Low-frequency (LF) data plays a key role in mitigating cycle-skipping in full waveform inversion (FWI). We propose a method to efficiently and accurately reconstruct LF seismic data for a large number of shot gathers based on multi-channel deconvolution (MD) and deep learning (DL). Specifically, we firstly propose a MD method to predict LF data for very limited shot gathers. Then, we use a deep neural network (called ‘acceleration network’) to learn the relation between a shot gather and its corresponding LF data, based on the labels provided by the MD method, enabling efficient prediction for all shot gathers. Next, another deep neural network (called ‘improvement network’) is proposed to improve the accuracy of the LF shot gathers predicted by the ‘acceleration network’. To do so, several horizontal layered velocity models are generated based on the statistical distribution of well logs, and several synthetic shot gathers with and without LF are generated by solving the acoustic wave equation. Based on these synthetic shot gathers, the MD predicted LF data and the corresponding true LF data form a data pair [predicted LF, true LF] for each shot gather, and these data pairs are used to train the ‘improvement network’. Finally, employing a cascade of ‘acceleration network’ and ‘improvement network’, we reconstruct the LF data of all shot gathers. Synthetic and field data examples verify that the proposed method exhibits superior accuracy compared to conventional MD method in LF data reconstruction.

Elastic full waveform inversion (EFWI) is able to simultaneously build multiple subsurface parameters. However, EFWI faces the ill-posed problem and the multi-parameter coupling effects. Building accurate initial P- and S-wave velocity models is crucial for mitigating these issues and ensuring the convergence of EFWI. Yet, limitations of acquisition systems and the different sensitivities of P- and S-waves to wavenumber components pose significant challenges in simultaneously building P- and S-wave velocity models with structural consistency. These issues may result in additional iterations, or in some cases, even non-convergence. Aiming to build accurate long-wavelength velocity models with high structural consistency, a novel structurally consistent elastic frequency controllable envelope inversion (SC-EFCEI) method is proposed in this paper. SC-EFCEI performs multi-scale inversion using elastic frequency-controllable envelope data to build long-wavelength models, and additionally introduces structural constraints between different velocity gradients via automatic differentiation (AD) to enforce consistency between the inverted P- and S-wave velocity models. Numerical experiments on the elastic Overthrust model, modified Marmousi2 model, and Chevron 2014 blind dataset verified the effectiveness of the proposed inversion method. The inverted P- and S-wave velocity models both successfully reveal the large-scale features of the velocity model while exhibiting good structural consistency, which can be used as good initial models for EFWI.

Distributed Acoustic Sensing (DAS) is a highly appealing technology for seismology, prized for its flexibility, durability, and high sensitivity to vibrations and strain field changes. However, despite these advantages, optical fibers are susceptible to external interference, which introduces incoherent noise during measurements. Recognizing that this noise in raw DAS data is unstructured and has a zero mean, we propose ZSN2N-DAS, a self-supervised learning method that achieves zero-shot Noise2Noise denoising for ground-based DAS data. The effectiveness of ZSN2N-DAS is underpinned by a mathematically proven equivalence. Results demonstrate its ability to effectively suppress incoherent noise and significantly enhance the Signal-to-Noise Ratio (SNR) of microseismic events, as validated using datasets from a DAS array on the Rutford Ice Stream in Antarctica. Furthermore, compared to the current leading deep learning model, N2N-DAS, ZSN2N-DAS achieves a 54% reduction in network parameters while simultaneously improving the SNR of seismic signals by approximately 20% and mitigating the issue of signal leakage. Consequently, in arrival time picking, ZSN2N-DAS enhances picking quality and increases the average number of effectively picked arrivals by roughly 28%. The denoised data produced by ZSN2N-DAS can benefit downstream seismological analyses like magnitude estimation, hypocenter location, and focal mechanism inversion.

Because of the viscoelastic properties of the Earth, seismic waves experience attenuation during propagation, resulting in decreased amplitude and phase distortion, ultimately reducing resolution. The inverse Q filtering method is an important way to compensate for attenuation and consequently improve the resolution of seismic data. However, the compensatory capability and stability of the existing inverse Q filtering methods present a paradoxical relationship, ensuring compensation ability may diminish stability, and vice versa. In other words, the existing methods can hardly work in scenarios characterized by high levels of noise or significant attenuation (low Q values). In this article, a physics-constrained deep-learning-based attenuation compensation (PCDL-AC) method is proposed. Specifically, we first establish a time-domain attenuation model, which delineates the relation among a stationary seismic trace, the Q model, and the corresponding attenuated seismic trace. Then, we use this model as the physics law and propose a physics-constrained deep learning method for attenuation compensation in a semisupervised or even unsupervised manner. Benefiting from the noise-resistance ability of deep neural networks and the physics law, the proposed method can achieve stable and accurate compensation even when strong noise is present in data. In addition, this method significantly improves the efficiency of attenuation compensation since the application of deep learning is very efficient once it is trained. Both synthetic and field data experiments verify the effectiveness of the proposed method and demonstrate its advantages over common methods.

Migration is the core link in reflection seismic exploration. Seismic images are often extended into angle domain for interpretations. However, affected by limited acquisition aperture and complex overburden, the generated images are far from ideal. The illumination is unbalanced, causing unreliable amplitude variation in angle gathers. Band-limited seismic data and wavelet stretch in large angles, lead to low-resolution angle gathers. Image-domain least-squares migration (IDLSM) implemented by point spread function (PSF) deconvolution is a promising solution. Extending the concept of IDLSM to the angle domain, we develop a new method to construct angle-dependent PSFs and optimize angle gathers. The essential element to construct PSFs is the Green’s function. The proposed method reconstructs Green’s functions using a bidirectional long short-term memory (LSTM) network. We use a ray tracing method to efficiently obtain wave propagation directions (travel-time gradients). And wave-equation forward modeling is used to accurately calculate wavefront amplitudes. The LSTM network is trained by labels composed of travel-time gradients and amplitudes to surrogate the solver of Green’s functions. Angle-dependent PSFs are constructed according to the mathematical model of the angular local Hessian. And inversions with PSFs are performed to optimize angle gathers. Numerical tests on a 3-D synthetic model demonstrate that the proposed method is able to improve the image quality of prestack angle gathers and poststack seismic images. The proposed method compensates illumination and improves the resolution of angle-dependent seismic images. Both vertical and lateral resolution are enhanced. Amplitude versus angle (AVA) responses can be corrected for further analysis and interpretations.

Seismic interpretation and reservoir characterization require the seismic data having faithful amplitudes that relate to subsurface physical parameters. Nowadays, the amplitude fidelity of seismic imaging becomes more important than ever. Although reverse time migration (RTM) adopts the full wave equation as true amplitude seismic wave propagator, it is still not sufficient for true amplitude seismic imaging since migration is only the adjoint operator corresponding to the forward modeling process. The complex overburden and limited migration aperture lead to unbalanced illumination of subsurface structures. Least-squares migration was proposed to correct amplitudes of seismic images, but it is computationally expensive and sometimes unstable. The illumination compensation is an available alternative which only considers the amplitude correction regardless of the resolution issue. In this article, we propose a true amplitude seismic imaging method with illumination compensation performed on both RTM stacked images and angle gathers. We derive the angle-dependent illumination intensity from the Hessian of least-squares migration in which Green’s functions are essential components. We propose a new method to estimate the Green’s function and its corresponding wave propagation direction based on wavefields excitation amplitudes and Poynting vectors at excitation times. Then, the illumination intensity is constructed as a function of dip and reflection angles to correct both angle gathers and stacked images. The proposed method is tested using two synthetic models and a real marine dataset. Numerical results demonstrate that the proposed method can effectively correct amplitudes of seismic images. Deep events beneath complex structures are enhanced with more balance illumination.

Low-rank approximation (LRA) is a powerful technique for seismic diffraction separation and imaging, providing higher-resolution images of subsurface discontinuities compared to traditional reflection imaging. However, in complex wavefields where reflections lack distinct low-rank characteristics, diffractions and reflections can overlap within the same eigenimages, making traditional LRA less effective for separation. To address this limitation, we propose a diffraction separation and imaging method based on multi-directional wavefield low-rank approximation (MDWLRA). The MDWLRA method employs multi-directional wavefield decomposition (MDWD) to divide complex wavefields into angular slices with similar dip angles. These slices are classified as either diffraction slices or reflection slices, with the latter containing mostly reflections and some residual diffractions. LRA is then applied to the reflection slices to separate the remaining diffractions from reflections. By reducing wavefield complexity using MDWD, reflections in the reflection slices exhibit clearer low-rank characteristics than those in the full wavefields, allowing for more effective separation using LRA. Numerical tests on synthetic data from the modified Sigsbee2A model and field data demonstrate that the MDWLRA method outperforms traditional methods, achieving more accurate separation with fewer leakages than traditional LRA, while also improving diffraction fidelity compared to the Curvelet-transform-based method.

Seismic travel-time tomography is an effective approach for exploring subsurface structures. In recent years, machine learning (ML) has been successfully applied in seismic travel-time tomography; however, the uncertainty quantification of predictive outputs has been less frequently addressed. To tackle these challenges, we adopt the deep ensemble of deep operator networks with randomized priors (DERP-DON) for travel-time tomography, based on measured travel-time data from surface and cross-well measurements. Deep ensembles provide informative uncertainty estimates, and the incorporation of randomized priors allows the network model to offer more conservative uncertainty quantification. Through numerical experiments, we demonstrate that DERP-DON can provide reasonable and conservative uncertainty estimates while accurately inferring the velocity field. Notably, DERP-DON is particularly effective in offering meaningful uncertainty estimates for out-of-distribution data.

The attenuation of seismic field noise using self-supervised deep learning has gained attention due to its label-free training process. However, common self-supervised methods are limited by the pixelwise independence assumption, which does not align with field seismic noise characteristics, and suffer from signal leakage due to receptive fields containing inherent blind spots or traces. In this paper, we propose a self-supervised random noise attenuation method based on the non-pixelwise independence assumption. By considering the spatial correlation map of field noise, we extend the blind spot to a generalized blind neighborhood, ensuring that the prediction pixel is not influenced by neighboring pixels with noise correlation greater than zero. The blind neighborhood size controls how much spatial correlation is disrupted, allowing our method to handle random noise with varying spatial correlation. Since larger blind neighborhoods may lead to signal loss, we introduce an automatic trade-off between noise correlation disruption and signal preservation during training. Experiments on real seismic noise attenuation (including random and tracewise coherent noise) demonstrate the superiority of our method in destroying the spatial coherence of noise and preventing useful signal leakage.

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.

Sedimentary cycles are the fundamental building blocks of sedimentary sequences, resulting from the superposition of periodic sedimentary events at different scales. Seismic reflection data contain multiscale sedimentary cycle information in the subsurface. Accurate extraction multiscale sedimentary cycle information from seismic data is key to realizing multiscale sequence stratigraphy analysis. This article proposes a workflow for multiscale sedimentary cycle characterization by combining variational mode decomposition (VMD) and synchrosqueezing optimal basic wavelet transform (SOBWT) methods. The workflow first derives the relationship between different-scale sedimentary cycles and their reflectivity amplitude spectrum and proposes a method for determining the number of intrinsic mode functions (IMFs) and center frequencies parameters of VMD. Subsequently, VMD is employed to decompose the different-scale seismic reflection from seismic data. Further, SOBWT and ridge extraction methods are introduced to extract instantaneous dominant frequency attributes from IMF profiles to characterize different-scale sedimentary cycles and to divide sedimentary cycle units. Applications on synthetic and field data demonstrate that the proposed workflow can effectively separate seismic reflection characteristics of different-scale sedimentary cycles from seismic data. The instantaneous dominant frequency attributes proposed based on SOBWT and ridge extraction methods can effectively characterize the thin bed thickness variation of different-scale sedimentary cycle and can assist in sedimentary cycle unit identification. This provides an important tool for subsequent sequence stratigraphy research.

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.

Accurately picking the first arrivals of acoustic logging curves (e.g., P-, S- and Stoneley waves) is crucial for stratigraphic lithology characterization. The conventional interpreter-dominated first arrivals identification methods frequently lead to an interpretation uncertainty and time burden. To reduce these deficiencies, we developed a dual attention PhaseNet (DA-PhaseNet) network to intelligently identify the first arrivals of acoustic logging curves. The field data test demonstrates that the DA-PhaseNet network can dramatically improve the result accuracy and its generality compared to other PhaseNet-based methods. Specifically, the DA-PhaseNet strategy can capture both local and global features of input logging curves simultaneously, resulting in a high identification accuracy of 99.4% and 94.5% for P- and S-wave respectively. Moreover, the proposed DA-PhaseNet network dramatically improves the accuracy of first arrival identification from 72.3% to 87.6% for the noise-contaminated Stoneley wave. Furthermore, it is important to mention that the DA-PhaseNet has a maximum noise tolerance of 0 dB for P- and Stoneley waves to ensure accuracy of first arrival identification, while has a maximum noise tolerance level of 10 dB for S-wave if the result F1 score limit is set at a level of > 0.8.

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.

Blind seismic acoustic-impedance (AI) inversion is a technique for obtaining the AI of the subsurface medium without given a wavelet. An effective way to solve the blind inversion problem is to split the multi-parameter problem into two single-parameter subproblems and solve them in an alternative iteration way. However, this method becomes time-consuming when dealing with large-scale 3D problems and faces challenges in selecting suitable regularization parameters. To overcome these shortcomings, we propose a deep learning accelerated blind seismic AI inversion (DLA-BSAII) method. It mainly has three steps: (1) Only a few 2D profiles are selected from the whole 3D data, and their corresponding AI models and wavelets are inverted using conventional blind seismic AI inversion method. (2) The results of the first step are used to train deep networks to realize the nonlinear mapping from a 2D seismic profile to AI and wavelet. In addition, the trained deep networks are used to generate predictions of AI models and wavelets for the remaining 2D profiles. (3) Benefiting from the predicted AI models and wavelets, a new alternative iteration method with fewer but more effective regularization terms is proposed to obtain the final inverted AI models and wavelets of the remaining 2D profiles. It has the advantages of easier selection of regularization parameters and faster convergence speed. Synthetic and field data examples verify that DLA-BSAII outperforms conventional methods in terms of both efficiency and inversion accuracy.

Seismic facies classification involves assigning geological meaning to seismic amplitudes based on distinct sedimentary facies responses. Various deep learning approaches have been developed for seismic facies classification. Currently, most deep neural networks applied for this task are manually engineered based on domain expertise. However, these human-designed architectures may not be optimal for seismic facies classification. To address this, we introduce differentiable architecture search with partial channel connections (PC-DARTS), enabling automated architecture search instead of manual design. We modify the PC-DARTS search space and propose PC-DARTS for seismic facies classification (PC-DARTS-SFC) to determine architectures tailored for this problem. We apply PC-DARTS-SFC on the Netherlands F3 seismic volume. The results demonstrate the superiority of the architecture discovered by PC-DARTS-SFC over original PC-DARTS, conventional networks, and a previous method. This confirms the potential of leveraging network architecture search (NAS) to find specialized networks surpassing human design for seismic facies classification.

Seismic facies classification is crucial in interpreting subsurface geological structures for oil and gas exploration. Traditional methods for seismic facies classification usually rely on handcrafted features and heuristic rules, limiting their ability to capture complex geological patterns. We suggest a label-integrated and VMD-augmented transformer (LIVAT) to address these issues, which refers to transformers’ embedding stage infused with seismic facies labels and uses variational mode decomposition (VMD) to augment training data. Four advanced time-series transformer models are selected to verify the effectiveness of our proposed label-integrated embedding and VMD-augmentation on F3 Netherlands and New Zealand Parihaka datasets. Moreover, we evaluate the performance of LIVAT by comparing it with convolutional neural networks (CNNs) and bidirectional long short-term networks (BiLSTM) in few-shot learning. Experimental results demonstrate that LIVAT achieves superior classification accuracy and outperforms existing deep learning methods, showcasing its potential as a powerful tool for automatic seismic facies interpretation.

Accurate classification and characterization of pore-crack structures are substantial to carbonate reservoirs in terms of reservoir exploration and development. Although experience-dominated manually classifying pore-crack structures achieves a milestone, these methods usually encounter significant uncertainties and heavily rely on the interpreter’s experience. Nevertheless, as a classification problem, using the 2D image input dataset, instead of 1D logging data, could achieve a higher accuracy. Consequently, we developed a Swin Transformer-Convolutional Neural Network (SWT-CNN) hybrid network to capture multi-level features of the pore-crack structure simultaneously using 2D resistivity imaging logging images as an input, thereby eliminating the uncertainty of manual interpretation and enabling automatic feature extraction. Furthermore, to fully utilize rare and valuable dataset, the proposed SWT-CNN model incorporates the data augmentation strategy which has been modified to fit the dataset. Also, the idea of transfer learning is introduced to improve the accuracy of pore-crack types classification in carbonate rock and accelerate convergence. Lastly, the field validation data test shows that the proposed SWT-CNN can achieve an accuracy rate of 95.92%. Moreover, the visualization of the feature map indicates the proposed SWT-CNN is more accurate in recognizing the position of pore-crack structures.

Seismic migration produces the migrated images of subsurface media using seismic data, which is important for geophysical exploration. However, the adjoint-based migration methods may produce a blurry image, convolved by a Hessian matrix. To address this problem, we propose a Hessian-assisted iterative self-training learning (HAISTL) method aimed at approximating the inverse Hessian matrix and deblurring the migrated image. First, we train a long short-term (LSTM) network using labeled images and use it as a teacher network to generate pseudolabels for the unlabeled images. Subsequently, we integrate the demigration and migration operators to identify the pseudolabels with high confidence levels and construct a dataset containing both the true and pseudolabels. The dataset is then used to train a student network with the injection of model noise into the network. Finally, we regard the student network as a new teacher and repeat the process in an iterative STL framework. We demonstrate the effectiveness of our proposed method using two synthetic datasets and field data. Compared with the supervised learning (SL) method, the proposed method exhibits superior generalization capabilities. This advantage stems from the incorporation of the demigration and migration operators, providing a valuable prior for the inverse Hessian matrix in training the model. In contrast to the model-driven least-squares migration (LSM) methods, the proposed method yields high-resolution images with significantly reduced computational costs. However, it may be less effective in recovering small-scale structures when confronted with an extremely limited number of labels.

The precise decomposition of P/S-waves in multi-component seismic data is critical for seismic imaging. Inaccuracies in this decomposition can result in migration images with biased amplitudes and undesirable crosstalk artifacts. Although vector-decomposition (VD) methods are effective, they rely on the availability of elastic parameters at the acquisition surface. Therefore, we propose a data-driven deep-learning (DL)-P/SVD(DL-PSVD) method that eliminates the need for prior elastic parameter information. We used publicly available elastic models to generate training datasets by simulating multi-component data and their amplitude-preserving P/S-wave components using the decoupled elastic wave equation. Our analysis explores the impact of the loss function type, output channel quantity, and direct wave removal on the generalization ability of DL-PSVD. The critical insights from the numerical experiments include the superior generalization ability of DL-PSVD using two channels when the P/S-wave energy distribution is highly unbalanced. Moreover, DL-PSVD exhibits improved generalization ability using four channels for observed data with removed direct waves. Finally, the L1 loss function is more effective for DL-PSVD’s generalization ability than the L2 loss function. Overall, the proposed DL-PSVD is a promising method for automatic P/S-wave VD without requiring prior elastic parameter information.

Horizon picking is of paramount importance in seismic interpretation because it has a significant impact on subsequent interpretation and inversion. Although manual and various automatic interpretation methods have been widely used for horizon picking, they still have several problems, such as being time-consuming and highly dependent on human experience. Recently, deep-learning (DL) methods have been implemented to solve these problems. However, traditional convolutional neural networks (CNNs) have a shortage of capturing global features, and vision transformers, recently proposed, aim to address this. To segment the seismic horizon accurately, we suggest a dense inception transformer (DIFormer) by combining the dense extreme inception network (DexiNet) and the inception transformer network. When implementing model training with the patch technique, the DIFormer can retrieve more information and interpret horizons smoothly. Furthermore, we utilize multiple attributes computed from seismic data to train basic DIFormer models and then adopt ensemble learning to obtain the fusion model, that is the ensemble DIFormer (EDIFormer). We implement qualitative and quantitative analyses to verify the effectiveness of the suggested model and compare it with the state-of-the-art (SOTA) SegFormer and basic DIFormer trained with a single attribute in trace- and patch-based modes.

With the rise of deep learning (DL), there are kinds of DL-based models proposed for addressing seismic data reconstruction, especially convolutional neural network (CNN)-based methods. However, most of these models are supervised, which require a large amount of training data and ground-truth labels that are difficult to obtain in real applications. We propose the polarity-constrained dual-cycle generative adversarial networks (PCDC-GANs) for reconstructing the irregularly sampled seismic data. We first adopt a traditional generative adversarial networks (GANs) framework as the base model, integrating with a dual-cycle mechanism. Instead of the conventional generator network, we suggest a self-prior generator that uses the prior information extracted by the generator in the first stage to enhance the reconstruction performance, i.e., the mask data of the irregularly sampled seismic data. In addition, we introduce polarity constraints to promote the recovery of sampled seismic traces, amplifying the model’s sensitivity to the locations of missing traces. Furthermore, our model incorporates various loss functions to promote its convergence. Numerical experiments on synthetic and field data show that our PCDC-GANs can reconstruct irregularly sampled seismic data more accurately than the SuperstarGAN and CycleGANs, and achieve comparable performance to the supervised U-Net.

Suppressing random noise is an effective way to improve the signal-to-noise ratio (SNR) of seismic data. Supervised deep learning methods have recently been widely applied to seismic image denoising. However, these methods require a large amount of noise-free data to train the network, which is unavailable in practical applications. Moreover, most of these denoising methods focus on removing random noise, assuming that the noise is zero-mean and independent of seismic signals. In field applications, real seismic noise often exhibits band-limited and spatial correlations. We propose an unsupervised learning method to train a denoising network using only noisy images, termed Pixel-shuffle Down-sampling and Visible Blind-Spots (PD-VBS). First, we propose to utilize Pixel-shuffle Down-sampling (PD) to destroy the spatial correlation of real seismic noise, followed by feeding the data into the blind-spots network. Next, we introduce additional input derived from the input data with a finer stride PD to compensate for the information loss induced by both the blind-spots network and PD mechanisms. Experimental results on both synthetic and field data show that our proposed PD-VBS can effectively remove noise while preserving valid signals, compared with traditional denoising methods and state-of-the-art deep learning models.

S-transform (ST) and its generalized versions are commonly used for seismic data processing and interpretation. Nevertheless, these transforms have several unavoidable drawbacks, including parameter selection and the Heisenberg uncertainty principle’s restriction. To overcome these drawbacks, we suggest a cycle-consistent generalized ST network (CGSTN), inspired by sparse-based transforms. The CGSTN contains four main modules, i.e., two generators and two discriminators. The forward generator is trained to convert a seismic trace into a 2-D high-resolution time–frequency (TF) spectrum, while the inverse generator is trained to reconstruct the seismic trace based on the generated TF spectrum provided by the forward generator. Similarly, one discriminator is trained to distinguish whether the TF spectrum generated by the forward generator is a true TF spectrum or not, while the other is utilized to distinguish the seismic trace generated by the inverse generator. After model training, we apply the well-trained CGSTN to a 3-D field data volume acquired in the Ordos Basin, Northwest China. The results show that the CGSTN can obtain the TF spectrum with higher resolution than the contrastive methods, benefiting further reservoir delineation.

Studying the statistical characteristics of primary reflection coefficients is crucial for gaining a deeper understanding of the structure of the Earth’s rock layers. In this study, we collected 686 logging data from scientific ocean drilling sites worldwide, and after careful data cleaning, 328 logging data remained. Using a data-driven approach, we constructed an overall score index to measure the quality of the fit for various distribution models. This index comprised metrics, including the residual sum of squares (RSSs), Kolmogorov–Smirnov (KS) statistics, Wasserstein distance, and energy distance. From 80 distribution models, top 5 with the best overall fitting performance were the Johnson SU (Johnsonsu),$T$, Tukey lambda, generalized normal, and double Weibull distributions. Further comparison of goodness-of-fit metrics that revealed the Johnsonsu distribution demonstrated the optimal fit for the primary probability distribution of reflection coefficients. In addition, logging data from three onshore wells in China’s Dongying Shengli Oilfield provided validation support for the Johnsonsu distribution. Our results illustrated the advantages of the Johnsonsu distribution for simulating primary reflection coefficients and provided approximate parameter ranges for fitting the distribution.

Seismic travel time plays a fundamental role in a wide array of geophysical applications. Traditionally, numerical simulation of travel time involves solving the eikonal equation. However, conventional methods are typically limited to simulating the travel-time field for a single source and velocity model at a time. This limitation poses challenges, particularly when dealing with inverse problems that necessitate multiple forward simulations to infer velocity models based on travel-time data excited by different sources. In recent years, machine learning has proven its effectiveness in tackling problems associated with partial differential equations (PDEs). Among these methods, the Deep Operator Network (DeepONet) has gained attention for its adaptable structure and minimal generalization error. In response to the challenges posed by solving the eikonal equation in heterogeneous media, we introduce a modified architecture known as the Fully Convolutional DeepONet (FC-DeepONet). This approach leverages convolutional operations to extract features directly from 2D data and avoid flattening operations that could lead to the loss of important spatial information. The FC-DeepONet model takes the velocity model and source location as input and generates the corresponding travel-time fields as output. Through numerical experiments, we validate the efficacy of our proposed method in accurately predicting travel-time fields induced by sources located at various positions across diverse velocity models. Besides, our approach demonstrates robustness by providing reasonably accurate predictions even in scenarios involving velocity models with irregular topography. This adaptability holds significant promise for practical applications, particularly in cases characterized by complex geological features.

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.

The data-driven approach has become significant in various scientific fields, such as climate modeling and weather forecasting, where a mechanistic description of physics and chemistry is either unavailable or insufficient for the desired purpose. However, the prominent nonstationarity poses a significant challenge to the accurate prediction of recent global average temperature (GAT) using conventional methods. To address this challenge, we draw inspiration from signal analysis’s moving-window approach, wherein we split the GAT into shorter segments to alleviate nonstationarity. These segments are transformed into a time-symmetric graph (TSG) structure in the non-Euclidean domain. Consequently, we introduce the GlobalTempNet model, which incorporates a graph convolutional network (GCN) embedded with a residual neural network (NN) and a long short-term memory (LSTM) network. In addition, we propose the entire graph node training (EGNT) process, optimizing parameters by treating each sample as a graph node for feature aggregation and information updating. Validation using the HadCRUT5 dataset demonstrates that GlobalTempNet outperforms nine established models, showcasing higher prediction accuracy. Furthermore, long-term estimation and future prediction analyses reveal GlobalTempNet’s capability to predict the climate change trend in the coming years. The model’s applicability is confirmed across ten different temperature datasets. Consequently, the proposed GlobalTempNet, coupled with the EGNT process, emerges as a robust, reliable, and open-source method for global temperature prediction, offering promising potential as a tool for univariate time series analysis using graph NNs (GNNs).

The acquisition and reconstruction of seismic data are fundamental to seismic exploration. The balancing data quality and acquisition cost is essential. To address this challenge, we propose Seis-PDDN, a novel framework that integrates edge-preserving piecewise undersampling design with diffusion null-space iteration, optimizing both survey design and data reconstruction. Seis-PDDN uses the prior distribution of seismic reflectivity to design a linear missing mask operator, guiding the undersampling process. Reconstruction is achieved through a diffusion null-space iteration, combining range-null space decomposition with a pretrained diffusion model, ensuring both consistency and fidelity in the reconstructed data. Extensive experiments on synthetic and public seismic shot gathers demonstrate that Seis-PDDN outperforms traditional random, jittered, and uniform sampling schemes. Further comparisons with other deep learning reconstruction methods confirm that Seis-PDDN achieves higher metrics in seismic reconstruction, especially with a spatial sampling rate as low as 10%. Overall, Seis-PDDN holds significant potential for advancing flexible, economical acquisition and accurate reconstruction in seismic exploration.

Reconstructing missing seismic data is crucial for seismic processing and interpretation. Recent methods struggle when seismic traces are regularly missing, such as near offset data. We proposed a classifier-guided conditional seismic denoising diffusion probabilistic model (CCSeis-DDPM) to enable consistent reconstructions. The CCSeis-DDPM adopts the Markov model architecture of denoising diffusion probabilistic models to generate high-quality results. The model involves classifier-guided training and tailored inference. During training, we employ a U-Net with embedded timestep and three class labels for noise prediction, utilizing classifier guidance to enhance reconstruction accuracy. In the inference phase, the model selectively samples unmasked regions using available seismic data. Our experiments on synthetic and field shot gathers with regularly missing near, mid and far offsets show the proposed CCSeis-DDPM reconstructs regularly missing traces more accurately than current state-of-the-art methods, demonstrated qualitatively and quantitatively. This successful integration of diffusion probabilistic models with classification guidance and conditioning underscores the immense potential of this approach for enhancing seismic data reconstruction processes.

Sparse coding (SC) has been proven effective in various geological tasks, such as seismic time-frequency (TF) analysis and seismic reflection inversion. Nevertheless, it inevitably has several drawbacks, e.g., low computational efficiency and difficulty in parameter selection. Recently, self-supervised learning (SSL) has emerged as a promising alternative to mitigate these issues, offering high computational effectiveness and requiring fewer labels. We suggest a generalized physically driven workflow for geophysical inversion based on SSL and SC, named the physically driven SSL network (PDSSLNet). This generalized PDSSLNet model comprises two main modules. One is the inverse model, generated by convolutional neural networks (CNNs), which can benefit from their high computational effectiveness and strong nonlinear fitting ability. The other one is the forward model based on the SC theory, ensuring the physical meaning of the geophysical applications with high accuracy. Afterward, we provide two typical geological inversion cases to demonstrate the validity and effectiveness of the suggested PDSSLNet, including sparse TF analysis and seismic reflectivity inversion. Three-dimensional (3D) field data volume applications confirm that the proposed inversion workflow may efficiently circumvent the drawbacks of the conventional SC-based approach while maintaining excellent computing efficiency.

Seismic attenuation, parameterized as quality factor Q, holds great significance in enhancing seismic resolution and reservoir characterization. Most methods for estimating Q values are performed in the frequency domain, however, the frequency spectrum of the seismic data may usually be influenced by the closely adjacent reflections and the seismic noise, leading to an unreliable Q estimation. To address this challenge, we propose a kernel-based regression method for Q estimation on manifolds. This supervised learning model computes the kernel function on the tangent space of the manifold. We apply this method to Euclidean space, Spherical manifold, and Wasserstein spaces, and provide a detailed comparison of their performance. Our experimental results using synthetic data demonstrate a significant improvement in both robustness and accuracy compared to conventional methods. Furthermore, the validation of our methodology using real data confirms its effectiveness and superiority. Notably, our method on Wasserstein space consistently outperforms others in all experiments.

Seismic frequency attributes are commonly used for describing geological structures and characterizing complex reservoirs. Although there are different kinds of machine learning based methods proposed, how to select appropriate attributes and how to map them to reservoir thickness is still an open issue. In this study, we suggest an adaptive multi-frequency attribute analysis (AMFAA)-based workflow to address these issues. We first utilize a generalized S-transform to extract multi-frequency attributes, which can describe local time-frequency features of seismic data. Then, we propose a sensitive attribute analysis method to reduce frequency attribute redundancy with the aid of hierarchical clustering and correlation analysis. Afterward, based on the selected sensitive attributes, we propose to adopt the potential of heat diffusion for affinity-based transition embedding (PHATE) for multi-frequency attribute analysis, which can map seismic multi-frequency attributes to reservoir thickness. To test the validity and effectiveness of our method, we first apply it to a synthetic wedge model and then post-stack field data in the Ordos Basin, Northwest China.

f–k filtering and Radon transform (RT) are classical methods for processing 2-D seismic signals. They assume that target signal events exhibit specific trajectories in the time–offset domain (linear, parabolic, and hyperbolic) and process them accordingly. In fact, seismic signals are nonstationary, with geometric and dynamic characteristics changing pointwise. This makes that these methods suboptimal for processing such signals. The 2-D nonstationary convolution filtering conducted in the time–space domain allows filter variations point-by-point, adapting to the nonstationarity of seismic signals. However, obtaining the filter factors involves complex calculations, making it not widely applicable. This article proposes an efficient method based on a two-dimensional nonstationary convolution model (TNCM) and termed two-dimensional nonstationary filtering by operator scaling (TNFOS). Leveraging the resemblance among filters, specific filter factors can be easily acquired by extracting and scaling the reference filter factors. Through the cascading of filters, TNFOS effectively fulfills nearly all design requirements for 2-D velocity or dip filtering, enabling the broad implementation of 2-D nonstationary filtering. Using synthetic and field experiments, we tested the efficiency of TNFOS and provided four successful applications in suppressing seismic interference.

Extracting a reliable model of quality factor$Q$from the spectral information of seismic signals is a significantly important step for seismic imaging and reservoir characterization. However, the conventional$Q$estimation approach based on the frequency domain is susceptible to the high oscillative spectrum created by the unavoidable random and coherent noise in the observed signal. To address this issue, we introduce an absorption-constrained wavelet power spectrum inversion (AWPSI) method. The inversion involves absorption constraint (AC) and spectrum constraint (SC), where the AC term is a novel constraint for estimating the wavelet’s amplitude spectrum or power spectrum. By treating medium absorption as a physical prior and utilizing information from all waveforms rather than individual ones, AWPSI can yield high-quality wavelet power spectra and ensure stable$Q$estimation results. In addition, the proposed method has no limitations on the type of wavelet. Since its inversion target is wavelet power spectra, AWPSI is broadly applicable to various frequency-based$Q$estimation approaches. We validate the effectiveness of the proposed method using both synthetic and actual vertical seismic profile (VSP) data.

High-dimensional time-frequency (TF) transforms are essential tools in seismic data processing. However, commonly used transforms such as Ridgelet, Curvelet, and Contourlet exhibit limitations in time-shifting invariance and basis function selection, which impacts on their effectiveness in seismic data analysis. To address these limitations, this study introduces optimal basic wavelet (OBW)-Ridgelet, a novel approach integrating the OBW with the Ridgelet transform. By combining OBW with Ridgelet, this method aims to enhance the TF localization for seismic structural analysis and time-shifting invariance property. We also present a workflow for seismic discontinuity detection, employing the C3 algorithm to the decomposed seismic data to get multiscale coherence and introduce the similarity coefficient for scale selection of the multiscale coherence. Synthetic and field data examples demonstrate the effectiveness and robustness of the proposed method, yielding promising results for seismic signal interpretation. The integration of OBW-Ridgelet enriches the toolkit for seismic signal analysis and holds the potential for refining seismic feature detection and interpretation in practical applications.

Improving the resolution of nonstationary reflection seismic data without well data is challenging, as it requires prior estimation of the$Q$-value. The coupling of reflectivity sequence and wavelet introduces spectral fluctuations, rendering the extraction of$Q$highly unstable. While some statistical wavelet amplitude estimation methods, such as spectral shaping (SS) and contraction operator mapping (COM), can yield smooth wavelet amplitude spectra, they do not contribute to$Q$analysis as they lack a physical mechanism for absorption attenuation. Therefore, we propose an absorption-constrained wavelet power spectrum inversion (AWPSI) method based on the segmented stationary convolution model (SSCM). The absorption constraint (AC) term incorporates prior knowledge of the medium’s$Q$-effect and enables simultaneous inversion of wavelet amplitude spectra for all windows. Incorporating AWPSI into COM and SS methods leads to AWPSI-COM and AWPSI-SS methods, which yield higher precision wavelet power spectra and remove the spectral fluctuations caused by reflectivity sequences. We demonstrate that AWPSI enables COM to extract wavelet amplitude spectra more accurately while preserving the attenuation characteristics caused by$Q$-effect. Using the equivalent$Q$field obtained by the AWPSI-COM method, an inverse$Q$-filter can be performed to generate accurate high-resolution seismic profiles. Synthetic and actual stacked seismic data verify the effectiveness of the proposed method.

Seismic lithology interpretation based on seismic data is an important task to delineate oil and gas reservoirs. However, this is an extremely unstable work when only utilizing seismic data, which would result in multiple solutions. We suggest a multiattribute integrated deep learning (MAIDL) workflow for automatic seismic lithology interpretation. To implement the proposed model, we first propose to apply the wavelet scattering transform (WST) to seismic data for multiscale features extraction. Note that the WST has local deformation stability and translation invariance for analyzing seismic data, which would be proven to promote seismic lithology interpretation. Next, the MAIDL model is suggested to combine the multiscale features extracted by the WST and seismic data simultaneously, which can improve the accuracy of automatic seismic lithology prediction. Afterward, the Res-UNet, which incorporates residual blocks into the UNet, is introduced to avoid the over-fitting and the degradation problem of the proposed MAIDL model. Finally, a 2-D synthetic data and a 2-D post-stack field data are adopted to test the effectiveness of the suggested MAIDL model for automatic seismic lithology interpretation.

Multifrequency attribute analysis is an effective tool to delineate sand bodies with different thicknesses. Conventionally, red–green–blue (RGB) blending technique is often used to fuse three frequency components for depicting reservoir thicknesses, that is, the low-, medium-, and high-frequency components. However, the seismic signal is a typically broadband signal, while RGB blending can only fuse three frequency components. Moreover, how to select these three specific frequency components is also a difficult and unsolved task. In this study, we suggest a multifrequency attribute analysis workflow for delineating sand bodies. First, we introduce the S-transform (ST) to extract multifrequency components of the analyzed seismic data. Then, the t-distributed stochastic neighbor embedding (t-SNE)-based workflow for fusing multifrequency components is proposed, which is used to capture the local structural features of the analyzed high-dimensional data and reveal the global structures simultaneously. Afterward, we adopt a synthetic trace and a 3-D field data volume to test the effectiveness of the proposed workflow. Compared with the contrastive methods, our workflow performs better in delineating the spatial distribution and thicknesses of sand bodies, which benefits further well deployment.

The bilinear based method is one of the commonly used tools in time-frequency analysis (TFA) fields. However, it suffers from the trade-off of high resolution and cross-term interference. We propose WVDNet, a semi-supervised learning model for time-frequency analysis based on the Wigner-Ville distribution (WVD), to reduce the cross-term existing in WVD and relax the requirements of the training data set. The proposed WVDNet is based on the Mean-Teacher model to enable the task model to exploit the unlabeled training data. We first build a synthetic data set for model training, that contains different kinds of amplitude-modulated and frequency-modulated (AM-FM) signals. Next, a task model of WVDNet is designed and the consistency regularization based method is utilized to promote model training. Finally, experiments are conducted on both synthetic and real-world data, showing the effectiveness of suppressing cross-term and strong generalization ability.

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.

The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty due to the noisy data and data scarcity is less discussed in conventional seismic tomography literature. To mitigate the uncertainty effects and quantify their impacts in the prediction, the so-called Bayesian Physics-Informed Neural Networks (BPINNs) based on the eikonal equation are adopted to infer the velocity field and reconstruct the travel-time field. In BPINNs, two inference algorithms including Stein Variational Gradient Descent (SVGD) and Gaussian variational inference (VI) are investigated for the inference task. The numerical results of several benchmark problems demonstrate that the velocity field can be estimated accurately and the travel-time can be well approximated with reasonable uncertainty estimates by BPINNs. This suggests that the inferred velocity model provided by BPINNs may serve as a valid initial model for seismic inversion and migration.

Amplitude-preserving angle gathers are ideal inputs for seismic prestack inversion. However, due to the limitation of computational efficiency, generating subsurface azimuth–reflection angle gathers from 3-D seismic imaging is still a very difficult task. In this article, we propose a new method to generate azimuth–reflection angle gathers from 3-D reverse time migration (RTM). The proposed method approximately reconstructs the source wavefield using high-dimensional wavelets and the excitation information. After using directional vectors to calculate the subsurface observation angles and applying the cross correlation imaging condition, we can generate azimuth–reflection angle gathers by angle binning. Without storing source wavefields or reconstructing source wavefields using boundary conditions, the proposed method has high computational efficiency. Numerical experiments on a synthetic model and a real marine seismic dataset demonstrate that compared with the excitation amplitude imaging condition, the proposed method can generate azimuth–reflection angle gathers with continuous complete events and high signal-to-noise ratio. The image quality and resolution of angle gathers are significantly improved. At the same time, the computational complexity does not increase much.

Diffraction separation and imaging are important for subsurface discontinuities characterization. However, conventional diffraction separation methods may loss validity when the diffractions and reflections do not have discernible differences in data domain. Moreover, due to limited acquisition geometry and narrow frequency band of seismic data, the diffraction imaging methods that use conventional ray-based or wave-equation-based migration operators may produce images with low resolution. We propose a diffraction separation and least-squares imaging method based on multi-scale and multi-directional wave-field and image decomposition. First, by using the multi-scale and multi-directional properties of the generalized curvelet transform, we reproduce the diffractions from the plane-wave sections according to the differences between the diffractions and reflections in terms of scale and angle. When the diffractions and reflections do not have discernible differences in data domain, their migrated images generally have different dip angles. Therefore, we propose a plane-wave least-squares diffraction imaging method with a curvelet-domain regularization which suppresses the images of residual reflections with small dip angles. Finally, we obtain high-resolution images of the subsurface discontinuities by using a regularized conjugate gradient method. Synthetic and field data examples verify the superiority of the proposed diffraction separation method over the plane-wave destruction filter in terms of better suppression of the reflections and better recovery of the diffractions. Compared with plane-wave reverse time migration, the proposed diffraction imaging method effectively suppresses the residual reflectors and produces images with higher resolution and signal-to-noise ratio.

Time-frequency analysis (TFA) is widely used to describe local time-frequency (TF) features of seismic data. Among the commonly used TFA tools, sparse TFA (STFA) is an excellent one, which can obtain a TF spectrum with good readability. However, many STFA algorithms suffer from expensive calculation time and unavoidable prior knowledge, such as the iterative shrinkage-thresholding algorithm (ISTA) and the sparse reconstruction by separable approximation (SpaRSA). Inspired by the unrolled algorithm and its successful applications in signal processing, we propose a deep learning-based ISTA unrolled algorithm, which is named the sparse time-frequency analysis network (STFANet). The STFANet contains two parts, i.e., the sparse time-frequency spectrum generator and the reconstruction module. The former learns how to transform a one-dimensional (1D) seismic signal from a large amount of unlabelled data into a two-dimensional (2D) sparse time-frequency spectrum, which is implemented based on the proposed unrolled iterative dynamic shrinkage-thresholding (UIDST) algorithm. Note that the UIDST algorithm is carried out by using a simplified deep learning network. The latter serves as a physical constraint of model training to ensure that our generator obtains an accurate TF spectrum, which is actually an inverse time-frequency transform. In this study, the traditional inverse short-time Fourier transform (STFT) is utilized in the reconstruction module. To test the effectiveness of the proposed model, we apply it to 3D post-stack field data. The results show that, compared with the traditional TFA tools, the STFANet can availably compute time-frequency spectrum with better readability, which benefits seismic attenuation delineation.

The stratigraphic correlation of well logs is crucial for characterizing subsurface reservoirs. However, due to the complexity of well logs and the huge amount of well data, manual correlation is time- and resource-intensive. Hence, various computerized stratigraphic correlation methods have been developed, especially regarding convolutional neural networks (CNNs). Recently, Transformer, a self-attention system that evolved from Natural Language Processing (NLP), has attained state-of-the-art performance over CNNs in a variety of domains because of its ability to perceive global features. We propose the Axial and Sliding window based attention with High-resolution Transformer (ASHFormer), combining the High-Resolution Network (HRNet) with an Axial and Sliding window self-attention Block (ASBlock) intended for stratigraphic correlation of well logs. ASBlock includes three different forms of Multi-Head Self-Attentions (MHSA), including sliding-window attention, horizontal-axis attention, and vertical-axis attention, therefore, it is possible to retrieve well logs’ long-range and local information. The experiments show that ASHFormer predicts more accurate stratigraphic correlation results than HRNet and CMT (a Transformer combining CNN and self-attention). The usefulness of the Transformer for well log feature extraction and automatic stratigraphic correlation is demonstrated by ASHFormer’s 9.74% improvement in correlation accuracy over HRNet with the same architecture.

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.

The well-known cycle-skipping problem in full-waveform inversion (FWI) can make the iterative solution fall into local minima and produce an undesired inverted result when reliable low-frequency components in seismic data and a good initial model are not available. The recovery of low-frequency data can effectively solve the cycle-skipping problem. However, hardware limitations have made it difficult to obtain reliable low-frequency components in seismic data. Thus, we adopt a multiscale and cross-scale convolutional neural network (MCCNN) to build the nonlinear mapping between high-frequency and low-frequency data from synthetic training datasets. The major benefit of MCCNN is that it can fully use the multiscale and cross-scale information in the high-frequency data to predict the low-frequency data. Several numerical experiments show the effectiveness and benefits of the low-frequency recovery of MCCNN. On one hand, introducing the in-stage multiscale and across-stage cross-scale information can accelerate the convergence rate in the training process and improve the low-frequency prediction accuracy. On the other hand, MCCNN has good generalization abilities in predicting the low-frequency data from the Marmousi and overthrust models, different model sizes, and wavelet types and frequencies. The acoustic FWI results show that the predicted low-frequency data can effectively prevent the inversion from falling into a local minimum and help FWI obtain an accurate velocity model even if we start from a poor initial model.

Recovering the useful signal from seismic field data is critical in seismic data processing. Seismic field data are usually coupled by a useful signal and field noise (random noise with unknown distribution), making them difficult to decouple. Unfortunately, subject to the assumption biases of data prior and noise prior, different random noise attenuation methods may have different performance biases. Suppose data-driven supervised deep learning methods have plenty of labeled [real noisy(field), clean(useful)] data pairs. In that case, they will learn useful information from the labeled dataset and relax the biases of the data-prior and noise-prior assumptions. To this end, we first use the invertible Neural Network (INN) to disentangle the field data in observational space into the latent variable in latent space. Then, by manipulating the latent variable’s partitions encoding high- and low-frequency information, INN can generate quality-controlled fake field data and decouple useful signal and field noise parts from field data in its backward pass. To gain decoupling and generative capabilities, the training of our INN only requires a relatively small labeled dataset containing field-useful data pairs. Sampling in latent space, the trained INN can generate an infinite number of paired [fake-field, useful] samples. Experiments show that our method can effectively decouple useful signal and field noise, and the noise of the fake field data is close to field noise. The generated paired dataset can benefit downstream tasks such as field noise attenuation.

Random noise attenuation is a critical step in seismic data processing. Since the distribution of field noise is complex and unknown, this poses a challenge to noise attenuation methods where the default noise distribution is known, such as a Gaussian distribution. To address this issue, we propose a method called Seismic Random Noise Gaussianization Framework (SRNGF) to attenuate random noise with unknown distribution. Specifically, SRNGF couples the Gaussianization subproblem and Gaussian denoising subproblem based on the Plug-and-Play (PaP) framework. The Gaussianization submodule with learnable parameters maps seismic data with the noise of unknown distribution to the one corrupted by Gaussian noise. The learnable parameters can be updated through unsupervised online training according to the noise of the unknown distribution on a single field data. The gaussian denoising submodule, which can be replaced by seismic denoiser, aims only for Gaussian noise removal, making SRNGF incorporate the denoiser prior for seismic data. Thus, we incorporate different kinds of seismic (non-deep/deep learning (DL)) denoisers into SRNGF and give their corresponding implementations of SRNGF. Experiments on noise with unknown distribution qualitatively and quantitatively validate the superiority of SRNGF. SRNGF improves the results of non-DL/DL seismic denoiser by a large margin.

The frequency-dependent amplitude-versus-offset (FAVO) method has great potential for reservoir parameters estimation. However, it is hard work to establish the FAVO inversion model. It is also difficult to solve the inverse problem for FAVO by traditional methods. In this paper, we propose a new workflow to extract the reservoir fluid parameters from the FAVO gathers based on a deep neural network (DNN). The proposed method is applied to predict the tight sandstone gas reservoir properties. Within the framework of this workflow, we generate the synthetic FAVO gathers. First, we establish the petrophysical model using the logging interpretation results. Then, the Backus average, Biot-Gassmann fluid substitution, velocity dispersion equations of the binary medium, and Rüger equation are applied to generate the FAVO reflectivity series. By introducing the DNN-based seismic wavelet estimation method and the optimal basis wavelet transform (OBWT), we can generate different frequency components of the seismic wavelet. These different frequency components are used to convolve the FAVO reflectivity series to obtain FAVO gathers that are used to generate the sample pairs for DNN training. At the same time, the OBWT is used to decompose the real AVO gathers to get the FAVO gathers. Finally, to testify its validity and effectiveness, the proposed workflow is applied to synthetic and field data.

Seismic facies classification plays an important role in oil and gas reservoir interpretation. In the past few years, convolution neural network (CNN)-based models have been widely used in supervised seismic facies classification. However, to improve some inherent limitations of CNNs, it is significant to explore alternative architectures, such as the Transformer with the self-attention mechanism. In this study, based on the Segformer, a cutting-edge semantic segmentation Transformer, we propose a U-shaped model of joint the Segformer and the Hypercolumn representation for seismic facies classification, named U-Segformer-Hyper. As the emerging lightweight variant of the Transformer for seismic facies segmentation, the proposed U-Segformer-Hyper consists of a specific encoder–decoder–hypercolumns scheme, which can extract various features in different layers and fuse the output features of different layers with different scales. In the application of the public F3 seismic data, compared with the CNN Benchmark model, the U-Segformer-Hyper model has fewer parameters, fewer floating-point operations per second (FLOPS), and higher accuracy of classification in both the section-based and patch-based training modes. Moreover, the proposed U-Segformer-Hyper is open source, which benefits to further explore alternative deep models in seismic interpretation.

Image-domain least-squares reverse time migration (IDLSRTM) through point spread functions (PSFs) is a suitable compromise between image quality and computational efficiency for inversion-based imaging tools. However, the conventional IDLSRTM method in acoustic approximation does not account for the subsurface attenuation effects, which may result in the unfocused migration image in attenuated geological environments. To incorporate the attenuation effects and improve the image quality, we develop a Q-compensated IDLSRTM method by using the hybrid PSFs rather than the acoustic PSFs as the blurring functions to deconvolve the adjoint migration image. These hybrid PSFs are estimated by a combination of computation between the viscoacoustic Born modeling and acoustic reverse time migration (RTM) using a series of uniform point scatterers. To further improve the quality of inverted images, we have applied a hybrid deblurring filter to the hybrid PSFs and acoustic RTM image, before the iterative inversion. Through some numerical examples of synthetic and field data, we have demonstrated that the proposed Q-IDLSRTM method combined with the hybrid PSFs and the hybrid deblurring filter can compensate for the attenuation effects and provide seismic images with improved spatial resolution and balanced image amplitudes. Relative to the conventional IDLSRTM methods through acoustic and hybrid PSFs, the proposed method can provide migration images with higher image resolution and better-balanced image amplitudes.

High-resolution seismic data allows us to better characterize the reservoir and detect the hydrocarbon. To improve the resolution of seismic data, in this article, we extend the conventional S transform to Hyperbolic spaces, and propose a hyperbolic spaces S transform (HS transform) and its deformed reconstruction. By considering the seismic signal as an element of hyperbolic spaces, the HS transform performs the time–frequency (TF) decomposition of the data in Hyperbolic space and the reconstruction in Euclidean space. The whole process from the TF decomposition to the reconstruction gives a natural nonlinear transformation to the spectrum of the original signal. By investigating the analytical relationship between the spectra of the original signal and its deformed reconstruction, we then propose the frequency-dependent curvature HS transform, which allows a desired change in the spectrum of the seismic data. By performing such decomposition and reconstructing iteratively, the final deformed reconstruction of the seismic data will have a broad and whitened band, and the resolution of the seismic data can be enhanced. The effectiveness of our proposed method is demonstrated through the comparison with the Wiener filter in the synthetic and field data examples. The significant advantage of our method is that it is nondeconvolutional, and requires no information about the seismic wavelet.

Seismic inversion is a significant tool for exploring the structure and characteristics of the underground. However, the conventional inversion strategy strongly depends on the initial model. In this work, we employ the physics-informed neural network (PINN) to estimate the velocity and density fields based on acoustic wave equations. In contrast to the traditional purely data-driven machine learning approaches, PINNs leverage both available data and the physical laws that govern the observed data during the training stage. In this work, the first-order acoustic wave equations are embedded in the loss function as a regularization term for training the neural networks. In addition to the limited amount of measurements about the state variables available at the surface being used as the observational data, the well logging data is also used as the direct observational data about the model parameters. The numerical results from several benchmark problems demonstrate that given noise-free or noisy data, the proposed inversion strategy is not only capable of predicting the seismograms, but also estimating the velocity and density fields accurately. Finally, we remark that although the absorbing boundary conditions are not imposed in the proposed method, the reflected waves do not appear from the artificial boundary in the predicted seismograms.

Time–frequency analysis (TFA) technology plays a significant role in seismic signal processing. The time–frequency representation (TFR) calculated using the TFA method is helpful for the localization of time-varying frequencies within the signal. Nevertheless, limited by the Heisenberg uncertainty principle, traditional linear TFA methods always provide blurred TFRs, which makes them difficult to distinguish details of time–frequency structures. Recently, the synchrosqueezing transform (SST) was designed to improve the concentration of the TFR. The SST can provide a much concentrated TFR for the weakly frequency-modulated (FM) signal, but it is not effective for the interpretation of strongly FM signals, such as the thin interbed in seismic exploration. In this work, we propose a new tool by introducing the multi-synchrosqueezing operator to the frame of wavelet transform (WT). Employing an iterative operator to correct the frequency estimation of the original SST step-by-step, it thus can calculate a TFR with better concentration and robustness. Synthetic signals and a field seismic data are employed to verify the performance of the proposed method for characterizing the time-varying frequency features.

Microseismic event picking is one of the key steps in seismic processing and imaging. Manually picking is a widely used way to pick the microseismic events, which is time-consuming. The standard short-term average/long-term average (STA/LTA) is a traditional method to pick the microseismic first arrivals, which would lead to inaccurate first-arrival picks in case of low signal-to-noise ratio (SNR). We developed a workflow to automatically pick the microseismic first arrivals by using the feature pyramid networks (FPNs). To train the proposed model, we first randomly select part of the microseismic traces and manually pick the time index of the first arrivals. Next, we segment every selected trace into two parts based on the time index of the manual picking and then assign each part a label. Afterward, we train the proposed fine-tuning FPN model by using the training data and the corresponding labels. It should be noticed that we proposed a loss function, named the point-aware loss, for solving the microseismic first-arrival picking issue. Finally, we predict the microseismic first arrivals by using the well-trained fine-tuning FPN model. The numerical examples demonstrate that our proposed model successfully identifies the microseismic first arrivals. The microseismic first arrivals predicted by using our proposed model are more robust and more accurate than those obtained by using the STA/LTA and the encoder–decoder network.

Seismic instantaneous frequency (IF), as one of the instantaneous attributes, is widely used for seismic interpretation and stratigraphy analysis. The Hilbert transform (HT)-based complex analysis approaches are commonly used to extract seismic IF, which are sensitive to kinds of noise contained in field data. Although the normalized HT (NHT) improves the antinoise property of HT by normalizing the original trace, the HT-based methods are a global operator that is not suitable for the local analysis. For example, IF calculated by using the HT-based method is unstable when meeting strong seismic events. In this letter, we propose a workflow to extract local IF (LIF) and then apply it to describe superposed sands. Note that the proposed workflow extracts a stable IF result even when processing a seismic trace with strong events. To demonstrate the effectiveness of the proposed workflow, we apply it to both synthetic and field data. Compared with results from HT and NHT, the proposed workflow provides a stable IF extraction and offers potentials in precisely highlighting superposed sands.

Seismic attenuation estimation is a significant task for characterizing reservoirs and improving the resolution of seismic data. The logarithmic spectral ratio (LSR) is one of the widely used tools for seismic attenuation estimation. However, how to select a suitable frequency bandwidth for the LSR is a difficult task, especially for field data. Moreover, field data are often contained kinds of noises, which makes seismic attenuation estimation difficult and unstable. We proposed an enhanced LSR (ELSR) workflow to estimate seismic attenuation. First, we built a sparse S-transform (SST) to obtain a sparse time-frequency (TF) spectrum of the analyzed seismic trace. Then, based on the SST spectrum, we introduced an ELSR workflow to estimate seismic attenuation. It should be noticed that we provided an adaptive frequency band selection for the LSR. To demonstrate the effectiveness of the proposed workflow, we apply it on both synthetic and field data. Compared with the results from several traditional attenuation estimation methods, the proposed ELSR provides a more stable and more accurate attenuation estimation result and offers the potentials in improving the resolution of post-stacked seismic data.

The time-frequency (TF) analysis (TFA) tools are usually used to analyze the seismic reflection signals to assist the sedimentary cycle division. The high-resolution TFA results are beneficial to characterize the dominant frequency changes caused by the variations of the stratum thickness. The multisynchrosqueezing transform (MSST) is an iterative version of the synchrosqueezing transform (SST), which provides a more concentrated TF representation than the SST. So, the MSST is suitable for the sedimentary cycle characterization. However, it is a hard task to construct an appropriate basic wavelet. In this study, by combining the MSST and optimal basic wavelet (OBW), we proposed a multisynchrosqueezing OBW transform (MSOBWT) to help the sedimentary cycle division. The proposed method first defines the dominant frequency location condition (DFLC) that ensures the MSST to reassign the TF spectrum to the dominant frequencies position. Further, the OBW is introduced to construct the basic wavelet that satisfies the DFLC. Finally, the synthetic traces and field data are used to testify its effectiveness for the sedimentary cycle division.

In this letter, we concern the acoustic impedance (AI) inversion from the known reflectivity based on the increasingly mature deconvolution techniques. For seismic data with the complicated geological structures, we first construct the regularization model for the AI inversion with the proposed regularizer consisting of the total variation (TV) seminorm and the Frobenius norm of the Hessian. Second, we develop the split Bregman (SB) iterative algorithm in the frequency domain for solving the proposed model. Finally, we verify the effectiveness of our proposed method via synthetic and field data. Experimental results demonstrate that our proposed method can not only preserve the lateral continuity and the impedance interfaces of the inverted AI section well, but also provide a higher resolution impedance section than the other related methods.

We propose a blind nonlinear acoustic impedance inversion method. The seismic wavelet is first extracted through the Euclid deconvolution method from multichannel seismic data. Then, the acoustic impedance is inverted based on the exact nonlinear forward operator. The conventional Euclid deconvolution can theoretically estimate the reflectivity without special prior assumptions, but the method is extremely inefficient and unstable in the case of a large amount of data. We optimize the method and propose a frequency-domain algorithm to improve its efficiency. Conventional impedance inversions are almost implemented based on the linearized approximate formula, but the inversion errors will increase sharply when there is a strong reflection interface. We build the inversion objective function by the accurate nonlinear formula to improve accuracy. The total variation (TV) regularization and low-frequency components of well-logging curves are added to the objective function to make the inversion result have a block structure and converge to the absolute impedance. The nonlinear optimization problem is finally solved by the Levenberg–Marquardt (LM) algorithm. The results of synthetic data and field data verify that our method has high accuracy and good practicability.

Building a reliable velocity model plays a vital role in seismic imaging and quantitative reservoir description. However, the current data-driven deep-learning-based velocity model building (VMB) approaches directly reconstruct the velocity model of the subsurface from prestack seismic recordings, which are very sensitive to the noise and amplitude mismatch in the data domain. In this letter, we propose a novel VMB approach based on common-source migration image gathers (CSMIGs) and convolutional neural networks (CNNs). The proposed CNN architecture uses the CSMIGs reconstructed by the reverse time migration approach and migration velocity model as the input data. It aims to capture the nonlinear relationship between the amplitude and phase information of CSMIGs and the optimal subsurface reflectivity model. Trained with realistic subsurface models, it can determine that the VMB approach is a computationally efficient solution for a high-resolution velocity reconstruction. In addition, the proposed approach has a better reconstruction performance, antinoise ability, and can be generalized much more easily than the data-driven VMB approach.

Least-squares reverse time migration (LSRTM) has the potential to retrieve a high-resolution subsurface image. However, the standard acoustic LSRTM approach may produce a blurred image, if directly applying it to attenuated seismic recordings. In this letter, we developed a novel 3D Q-compensated image-domain LSRTM approach, denoted as Q-IDLSRTM. The Hessian matrix in the proposed approach is efficiently estimated from the point spread functions (PSFs) which are calculated by a combination of viscoacoustic Born modeling and reverse time migration (RTM) based on the generalized standard linear solid (GSLS) wave equation. The major advantage of the proposed image-domain inversion is that it is much faster than data-domain inversion. The L1 norm constraint and total variation (TV) regularization are used to produce a sparse solution and maintain the structural continuity of the inverted image. We determine the effectiveness of the proposed approach with a part of the 3D Overthrust model and the resulting images demonstrate the ability of our approach to image subsurface structures with enhanced resolution and balanced amplitude relative to the RTM image and inverted image from the acoustic image-domain LSRTM approach.

In the zero-offset vertical seismic profile (VSP), if the data noise is weak, the spectral ratio method (SRM) is considered to be the most reliable and commonly used method for estimating the medium$Q$factor. However, due to the possible picking error in the first-arrival time of the downgoing waveform, the estimated$Q$value fluctuates, which affects the subsequent attenuation compensation and lithology analysis. In order to overcome this fluctuation, we present an iterative maximum posterior probability (IMAP) method that uses zero-offset VSP data to invert the medium$Q$factor. Based on SRM, this method gives the maximum posterior probability (MAP) method for inverting the quality factor$Q$, establishes the update formulas of quality factor$Q$and travel time difference$\Delta t$, and performs alternate iterations on them. Since the prior information of the formation is introduced and$\Delta t$is corrected in each iteration, the inversion result can eliminate the fluctuations in the$Q$value and velocity caused by the$\Delta t$error. Two synthetic experimental examples and one field experiment verify the effectiveness and superiority of the proposed method.

The time-frequency (TF) analysis method plays a significant role in the detection of natural gas hydrates. As a data-driven method, compressed sensing (CS) has been widely used in the TF methods due to the sparsity of the TF representation. This study proposes a data-driven TF method based on the CS theory and a non-convex regularization. In the implementation, a continuous wavelet transform (CWT) with a generalized beta wavelet (GBW) is formulated as an inverse problem based on the CS theory. The selection of appropriate parameters enables the GBW to match the seismic wavelets better than the widely used Morlet wavelet. The GBW can constitute a tight frame to reduce calculation time, particularly for large-scale field data processing. Additionally, the proposed TF method introduces the generalized minimax concave (GMC) penalty function as a non-convex regularization term. Compared with the classical sparse approximation method with$\ell _{1} $regularization, the GMC regularization term can enhance the sparsity in sparse inverse problems and ensure the convexity of sparse inversions. This article also presents an exponentially decreasing threshold scheme to adaptively select the regularization parameters. Three synthetic examples are investigated to demonstrate the performance of the proposed sparse TF representation with GMC regularization. Finally, the proposed TF method’s performance in detecting free gas of gas hydrates is validated using field seismic data obtained from the Blake Ridge.

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.

Seismic full waveform inversion (FWI) is able to build high-resolution velocity model based on the full information carried by seismic wave. However, FWI requires an accurate enough initial model to ensure convergence. In this paper, we propose a new nonlinear FWI method to mitigate the initial model dependence problem. Specifically, we firstly propose a nonlinear operator within the hybrid model- and data-driven framework based on the frequency controllable envelope operator (FCEO) and a deep learning architecture U-Net. FCEO is used to obtain the envelope of a band-limited data and U-Net realizes the mapping from this envelope to that corresponding to a lower frequency band. The U-Net is trained in a self-supervised manner that avoids the reliance on labeled data and benefits the generalization ability. Based on the nonlinear operator, a nonlinear FWI method is proposed by defining a new misfit function. In addition, the calculation of gradient is derived using the adjoint-state method. Using numerical examples, we investigate the performance of the proposed nonlinear operator and the new nonlinear FWI method. The results clearly demonstrate that the proposed nonlinear operator is effective in obtaining low-frequency envelope data, and the new nonlinear FWI method has advantages over common method in mitigating cycle-skipping and building an initial model for conventional FWI.

Least-squares reverse time migration (LSRTM) is an amplitude-preserving seismic imaging technique that aims at finding the subsurface reflectivity model. It is often performed iteratively using an inversion algorithm, such as the conjugate gradient method. Such an implementation requires a huge amount of calculation as it may converge slowly. Preconditioning plays a crucial role in seismic inverse problems. In this study, we propose a novel preconditioning method for LSRTM. The proposed method estimates a new guided curvelet-domain deblurring filter for one-step LSRTM and preconditioned LSRTM. Then, the filter is applied to migrated images and gradients in LSRTM. Such a deblurring filter acts as a curvelet-domain local linear approximation of the least-squares functional inverse Hessian, which can improve the image quality and accelerate the convergence. Numerical tests on the synthetic model and a field data example demonstrate that the preconditioning operator can effectively accelerate the convergence of LSRTM. One-step LSRTM can obtain comparable image quality to that of conventional iterative LSRTM with only a single iteration. The comparison of the convergence curves demonstrates that the curvelet-domain preconditioning operators accelerate the convergence of LSRTM. Furthermore, the preconditioned LSRTM achieves better image quality than the conventional LSRTM. We compare preconditioning operators based on diagonal and local linear approximations. The preconditioning operator based on the local linear approximation has more robust performance and more stable convergence curves than the diagonal-based approximation.

Delineating seismic faults is one of the main steps in seismic structure interpretation. Recently, deep learning (DL) models are used to automatic seismic fault interpretation. For the DL-based models, there are two widely used techniques, which can enhance the model performance, that is, data augmentation (DA) and ensemble learning (EL). Qualitatively and quantificationally analyzing the performances of these two techniques is a rarely studied domain. In this study, we make detailed comparisons between the DL models using DA and EL. For the DL model with DA, we first build a holistically nested Unet (HUnet) model by adopting the holistically nested module to the widely used Unet model. Then, we train a HUnet model by using the original and its augmented synthetic datasets (HUnet-D model for short). Besides, we train a Unet model in the same way as a comparison (Unet-D model for short). On the other hand, for the DL model with EL, we first obtain several individual HUnet models separately trained by only using a type of the augmented datasets for each time. Next, we propose a data-driven EL model to integrate these HUnet models. Specially, we propose an adjoint-net module for the EL model to extract the multi-scale features from seismic data, which benefits for checking and fine-tuning the fusing results. Finally, we qualitatively and quantificationally evaluate these DL models (Unet-D, HUnet-D, and EL-HUnet) using the synthetic validation dataset. Moreover, we apply these models to 3-D field data volumes for automatic fault interpretation. Compared with the coherence attribute, Unet-D and HUnet-D models, we find that the EL-HUnet model achieves the comparable model performance for effectively enhancing the precision and continuity of the detected faults.

Traditional optimization algorithms are usually applied to estimate the elastic parameters of the subsurface by using field seismic data. However, these optimization algorithms highly depend on prior knowledge (e.g., the initial model setup and sparsity), leading to serious inversion uncertainties. Nowadays, with the rapid development of neural networks, convolutional neural networks (CNNs) have been widely imposed on estimating elastic parameters from field data. However, the deficiency of labeled seismic data impedes the CNNs application in seismic inversion. Moreover, both the size and diversity of labeled datasets are also critical factors influencing the accuracy and resolution of predicted parameters when using the CNNs-based inversion techniques. In this work, taking the unconventional tight sandstone formation as an example, we develop a geological and geophysical model driven CNNs (GGCNNs), named as GGCNNs. The proposed GGCNNs allow us to take advantage of both the prior geological information and basic geophysical model from the generated synthetic labeled prestack seismic datasets, representing essential characteristics of the subsurface. Moreover, under the consideration of data diversity, the GGCNNs model enables us to make a tradeoff between the inversion accuracy and labeled data size. Applications on both synthetic and field data clearly demonstrate the effectiveness of the proposed GGCNNs model for predicting elastic parameters by using prestack seismic data, i.e., its predicted results are with high accuracy in the vertical profile and continuity and smooth in the horizon slice.

Accurate estimation of petrophysical properties (e.g., porosity, clay volume) of subsurface rock from seismic data/elastic properties is significant to reservoir characterization. Conventional model-driven inversion strategies for estimating petrophysical parameters confront with the deficiency of prior knowledge. In contrast, machine learning-based approaches are adapted to account for reservoir parameter estimation through developing nonlinear mapping and quantifying uncertainty. However, most of the current researches mainly concentrates on the single parameter prediction with different neural network architectures, which, in turn, conflicts with the truth of coupling multiple reservoir properties. To quantify the sensitivity of input-output parameters and the effects of network architecture on the accuracy of petrophysical parameter inversion, we propose a CNN-based network strategy to estimate multiple reservoir parameters simultaneously. The results from both synthetic labeled data and field data and uncertainty analysis strongly demonstrate that SopenCNN, abbreviated from multiple input and single output openCNN, exhibits the highest prediction accuracy, while the cycleCNN with multiple input and multiple output, referred to as McycleCNN, is superior to the MopenCNN, which means that an openCNN contains multiple input and multiple output. It means that, for similar network architecture, the number of input and output parameters makes a significant impact on prediction accuracy. Moreover, for similar multiple inputs and outputs, the fine-tuning McycleCNN, parallelly updated in each intermediate closed-loop step, behaves much better accordingly. The application of the three workflows with varying architecture on field tight sandstone reservoirs demonstrates that network based inversion strategy could establish a mapping function to characterize spatially varying reservoir parameters.

Least-squares reverse time migration (LSRTM) can estimate high-quality reflectivity of subsurface medium from seismic data. However, the subsurface reflectivity depends on reflection angles, and its variations over reflection angles are extremely important because they can be used to estimate sub-surface physical properties for seismic interpretation. We present a new formulation of the LSRTM method that can estimate reflection-angle-dependent reflectivity from seismic data. We derive a forward modeling operator which predicts the reflection data without calculating the reflection angles, and verify that it approximately equals to the reflection-angle-dependent wave-equation-based Kirchhoff modeling operator under the assumption that the velocity perturbation is small and the reflection angle is smaller than the critical angle. Based on the proposed modeling operator associated with the adjoint of the angle-dependent wave-equation-based Kirchhoff modeling operator, we reformulate LSRTM as an inverse problem to invert for reflection-angle-dependent reflectivity using a preconditioned conjugate gradient algorithm. The algorithm uses a low-rank filter as the preconditioner to attenuate migration artifacts. Imaging tests on synthetic and field seismic data are used to verify validity and superiority of the proposed method. The tests illustrate that the proposed method can produce the reflection-angle-dependent reflectivity with much higher signal-to-noise ratio, resolution and amplitude fidelity than reverse time migration. Compared with conventional LSRTM, it can produce more focused stacked image when the migration velocity contains errors. Moreover, conventional LSRTM only produces the angle-independent reflectivity, whereas the proposed method has the feasibility to produce the reflection-angle-dependent reflectivity.

Lithology interpretation is important for understanding subsurface properties. Yet, the common manual well log interpretation is usually with low efficiency and bad consistency. Therefore, the automatic well log interpretation tools based on machine learning and deep learning have been developed. Although the state-of-the-art sophisticated models can show fine interpretation performance with acceptable accuracies, “blind” tests do not always exhibit satisfactory results because of the complexity of lithology interpretation with respect to subsurface rock properties and the data-labeling quality. To solve this generalization challenge, we propose to leverage the parameterized quantum circuits in the deep-learning model. The quantum computing takes advantages of the superposition and entanglement quantum systems, which could potentially endow the generalization power or capability to the deep-learning model. Using the proposed quantum-enhanced deep-learning (QEDL) model, we have tested the model performance on field well log data from different wells. Compared with the classic fine convolutional neural network (CNN) model and the long short-term memory (LSTM) model, the proposed QEDL model achieves comparable model performance with a clearly improved generalization power for interpreting both thin and thick lithology layers. In addition, because of the quantum circuit structure, the QEDL model needs much fewer model parameters than LSTM and CNN models, i.e., the QEDL parameter number in our study can be approximately 75% less than that of LSTM and 89% less than that of CNN.

Ground roll, a source-generated surface wave, is a main type of coherent noise in a land seismic survey. Low-frequency and high-amplitude ground roll often overlays valid reflection events, resulting in obscuring seismic reflections. Ground-roll attenuation is an essential step for seismic data processing, which is based on the accurate separation of the ground roll and reflections without damaging their morphological characteristics. In this study, we effectively separate and suppress ground roll in shot gathers through a proposed workflow. We first identify the major components of the ground roll adopting the multichannel variational mode decomposition (MVMD), which shows significant improvements compared to the conventional single-channel VMD. Ground roll can be identified on the decomposed band-limited intrinsic mode functions (IMFs). Moreover, we propose an adaptive criterion to determine the number of decomposed IMFs. Due to the narrowly concentrated frequency components with the multichannel continuity constraint from MVMD, ground roll is mainly contained in low-frequency IMFs, which benefits the accurate ground-roll suppression. Next, we separate ground roll and reflections on the selected low-frequency IMFs through a curvelet based block-coordinate relaxation method. Afterward, we can obtain a filtered gather by removing the separated ground roll from the original shot gather. Finally, we apply the proposed workflow to synthetic and field gathers to testify its validity and effectiveness for simultaneously attenuating ground roll and preserving valid seismic reflector information.

Seismic image denoising is essential to enhance signal-to-noise ratio (SNR) of seismic images and facilitate seismic processing and geological structure interpretation. With the development of deep learning (DL), several DL based models have been proposed for seismic image denoising. However, the commonly used supervised DL based denoising models require noise-free data as training labels, yet noise-free data is often difficult to be obtained in field application scenarios. By considering the similarity of seismic images, we propose a similarity informed self-learning (SISL) to address seismic image denoising in the absence of noise-free seismic images. To accurately preserve valid seismic signals when constructing training pairs, we develop a specialized workflow, termed the similar image sampler. In this way, we can fully use the self-similarity of noisy seismic images to build training pairs and then train a denoising model. Moreover, to effectively attenuate random noise, we propose a hybrid loss function with a regularization constraint to availably retain valid seismic events. After comparing with traditional denoising methods and several state-of-the-art unsupervised DL models, the experiment results from synthetic and field data quantitatively and qualitatively demonstrate the effectiveness and the stability of the proposed SISL model for seismic image denoising.

Attenuation of incoherent noise is an effective way to improve signal-to-noise ratio (SNR) of seismic data. Recently, supervised deep learning based methods have been widely utilized for seismic image denoising, which often need plenty of noise-free data as training labels. However, noise-free seismic data are often unavailable in field applications. We propose an unsupervised learning method (NS2NS) to train a denoising network by using single noisy seismic data. The proposed model is based on two basic truths of seismic data: (1) High self-similarity of seismic data; (2) Spatially independence of incoherent noise in seismic data. To implement the proposed method, we first build a sampling workflow to generate paired noisy images based on single noisy seismic image. Moreover, we create similar noisy images that are similar but different with the original noisy image by using the proposed self-similar sampler. The original noisy images and generated similar noisy images are then fused by using a suggested Bernoulli sampler to create new paired noisy images. These new paired noisy images are used as the input and target of the denoising model, respectively. Next, an end-to-end convolutional neural network (CNN) is built for seismic image denoising, which aims to learn features of valid signals and suppress unpredictable random noise. Finally, we apply the proposed NS2NS method to both synthetic and field data. The results show that our proposed method can effectively suppress incoherent noise while preserving valid signals.

Time-frequency (TF) representations achieve better TF localization properties compared with Fourier transform (FT) and perform well for Q estimation via methods such as spectral ratio (SR), centroid frequency shift (CFS), and peak frequency shift (PFS). However, these attenuation estimation methods all require a given frequency band or certain source wavelet assumptions, also heavily interfered by noise. In addition, the resolution and accuracy of TF spectrum also determine whether the extracted spectrum can accurately characterize the frequency properties of seismic wavelets, thus affecting the accuracy of seismic estimation results. In this study, we propose an unscaled generalized S-transform (UGST), which achieves better TF localization while avoiding the dominant frequency shift of S-transform (ST). Next, we build a Q estimation method based on the weighted Kullback-Leibler (WKL) divergence and then give an estimation workflow combined with the proposed UGST. Note that the proposed workflow does not need to make specific wavelet assumptions or consider the frequency band selection, which is also proved to be not sensitive to noise. Finally, to demonstrate the effectiveness of the proposed workflow, we apply it to synthetic and field data. Compared with the contrastive methods, our proposed workflow can achieve more accurate estimation results and show better noise immunity, which can benefit delineating seismic hydrocarbon reservoirs.

Seismic data reconstruction is one of the essential steps in the seismic data processing. Recently, the deep learning (DL) models have attracted huge attention in seismic exploration, which has been applied to seismic data reconstruction, especially the convolutional neural network (CNN)-based methods. However, the general CNN-based models only consider seismic features in the time domain and do not take into account the frequency features. Moreover, there are detailed features lost due to the downsampling scheme. We propose a wavelet-based residual DL (WRDL) network to reconstruct the incomplete seismic data. By selecting the U-Net as the backbone, we introduce the discrete wavelet transform (DWT) to replace the pooling operations, whose invertibility property benefits reserving the detailed features. Furthermore, the inverse wavelet transform (IWT) with the expansion convolutional layer is introduced to restore the feature maps. In addition, we adopt the residual blocks into the proposed model to promote the training accuracy and avoid the overfitting issue. To accurately and effectively reconstruct the missing seismic data, we propose a hybrid loss function based on the structural similarity (SSIM) loss and the Huber loss. Numerical experiments on synthetic data and field data show that the WRDL model reconstructs the missing seismic data more accurately than the U-Net and MWCNN models, including the irregularly missing seismic data and the consecutively missing seismic data with a big gap. Furthermore, the qualitative and quantitative results demonstrate the advantages of the proposed hybrid loss function over the commonly used traditional loss for seismic data reconstruction.

Time-frequency analysis (TFA) is a powerful tool for describing time-frequency (TF) features of seismic data, such as short-time Fourier transform and S-transform. Recently, sparse time-frequency analysis (STFA) is proposed for enhancing TF readability of commonly used TFA tools. However, STFA is often solved via an optimal inverse problem with a prior regularization term, which is difficult to set in practice, where the key regularization parameters are sensitive to noise. Moreover, it often takes expensive calculation time, especially for 3D field data application. We build a deep learning based workflow for implementing STFA to obtain sparse time-frequency (STF) spectra, termed the sparse time-frequency network with transfer learning (STFNTL). We first adopt a Marmousi II reflectivity model and Ricker wavelets with different dominant frequencies to generate synthetic training data set. Then, we adopt a simplified STFA method with optimized parameters to generate synthetic training labels, i.e., sparse TF spectra. Afterward, we propose the sparse time-frequency network (STFN) based on a simplified Unet model, which is trained using synthetic training data and corresponding STF labels. Moreover, to enhance the generalization of STFN, we introduce an adaptive transfer learning strategy based on small samples of field data and their corresponding STF labels. Finally, synthetic and field data are utilized to illustrate the effectiveness and generalization ability of our proposed model.

Random noise attenuation is a key step in seismic field data processing. With the rise of artificial intelligence, deep learning (DL) algorithms are gradually introduced into seismic random noise suppression. The most commonly used DL paradigm takes mean squared error (MSE) as loss function, the default assumption is that its error term obeys independently identically distribution (IID) Gaussian, and its noise level involved preset-hyperparameters in the local area of data cannot be adjusted adaptively in the training phase. This leads to the poor generalization of deep denoiser on Non-IID noises. In this study, we propose a deep learning framework based on Non-IID pixel-wise Gaussian noise modeling, which integrates noise attenuation and noise level estimation into a unique Bayesian framework. The framework can adaptively characterize the noise and data distribution in the local area of noisy data through the variational inference (VI) technique, which allows the network to see more noises of varying degrees and learn effective information from them. Thus, our proposed framework called VI-Non-IID inclines to have better noise characterization and generalization capabilities, which brings better performance on seismic field noise attenuation. Furthermore, we conduct a series of experiments on seismic synthetic and field data to test the performance of two implementations of VI-Non-IID: VI-Non-IID(Unet) and VI-Non-IID(DnCNN). A lot of results validate the superiority of our proposed VI-Non-IID framework. Specifically, VI-Non-IID can explicitly predict the denoised data and its corresponding noise level map simultaneously, and succeed in attenuating unknown field noises while preserving the useful seismic signals.

Sedimentary cycle division is an important step for sequence stratigraphy analysis. For the division of sedimentary cycle using seismic data, a key issue is characterizing the changes of dominant frequencies caused by the changes of stratum thickness with high accuracy and high resolution. The synchrosqueezing transform (SST) can provide a time–frequency (TF) representation with high resolution by synchrosqueezing the TF spectrum, which helps the sedimentary cycle identification. Unfortunately, it is a hard task to choose an appropriate basic wavelet, which influences the accuracy of the SST to characterize the sedimentary cycle. To solve this issue, we construct a synchrosqueezing optimal basic wavelet transform (SOBWT) to optimally characterize the sedimentary cycle. We first propose a criterion to construct the basic wavelet of SST by deriving the dominant frequency location condition and defining the similarity coefficient condition of the basic wavelet. Then, we introduce the optimal basic wavelet (OBW) to construct the basic wavelet that satisfies the dominant frequency location condition and the similarity coefficient condition. Note that we term the SST with a basic wavelet that satisfies the dominant frequency location condition and the similarity coefficient condition as the SOBWT. Finally, we apply the proposed SOBWT to synthetic and field data to testify its validity and effectiveness and compare it with conventional SST-based methods. The application results illustrate that it is much more convenient and easier for the sedimentary cycle division based on the SOBWT results.

Continuous wavelet transform (CWT) is often used to extract the peak frequency attribute for characterizing the thin-bed thickness. Good joint time-frequency (TF) resolution is beneficial for the extraction of peak frequency. However, due to the Heisenberg’s uncertain principle, the time and frequency resolution of CWT cannot be obtained simultaneously. In this paper, combining the adaptive superlet transform and the optimal basic wavelet, a super-resolution optimal basic wavelet transform (SROBWT) is proposed to obtain the best joint TF resolution. The optimal basic wavelet matching the seismic wavelet is constructed as a basic wavelet of the adaptive superlet transform. Herein, taking the best joint TF resolution of the seismic wavelet as the target, a parameter selection method is proposed for the adaptive superlet transform. Furthermore, based on the proposed SROBWT and wedge model, a workflow is proposed to characterize the thin-bed thickness. The synthetic and field seismic data are employed to demonstrate the validity of the proposed methods. All the corresponding results show that the SROBWT has a better joint TF resolution than the conventional methods and the proposed workflow can correctly characterize the spatial variation of the thin-bed thickness, which is beneficial for further sediment sources analysis and reservoir prediction.

Building reflectivity and quality factor (Q) using nonstationary post-stack seismic data is important for vertical resolution enhancement of seismic data and reservoir identification. However, it is well-known that both reflectivity and Q affect the waveform of seismic data, leading to the fact that simultaneously estimating them is a strong ill-posed multi-parameter inverse problem which faces the crosstalk problem. In this paper, we propose a new method for simultaneous inversion of reflectivity and Q. A deep-learning-based data decoupling operator is proposed to decouple the effects of the two parameters on nonstationary seismic data. Based on the decoupled data, we transform the original multi-parameter inverse problem into two independent singe-parameter inverse problems that are immune to crosstalk and can build reasonable initial models for reflectivity and Q. Then alternative iteration is conducted to update the two built initial models to obtain the final models. A few well-logs are used to train the deep learning architecture and specific regularization terms are constructed for the inverse problem to ensure physically reasonable results. Synthetic and field data examples verify the effectiveness of the proposed method and its advantages over a conventional model-driven joint inversion method.

Wavelet and reflectivity inversion (WRI) is an important issue in seismic data processing. To overcome the ill-posedness of WRI inversion with more efficient parameter selection and better lateral continuity of reflectivities, we propose a new WRI algorithm named compact smoothness and relative sparsity (CSRS) algorithm, where a normalized compact constraint and a normalized smooth regularization is proposed for the wavelet inversion, and a relative sparsity constraint is proposed for the reflectivity inversion. The proposed constraints and regularization make the parameters of WRI easy to be selected. The proposed relative sparsity constraint can lead to a reflectivity profile with good lateral continuity as it can be suitable for various seismic data with a fixed sparsity parameter. We also propose an efficient algorithm for solving corresponding WRI optimization problem. The whole WRI problem is divided into reflectivity inversion subproblem and wavelet inversion subproblem by using alternating iterative method, where the initial wavelet is estimated by smoothing the absolute amplitude spectrum of averaged seismic data. The proximal algorithm is applied to solve both reflectivity inversion subproblem and wavelet inversion subproblem. By replacing Toeplitz matrix multiplication with fast Fourier transform (FFT) and using compact wavelet, our algorithm can be efficient for 3D seismic data. The numerical examples on 2D synthetic data, 2D offshore field data and 3D onshore field data demonstrate that, compared to Toeplitz-sparse matrix factorization (TSMF) algorithm, the CSRS algorithm with fixed default parameters can get high-resolution reflectivities with better lateral continuity, and requires much less computational time.

The time-frequency (TF) analysis is an effective tool in seismic signal processing. The sparsity-based TF transforms have been widely used to obtain high localized TF representations in recent past years. These TF transforms formulate a sparse TF representation as an inverse optimization problem using simple mathematical models, which are typically based on a hand-crafted prior knowledge. Unlike the traditional sparsity-based TF transforms, the supervised deep learning (DL)-based sparse TF representations don’t require this prior knowledge and instead use a large amount of labeled data set, which is difficult to label for seismic data. In this study, to bridge the gap between the traditional sparsity-based transforms and the supervised DL-based transforms, we propose a DL-based sparse TF analysis approach based on a physically informed autoencoder model, named the SparseTFNet. The proposed SparseTFNet includes two modules: a convolutional neural networks (CNN)-based encoder and a traditional inverse TF representation-based decoder. The CNN-based encoder is implemented by training the inverse optimization problem in the absence of the “ground-truth" TF representation, which can be trained with only seismic traces. The traditional inverse short time Fourier transform (STFT) is utilized as the decoder module in this study, which is used as a physical constraint to ensure the high accuracy of the calculated TF representation. Finally, after training and validating the proposed model using the noise-free and noisy synthetic seismic traces, the model is applied to three-dimensional (3D) offshore seismic data. The results show that the proposed SparseTFNet model has good performance in the delineation of the depositional fluvial channels.

Data-driven deep-learning full-waveform inversion (DD-DLFWI) can efficiently reconstruct a velocity image of the subsurface from prestack seismic recordings, once the deep-learning (DL) model is well-trained based on the self-designed geological structures and simulated recordings. However, the key problem of this approach is that it usually discards the knowledge about the forward and adjoint operators, which leads to poor reconstruction quality and generalization ability. To mitigate these problems, we have developed a deep-learning full-waveform inversion (DLFWI) approach using seismic migration images. This approach includes two key points. The first key point is that, unlike the conventional DD-DLFWI approach based on the seismic recordings in the common-source data domain, our approach utilizes the reverse time migration (RTM) images of seismic recordings in the common-source image domain as the data engine of the convolutional neural network (CNN) to reconstruct the background velocity. The second key point is that we utilize the iterative neural network architecture to reconstruct the high-resolution velocity model based on the reconstructed background velocity. Specifically, the high-resolution velocity model can be recovered by using the reconstructed velocity model, RTM image, and gradient of regularization term as the input of neural network architecture. Through synthetic experiments with various layered and fault velocity models, we have confirmed that the proposed approach can reconstruct a high-resolution velocity of the subsurface from prestack seismic recordings. Meanwhile, it outperforms the conventional DD-DLFWI approach in terms of reconstruction accuracy, antinoise, and generalization ability.

The enormous computational overheads and excessive storage requirements are two obstacles to the data-domain least-squares reverse time migration (RTM) approach for the application of large-scale 3-D seismic data. To alleviate this problem, we have developed an image-domain least-squares RTM (IDLSRTM) approach through point spread functions (PSFs) and excitation-amplitude (EA) imaging condition, denoted as EA-IDLSRTM. The key point is that the EA imaging condition, as a cost-effective and practical imaging condition, is used to reconstruct the RTM image and localized PSFs. There are two benefits to this combination. One is that the EA imaging condition can effectively reconstruct the RTM image and localized PSFs with less computational overhead and storage requirement, relative to the zero-lag cross correlation (CC) imaging condition. Another important benefit is that the redundant source wavelets in both the RTM and PSF images computed by the CC imaging condition can be removed by the EA imaging condition, prior to the image-domain inversion. As a result, the proposed approach can explicitly reduce the condition number of the Hessian matrix used in the conventional IDLSRTM approach, which will produce a less ill-conditioned inverse problem. In addition, we introduce an angle-dependent filter for the attenuation of low-wavenumber artifacts to accelerate the convergence. Several experiments with synthetic and field data demonstrate that the proposed EA-IDLSRTM approach can efficiently and effectively recover the high-resolution and high-fidelity reflectivity image. Meanwhile, EA-IDLSRTM can provide better imaging quality than the conventional IDLSRTM approach in the case of relatively smoothed velocity.

Data-domain least-squares reverse time migration (DDLSRTM) has been proved to be a more effective imaging tool for complex structures, relative to the standard reverse time migration (RTM) approach. One of the difficulties in DDLSRTM is that the enormous computational costs may impede its application in large-scale 3D data. To mitigate this problem, with the help of point spread functions (PSFs) and spatial interpolation, we have developed a novel 3D image-domain least-squares reverse time migration (IDLSRTM) approach, which requires once migration and modeling calculations. However, because of the incomplete acquisition geometry of seismic recordings, IDLSRTM is a highly ill-posed inverse problem. The inverted image from the conventional IDLSRTM approach may suffer from the migration artifacts caused by the coarse source and receiver sampling and spatial discontinuity and instability caused by the truncated PSFs. To solve the ill-posedness and improve image quality, the L1 norm constraint and total variation (TV) regularization are introduced into the objective function of IDLSRTM. The alternating direction method of multipliers (ADMM) algorithm is developed to solve this optimization problem. Through some 3D synthetic and field data, it can determine that the proposed IDLSRTM approach computationally efficient produces a high-fidelity reflection image with good spatial continuity and fewer migration artifacts. It has shown this approach to be a cost-effective and practical inversion-based imaging tool for 3D field datasets.

The data-consistency item is a necessary condition for a reliable solution to the inverse problem. However, the current supervised-based deep-learning reconstruction approaches generally lack the data-consistency item, which directly leads to unreliable subsurface images for field data. To resolve this problem, we have developed a consistent least-squares reverse time migration (CLSRTM) approach using convolutional neural networks (CNNs), which is referred to as CNN-CLSRTM. The key point is that we have enforced that the predicted recording via the inverted image from the CNN model is consistent with the observed recording in the least-squares sense. We utilize the standard reverse time migration (RTM) image of single-shot recording as the input of the constructed CNN model. As a result, the optimal reflection image can be obtained by iteratively updating the parameters of CNN by minimizing the data residuals. Benefiting from the similarity of RTM images of adjacent recordings and the representation ability of the well-trained CNN model, we can directly predict the optimal reflection image for the testing datasets in a very fast way, which can greatly improve computational efficiency. Through synthetic and field data sets, we have determined that the proposed CNN-CLSRTM approach can retrieve high-resolution images with balanced amplitudes and continuous events. At the same time, our approach has better antinoise ability inherited from the benefit of CNN model compared to the standard LSRTM approach. In addition, we analyze the generalization ability of the CNN model for synthetic and field datasets.

Seismic attenuation is one of the crucial attributes for seismic resolution enhancement and reservoir characterization, which is often described by quality factor Q. Among the commonly used methods for Q estimation, the frequency based method is demonstrated for effectively estimating Q factor, mainly including the frequency shift (FS) based, and the spectral correlation (SC), and the logarithm spectral ratio (LSR) based methods. However, the frequency spectrum of the received wave may be affected by the closely adjacent reflections, which may result in an unreliable Q estimation. To handle this limitation, the error modeling based discriminative approach in machine learning is proposed in this study. We utilize the seismic wave first received to construct the classifier based on the reproducing kernel Hilbert spaces representer theorem, then give an effect Q estimation by applying the classifier to the wave second received. Furthermore, to improve the robustness of the estimation results, the error models of the classifier are introduced. The loss functions are proposed to correspond to the distributions of the error models, from which two different implementations of Q estimation are derived. When applying to the synthetic data, the corresponding results show that the proposed method greatly improves the robustness and accuracy of the conventional methods. Field data test is also provided and demonstrates the effectiveness of our proposed method.

Seismic noise separation and attenuation is a fundamental topic in the seismic signal processing and geological interpretation. Several kinds of algorithms are proposed for separating and attenuating seismic random noises. However, the conventional methods often handle a seismic volume trace by trace, which ignores the lateral continuity of seismic data. Moreover, seismic signal is a typical broadband signal, which makes it difficult to separate and attenuate random noises contained in the whole frequency bands of the raw seismic data. Additionally, the tuning parameters for the denoising methods are also a difficult task to filter a broadband seismic signal. In this study, we propose a multi-channel scheme which is referred as the multi-channel variational mode decomposition (MVMD) based on multi-channel singular spectrum analysis (MSSA), to efficiently and effectively separate and attenuate seismic random noises. The proposed workflow first adopts the MVMD to decompose a 2-D seismic data into several band-limited intrinsic mode functions (IMFs) with different center frequencies and different bandwidths. Then, we leverage the MSSA for each decomposed IMF to separate and attenuate random noises. It is worth to be noted that we can select the tuning MSSA parameters for each IMF based on their different center frequencies and bandwidths. Finally, we restore the valid seismic data by summing all filtered IMFs. Through detailed comparisons with the traditional denoising methods, the results from the synthetic examples and field data quantitatively and qualitatively demonstrate the effectiveness and accuracy of the proposed workflow for separating and attenuating seismic random noises.

Time-frequency (TF) analysis is an available tool to estimate seismic absorption qualitatively. The high TF concentration is a key factor for the seismic attenuation qualitative estimation. To obtain a more concentrated TF representation, we propose a sparse TF method based on sparse representation (SR) and sparse Group-Lasso (GL) penalty function. Based on the SR theory, TF representation can be regarded as an inverse problem, and thus, sparse GL penalty function can be added in this inverse problem to enhance the TF concentration. Sparse GL penalty function, includingl1penalty andl2,1penalty, can provide group-wise and within-group sparsity for TF coefficients. Using the proposed sparse GL-based TF (GLTF) method, we develop a workflow to characterize seismic attenuation qualitatively. Finally, a synthetic data of viscoacoustic model and a 2-D field data are applied to test the validity and effectiveness of the proposed workflow for indicating the gas and oil reservoirs.

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.

In this letter, we propose a new global optimization method for nonlinear seismic inversion problems. The proposed method is a development of the existing method MMDE-Net by introducing a learnable strategy for choosing problem-dependent basis vectors and regularization parameters that are considered to be fixed in MMDE-Net. We name the proposed method as the optimized MMDE-Net (OMMDE-Net) and investigate its performance in seismic inversion through both synthetic and field data examples. The experimental results demonstrate that OMMDE-Net has advantages over MMDE-Net in effectiveness and efficiency.

Lithology classification in well logging plays a significant role in evaluating the quality of oil and gas reservoirs. Conventionally, the manual interpretation method is of much more limited use, partly because it is time-consuming, but mainly because it is subjective. This is due primarily to the massive volume of logging data and the dependence of the experience of geophysical practitioners. By considering the features that logging data are typically sequential and long short-term memory (LSTM) network is well-suited to process a sequential signal, an LSTM-based architecture is proposed to identify rock facies based on borehole data automatically in the study area. The tests based on data from one well of the tight gas sandstone reservoir demonstrate that, when the sample size and the number of hidden layer neurons are appropriately set, the trained LSTM-based Adam optimizer can precisely recognize the rock facies boundaries than that based on Sgdm and Rmsprop optimizers. Additionally, results on another eight wells in the same study area statistically show a good generalization of the trained LSTM. Moreover, another complex reservoir with similar lithology interbedding also demonstrates the usefulness of the LSTM-based network.

Continuous wavelet transform (CWT) is an effective tool for seismic time-frequency (TF) analysis. Selecting a matched wavelet to the analyzed seismic wavelet is a key issue for accurately characterizing TF features of seismic data. The three-parameter wavelet (TPW) can match different seismic wavelets by adjusting the three parameters. However, it is difficult to select appropriate parameters for matching TPW to seismic wavelets in real applications. In this letter, we propose a basic wavelet construction method by using the TPW and the deep learning network. The proposed workflow first builds a mapping relationship between seismic wavelet and seismic data by using the alternating iterative deep neural network (AIDNN). Based on this relationship, we then estimate a seismic wavelet. Using the estimated seismic wavelet, we can finally construct an analytical basic wavelet by matching the TPW to the extracted wavelet. Note that we named the TPW with optimal parameters as the optimal basic wavelet (OBW), and its wavelet transform is OBWT. To demonstrate the validity and effectiveness of the proposed approach, we apply it to synthetic traces and field data for characterizing their TF features. The results show that OBWT preserves the amplitude better and has a higher resolution than the CWT with mismatched basic wavelets to the seismic wavelet, which is helpful for seismic data analysis in the future.

Seismic inversion problems often involve strong nonlinear relationships between model and data so that their misfit functions usually have many local minima. Global optimization methods are well known to be able to find the global minimum without requiring an accurate initial model. However, when the dimensionality of model space becomes large, global optimization methods will converge slow, which seriously hinders their applications in large-dimensional seismic inversion problems. In this article, we propose a new method for large-dimensional seismic inversion based on global optimization and a machine learning technique called autoencoder. Benefiting from the dimensionality reduction characteristics of autoencoder, the proposed method converts the original large-dimensional seismic inversion problem into a low-dimensional one that can be effectively and efficiently solved by global optimization. We apply the proposed method to seismic impedance inversion problems to test its performance. We use a trace-by-trace inversion strategy, and regularization is used to guarantee the lateral continuity of the inverted model. Well-log data with accurate velocity and density are the prerequisite of the inversion strategy to work effectively. Numerical results of both synthetic and field data examples clearly demonstrate that the proposed method can converge faster and yield better inversion results compared with common methods.

Angle-domain common image gathers (ADCIGs) describe the reflectivity variation over reflection angles which are important for seismic exploration. The ADCIGs could be obtained using reverse time migration (RTM). However, because of the limitation of seismic frequency band and acquisition geometry, RTM produces the ADCIGs with low fidelity. We propose a reflection angle-domain pseudoextended least-squares RTM method to improve the quality of the ADCIGs in which the Poynting vector is used to efficiently calculate the angles. We first extend the inverted model in the reflection angle domain and derive a feasible pseudoextended Born modeling operator which can map the reflection angle-domain extended model to seismic data. The modeling operator, associated with an adjoint operator, are then used to build a pseudoextended linearized inversion framework for inverting the angle-dependent reflectivity. Taking advantage of the simplicity and coherency of the ADCIGs, we impose a series of low-rank constraints on the extended angle dimension and a sparse constraint on the whole dimension to ensure the production of high-quality ADCIGs. The proposed method is finally solved by a regularized conjugate gradient algorithm. We conduct several numerical examples on a flat layer model, the Marmousi model, and the Sigsbee2A salt model to test the validity and superiority of the proposed method. The results demonstrate that the proposed method could produce the ADCIGs and the stacked image with higher fidelity than RTM, which provides a reliable input for migration velocity analysis, anisotropic model building, and amplitude versus angle analysis.

Full waveform inversion (FWI) is a powerful tool to understand the real complicated earth model. As FWI is a highly nonlinear problem and depends strongly on the initial model, how to effectively retrieve the large-scale background model is critical for the success of FWI. For elastic FWI (EFWI), the inversion challenge increases because the P-wave and S-wave are coupled together if no mode separation technologies are applied. In this article, we develop a new EFWI strategy, where we simultaneously implement the angle decomposition and mode separation for the wavefield. Based on the analysis of radiation patterns of different parameters and the fact that small scattering angles correspond to large-scale model perturbations, we can retrieve the large-scale background model of the P-wave velocity with pure small scattering angle P-P mode wavefield. On the other hand, the pure small scattering angle S-S, S-P, and P-S mode wavefields are used to estimate the large-scale background model of the S-wave velocity. The correctly retrieved large-scale background models further guarantee the success of subsequent fine structure retrieving for the P- and S-wave velocity models by using different wave modes. The proposed method is able to reduce the cycle-skipping problem and the multiparameter crosstalk problem simultaneously. Numerical examples show that the proposed method provides much improved inversion results than the conventional EFWI, which demonstrates the validity of the proposed method.

Noise attenuation is a very important step in seismic data processing, which facilitates accurate geologic interpretation. Random noise is one of the main factors that lead to reductions in the signal-to-noise ratio (SNR) of seismic data. It is necessary for seismic data, including complex geological structures, to develop a number of new noise attenuation technologies. In this article, we concern with a new variational regularization method for random noise attenuation of seismic data. Considering that seismic reflection events often have spatially varying directions, we first employ the gradient structure tensor (GST) to estimate the spatially varying dips point by point and propose the structure-oriented directional total generalized variation (DTGV) (SODTGV) functional. Then, we employ the SODTGV as a regularizer to establish an ℓ2-SODTGV model and develop the primal-dual algorithm for solving this model. Next, the choice of the model parameters is discussed. Finally, the proposed model is applied to restore noisy synthetic and field data to verify the effectiveness of the proposed workflow. For contrastive methods, we select the structure adaptive median filtering (SAMF), anisotropic total variation (ATV), total generalized variation (TGV), DTGV, median filtering, KL transform, SVD transform, and curvelet transform. The synthetic and real seismic data examples indicate that our proposed method can preferably improve the vertical resolution of seismic profiles, enhance the lateral continuity of reflection events, and preserve local geologic features while improving the SNR. Moreover, the proposed regularization method can also be applied to other inverse problems, such as image processing, medical imaging, and remote sensing.

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.

For oil and gas exploration, seismic wave propagation in coupled acoustic, elastic, poroelastic, and even anisotropic media is a valuable aspect. However, it is a challenging task to deal with the interfaces of the coupled model. In order to tackle the specific issue, a unified numerical scheme is developed, which is based on the discontinuous Galerkin method. The acoustic, elastic, poroelastic, and anisotropic elastic wave equations are unified into a first-order velocity–stress system. The numerical simulation at the interfaces in the coupled model is conveniently handled by the Godunov flux without any extra operations. Numerical results from the coupled acoustic–elastic and acoustic–poroelastic model are compared with the analytic solutions. In addition, the rates of convergence from different orders are analyzed, which demonstrates the accuracy of the proposed numerical scheme. The surface waves at the fluid–solid interface are studied. Moreover, the proposed scheme is applied to a more complex coupled model, including the coupled acoustic–elastic–poroelastic model and the coupled acoustic–anisotropic elastic model. The corresponding results demonstrate that the proposed numerical scheme is capable of dealing with the coupled model.

Time-frequency (TF) analysis algorithms are widely used to process seismic data. Unfortunately, most TF analysis algorithms cannot process 2-D seismic data, which contain more information than 1-D data. In fact, 2-D x-t domain seismic data should be analyzed in the multi-dimensional phase space (MDPS). In this letter, we develop and explain an MDPS analysis method for 2-D seismic data. In order to map the 2-D seismic data into MDPS, the synchrosqueezed curvelet transform (SSCT) is extended from the x-y domain to the x-t domain. By comparing the 2-D synchrosqueezing transform (SST) with the 1-D SST, we explain how the 2-D SST makes the connection between the 4-D curvelet domain and the 4-D space-time-wavenumberfrequency domain (xt-kf domain). This new analytical method can help us to obtain the angle, scale, frequency, and wavenumber information, which are useful to separate the overlapped seismic data. The numerical example and real data example illustrate the effectiveness of this method.

One important application of time-frequency analysis (TFA) is seismic spectral decomposition for reservoir characterization. However, traditional seismic TFA techniques are usually limited by diffused TF distribution, which can result in unreliable seismic interpretations. Synchrosqueezing transform (SST) is an effective TFA method that improves the concentration of the TF representation (TFR) of nonstationary signals. However, for the signal with a rapidly varying instantaneous frequency, the SST method suffers from a blurred TFR. In this letter, we propose a novel TFA method called time-synchroextracting transform (TSET) that provides highly concentrated TFR for transient signals where the TF curve is nearly parallel to the frequency axis. We applied the proposed TSET to synthetic signals and field seismic data to verify its validity of time localization and effective delineation of subsurface geological information.

Subsurface scatters are sometimes masked by reflectors in seismic migration images, because the diffractions are much weaker in energy than the reflections. We propose a novel imaging method, named reflection-damped plane-wave least-squares reverse time migration (RD_PLSRTM), to enhance the scatters in the migration image. We formulate seismic imaging as an inverse problem that minimizes a weighted residual between the modeled and observed seismic data. In the proposed approach, we use the plane-wave destruction filter to separate the diffractions from the reflections in the data residual. A reflection-damped weighting matrix is then used to govern the fitting of the diffractions and the reflections, and therefore emphasize the updates of the scatters. The inverse problem is finally solved by using an iteratively reweighted least-squares (IRLS) algorithm. The proposed method provides a generalized formulation that could be reduced to conventional PLSRTM and PLSRTM of diffractions (PLSRTM_D) by using specific damping factors. We conduct imaging tests on synthetic and field data that prove the superiority of the proposed method over PLSRTM in imaging deep scatters and subsalt scatters. Compared with PLSRTM_D, it could produce high-quality images of not only the scatters but also the reflectors.

To better describe features of nonstationary seismic signals, mode decomposition-based approaches are widely used for seismic processing and analysis, such as empirical mode decomposition (EMD) and empirical wavelet transform (EWT). EWT builds an adaptive filter bank and then decomposes a nonstationary seismic trace into several intrinsic mode functions (IMFs), which has been applied for analyzing the nonstationary seismic signal. In this letter, we propose an enhanced EWT (EEWT) using Hankel transform (HT), which is an integral transform whose kernels are Bessel functions. Compared with sinusoidal functions of Fourier transform (FT), Bessel functions are more effective for describing features of nonstationary signals. Moreover, HT obtains a more compact spectrum than FT for wideband and nonstationary signal analysis, which contributes to the detection of spectral segmentation. To demonstrate the effectiveness of the proposed algorithm, we apply it to both synthetic and field data. Compared with the results provided by EWT, EEWT provides a time-frequency spectrum with higher resolution and offers potentials in precisely highlighting reservoirs.

In[1], the grant number in the first footnote for the National Postdoctoral Program for Innovative Talents should be BX20190279.

Time-frequency (TF) analysis is a powerful tool in seismic data processing and interpretation, and it characterizes the frequency response of subsurface rocks and hydrocarbon reservoirs effectively. In this letter, we proposed a new method called the second-order synchrosqueezing wave packet transform (SSWPT2) for seismic TF analysis. The proposed approach introduces two posttransform, i.e., reassignment method (RM) and synchrosqueezing transform (SST), into the wave packet transform. Such a technique achieves a highly concentrated TF representation by using a second-order local estimate of the instantaneous frequency (IF). We validate the proposed approach with a synthetic example and compare the result with the existing methods, and field data examples also illustrate its effectiveness in delineating more distinct channels in the horizon slices.

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.

Synchrosqueezing transform (SST) is an effective time-frequency analysis (TFA) approach for the processing of nonstationary signals. The SST shows a satisfactory ability of the TF localization of the nonlinear signal with a slowly time-varying instantaneous frequency (IF). However, for the signal of which ridge curves in the TF domain are fast varying, or even almost parallel to the frequency axis, the SST will provide a blurred TF representation (TFR). To solve this issue, the transient-extracting transform (TET) was recently put forward. The TET can effectively characterize and extract transient features in the much concentrated TFR for the strongly frequency-modulated (FM) signal, especially the impulse-like signal. However, contrary to the SST, it is not suitable for weak FM modes. In this study, we propose a TFA method called the time-synchroextracting general chirplet transform (TEGCT). The TEGCT can achieve a highly concentrated TFR for strong FM signals as well as weak FM ones. Quantized indicators, the concentration measurement and the peak signal-to-noise ratio, are used to analyze the performances of the proposed method compared with those of other methods. The comparisons show that the TEGCT can provide a result with better TF localization. Then, the proposed method was applied to the spectrum analysis of the seismic data for oil reservoir characteristics. The horizontal slices of the offshore 3-D seismic data show that the TEGCT delineates more distinct and continuous subsurface channels in a fluvial-delta deposition system. All the results illustrate that our proposed method is a good potential tool for seismic processing and interpretation in the geoscience.

In this article, we present one numerical approach to infer the model parameters and state variables of acoustic wave equations. The method we consider is based on the recently proposed method-the so-called hidden physics model. With placing Gaussian process (GP) prior on the state variables, the structure and model parameters of acoustic wave equations are encoded into the kernel function of a multioutput GP. The purpose of this article includes: 1) testing the applicability of hidden physics model to infer the velocity, density, and state variables of the acoustic wave equation, which is important for many applications in geophysics; 2) adapting the method to handle for both homogeneous and heterogeneous media that are of practical interest; and 3) exploring efficient sequential sampling methods to improve the sampling efficiency. We suggest that the expected-improvement-based sequential sampling method would be effective for most practical problems related to acoustic wave propagation. Besides, we demonstrate the performance of the proposed scheme via several benchmark problems.

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.

By building an adaptive filter bank, the empirical wavelet transform (EWT) decomposes an analyzed signal into several intrinsic mode functions (IMFs). Although some applications have certified the effectiveness of the EWT, the effectiveness of the EWT is affected obviously when analyzing nonstationary signals (e.g., seismic data). In this letter, we propose an improved EWT (IEWT) to decompose a nonstationary seismic signal into several IMFs and describe its frequency features. After computing the Fourier spectrum of the seismic signal, the scale-space representation (SSR) is used to extract the slowly varying component of the Fourier spectrum. Then, the frequency components contained in the seismic signal and the boundaries can be obtained using the central frequency information. Finally, we obtain an adaptive spectrum segmentation using detected boundaries based on the SSR. Afterward, the proposed algorithm obtains accurate and stable IMFs in decomposing the nonstationary seismic signal. To demonstrate the effectiveness of the proposed IEWT, we apply it to synthetic seismic signal and field data.

Quality factor$Q$can be used for hydrocarbon detection and reservoir characterization. The commonly used methods for$Q$estimation include the logarithm spectral ratio (LSR) method, the centroid frequency shift (CFS) method, and the peak frequency shift (PFS) method. However, all these methods are existing limitations respectively. The LSR method is sensitive to random noise. The CFS and PFS methods are lack of applicability owing to their assumptions of the source wavelet type. To overcome these limitations, we derived a new formula without any wavelet assumption. This formula establishes a relationship between the$Q$factor and the spectral centroid downshift concisely through the Jeffery divergence. The proposed method is named the generalized centroid frequency shift (GCFS) method. Compared with the conventional methods, the proposed method can achieve higher accuracy and better antinoise performance. In addition, the proposed method is suitable for various source wavelet types. Synthetic and field examples demonstrate the effectiveness and potential of the proposed method.

Coherence algorithm is widely used to describe geological discontinuity and subtle features of seismic data. Traditional coherence algorithms often use the linear correlation measurement to measure the relationship between two seismic traces. It does not work well because seismic data do not obey the normal distribution. To describe the coherence measurement of seismic data, we propose an improved coherence algorithm by combining the mutual information (MI) and third-generation coherence (C3) algorithm. The MI is a measurement of the general dependence and used to describe nonlinear relationships between two variables. Note that, the MI does not require that variables obey specific distribution (e.g., the normal distribution). Note that, we calculate precise MI values using the copula function. In addition, we introduce the information divergence to save calculation time by replacing the eigenvalue decomposition of the C3 algorithm. To demonstrate the effectiveness of the proposed algorithm, we apply it to field data. Field data experiments demonstrate the effectiveness of the proposed algorithm to describe geological discontinuity and heterogeneity, such as channels with different thicknesses.

Full-waveform inversion (FWI) attempts to find optimal models of subsurface by using full information of the observed data. One difficulty in conventional FWI is that the misfit function has many local minima because of cycle skipping. Envelope inversion (EI), which uses the envelope operator (EO)-based misfit function, has been proven to be effective in mitigating cycle skipping and recovering long-wavelength velocity model. However, EI ignores the fact that the information within different frequency bands plays different roles in inversion. In this paper, a frequency controllable EO, which can control the frequency components being used to construct envelope, is proposed. We propose a new misfit function and a multiscale FWI method. Using synthetic experiments based on the Marmousi model, we demonstrate that the proposed method is better than EI in mitigating cycle skipping and in building an accurate initial model for conventional FWI to significantly improve its final result. In addition, this method can tolerate a wide range of noise levels. Its effectiveness has also been successfully demonstrated using a field data set.

Seismic inversion problems are well-known to be nonlinear and their misfit functions often involve many local minima. Global optimization methods are capable of converging to the global minimum of a misfit function, thus, they are promising in seismic inversion. As a global optimization method, multimutation differential evolution (MMDE) has been proven to be effective in solving high-dimensional seismic inversion problems. However, it is challenging to choose the optimal parameters for MMDE to achieve the best performance in seismic inversion. In this paper, we propose a new deep network based on MMDE and name it as MMDE-Net, which enables us to learn the optimal parameters by using a network training procedure rather than empirically choosing them. Benefiting from the learned parameters, MMDE-Net has advantages over MMDE in applications. Numerical examples based on synthetic and field data set clearly indicate that MMDE-Net can provide faster convergence speed and better inversion result than conventional methods in seismic inversion.

Achieving a proper time-frequency (TF) resolution is the key to extract information from seismic data using TF algorithms and characterize reservoir properties using decomposed frequency components. The generalized S-transform (GST) is one of the most widely used TF algorithms. However, it is difficult to choose an optimized parameter set for the whole seismic data set. In this paper, we propose to set the parameters of the GST adaptively using the instantaneous frequency (IF) of seismic traces. Our workflow begins with building a relationship between the parameter set of the GST and IF using a synthetic wedge model. We use the IF as an indicator for the time thickness of each trace in the wedge model. We then compute the TF spectrum of each trace using the GST with different parameter sets and compare the similarity between the computed TF spectrum and theory TF spectrum. The parameter set with the largest similarity is regarded as the best parameter set for each trace in the wedge model. In this manner, we build a relationship between the parameter set and IF value. We can finally choose the optimum parameter set for the GST according to the IF values of seismic traces. We name the proposed workflow as the self-adaptive GST (SAGST). To demonstrate the validity and effectiveness of the proposed SAGST, we apply it to synthetic seismic traces and field data. Both synthetic and real data examples illustrate that the SAGST can obtain a TF representation with a high TF resolution.

The second generation bandelet transform uses the two‐dimensional (2D) separable wavelet transform to improve its image denoising and compression performance. However, the 2D separable wavelet transform is not a shift‐invariant transform and therefore cannot capture geometric information well. The authors propose a hybrid image denoising method in which the 2D separable wavelet transform in the second generation bandelet transform is replaced with the non‐subsampled contourlet transform. The results of the application of the proposed method to several greyscale and colour benchmark images contaminated with various levels of Gaussian white noise and Poisson noise indicate that the proposed method has good peak signal‐to‐noise ratio and visual quality performance.

The S transform (ST) is one of the most commonly used time-frequency (TF) analysis algorithms and is commonly used in assisting reservoir characterization and hydrocarbon detection. Unfortunately, the TF spectrum obtained by the ST has a low temporal resolution at low frequencies, which lowers its ability in thin beds and channels detection. In this letter, we propose a three parameters ST (TPST) to optimize the TF resolution flexibly. To demonstrate the validity and effectiveness of the TPST, we first apply it to a synthetic data and a synthetic seismic trace and then to a filed data. Synthetic data examples show that this TPST achieves an optimized TF resolution, compared with the standard ST and modified ST with two parameters. Field data experiments illustrate that the TPST is superior to the ST in highlighting the channel edges. The lateral continuity of the frequency slice produced by the TPST is more continuous than that of the ST.

In this letter, a new method is introduced for a seismic time-frequency (TF) analysis. The proposed method is called synchrosqueezing generalized S-transform (SSGST), which belongs to a postprocessing procedure of the GST. The frequency-dependent Gaussian window used in the standard S-transform may be not suitable for real applications. In order to overcome this limitation, the frequency-dependent Gaussian window is replaced by a parameterized function containing three parameters. These three parameters result in flexibility in the variation of TF resolution. Then, the synchrosqueezing transform is employed to squeeze the TF coefficients of the GST to achieve an energy-concentrated TF representation. Synthetic examples and field data show that the SSGST achieves a high resolution and has the potential in highlighting geological structures with high precision.

Attenuation is a fundamental mechanism as seismic wave propagates through the earth. The loss of high-frequency energy and concomitant phase distortion can be compensated by inverse Q filtering to enhance the resolution of seismic data. Since the attenuation process depends on time and frequency, it is routinely performed in the time-frequency domain. The synchrosqueezing transform (SST), which provides highly localized time-frequency representations for the nonstationary signals due to reduced spectral smearing, is applied to implement the inverse Q filtering scheme. However, the amplitude compensation process is unstable because energy amplification is involved. To stabilize it, the amplitude compensation is regarded as an inverse problem with an L1-norm regularization term in the SST domain. The iteratively reweighted least-squares algorithm is used to solve the regularized inverse problem. Synthetic and real data examples illustrate the stability and effectiveness of the proposed method.

The numerical simulation of wave fields in 3-D poroelastic media can give a better understanding of elastic properties, deformation characteristics of rocks, and interaction with pore fluids. However, the wave equations in 3-D poroelastic media include more equations, and the size of geophysical model for practical reservoir is immense. Therefore, numerical simulation is time consuming. In order to improve the efficiency, we proposed variable-order staggered-grid (SG) finite difference (FD) method to solve 3-D poroelastic wave equations. In this method, different orders of SGFD scheme can be selected for different velocities in a heterogeneous poroelastic model by restricting the dispersion parameters within a tolerable threshold. We derive the dispersion relation, numerical dispersion relation, and stability condition for 3-D poroelastic media using plane wave analysis and SGFD scheme. Based on the numerical dispersion relation of slow P-wave, S-wave, and fast P-wave, we restrict the average of dispersion parameters of the three waves within a given range; the orders of the SGFD scheme can be calculated for different velocities. Dispersion analysis shows that the variable-order SGFD method can maintain the accuracy compared with the fixed-order SGFD method. We use three numerical examples, which include laterally homogeneous model, a simplified overthrust model, and a geophysical model in a desert area in China, to demonstrate the accuracy and efficiency of the proposed method. The numerical results confirm that the variable-order SGFD method can reduce the computation time efficiently and still ensure the accuracy.

Time-frequency (TF) analysis can reveal local variations in seismic data processing and interpretation, where seismic signals are nonstationary and time varying. High-quality TF representation (TFR) is important for revealing the local information about these nonstationary seismic signals and describing geological structures. Due to the Heisenberg uncertainty principle, traditional TF methods (e.g., short time Fourier transform and continuous wavelet transform) cannot get the finest time resolution and the best frequency resolution at the same time, which leads to ambiguous TFR with a negative effect on the seismic signal analysis. Concentration in frequency and time is proposed to distinguish the different TF contents of time-dependent signals with time-varying amplitude and instantaneous frequencies. We introduce this promising TF analysis tool to seismic data processing. Experiments on synthetic signals and seismic data show its validity and effectiveness, which is helpful for seismic data interpretation in the future.

Seismic inversion problems often involve nonlinear relationships between data and model and usually have many local minima. Linearized inversion methods have been widely used to solve such problems. However, these kinds of methods often strongly depend on the initial model and are easily trapped in a local minimum. Global optimization methods, on the other hand, do not require a very good initial model and can approach a global minimum. However, global optimization methods are exhaustive search techniques that can be very time consuming. When the model dimension or the search space becomes large, these methods can be very slow to converge. In this paper, we propose a new global optimization algorithm by incorporating a new multimutation scheme into a differential evolution algorithm. Because mutation operation with the new multimutation scheme can generate better mutant vectors, the new global optimization algorithm has a very good ability of exploring the search space and can converge very fast. We apply the proposed algorithm to both synthetic and field data to test its performance. The results have clearly indicated that the new global optimization algorithm provides faster convergence and yields better results compared with the conventional global optimization methods in seismic inversion.

The concept of simultaneous source has recently become of interest in seismic exploration, due to its efficient or economic acquisition or both. The blended data overlapped between shot records are acquired in simultaneous source acquisition. Separating the blended data and recovering the single-shot seismic signals (the recovery) are of great importance in the scenario of current workflows, which can be called seismic simultaneous source separation. In the context of general random time-dithering firing, we propose an alternative method to separate the blended data by combining patchwise dictionary learning with sparse inversion, in which the dictionary is directly learned from the measured blended data. Apart from the sparse coding used for the coefficients, an additional regularization term on the dictionary is particularly designed to remove the severe interference noise. The efficient and flexible alternating direction method of multipliers (ADMM) is used to update the dictionary in the used alternating optimization scheme. The results obtained from the synthetic and real examples reasonably suggest that the separated seismic signals by using dictionary learning are more accurate and robust compared with that using the fixed transform basis, such as the local discrete cosine transform. The learned dictionary tailors for the recovery and is similar to the local seismic waveform, which improves the sparsity of the recovery substantially and is highly advantageous for producing the promised results.

Seismic records are often contaminated with various kinds of noise, which makes it very difficult to distinguish the expected geological features. In this paper, we introduce a novel adaptive variable time fractional-order anisotropic diffusion equation for seismic data noise removal and strongly oriented structure enhancement. Since the time fractional-order differential equation interpolates a parabolic equation and a hyperbolic equation, the solution benefits both of these approaches. The presented differential equation can be written as a Volterra integral equation, and its well-posedness can be guaranteed for all time. We employ a structure tensor to analyze the flow-like texture characteristic which is typical in seismic data. Then, the diffusion process is guided reasonably by a diffusion tensor based on the structure tensor analysis which allows real anisotropic behavior comparing to the classical scalar diffusion approach. In reference to the numerical implementation, we utilize the predictor-corrector algorithm to solve the Volterra integral equation which provides high-order numerical precision jointly with good stability property. Finally, numerical experiments involved with synthetic and prestacked real seismic data are presented. The obtained results demonstrate that the noise is effectively removed, and the coherent seismic events that express some important geological structures are not only preserved but significantly enhanced.

In this letter, a new adaptive differential evolution (DE) for high-dimensional waveform inversion is proposed. In conventional DE algorithms, individuals are treated as a whole and share the same fitness function and parameters. However, conventional DE algorithms have ignored the huge difference among the subcomponents in an individual and are not effective for high-dimensional problems. Therefore, for high-dimensional problems, we expand the unit of crossover rate from the whole individual to its subcomponents and propose a new adaption algorithm by adjusting the crossover rate of each subcomponent. In our algorithm, both kinds of crossover rate, including individual crossover rate and subcomponent crossover rate, play important roles in crossover operation. Based on local fitness function, the subcomponent crossover rate is adaptively obtained to improve the efficiency of crossover operation. On the other hand, the individual crossover rate is used to prevent the population diversity from decreasing in crossover operation. We embed the adaption algorithm into cooperative coevolutionary DE (CCDE) and propose a new adaptive DE by adjusting the subcomponent crossover rate named CRsADE. We have conducted experiments on waveform inversion to test the performance of the proposed algorithm. The results show that CRsADE performs better than CCDE significantly both on convergence speed and accuracy. In order to estimate the validity of CRsADE, we have also applied it to real seismic data.

In this letter, a new differential evolution (DE) algorithm is proposed and applied to waveform inversion. The traditional evolution strategy of this algorithm is not efficient because it treats the individuals in a population equally and evolves all of them in each generation. In order to overcome this shortcoming, we propose a new population evolution strategy (PES) to decrease the population size based on the differences among individuals during an evolution process. We embed the new strategy into the cooperative coevolutionary DE (CCDE) and obtain a new highly efficient DE (HEDE). We apply this new algorithm to waveform inversion experiments of both synthetic and real seismic data to test its performance and demonstrate its validity. The results have clearly shown that, under the same inversion precision, the HEDE can reduce the runtime by about 50% compared with the CCDE.

Stacking is a fundamental concept that can be found in geosciences and seismic signal processing. The performance of random noise suppression and residual moveout correction by traditional amplitude-based stacking process is always far from satisfactory. In this letter, we present a time-frequency-domain phase-based stacking approach to exploit the similar spectral content of the different traces in seismic array data. The method can overcome the disadvantages of many existing stacking methods. The phase is derived from the well-known time-frequency-domain technique S transform, and the average of the phase spectrum is used to weight the spectrum of prestack seismic traces. As a coherency measure, the weighted phase spectrum can better reflect the lateral coherence of effective signal between individual traces. Meanwhile, the unique time-frequency properties of S spectrum make the weighting process more competitive in suppressing random noise and nonuniform artifacts. The analysis results of synthetic and real field data show the effectiveness of the proposed stacking approach.

Time-frequency analysis can provide useful information in seismic data processing and interpretation. An accurate time-frequency representation is important in highlighting subtle geologic structures and in detecting anomalies associated with hydrocarbon reservoirs. The popular methods, like short-time Fourier transform and wavelet analysis, have limitations in dealing with fast varying instantaneous frequencies, which is often the characteristic of seismic data. The synchrosqueezing transform (SST) is a promising tool to provide a detailed time-frequency representation. We apply the SST to seismic data and show its potential to seismic signal processing applications.

The recent progress of compressive sensing (CS) theory shows that perfect reconstruction is possible when the data are sampled randomly and compressed greatly. This revolutionary theory strongly advocates the irregular sampling pattern in the process of seismic data acquisition, leading to a highly reduced acquisition cost. The complete seismic record can be reconstructed from the sparsely few sampled seismic data. In this paper, an analysis version of iterative half thresholding algorithm is introduced to interpolate the seismic data, using the tight frame dictionary. Inspired by the newly proposed spectral compressive sensing theory and the favorable characteristics of tight frame, we employ the redundant Fourier transform to sparsely represent the oscillating seismic data. A double zero-padding strategy in spatial direction of seismic data is suggested to further enhance the reconstruction quality, allowing for the improved interpolation performance and the increased computational cost and storage requirement. The validity of the proposed method is demonstrated by experimental result.

Monochromatic noise always interferes with the interpretation of the seismic signals and degrades the quality of subsurface images obtained by further processes. Conventional methods suffer from several problems in detecting the monochromatic noise automatically, preserving seismic signals, etc. In this letter, we present an algorithm that can remove all major monochromatic noises from the seismic traces in a relatively harmless way. Our separation model is set up upon the assumption that input seismic data are composed of useful seismic signals and single-frequency interferences. Based on their diverse morphologies, two waveform dictionaries are chosen to represent each component sparsely, and the separation process is promoted by the sparsity of both components in their corresponding representing dictionaries. Both synthetic and field-shot data are employed to illustrate the effectiveness of our method.

With the development of seismic attribute analysis technique, the fidelity of waveform and amplitude becomes important to wavefield separation method. In this paper, we present a zero-offset vertical seismic profiling (VSP) wavefield separation method with good fidelity. The method is based on singular value decomposition(SVD) filtering and have four stage: first, aligning events of downgoing wave by static time shifting each trace of VSP; second, suppressing downgoing wave by high-pass SVD filtering; third aligning events of upgoing wave by static time shifting each trace of downgoing wave suppressed wavefield; fourth, extracting upgoing wave by low-pass SVD filtering. It is difficult to calculate the time shift of each trace for aligning events of upgoing wave, as the residual downgoing wave in downgoing wave suppressed wavefield is not very week. In this paper, we calculate the time shift via the largest singular value maximization algorithm. I demonstrate with synthetic data and real data example that the results of our method have good fidelity and are better than the results of traditional SVD method.

Seismic thin bed thickness approximation has been a hot topic for many years in seismic data processing. The variation of bed thickness can usually indicate some geologic structure anomalies. Generally it's difficult to distinguish and estimate the thin bed when the thickness is below the tuning thickness (resolution limit). But there is a close relationship between bed thickness and its frequency domain response characteristics. Both of the reflectivity series and seismic wavelet influence the thin bed frequency response. Peak frequency attribute of two common bed types is studied and an analytical expression of thickness and peak frequency is obtained through different order of estimate. The influence of random noise is also discussed. The synthesized model results demonstrate the effectiveness of our proposed method. In the real data applications, this method should be combined with many other preprocessing operations.

In this paper, a robust method for the extraction of instantaneous attributes is proposed in wavelet domain. A new class of analytic wavelets, the Generalized Morse Wavelets (GMWs), which have some desirable properties, are applied during the procedure of the proposed method. Compared to the conventional method based on Hilbert transform (HT), the new method is proved to yield higher precision and better anti-noise performance. Experimental results on synthetic signals and real seismic data show the validity of the method.

This paper is on the use of the framelet transformation for noise surpression of geophysical data. The main contribution lies in the application of the transformation for geophysical data. The results of the proposed approach are compared to the use of f-x deconvolution filtering and the curvelet transformation for the same purpose on seismic data. Visually, an improvement in noise reduction is detected.

This paper realized the forward calculation with the ray tracing algorithm, and applied WEPIF (the wavelet envelope peak instantaneous frequency) analysis for absorption tomography. The paper presents a rapid and valid adaptive angle step ray tracing algorithm to overcome the problems of low accuracy and computational efficiency of the existing methods. The new algorithm is developed for pre-stack CMP data forward modeling. We deduce successive linearization absorption tomography algorithm combining WEPIF method and Gauss weighted interpolation, and use ART, SIRT and LSQR for iterative solution of linear systems. Applied to single and multi trace gather synthetic data, the results indicate the validity of the method.

Seismic numerical modeling is a valuable tool for seismic interpretation and an essential part of seismic inversion algorithms. The aim is to predict the seismogram, given an assumed structure of the subsurface. Real subsurface structure is often multi-phase media because of fluid saturation, so the commonly used models such as acoustic media, elastic media can't characterize the information of real subsurface structure. The diffusive-viscous model can be used to describe seismic wave propagation in fluid-saturated rocks, and it is also used to investigate the relationship between the frequency dependence of reflections and the fluid saturation in a porous rock. In this paper we simulate the propagation of diffusive-viscous waves in fluid-saturated media using the Flux Corrected Transport-Finite Difference Method (FCT-FDM). The numerical results show that the propagating waves in fluid-saturated media greatly attenuate by comparing with those of acoustic case.

In this letter, an improved differential evolution (DE) for high-dimensional waveform inversion is proposed. In conventional evolutionary algorithms, an individual is treated as a whole, and all its variables (genes) are evaluated with a uniform fitness function. This evaluation criterion is not effective for a high-dimensional individual. Therefore, for high-dimensional waveform inversion, we incorporate the decomposition strategy of cooperative coevolution into DE to decompose the individual into some subcomponents. Another novel feature that we introduce is a local fitness function for each subcomponent, and a new mutation operator is designed to guide the mutation direction of each subcomponent with the corresponding local fitness value. Coevolution among different subcomponents is realized in the selection operation with the global fitness function. Many experiments have been carried out to evaluate the performance of this new algorithm. The results clearly show that, for high-dimensional waveform inversion, this algorithm is effective and performs better than some other methods. Finally, the new method has been applied to real seismic data.

A desirable property when dealing with frames is that the low and up bounds of frames should be close to each other. This can accelerate the convergence speed in computing the dual-frame and simplify the process of recovering the signal from its frame coefficients. In this letter, a new 2-D continuous wavelet transform tiling scheme, which uses different rotation factor sampling methods for different scales, is proposed. The upper/lower bound of the 2-D wavelet family based on this new tiling scheme is derived. The upper/lower bound of the 2-D Morlet wavelet family is estimated, and the results show that the 2-D wavelet family based on the new tiling scheme can provide a higher lower bound and a lower upper bound compared with the 2-D wavelet family based on the old tiling scheme.

In some seismic numerical applications we have to simulate wave propagation with sharp medium discontinuities. The rotated staggered grid (RSG) finite difference (FD) scheme and the arbitrary high-order derivatives discontinuous Galerkin (ADER-DG) finite element (FE) scheme can both be used for the problem of strong material heterogeneities. In this paper we study their behavior in a two-layer model with a varying ratio of the material parameters in the first layer to the second. We compared the results of the numerical schemes with the exact solution. The FD method and the FE method can both get small envelop misfits. The FE scheme has advantage over the FD method on phase misfits, but it needs a high CPU effort.

An approach is proposed to improve the resolution of nonstationary seismic data by adaptive molecular decomposition. For each seismic trace, a set of nonuniform molecular windows is constructed according to the attenuation trend described by smoothed weighted and damped instantaneous frequencies (WDIF) located at the trace's envelope peaks. Such that in each window, the seismic trace is approximately stationary. These nonuniform molecular windows are used to produce a couple of Molecular-Gabor frames. For the trace segment in each window, the spectrum-broadening and energy compensation are performed in Molecular-Gabor domain. Subsequently, a high-resolution version of the nonstationary seismic data can be obtained after inverse Molecular-Gabor transform. Applications of this method to both synthetic and real data show that the proposed method works well for a general earth Q-model that varies with travel time, and can expand the frequency band and recover the absorbed energy of the nonstationary seismic trace effectively.

In this paper, we propose an improved differential evolution (DE) for seismic waveform inversion. In the selection step, we decompose the individual into some subcomponents with the decomposition strategy of Cooperative Coevolution, and a local fitness function is assigned to each subcomponent. Then a mid offspring is selected one subcomponent by one subcomponent according to the local fitness value. Considering the interdependence among subcomponents, coevolution is needed, the final offspring is still selected according to the global fitness values of the parent individual and the mid offspring. In addition, the probability concept of the selection operator of SA is incorporated into the selection operator of DE.

We propose a seismic discontinuities detecting method based on wavelet transform in this paper. First we do 1DCWT to seismic cube to obtain instantaneous phase cubes for three interested scale. Then we use 3D CWT as a novel tool to detect seismic discontinuities on these three instantaneous phase cubes. The result on synthetic signal and real field data show our method's depicting ability of large fault and tiny discontinuities.

In this paper, seismic quality factor Q estimation from vertical seismic profile (VSP) data is discussed, by using continuous wavelet transform (CWT). We suppose that source signature is a general constant-phase wavelet which matches the real one better. Based on the CWT of a reference and a target recording, we derive the formula of frequency-independent Q estimation by the ratio of wavelet-domain peak amplitude of these two recordings. Wavelet-domain peak amplitude denotes the peak module of CWT of the recording with every fixed scale. The formula is related to the dominant frequency and standard deviation of source signature. And the Q estimation formula with impulse source can be considered as its specific case that the standard deviation of source approaches the infinity. The synthetic zero-offset VSP and real field tests demonstrate that in the condition of constant-phase source signature, estimated Q from our formula can provide more accurate information than that by the formula with impulse source.

An approach is proposed for quality ($Q$) factor estimation from the variation of envelope peak instantaneous frequency (EPIF). For a frequency-independent$Q$model, assuming that the propagating wavelet can be modeled by a Gaussian function with constant phase, an approximate analytic relation between$Q$and EPIF variation is derived. Synthetic tests show that the EPIF method has higher resolution and is less sensitive to noise and interference reflection than common methods. The field test of reflection seismic data indicates that the zone of lower$Q$-factors corresponds well to the gas reservoir.

Support vector machine(SVM) has become a powerful and widely used machine learning method in resent years. Gaussian kernel is the most commonly used kernel function. However, model selection including setting the width parameter sigma in kernel function and the regularization parameter C is essential to generalization performance of SVM. In this paper we proposed a new parameter selection method for Support Vector Machine. The key idea of our method MSKD in selecting the Gaussian kernel parameter is that convergent character between pattern's similarity measurement in feature space will decrease the classification ability of SVM. In addition, We combined MSKD algorithm with one-dimension search strategy based on cross-validation and developed a complex parameters selection method named MSKD-GS. Experiments on eight real world data sets from UCI have been carried out to demonstrate the effectiveness and efficiency of this method.

This paper presents a structure-oriented Gaussian (SOG) filter for reducing noise in 3D reflection seismic data while preserving relevant details such as structural and stratigraphic discontinuities and lateral heterogeneity. The Gaussian kernel is anisotropically constructed based on two confidence measures, both of which take into account the regularity of the local seismic structures. So that, the filter shape is well adjusted according to different local geological features. Then, the anisotropic Gaussian is steered by local orientations of the geological features (layers) provided by the Gradient Structure Tensor. The potential of our approach is presented through a comparative experiment with seismic fault preserving diffusion (SFPD) filter on synthetic blocks and an application to real 3D seismic data.

This letter describes an attenuation tomography method via variations in the envelope peak instantaneous frequencies (EPIFs) of seismic signals. For a linear frequency-attenuation model, assuming that the propagating wavelet can be modeled by a Gaussian function with constant phase, an imaging formula using EPIF variation is derived. In tomography, the simultaneous iterative reconstruction technique (SIRT) with travel-time weighting is proposed for tomographic inversion. Numerical simulations of both noise-free and noise-added data show the validity of attenuation tomography from EPIF variation. SIRT with travel-time weighting yields a better reconstruction and lower residual.

Conventional ensemble learning algorithms based on ambiguity decomposition and negative correlation learning theory are carried out on the basis of empirical risk minimization principle. When SVM is used as the component learner, the generalization ability of ensemble learning system may not be improved. In this paper, based on the estimation of the generalization performance of SVM and negative correlation learning theory, a new selective ensemble SVM learning method is proposed. Experiments on real world data sets from UCI were carried out to demonstrate the effectiveness of this method.

Reduction of feature dimensionality is of considerable importance in machine learning. The generalization performance of classification system improves when correlated and redundant features are removed. In order to reduce the dimensionality of pattern representation, A new feature election method for support vector machine is proposed. Based on pattern similarity measurement in kernel space, lass separability is deduced and we explore the use of the lass separability in feature selection. The key idea of our ethod is that the feature whose removal downgrades the class separability in kernel space most is relevance to the classification. Experiments on linear and nonlinear synthetic problems and real (world data sets have been (carried out to demonstrate the effectiveness of this method.

This letter describes a method for estimating seismic quality$(Q)$factors from spectral correlation (SC). For a linear frequency attenuation model, the SC coefficient is examined between the amplitude spectrum of a reference pulse multiplied by an absorption filter and that of a target pulse, and then, the$Q$factor can be determined from the absorption filter which yields the maximum SC coefficient. In this way,$Q$-factor estimation is converted into an optimization problem which can be quickly implemented by the Newton iteration scheme. Synthetic tests with different source signatures show that the SC method is free of the type of source wavelet. Noisy tests indicate that the SC method has higher noise resistance than the logarithm spectral ratio and the centroid frequency shifting methods. Field test indicates that the depth range of lower$Q$values estimated by the SC method well corresponds to the distribution of gas reservoirs. With better$Q$-factor evaluation, the SC method may become a more practical tool for gas reservoir characterization than before.

A novel theorem on the wavelet transform and Hilbert transform (HT) is proposed and applied to extract the instantaneous parameters of energy-limited, real signals. Numerical simulations shows advantages of the presented method in both precision and antinoise performance.