Seismic impedance inversion is essential for sub-surface exploration, facilitating precise lithological interpretation by reconstructing subsurface impedance. Although recent deep learning-based methods have advanced this field, many rely on direct mapping from observation to model space, which increases solution uncertainty due to the presence of a large null space, impacting inversion accuracy. To address this issue, we propose an iterative method that operates within the model space, applying progressive gradient correction to incrementally refine the current model towards a physically plausible solution, effectively reducing non-uniqueness and improving inversion robustness compared to single-step updates. The effectiveness of this iterative framework is further strengthened by a semi-supervised learning approach, which critically depends on both the network architecture and the design of the loss function. While most DL methods use convolutional architectures, their localized nature limits the capture of long-range dependencies critical for seismic inversion. To overcome this, we introduce USTNet, a hybrid UNet-Swin Transformer architecture that captures multi-scale features, improving inversion precision. To further ensure consistency with subsurface structure, structural priors are incorporated into the loss function, reinforcing spatial coherence. Experiments on synthetic and field data confirm that the proposed method significantly outperforms conventional and several state-of-the-art deep learning approaches in accuracy.

Migration artifacts are usually presented in the migrated image or angle-domain common-image gathers (ADCIGs) recovered from the seismic migration operators. When these migration artifacts are not properly suppressed, they may significantly degrade the accuracy of subsequent structure interpretation, amplitude-versus-angle inversion, and reservoir characterization. In this article, we apply an angle-domain least-squares migration (ADLSM) method to suppress these migration artifacts presented in the migrated ADCIGs. There are two key points in this proposed method. The first point is that we explicitly compute the angle-domain Hessian matrix and invert it by the regularized linear inversion technique. Thanks to the introduction of diagonally band Hessian matrix, the migration artifacts at the far-field can be effectively suppressed. The second point is that we have incorporated the smoothness prior of the reflection-angle-dependent reflectivity image along the reflection angle direction into the linear inversion. We determine the validity of the proposed ADLSM method within the Kirchhoff migration. Through the SEG/EAGE Salt model and field data, we demonstrate that the proposed ADLSM method can effectively and efficiently suppress these migration artifacts in the migrated ADCIGs recovered from the Kirchhoff migration. In addition, even when the migration velocity is less than the true velocity model, this method remains valid.

Seismic facies classification is pivotal for analyzing geological environments and predicting reservoirs. The transformer architecture has been widely applied in seismic facies classification due to its powerful feature learning capabilities. However, most existing transformer architecture has limitations in learning fine-grained features of seismic data, due to the high local correlation and low global correlation characteristics of seismic data. Meanwhile, they generally perform feature extraction at a single scale and fail to fully utilize the inherent multi-scale property of seismic data, which may lead to a decrease in classification accuracy. To overcome these two problems, we propose a seismic facies classification method that integrates multi-level wavelet transform with a multi-resolution transformer architecture. First, we employ the Haar wavelet decomposition algorithm to decompose the seismic data into three distinct levels of features, which are then input into a multi-scale network for feature extraction. Next, we propose a multi-resolution transformer module for fine-grained feature extraction of first-level decomposed features. It can capture both global and local spatial attention features through two branches: the global attention branch and the local attention branch. The enhanced features are merged with intermediate outputs from the other two branches to achieve feature integration. The final step involves a decision-level fusion of the classification outcomes from all three branches. Numerical experiments on synthetic and field datasets confirm the effectiveness of the proposed architecture. The classification results show that the proposed method outperforms the comparison methods and performs particularly well in classes with fewer samples.

The deep learning method has been proven to be an effective way to recover high-precision classification of seismic facies. However, the existing methods often ignore the temporal and spatial correlation of seismic data, leading to insufficient extraction of relevant features in seismic facies classification. To address these problems, we propose a lightweight cooperative attention network for high-precision classification of seismic facies. The proposed lightweight architecture includes two key points. On the one hand, the proposed architecture employs only five convolutional layers to reduce feature redundancy and improve computational efficiency for the classification of seismic facies. On the other hand, a cooperative attention module (CAM), which comprises of two parts: self-channel and self-spatial operations, is proposed to improve the extraction ability of long-distance features and expand the receptive fields. The major benefit of the proposed attention module is that it can improve the classification accuracy of the lightweight network. Through numerical experiments with a synthetic and a field dataset, we demonstrate the effectiveness of the proposed lightweight architecture and highlight two key benefits. First, the proposed CAM can improve the prediction accuracy of the proposed lightweight architecture for the classification of seismic facies. Second, the proposed lightweight architecture embedded with the proposed attention module outperforms the standard UNet network while reducing the number of parameters by 99.5%. It has shown the proposed architecture to be a cost-effective and practical classification tool for seismic facies.

Petrophysical seismic inversion is a challenging problem due to its intrinsic nonlinearity and ill-posedness. Deep learning emerges as a promising solution to tackle this intricate problem, with semi-supervised learning proving particularly valuable in scenarios with limited labeled data. However, many existing semi-supervised learning approaches applied to reservoir parameters inversion are unidimensional or focus on single model parameters, potentially hindering the attainment of highly accurate predictions for multiple petrophysical parameters. To this end, we introduce a novel knowledge-driven semi-supervised deep learning approach for multidimensional petrophysical seismic inversion. This framework features a lightweight 2-D UNet, incorporating prior knowledge about the range of model parameters, to parameterize the set of pseudo-inverse operators, enabling effective multitask learning. By leveraging the low-frequency porosity as the sole initial model input, our approach enhances the information-sharing capabilities of the neural network. We also introduce Hermite cubic splines to parameterize source wavelets varying with angles, ensuring smooth and compactly supported waveforms. In addition, we develop a semi-supervised training loss function that integrates deterministic forward operators and sampling operators, allowing simultaneous updating of weights in both forward and pseudo-inverse operators. The proposed method facilitates the simultaneous inversion of wavelets, porosity, water saturation, and clay volume. Synthetic and field data tests are conducted to validate our approach, demonstrating that it significantly enhances inversion accuracy compared to 1-D semi-supervised deep learning methods.

Usually, inverse problems are ill-posed. The solution to the inverse problem is indeterminate, meaning that for given observational data, there may be multiple possible solutions. It is not sufficient to give a definite solution to common seismic inverse problems. In this study, we provide stochastic solutions for seismic inverse problems (denoising and reconstruction). We sample a range of possible and high-quality solutions for a given observation with various degradations from the posterior distribution through Langevin dynamics with conditional score function, all shown to be reasonable results; for example, the stochastic solutions we sampled may contain as many geological structures of interest to the expert as possible. Experimental results on synthetic and field data verify the superiority of posterior sampling. In particular, our method has obvious advantages over other methods, such as traditional and (supervised, self-supervised, and unsupervised) deep learning (DL) methods, especially in denoising under extremely low signal-to-noise ratio (SNR) and reconstruction for data with consecutively missing traces and noise. We also analyze the advantages of our approach and concluded that successful generative modeling of seismic data by the score-based generative models (SGMs) is the key to posterior sampling for the inverse problems, which all benefit from the seismic data prior implicit in the trained score network in the SGM.

Convolutional dictionary learning (CDL) can represent signals and images via the superposition of components given by the convolution of sparse coefficients (features) and the elements of a dictionary (filters). The filters represent universal signals that can model different images, whereas the coefficients are intrinsic to one particular image. Estimating the coefficients and the filters from a set of observed signals is similar to a blind deconvolution problem where we aim to simultaneously represent a signal via the convolution of two unknown signals. Classical CDL provides data-dependent filters that, in the seismic data processing case, might not have a solid resemblance to typical waveforms that one observes in seismic records. This limits the dictionary’s representation and discriminability, thus suffering from suboptimal denoising or reconstruction results. To address this challenge, we propose a new CDL algorithm. The proposed approach introduces a parametric constraint to enforce simplicity on the filters, guiding the learning process toward a more efficient and structured representation of the data. Specifically, we restrict each filter to include one single waveform parametrizable via a second-order traveltime curve and a seismic wavelet. The learned dictionary comprises linear and parabolic events that adapt adequately to observed seismic waveforms and resemble local Radon transform basis functions. The alternating direction method of multipliers (ADMMs) is adopted to solve the proposed parametric convolutional learning problem. The experimental results demonstrate that the proposed method achieves superior reconstruction results compared to the existing convolutional and patch-based dictionary learning methods.

Seismic inversion can be used to invert the subsurface acoustic impedance leveraging migrated seismic section, which can help lithology interpretation. It is not easy to predict impedance directly from post-stack seismic data. In the field data, the interference of random noise aggravates the difficulty of impedance inversion. Previous work mainly focused on trace-by-trace strategy leading to poor lateral continuity. We propose a two-dimensional (2D) temporal convolutional network (TCN)-based post-stack seismic low-frequency extrapolation and a TCN-based impedance prediction method. We use a two-step workflow for acoustic impedance prediction from post-stack seismic data. First, we use a neural network (LE-Net) for the low-frequency extrapolation of seismic data, and then we use another neural network (AI-Net) to predict acoustic impedance. The input to LE-Net is high-frequency band-limited seismic and low-frequency impedance data. Seismic data after low-frequency extrapolation and low-frequency impedance are used to predict impedance. 2D TCN and multi-trace input data can introduce spatial information from surrounding traces. The output of the network is single-trace data. The proposed network can ensure the single-trace prediction accuracy and improve lateral continuity. Numerical experimental results show that our proposed two-step workflow, named AI-LE, performs well on Marmousi II and has a certain generalization on the SEAM model. The results on field data show that AI-Net can predict relatively accurate impedance. The low-frequency extrapolation of seismic data can help improve the performance of impedance prediction.

Seismic acoustic impedance inversion (SAII) aims at recovering the subsurface impedance to achieve lithology interpretation. However, its ill-posedness and nonlinearity pose a great challenge to find an optimal solution. Regularization is an effective method to solve SAII by imposing prior information, but it suffers from high computational complexity and limited inversion performance. To mitigate the above limitations, we propose an optimization-inspired semisupervised deep learning SAII approach that incorporates the advantages between the model-driven optimization algorithm and the data-driven deep learning method. Specifically, it is implemented by parameterizing the alternating iterative method (AIM) by splitting it into two parts where the convolutional neural networks are adopted to learn the regularization terms and a nonlinear mapping and thus called the proposed network as AIM-SAIINet. The proposed method can not only simultaneously invert the seismic wavelet and impedance but also obtain high-resolution data as an intermediate product to facilitate the training of AIM-SAIINet and enhance the inversion accuracy. In addition, we introduce a joint semisupervised training scheme in which the network is first jointly pretrained in a supervised manner using the synthetic training data to provide good initial values, and then, a semisupervised training scheme is adopted to fine-tune it using few labeled data pairs to achieve high inversion accuracy. The synthetic and field data examples are conducted to validate the effectiveness of AIM-SAIINet, which achieves higher inversion accuracy at a fast computational speed compared with the traditional methods.

The convolutional model, which describes the relation among poststack seismic data, wavelet, and reflectivity, is the foundation of seismic deconvolution (SD). However, this model is only an approximation of the seismic wave equation, and it may not work in complex cases especially when the medium is anelastic, heterogeneous, and anisotropic. In this article, we propose a generalized convolutional model for poststack seismic data. A deep-learning-based data correction term is added to characterize the data ingredients that cannot be characterized by the convolutional model. The data correction term of the new model is realized using the long-short term memory (LSTM)-based deep learning architecture, of which parameters are learned based on the dataset from several well logs. Based on the new model, we propose an SD method and investigate its performance in building reflectivity models using complex numerical examples. The results verified that the new model can accurately characterize complex seismic data, which cannot be characterized by a convolutional model. In addition, the proposed SD method has significant advantages over traditional methods in building high-fidelity reflectivity models in complex cases.

The time-varying seismic super-resolution inversion technique becomes more and more attractive in seismic exploration. However, most existing inversion methods suffer from amplitude loss and manual adjustment parameters. In this letter, we present an adaptive time-varying seismic super-resolution inversion method based on the Lp(0p-norm with 01regularization. To solve the nonconvex inversion problem adaptively, second, we provide a new algorithm called singular value decomposition (SVD)-Hadamard product parametrization (HPP). The idea of the new algorithm is to apply an HPP to express the Lp(02regularizations that are easy to be programed and solved. Then, the SVD is adopted to solve each L2regularization. It is convenient to apply the L-curve method or its variants to determine the regularization parameters at each iteration for finishing the inversion adaptively. Finally, synthetic and field data examples are tested to validate the effectiveness of the proposed method.

With the emergence of the fog computing and the sensor-cloud computing paradigms, end users can retrieve the desired sensory data generated by any wireless sensor network (WSN) in a fog-based sensor-cloud system transparently. However, the fog nodes and the cloud servers may suffer from many kinds of attacks on the Internet and become semitrusted, which threatens the security of query processing in the system. In this paper, we investigated the problem of secure, fine-grained spatial-temporal Top- k query in fog-based mobile sensor-cloud systems (FMSCSs) and proposed a novel scheme named STQ-SCS to tackle the problem based on the virtual grid construction and the size-order encryption-binding techniques. STQ-SCS can preserve the privacy of the sensed data items and their scores and make end users verify the completeness of the query results of fine-grained spatial-temporal Top- k queries with a 100% successful rate even if the fog nodes and the cloud servers are not totally trustworthy. Besides the good security performance, simulation results indicate that STQ-SCS is also an efficient scheme that incurs a much lower communication cost than the state-of-the-art schemes on securing fine-grained spatial-temporal Top- k query in FMSCSs.

Seismic full-waveform inversion (FWI) aims to build high-resolution images of the physical properties of the subsurface. However, the ill-posedness and nonlinear problems pose a great challenge to the high-resolution reconstruction. Although the nonlinear problem can be mitigated by matching a subset of observation data, the resulting images are generally low-resolution background structures. Regularization-based techniques can mitigate the ill-posedness of FWI, but the iterative method suffers from the cycle-skipping and computational burden problems. To overcome these problems, we develop an adjoint-driven deep-learning FWI (AD-DLFWI) approach which utilizes the fully convolutional network (FCN) to invert subsurface velocity from reflection seismic data. Specifically, AD-DLFWI is implemented in a two-step iterative scheme, in which an optimal update result at each step is learned via a FCN-based learned updating operator. The proposed approach uses the seismic image of applying the adjoint operator of the scattering wave equation, which is equivalent to the gradient of classical FWI, as the data engine of FCN. Inspired by the wave-equation migration velocity analysis approach, we propose to unfold the gradient of FWI into the common-source domain to keep the information about the measure of velocity error. To ensure the interpretability of each network’s role, we design a two-step training scheme to successively reconstruct the low and high wavenumber components of subsurface velocity. Using synthetic experiments with reflection-dominant seismic data, we have confirmed that the proposed FWI approach not only can provide a reliable velocity estimation but also is not sensitive to the cycle-skipping problem.

We proposed a multichannel deconvolution method. The method uses a mixed norm to promote structured forms of sparsity. To solve this deconvolution problem, we develop a new algorithm called the Hadamard product parametrization (HPP) sparse-group (HPPSG) algorithm. We define each layer of seismic profile as a group, and perform$L_{p}$-norm for all elements within each group to preserve the lateral continuity. Based on the assumption that the reflectivity is sparse,$L_{q}$-norm is applied among groups along the time direction. Then, we construct an$L_{p,q}$optimization problem. After that, we solve this problem using the proposed HPPSG algorithm. The HPPSG algorithm is formed by converting the$L_{p,q}$optimization function into the$L_{1}$optimization function which is solved with the help of the HPP algorithm. The proposed algorithm is simple and applicable for an arbitrary$L_{p,q}$-norm inverse problem. Synthetic and real data examples demonstrate the effectiveness of the proposed method in improving the lateral continuity of seismic profiles.

We proposed a multitrace semiblind nonstationary deconvolution method. The proposed method estimates reflectivity and source wavelet simultaneously for pursuing high-resolution seismic processing. The mathematical framework is derived based on convolution exchange law and Fourier transform property. In this framework, seismic records are treated as the convolution of a time-varying wavelet and nonattenuated reflectivity or the convolution of a constant wavelet and attenuated reflectivity. Using these two equivalence relations, we devise an objective function containing two variables, the reflectivity and wavelet. In addition, we add the 2-D total variation constraint to the cost function, which preserves lateral and vertical continuity of the estimated reflectivity. The cost function is solved by alternating iteration and proximal splitting methods, under the assumptions of a known attenuation model and sparse reflectivity. In addition, the mathematical framework is extended to implement semiblind deconvolution in an approximate layered earth model. To demonstrate the effectiveness of the proposed method, we apply the proposed method to synthetic data and field data and confirm that the proposed method can achieve better reflectivity and source wavelet.