erratic noise follows the non-Gaussian distribution and has high amplitude, which is a challenge to the conventional denoising frameworks based on deep learning (DL). In this study, we propose an unsupervised learning framework with a multi-branch attention mechanism (MANet) to attenuate the erratic and random noise in 2-D and 3-D seismic data. MANet can adaptively attenuate noise in multi-dimensional seismic data without the need to manually generate labels to train the network. MANet integrates global features of waveforms extracted from multiple branches in a weighted way to enhance attention to significant features, thus obtaining a global and comprehensive representation of weights. To enhance the migration ability of shallow-level to deep-level features, we add some skip connections in the corresponding encoder and decoder. We use a robust mean-Huber loss function that is less sensitive to outliers to improve the denoising performance of erratic noise. We apply the proposed network for both 2-D and 3-D synthetic and field data. The denoising results demonstrate that the proposed method has better signal preservation and noise attenuation abilities compared with the conventional denoising methods and the state-of-the-art unsupervised learning framework. We improve the interpretability of the network by visualizing the weight matrices and different encoders. Besides, the visualization schemes proposed in this paper can be applied to more research, such as geological event interpretation, geological resource detection, and surface morphology analysis.

Salt body segmentation is a critical part of structural interpretation and oil and gas exploration for subsalt reservoirs. Existing automatic salt body segmentation techniques mostly use supervised learning strategies. It is challenging to generate a large number of labels by manual labeling, especially for 3-D salt bodies. Here, we propose a self-supervised learning (SSL) framework called Salt3DNet, for 3-D salt body segmentation. This framework is divided into two stages: pretraining and fine-tuning of downstream tasks. In the pretraining stage, we use the Barlow twins (BTs) method to pretrain the encoder and reduce redundancy in a contrastive learning manner to learn high-level data representations. In the fine-tuning stage, we construct two encoders to reconstruct 3-D seismic data and segment salt bodies in a multitask collaborative learning way. The encoder and decoder are composed of the 3-D fully convolutional DenseNet and soft attention mechanism, where the latter represents the selective kernel block (SKB) with multiple kernels of different sizes. Salt3DNet calculates the correlation matrix of features from different perspectives in the pretraining stage and makes it close to the identity matrix to obtain a more prosperous feature representation. Then, Salt3DNet uses a limited number of labeled samples for training. According to the evaluation metrics, the proposed network has demonstrated promising salt segmentation performance in 3-D SEG advanced modeling (SEAM) synthetic data and$F3$block real seismic data. In addition, the proposed network is demonstrated to have higher prediction accuracy than state-of-the-art salt segmentation frameworks through ablation experiments.

Gaussian pyramid (GP) has the property of decomposing the 2-D data into multiple scales. It has been successfully applied in image processing, but rarely used in seismic data processing and interpretation. Specifically, seismic data are not just a 2-D image in one time slice or horizon. Moreover, the pattern of geological body varies rapidly in 3-D spaces. Hence, the classical GP method exists a limitation in processing 3-D seismic data. Especially in fracture detection, the 2-D isotropic Gaussian kernel used in GP tends to blur the fracture details. In this letter, to match the high-dimensional seismic data, we propose a structure-oriented adaptive Gaussian pyramid (SOA-GP) algorithm, which expands the 2-D GP method to the 3-D situation. In this case, to eliminate the influence of transverse change of wave impedance and consider stratigraphic characteristics, the 2-D Gaussian filter is also substituted by the 3-D structure-adaptive anisotropic Gaussian kernel, which is constructed by instantaneous phase-based gradient structure tensor (GST) method. Meanwhile, seismic attributes are applied to the multiresolution seismic data decomposed by the SOA-GP method to realize multiscale fracture detection. Finally, we apply this new 3-D SOA-GP method to field data. It demonstrates that the multiscale decomposition of the new method could produce more details of fracture and less disturbance from noise.

The geostatistics stimulation method, as an important tool in subsurface modeling, is crucial for hydrocarbon reservoir characterization. Using geostatistical methods to reproduce complex heterogeneous structures is still challenging because of nonstationarity and computational consumption. We develop a stabilized stochastic simulation method by introducing the generative adversarial network based on a single image (SinGAN). It can preserve multiscale features contained in an individual training image by using a multistage training framework. In order to stabilize the training of the discriminator, the spectral normalization is integrated. We also introduce spatial attention and channel attention mechanism into the network to focus on the most significant features in each training stage, so that these features can be reproduced in the realizations. An adaptive strategy is adopted to automatically choose training stages, which balances the diversity and quality of simulation results and decreases the man-made factor on SinGAN. Several experiments are tested on synthetic and actual training images, respectively. We evaluate the simulation results from many perspectives, including variability, connectivity, probability density distribution, and time-consuming. The successful application of the new method on both categorical and continuous variables indicates that it has a strong ability to reproduce complex subsurface models, even for nonstationary geologic phenomena.

Accurate estimation of reservoir parameters (e.g., permeability and porosity) helps to understand the movement of underground fluids. However, reservoir parameters are usually expensive and time-consuming to obtain through petrophysical experiments of core samples, which makes a fast and reliable prediction method highly demanded. In this article, we propose a deep learning model that combines the 1-D convo- lutional layer and the bidirectional long short-term memory network to predict reservoir permeability and porosity. The mapping relationship between logging data and reservoir parameters is established by training a network with a combination of nonlinear and linear modules. Optimization algorithms, such as layer normalization, recurrent dropout, and early stopping, can help obtain a more accurate training model. Besides, the self-attention mechanism enables the network to better allocate weights to improve the prediction accuracy. The testing results of the well-trained network in blind wells of three different regions show that our proposed method is accurate and robust in the reservoir parameters prediction task.

Prestack seismic inversion has emerged as a powerful technique for reconstructing parameters attribute to the subsurface properties and building the geophysical parameter models. However, the inversion algorithms always suffer from spatial blur and low resolution. Total variation (TV) regularization preserves the spatial variation boundary of data by highlighting the sparsity of the first-order difference, which is regarded as an important technical means for image restoration. However, when the data do not change along the spatial grid direction, TV regularization is prone to a staircase effect. In this article, a directional TV (DTV) method is proposed to conduct the prestack amplitude variation with offset/angle (AVO/AVA) inversion. The method consists of three essential steps: estimating the seismic slope attribute from the seismic data, introducing seismic slope attribute to the TV regularization to establish the objective function, and optimizing the objective function by the split-Bregman algorithm. Finally, the conventional and proposed methods are applied to the synthetic and the real seismic data. The comparison of different methods demonstrates that the proposed method is applicable to reveal the detailed subsurface models, alleviate the staircase effect or artifact substantially, and further upgrade the quality of prestack inversion results.

Seismic inversion is a method used to identify spatial structure and obtain physical properties of underground strata by processing seismic data. As a data-driven approach, deep learning (DL) is widely used in pre-stack three-parameter inversion to solve its non-linearity and ill-posed problems. However, traditional DL-based methods involve the construction of a separate network for each task and thus ignore the correlations between different tasks. Multi-task learning (MTL) aims to promote the effectiveness of each task with implicit information amplification by training multiple tasks simultaneously. However, information sharing in conventional MTL may cause negative effects on parallel tasks. To solve this problem, a novel multi-task learning method, called pertinent multi-gate mixture-of-experts (PMMOE), was proposed for pre-stack three-parameter inversion. PMMOE introduces mixture-of-experts (MOE) structure for multi-task learning and creatively divides experts into three special experts and a shared expert. In PMMOE, the input data of different experts are discrepant, enabling the retrieval of different features for different tasks. Experiments revealed that our proposed method has higher accuracy than other methods, and the inversion results of synthetic data and field data further demonstrate the effectiveness of our proposed method.

High-amplitude noise could interfere with useful seismic signals, affecting our ability in processing and interpreting seismic data. Thus, attenuating seismic noise is an important task in seismic processing. Total variation (TV) has played an important role in many steps of seismic data processing but always neglected the seismic structural information. Directional TV (DTV), however, considers the structural direction of seismic events but tends to cause the staircasing effect on seismic records based on the first-order formulation. Here, we develop a high-order DTV (HDTV) method for seismic denoising. It considers the local structural direction of the seismic data and calculates the higher order derivatives of seismic images to avoid the staircasing effect. We design several synthetic models that are contaminated by various types of random noise to test the denoising ability. The denoising performance of our new method is compared with the first-order DTV, conventional high-order TV, and TV regularization methods from two aspects, i.e., the signal-to-noise ratio and the effective signal leakage degree. Then, the advantages of the proposed method are further validated via several field seismic data sets.

Lithofacies classification is an indispensable procedure in well logging and seismic data interpretation. We propose a novel deep classified autoencoder learning approach to identify lithofacies for high-dimensional data and complex problems. Deep autoencoder (DAE) is an unsupervised learning method via layerwise pretraining multiple autoencoders. It can learn deep data features automatically and reconstruct the original data with a small error. Introducing sparse constraint (i.e., sparse autoencoder) potentiates the learning ability of autoencoder. On this foundation, additional regularization terms constructed by labeled samples are considered in the new DAE approach in order to boost the performance. The new method can adaptively preserve the most significant input features and remove insensitive properties to decrease computational complexity. At the same time, we embed the class information into the loss function of autoencoder to measure intraclass similarity and improve the classification accuracy. Several experiments on well data and seismic data show that the proposed method achieves promising results. Compared with the traditional deep autoencoder (DAE), the proposed method is more competitive in terms of classification accuracy and robustness.

Seismic multicomponent, here refers to P-P wave (PP) and P- shear wave (SV), joint inversion is an important approach to improve the accuracy of S-wave velocity and density prediction. Compared with P-P wave data, converted wave data are more sensitive to these parameters. Thus, introducing these data to the seismic inversion could improve the inversion accuracy of S-wave velocity and density. Due to the travel-time gap between the multicomponent data, multicomponent inversion usually needs to be prepared for registration processing in advance. However, registration methods often suffer from matching errors, which ultimately affect the quality of the inversion results. Based on the optimal transmission idea, a registration-free multicomponent joint amplitude variation with offset/angle (AVO/AVA) inversion algorithm is developed in this article. The proposed method adopts the Earth mover’s distance between the synthetic P-SV wave and the observed P-P wave by calculating the optimal transport path. Besides${\ell _{1-2}}$norm is exploited as the penalty norm, where the regularized misfit function is minimized by the alternating direction method of multipliers (ADMM) algorithm. The synthetic data test and real seismic data application show that the proposed method can retrieve the S-wave velocity and density information better than the conventional method. The proposed method can not only effectively avoid the cumbersome registration steps, but also minimize the registration error and avoid the subsequent error accumulation.

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.

Effective random noise attenuation is critical for subsequent processing of seismic data, such as velocity analysis, migration, and inversion. Thus, the removal of seismic random noise with an uncertainty level is meaningful. Attenuating 3-D random noise in a supervised way based on deep learning (DL) is challenging because clean labels are difficult to obtain. Therefore, it is necessary to develop an adaptive unsupervised-based method for random noise attenuation. In this article, we propose a deep-denoising unsupervised learning (DDUL) network to attenuate random noise in 2-D/3-D seismic data. A patching technique is used to split 2-D/3-D seismic data into several patches to be fed into the network, which helps to expand the number of samples for training. We use the fully symmetrical structure of the autoencoder to construct the network. In each corresponding encoder and decoder layer, skip connections are added to enhance the learning of seismic data features. We construct three blocks to extract waveform features in seismic data, i.e., encoder, decoder, and skip blocks. Among them, the skip is connected between the encoder and decoder blocks of each hidden layer. The use of multiple blocks not only improves the network’s ability to extract seismic data features but also solves the problem of excessive training parameters caused by hidden layer stacking. Five 2-D/3-D synthetic and field seismic datasets are used to test the denoising performance of our proposed method. The denoising results demonstrate that our proposed method has good signal-preserving and noise attenuation capabilities in real-world applications.

Unconventional reservoirs usually have strong anisotropy. Generally, they can be regarded as transversely isotropic media with a vertical symmetry axis [(VTI) media] in the absence of fractures. Therefore, it is of great significance to develop high-accuracy inversion method for VTI media. The three elastic parameters and two Thomsen anisotropy parameters of VTI media are usually obtained by indirect calculation or inversion methods based on the approximate formulas. However, the cumulative errors caused by indirect calculation and low calculation accuracy of the approximate formulas limit the estimation accuracy of these parameters. In this article, we propose a new method based on the exact reflection coefficients equations (ERCEs) of VTI media to improve the inversion accuracy of these elastic and anisotropy parameters. The new method adopts the Bayesian deterministic inversion (BDI) strategy to solve the inversion problem, which becomes highly nonlinear when using the ERCEs. We analyze the feasibility of the new method using the residual function maps (RFMs) and eigenvalue analysis of Hessian matrix. The analysis results show that the BDI strategy can well solve a series of problems brought by the ERCEs for nonlinear inversion, such as strong nonlinearity and more target parameters need to invert. Both synthetic and field data examples show that the proposed method can accurately estimate the elastic and anisotropy parameters, which verifies the feasibility and effectiveness of the method.

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.

Prediction of lithology/fluid (LF) properties from seismic data can be very valuable in all phases of oil and gas exploration and production, but the resolution and accuracy of predicted results are reduced due to band-limited wavelet and noise of seismic data. Deep learning can review data, discover specific trends and patterns that would not be apparent to humans, and has been successfully used in many applications, including geophysics. Also, time-frequency (T-F) analysis tools can show how the energy of the signal is distributed over the 2-D T-F space, which helps to exploit the features produced by the concentration of signal energy. In this letter, we propose a novel hybrid approach for predicting LF properties, including oil-sand, brine-sand, and shale and evaluating their uncertainty, which aims at combining the benefits of T-F analysis method based on inverse spectral decomposition (ISD) and one-dimensional convolutional neural network (1D-CNN). The proposed method can provide more details about thinner layers and suppress noise to some extent using T-F spectrum obtained by ISD, and capture more relevant features from the input using 1D-CNN at different levels similar to a human brain, and thus, can significantly improve the resolution and accuracy of the predicted results. The proposed method was applied to a real 3-D post-stack seismic data and validated through a blind well test and comparison with the conventional methods.

S-wave velocity and mass density, which are two essential parameters in distinguishing lithology and hydrocarbon detection, are very difficult to retrieve even when long-offset gather data are used. P-P and P-SV waves joint inversion has been verified as an effective tool to accurately extract such fluid related parameters. However, registering the travel-time of P-P and P-SV waves on the identical coordinate is a significant but knotty problem for the joint inversion. Therefore, an improved strategy of prestack seismic joint inversion is proposed for accurately transforming the recorded data to elastic-parameter-based interpretive information. First, to overcome the weaknesses of artificial strenching and the local cross correlation-based method, a nonstrenching and globally optimal registration algorithm, i.e., dynamic time warping (DTW), is exploited to match the P-P and P-SV waves. Then, a new method has been developed for the joint inversion method by combining the logarithmic absolute-criterion-based misfit function withl1-2norm-based penalty, which can significantly improve the vertical resolution and stability of inversion results. The numerical examples demonstrate that the DTW algorithm can obtain better registered results than the conventional method. Moreover, the proposed joint inversion method performs better than the conventional prestack inversion in both resolution and accuracy, especially for the S-wave velocity.

Time-lapse (4-D) seismic exploration is one of the essential means for accurately reconstructing the underground geological model, enhancing oil/gas recovery (EOR), and predicting remaining oil distribution. Under the assumption that the rock skeleton is almost unchanged in the process of development, inversion of time-lapse seismic difference data can be used to characterize the dynamic reservoir parameter. However, the inaccuracy of the forward operator, lack of constraints, and inappropriate regularization weight may lead to ill-posedness. Thus, the ill-posedness is still a key factor affecting the accuracy and stability of time-lapse seismic inversion. In this article, an improved difference-and-joint inversion strategy is proposed using the modified linear approximation as the forward operator. First, based on the modified approximation as the forward operator, time-lapse seismic difference inversion is exploited to obtain the variations of elastic parameter reflectance caused by the production-induced model perturbation. Then, we innovatively proposed to take the production-induced model perturbation as constraints, thereby achieving more accurate geological models for multiperiod seismic data joint inversion. Moreover, the L-curve method is exploited in this article to acquire the optimal regularization weight adaptively in each iteration step. Finally, the difference inversion results are used as constraints to precisely invert the geological model by combining multiperiod seismic data.

Reconstructing an accurate and high-resolution subsurface model is attractive in the fields of both geology and seismology. However, due to the band-limited characteristics of seismic data, the inversion greatly depends on the reliability of the initial model. A fairly acceptable initial model could lay a good foundation for seismic inversion. In this article, we first introduce a well-log interpolation method with the local slope as a constraint for building a high-fidelity starting model in prestack amplitude versus offset/angle (AVO/AVA) inversion. First, we briefly review the basic theory of general seismic inversion. Then, instead of using the conventional preconditioned least-squares method, we introduce shaping regularization theory into the geological structure-guided well-log interpolation to accelerate the convergence. We use the plane-wave destruction (PWD) algorithm to extract the slope attribute from seismic data, images, or velocity models. The slope is used as the constraint to solve the inverse problem based on the shaping regularization method. Numerical examples demonstrate that the proposed initial model building method performs better than the conventional ones. It greatly improves the accuracy of inversion results. Furthermore, we apply the proposed model building method to the inverse problems of AVO/AVA inversion and reservoir parameter estimation of several field data sets for the first time, which demonstrate encouraging performance.

Dynamic changes of reservoir parameters within a reservoir are usually estimated by a history matching process based on the production data. However, it is difficult to accurately acquire the spatial distribution using production data as the constraints. We formulate a nonlinear inversion method to dynamically characterize the reservoir parameter variations from time-lapse prestack seismic data. Besides, we introduce the modified Hertz-Mindlin (H-M) model to simulate the changes in the elastic behavior of a turbidite sandstone during production by establishing a link between reservoir parameters and elastic parameters. Then, the exact Zoeppritz equation is exploited as a forward engine to convert these parameters into synthetic time-lapse seismic data. Numerical examples verify that the porosity parameter has a higher reflection sensitivity than the other two parameters, which is followed by the effective pressure. The water saturation parameter, however, is the least sensitive. Following a Bayesian approach, the baseline and monitor seismic data are used in the seismic inversion to establish the regularized augmented function. Combining the modified H-M rock physics model with the exact Zoeppritz equation as a forward operator, a regularized function is minimized with the Gauss-Newton optimization method to determine a model update. We further apply the proposed inversion algorithm to a real seismic data set, including baseline and monitor seismic data. The results demonstrate that the proposed inversion method can not only yield an accurate description of subsurface static reservoir properties but also improve the accuracy of dynamic reservoir parameter characterization.

Patchy saturation of gas and brine within the porous rock can induce significant attenuation and velocity dispersion effects, which in turn have a profound impact on seismic data. Thus, there should be a close relationship between dispersion and reservoir parameters, such as saturation, porosity, and permeability. Hence, using seismic data to determine dispersion information has been the subject of intensive research in recent years. It can help quantitatively predicting gas saturation and monitoring CO2sequestration, a key strategy for mitigation of global warming. Here, a frequency-dependent prestack waveform inversion workflow was proposed to extract the wave-induced fluid flow (WIFF) effect from seismic data (WIFF prestack waveform inversion strategy). The proposed approach consists of three essential parts, comprising spectral decomposition,$Q$-compensated prestack waveform inversion, and frequency-dependent prestack waveform inversion. First,$\ell _{1}$norm constrained inverse spectral decomposition is exploited to provide time-frequency amplitude and phase spectra with high resolution and reliable accuracy. Then, constant-$Q$compensated prestack waveform inversion is used to generate relatively precise$P$- and$S$-wave velocities, density, and Fréchet derivative for the subsequent dispersion inversion. Finally, frequency-divided seismic data and the estimated parameters and Fréchet derivative are used to invert the$P$-wave velocity dispersion. A comparison between the inversion results and band-limited rock physics analysis results shows that the proposed method can provide a quantitative inversion of the velocity dispersion to some extent. The proposed strategy provides a possibility for quantifying dispersion and further estimating gas saturation.

Seismic data are usually contaminated by various noises. Noise suppression plays an important role in seismic processing. In this article, we propose a new denoising method based on the nonlocal weighted robust principal component analysis (RPCA). First, seismic data are divided into many patches and grouped based on the nonlocal similarity. For each group, then, we establish a similar block matrix and set up the objective function of the RPCA. Next, we introduce the iterative log-thresholding algorithm into the augmented Lagrangian method to solve the problem. Furthermore, varying weights are specified to different singular values when minimizing the objective function. Finally, aggregating all recovered matrices can obtain the denoised seismic data. The proposed method considers the nonlocal similarity and adaptively sets weights with local noise variance. It performs well also owing to the superiority of the iterative log-thresholding method. The presented method is assessed using a synthetic seismic section with several crossover events. We also apply this novel approach to a real seismic data, which shows good results. Comparison with other approaches reveals the effectiveness of the proposed approach.

Prediction of lithology/fluid (LF) characteristics is always the bottleneck problem and difficulty of reservoir characterization. Deep-learning-based data-driven methods can review data and find specific trends and patterns that would not be apparent to humans, and have been successfully used in many geophysical applications including LF prediction (LFP). However, the above methods mostly predict LF point-by-point, which means that the spatial correlation of LF is not considered. When the predicted LF results are combined to form a 2-D/3-D image, the resulting image will be noisy or even geologically unreliable. To overcome these issues, we proposed a spatially coupled data-driven (convolutional neural network, CNN) approach for LFP from the poststack seismic data and well observations. Here, the vertical couplings of the LF are modeled by a Markov chain (MC) prior and the lateral continuity of the LF is further defined by a Markov random field (MRF) prior. We also proposed to perform spectral decomposition via inversion strategies (ISD) to get a time-frequency (TF) spectrum as the input of CNN. ISD helps make full use of the information hidden in the frequency domain of the poststack seismic data. Well-logs and poststack seismic data are integrated in a consistent manner to obtain predictions of the LF classes with the associated uncertainty statements. The LFP results of the proposed approach are more laterally continuous and geologically reliable than the LFP results of the point-by-point. We determined the effectiveness of this methodology on a 2-D synthetic model and a 3-D field seismic data set.

Facies identification is a powerful means to predict reservoirs. We achieve facies identification using a relevance vector machine (RVM) and develop a facies discriminant method based on a multikernel RVM (MKRVM). An RVM has the same functional form as a support vector machine (SVM) that is widely used in geophysics and shows a promising performance in disposing of small-samples, nonlinear and high-dimensional problems. The RVM inherits these superiorities, and its training is implemented under the Bayesian framework. Thus, it can provide probability information about the classified facies, which is critical to evaluate uncertainty of the result. Besides, the penalty parameter of the RVM does not depend on human experience. Compared with single-kernel learning, multikernel learning (MKL) is more flexible. After mapping the original data into a combined space by MKL, the features can be more accurately expressed in the new space, thereby improving the classification accuracy. Therefore, we introduce the RVM into facies classification and extend it to the MKRVM-based facies identification. The proposed method has advantageous properties such as strong generalization ability and high accuracy. First, we apply the approach to well log facies classification with different input features. Then, it is applied to seismic lithofacies identification with inverted elastic attributes to predict the target reservoirs. All the examples verify the effect and potential of the new method.

Seismic waveform inversion has been one of the most studied topics in recent years, which can be implemented both in common shot gather and prestack common midpoint gather. However, there are still several intractable issues to be addressed urgently, such as high-computational complexity, nonuniqueness, and robustness. In this paper, we have developed a model-based prestack waveform inversion (PWI) with a generalized propagation matrix scheme as forward operator, where a regularized function is minimized with the limited memory-Broyden-Fletcher-Goldfarb-Shanno technique to determine a model update corresponding to an adaptively determined regularization weight in each iterative step. To avoid falling into local extrema in the process of solving the objective function, we introduce an optimal transport method into the objective function to improve its convexity and use L-curve method to acquire the optimal regularization weight adaptively. The model tests show that the proposed scheme performs better than the conventional method significantly both on convergence and on accuracy. Furthermore, we apply the PWI with the proposed inversion scheme to the well-logging data and real seismic data. The results demonstrate that the proposed inversion scheme is not only capable of obtaining an accurate description of subsurface properties but also has a good convergence and robustness.

Since most information on S-wave velocity and density exists in the middle to large angle range of seismic data, traditional inversion methods based on the Zoeppritz approximation have difficulty in obtaining satisfactory results. Therefore, as a high-accuracy amplitude varied with angle (AVA) inversion, exact Zoeppritz (EZ) equation inversion has aroused a lot of attention in recent years. As for any other nonlinear inversion, iterative convergence and error are the important problems. In this letter, based on a Bayesian framework, we introduce optimal transport into EZ equation AVA inversion. Then, the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is adopted to solve the regularization-constrained least-square argument function to obtain the inversion results, including P-wave velocity, S-wave velocity, and density. We compare this method with a conventional method, which is based on an L2 norm or weighted L2 norm as a residual method in the model test. The results show that the proposed method not only reduces the error of the results to be smaller than L2 norm, but it also improves the convergence rate.

We devised a new filtering technique for random noise attenuation by weighted multistep adaptive autoregression (WMAAR). We first obtain a series of denoised results by means of different steps adaptive AR, and then we sum these results with different weights. The adaptive AR coefficients are obtained by solving a global regularized least squares problem, in which regularization is used to control the smoothness of these coefficients. The adaptive AR can estimate seismic events with varying slopes since AR coefficients have temporal and spatial variabilities. We derive the weights from the normalized power of local similarity by comparing the result of the nearest step with the ones of other steps. The application of these weights makes the proposed algorithm more effective in fault information conservation. The proposed WMAAR can be implemented both in the frequency-space and in time-space domains. Multidimensional synthetic and field seismic data examples demonstrate that, compared with conventional methods in frequency-space or time-space domain, multistep adaptive AR is more effective in suppressing random noise and preserving effective signals, especially for complex geological structure (e.g., faults).

Seismic data interpolation and reconstruction play an important role in seismic data processing. Seismic data are often inadequately sampled along various spatial axes. We have developed a new approach to interpolate aliased multidimensional seismic data based on the multidimensional adaptive prediction-error filter in frequency domain. First, we estimate the adaptive prediction-error filter coefficients, then interpolate missing traces using the estimated coefficients. Shaping regularization is used to control the smoothness of frequency-domain multidimensional adaptive prediction-error filter coefficients. Instead of estimating prediction-error filter coefficients only along one direction space, we estimate the prediction-error filter coefficients using more information along different direction spaces. So, multidimensional adaptive prediction-error filter using regularized nonstationary autoregression can adaptively estimate seismic events whose slopes vary in multidimensional space. The frequency-domain multidimensional interpolation method can input data at temporal frequency, which can save computer memory and time. For multidimensional seismic data, which miss different number of traces regularly in different axes, the proposed method can be used to interpolate missing traces to obtain more accurate results. The proposed method improves the calculation efficiency by applying shaping regularization and implementation in the frequency domain. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.