The suppression of surface-related multiples has become a critical step in seismic data processing. In fact, the absence of near-offset traces acquisitions significantly compromises the accuracy of conventional surface-related multiple suppression techniques. This study presents a wavefield extrapolation deep neural network (WEDNN) for pre-stack seismic data regularization by extrapolating the far-offset to the near-offset after an initial SRME. This approach enables effective suppression of surface-related multiples in pre-stack seismic data. Validation results from some synthetic examples including the Pluto model, and a field data example confirm the effectiveness and robustness of this developed approach. The WEDNN reduces 48.83% of the seismic data information loss in the spatial domain using wavefield extrapolation, which is caused by near-offset trace deficiency. And for synthetic examples in complex work areas, computational efficiency is enhanced by 88.3%.

Surface waves, usually referred to as Rayleigh waves and also called ground roll, generated near the surface are a kind of strong coherent noise to disturbs the accuracy of subsurface images with the recorded data from a seismic survey. In the case of the further challenges posed by rugged topography and variable near-surface velocities, the surface waves and other near-surface-related noises in the field data exhibit nonstationary characteristics, and their amplitude, frequency, and velocity vary with recorded time. Currently, the conventional methods to suppress this type of surface wave noise are based on steady-state assumptions. This article develops a nonstationary surface wave suppression method utilizing a deep neural network constrained by physical information. This method leverages the physical characteristics of surface waves and data-driven labels to constrain neural network training jointly. It enables effective training under small-sample conditions and effectively suppresses nonstationary surface waves in each prestack seismic data gathered. It also effectively decreases near-surface-related nonstationary interferences such as single-frequency noise and linear noise. Examples for both numerical and field datasets demonstrate that this near-surface-related noise suppression technology can precisely eliminate nonstationary interference signals such as surface waves, reconstructing effective waves with high efficiency, robustness, and generalization capability. Comparisons between the processing results of field data and those obtained using some typical commercial software confirm that the proposed deep neural network method surpasses traditional label-constrained network training limitations, offering superior suppression of surface waves, single-frequency noise, and linear interference in field data efficiently and stably with much less cost.

Adaptive subtraction plays a crucial role in the surface-related multiples elimination (SRME) method. Following the acquisition of predicted surface multiples, the traditional adaptive subtraction method, based on a matching algorithm, needs to identify suitable filter operators to optimize the predicted surface multiples with the actual surface multiples present in the original data. To enhance the suppression of surface multiples, we have developed an adaptive subtraction method using the pseudo-seismic-data-based convolutional neural network (P-CNN). P-CNN takes collections of predicted surface multiples as input and can produce an output that matches the actual surface multiples after training. Application to both synthetic and field data demonstrates that the P-CNN method effectively suppresses surface multiples in seismic data. Results from complex synthetic data reveal that compared to the traditional adaptive subtraction method, the P-CNN method enhances the signal-to-noise ratio (SNR) by 3.41dB while reducing the computation time by approximately two-thirds. Furthermore, in comparison to the CNN method, the P-CNN improves suppression results without significantly increasing computational costs.

Enhancing weak seismic signals in seismic data processing with a low signal-to-noise ratio (SNR) is a critical task, and it is imperative to attenuate random noise without damaging effective signals. One effective approach to achieving this is through the application of multichannel singular spectrum analysis (MSSA). However, the inherent non-stationary nature of weak signals poses a challenge for MSSA, as it struggles to completely attenuate random noise via the truncating singular value decomposition (TSVD). This study introduces a novel method referred to as adaptive non-stationary signal decomposition (ANSSD) to significantly improve the attenuation ability of seismic random noise of MSSA and enhance weak signals. Recognizing the non-stationary, non-Gaussian, and nonlinear random noise, our proposed method begins by decomposing the prestack data using singular value decomposition (SVD). Subsequently, each column of the left singular vector matrix is subjected to adaptive non-stationary signal decomposition. Finally, the data undergoes processing through truncated singular value decomposition in the frequency domain. For the synthetic data experiment, the SNR of the raw data is -14.03 dB, -4.38 dB after MSSA processing, and 0.29 dB after ANSSD processing. Meanwhile, the filed data processing results also prove that the ANSSD method is superior to the MSSA method in suppressing random noise and enhancing weak signals.

Internal multiple attenuation is a kind of significant coherent noise for imaging and comprehending subsurface structures from primaries in exploration seismic data. Traditional prediction-subtraction strategy heavily relies on predicting the traveltimes and matching the amplitudes for internal multiples, which poses a risk of primary distortions. Neural network methods face challenges about missing primary labels, limited applications on prestack field data, and high demand for prior information and manual intervention. To alleviate these problems, this article develops a physics-informed self-supervised neural network (SSN) to attenuate internal multiples by reducing requirements for prior information and employing the phase resemblance (PR) as the physics loss to adaptively prevent primary distortions. First, the initial internal multiples (IIMs) predicted by the virtual event (VE) method are taken as inputs for SSN to provide prior information, where no authentic primaries are required for training labels. Then, a U-shaped SSN equipped with attention mechanisms and a pyramid dilated convolution (PDC) unit is constructed to map IIMs to the estimated true internal multiples (EIMs) under a physics-informed hybrid loss. We introduce the PR constraint as the physics loss by cross-coherence of traces and kurtosis calculation to adaptively prevent primary distortions and constrain the network training. The result without internal multiples is finally obtained by subtracting EIMs from the recorded data. Synthetic and field data examples demonstrate the superior performance of our method in internal multiple suppression and primary retention ability compared with traditional workflow and the purely data-driven neural network.

The seismic coherence attribute is one of the most typically used seismic discontinuity feature detection technologies, which is widely used in fault detection, channel boundary characterization, and other occasions. The eigen-structure-based coherence algorithm possesses the property of stability by using the eigenvalues of seismic data’s covariance matrix, but in the algorithm, only the eigenvalues are used to calculate the final coherence value, and the information contained in eigenvectors is ignored. Through analysis, it is found that the elements in the eigenvectors represent the energy differences of seismic traces. By directly measuring the difference of different elements in an eigenvector, the energy differences between different seismic records can be effectively measured. Since the seismic data on both sides of some discontinuous boundaries, such as channel boundaries, principally show amplitude differences, the coherence properties based on eigenvectors can better characterize them. Through theoretical analysis, model testing, and case application, this letter illustrates the reliability of the proposed algorithm.

Internal multiples seriously affecting seismic inversion and imaging need to be suppressed. To suppress internal multiples, we propose a self-supervised deep learning method based on a local orthogonalization constraint (SDL-LOC). The self-supervised deep learning (SDL) consists of one multi-attention-based U-net (MA-net), two input data, and one output data. The predicted internal multiples (PIMs), obtained by the adaptive virtual event (AVE) method, and the original data are used as input data. SDL utilizes the excellent nonlinear optimization capability of MA-net to transform PIMs into the estimated true internal multiples that are the output data of SDL. Finally, the de-multiple result can be obtained by subtracting the output data from the original data. The proposed SDL-LOC uses the local orthogonalization constraint (LOC) function as part of the total loss function. The LOC function can help SDL to correctly maps PIMs into the true internal multiples with the right amplitudes and phases and prevent the output data from containing residual primaries and leaked internal multiples. Our proposed SDL-LOC method does not require true primaries or true internal multiples as the training dataset. Therefore, our proposed method has a wide range of applications and can well solve the problem of missing training datasets. We use the synthetic and land field data examples to demonstrate that our proposed method has a good internal multiple suppression effect.

In seismic data processing, the suppression of internal multiple is a challenging direction. To suppress internal multiples, we propose an unsupervised deep neural network (DNN) method based on adaptive virtual events (AVEs) and joint constraints of multi-DNNs (JCMDNNs). First, we use an AVE method to obtain predicted internal multiples by convolution and cross correlation. The predicted internal multiples can well calibrate true internal multiples and provide good prior information. Second, we use the unsupervised DNN (UDNN) to map the predicted internal multiples to the estimated true internal multiples. Finally, the demultiple results can be obtained by subtracting the estimated true internal multiples from the data containing internal multiples. Three DNNs, one input data, six output data, and six pseudo-labels (PLs), are combined into the base learners and auxiliary learners of UDNN. UDNN uses the nonlinear optimization ability of DNNs to map predicted internal multiples to true internal multiples through the JCMDNNs. Three auxiliary learners correct the outputs of the base learners to reduce the nonlinear mapping deviation of UDNN. Using JCMDNNs by combining all base learners and auxiliary learners is called ensemble learning. Our proposed JCMDNN method does not need true internal multiples and true primaries as the input and output data, which solves the problem of missing training datasets and has wide use ranges. The effectiveness and superiority of our proposed method to suppress internal multiples are demonstrated through two synthetic and one field data examples.

Random noise suppression can greatly improve the signal-to-noise ratio (SNR) of seismic signals. To suppress random seismic noise, we propose an unsupervised deep neural network (UDNN) method based on the local cross-correlation (LCC) loss function and ensemble learning. UDNN with two base learners mainly consists of one input data, two deep neural networks (DNNs), and two output data. The proposed UDNN based on the LCC loss function and ensemble learning (UDNN-LCCEL) method takes full advantage of the nonlinear mapping capabilities of DNNs and maps noisy data into effective noise-free signals by minimizing the total loss function. The total loss function includes the LCC and mean-absolute-error (MAE) loss functions. LCC calculates the local correlation or orthogonalization between output data and the removed noise. By reducing the value of the LCC loss function, we automatically reduce the residual noise and leakage of effective signals in the output data, thus avoiding the overfitting of UDNN. UDNN-LCCEL combines the advantages of two DNNs to obtain ensemble denoised results by ensemble learning. The biggest advantage of our proposed UDNN-LCCEL method is that it does not need to use noise-free data as label data, which can well solve the problem of missing training datasets. The synthetic and field data examples are used to demonstrate that UDNN-LCCEL can achieve good random noise suppression effectiveness.

By increasing the source density, the blended data can significantly improve the seismic data quality. However, the blended data cannot be directly used in the subsequent seismic processing process, and it is necessary to separate the useful signals from the crosstalk noise. For a high-density acquisition with the denser shot coverage survey (DSCS), we propose an unsupervised deep learning (UDL) method to directly deblend the blended data in the common shot gather (CSG). Both the useful signal and the crosstalk noise in the pseudo-deblended data (PDD) are continuously coherent in CSG. By minimizing the final total loss function, the similar coherent signals from the PDD of the main and second sources are extracted using the proposed UDL method. The UDL consists of two U-nets, which extract similar features from the PDD of the main and second sources in the training stage, and directly obtain the deblended results in the test stage. The original unblended data, which may be needed for supervised learning, are not available from the actual collected blended data. However, the proposed UDL method does not require the original unblended data as training data, which solves the lack of training data. The proposed UDL method can be applied to the CSG without providing the delay time and the blending operator, so it has more flexibility. Synthetic data and field data examples show that the proposed UDL method can effectively and directly deblend the blended data in CSG under DSCS.

Normal moveout (NMO) correction is an important step in seismic data processing. Conventional NMO methods, however, suffer from serious stretching distortions, especially at the shallow layer and far-offset traces. These distortions are not conducive to subsequent data processing at all. Reflection seismic interferometry, the cores of which are cross-correlation and stacking, is the latest technology to achieve noise suppression and signal enhancement. Compared with cross-correlation, higher-order cumulants (HOCs) have a better performance of time delay estimation and signal enhancement. To fully exploit its advantages, we propose reflection seismic interferometry based on HOC instead of cross-correlation to solve NMO stretching in this letter. Our proposed method is first tested on synthetic examples and then applied to field data from eastern China. The corresponding results demonstrate that the proposed data-driven method, without the need for velocity information, not only solves the far-offset traces’ stretching distortions of NMO correction, but also has a better noise suppression effect compared with the other two existing methods. These advancements are important to improve the resolution of seismic data and increase amplitude fidelity.

Adaptive surface-related multiple subtraction is an important step of surface-related multiple elimination (SRME) method. Generally, the traditional methods match the predicted multiples with the original data using obtained filter. In this letter, we propose a matching algorithm based on convolutional neural network (CNN) to strike a balance between the attenuation of multiples and the protection of primaries. Taking the predicted surface-related multiples as input, CNN’s output can better match with the original data. From the processing results of synthetic data, compared with the traditional$L_{1}$-norm or$L_{2}$-norm method, CNN method has lower calculation cost and the signal-to-noise ratio (SNR) of the primaries obtained after matching and subtraction is increased by 3 dB. The test of Pluto data and physical simulation data show that the proposed method can effectively remove surface-related multiples in seismic data.

Internal multiple suppression remains a key challenge in seismic processing due to the tiny velocity and periodicity difference between primary reflections and internal multiples. Existing methods suppress internal multiples with poor adaptivity and efficiency. Internal multiple suppression based on artificial intelligence (AI) faces challenges about highly demanded computing resources and the lack of sufficient labels. This letter redesigns a convolutional neural network (CNN) scheme for internal multiple suppression in terms of training set construction and input strategy to alleviate these problems. We adopt the virtual event (VE) method to generate a few primary labels and develop an internal multiple augmentation strategy to expand the training set and improve the network performance based on small data set. The U-shaped CNN is trained based on augmented datasets and then applied to new seismic data. During the training and prediction process, the entire seismic data are split into vertical patches as network inputs for less computing resources and better demultipling performance. Tests on synthetic and field data demonstrate that our method effectively suppresses internal multiples and exhibits a competitive performance in comparison with existing methods and original demultipling CNN in efficiency, memory cost, and primary retention ability.

The dips of underground reflectors indicate their trends and provide a wealth of information about geological structures. It is widely used in seismic data processing and interpretation. The time-frequency spectrum (TFS) can be directly used for dip estimation, and TFS can be obtained by spectrum decomposition techniques such as short-time Fourier transform, Stockwell transform, and continuous wavelet transform. In spectrum decomposition technologies, seismic data are usually multiplied by a window function in the time domain. At the same travel time, all traces in the seismic data are multiplied by the same window function, which burrs the difference in dip and leads to errors in dip estimation. To solve this problem, this letter advocates an algorithm that uses the dip to guide the window function. To enhance the robustness of the algorithm, we introduce the energy weighted average algorithm, and Hilbert transform, into the algorithm. The model testing has verified that our algorithm can estimate dips accurately, and the application of field seismic data has proved the practicability of this algorithm.

The simultaneous source acquisition method, which excites multiple sources in a narrow time interval, can greatly improve the efficiency of seismic data acquisition and provide good illumination. However, the simultaneous source data, also known as the blended data, contain the crosstalk noise from other sources, which brings trouble to the subsequent processing flow. Therefore, an effective deblending method for the simultaneous source data is needed. In order to suppress crosstalk noise, an iterative deblending method using a deep neural network (DNN) trained in the common shot gather (CSG) is developed in this article with the double-blended simultaneous source (DBSS) data being the input data and the blended CSG data being the label data. The proposed training method can not only solve the problem of difficult acquisition of the label data but also make the DNN applicable to any complex formation conditions without considering whether the DNN has the generalization ability of deblending in different work areas. In the test phase, the trained DNN is embedded into the iterative separation framework to deblend the data in the common receiver gather (CRG), which can achieve convergence in a few iterations and achieve a better separation effect. The synthetic and field data examples are tested to verify that the proposed method can effectively suppress the crosstalk noise when deblending the simultaneous source data.

Seismic internal multiples are the key factors affecting the accuracy and reliability of velocity analysis and migration. The removal of internal multiples is a challenging direction. To effectively remove the internal multiples from the seismic data, we propose the unsupervised deep neural network (DNN) combined with the adaptive virtual events (AVEs) method. First, we use the AVE method to get the predicted internal multiples, which can calibrate the true internal multiples in the original data, also called the full wavefield data. Second, the unsupervised learning with the DNN is used as a nonlinear operator to minimize the difference between the estimated internal multiples and original data. The trained DNN can obtain the estimated internal multiples through the predicted internal multiples, thereby completing the suppression of the internal multiples. Since our proposed unsupervised learning is essentially an optimization process, it does not require true primaries as the label data to participate in the training process for the DNN. Therefore, our proposed method can deal with the problem of lack of training set and would have some good practical application value with low computational cost. The effectiveness and efficiency of our proposed method are verified through two sets of synthetic data and one land field data examples.

Surface-related multiples are generally removed as noise. To suppress surface-related multiples, we propose an unsupervised deep neural network approach based on ensemble learning (UDNNEL). The unsupervised deep neural network (UDNN) has excellent nonlinear mapping ability, which maps the predicted surface-related multiples to true surface-related multiples, thereby completing the separation and estimation of multiples and primaries. UDNN consists of three deep neural networks (DNNs), one input data, six outputs, and six pseudo-labels (PLs). In practical use, input data are the predicted surface-related multiples, PLs consist of full-wavefield data and 0 matrices, and outputs are the desired results of estimated true surface-related multiples and differences between these desired results. Input data, one DNN, and corresponding output data are combined into a single base learner. Each base learner corrects amplitudes and phases of the predicted surface-related multiples and maps predicted multiples to true surface-related multiples under the minimization of the total loss function. The principle ensures that our UDNNEL method does not need true primaries or true multiples as training data and solves the problem of missing training datasets. Ensemble learning combines the advantages of three base learners and integrates the nonlinear optimization capabilities of three DNNs to achieve better multiple suppression effectiveness than a single base learner. Therefore, UDNNEL is better than UDNN based on a single base learner (UDNNSBL). Two synthetic data examples verify that our proposed method has good surface-related multiple suppression effectiveness. Another field data example demonstrates that our proposed method can efficiently suppress multiples under complex conditions.

Acquisition technology of multisource data has outstanding advantages in enhancing collection efficiency and reducing cost. However, traditional seismic data processes cannot be applied to multisource blended data. Therefore, deblending technology of multisource data is the key to the research. In this letter, we propose a deblending method of multisource seismic data based on a periodically varying cosine code (PVCC). First, we design a PVCC to blend the seismic data. Next, the blending model is transformed into the minimum problem of the objective function. Then, the blended data are decomposed in the curvelet domain. Finally, the main source data are separated based on sparse inversion. Furthermore, we use the edge processing to eliminate the boundary effect in the processed seismic data. The examples of synthetic data and field data are adopted to demonstrate that the proposed method has great potential in the deblending of multisource data. In addition, the edge processing can effectively suppress the boundary effect.

To eliminate ghost effects, a compressed sensing (CS) pseudo-vertical velocity method is proposed. Based on pressure data acquired using a conventional acquisition configuration, the vertical component of particle velocity at the same receiver positions is estimated using an expanded CS deghosting method. The pseudo-vertical velocity data, combined with the pressure data, are then used for deghosting. The proposed technique is applied to complex synthetic and field data, and improvements in resolution and infilling of frequency notches are achieved for shallow-sea single-component seismic data. In addition, the energy of the low-frequency signal is enhanced. Therefore, this proposed deghosting method has great potential in seismic data processing and subsurface imaging for offshore exploration.

At present, a primary challenge of seismic data processing is the ability to recognize and identify first-break seismic signals with low signal-to-noise ratio (SNR) in mountainous areas. Correlation-based supervirtual interferometry (SVI) can improve the SNR of refractions and diffractions to achieve high-quality results in velocity model construction and diffraction imaging from low SNR data. However, SVI is susceptible to coherent Gaussian noise and is limited to 2-D cases. This paper develops the cumulant-based coherent integration (CCI) method to enhance the first-break signals by using cumulant functions and multiple convolutions for both 2-D and 3-D land seismic data. The 2-D synthetic data example demonstrates that CCI can suppress coherent Gaussian noise and obtain results with higher SNR than SVI. The 3-D synthetic data example demonstrates the effectiveness of the 3-D CCI. Its application to 3-D field exploration seismic data measured in the mountainous areas of western China illustrates that the SNR of the first-break signals is much higher than that obtained by bandpass filtering, which is commonly employed in commercial software today.