Common-receiver Gathers Research Articles

Inversion-Based Deblending in Common Midpoint Domain Using Time Domain High-Resolution Radon

We implement an inversion-based deblending method in the common midpoint gathers (CMP) as an alternative to the standard common receiver gather (CRG) domain methods. The primary advantage of deblending in the CMP domain is that reflections from dipping layers are centred around zero offsets. As a result, CMP gathers exhibit a simpler structure compared to common receiver gathers (CRGs), where these reflections are apex-shifted. Consequently, we can employ a zero-offset hyperbolic Radon operator to process CMP gathers. This operator is a computationally more efficient alternative to the apex-shifted hyperbolic Radon required for processing CRG gathers. Sparse transforms, such as the Radon transform, can stack reflections and produce sparse models capable of separating blended sources. We utilize the Radon operator to develop an inversion-based deblending framework that incorporates a sparse model constraint. The inclusion of a sparsity constraint in the inversion process enhances the focusing of the transform and improves data recovery. Inversion-based deblending enables us to account for all observed data by incorporating the blending operator into the cost function. Our synthetic and field data examples demonstrate that inversion-based deblending in the CMP domain can effectively separate blended sources.

The influence of simultaneous-source survey parameters on deblending performance

Deblending is the dominant way to deal with simultaneous-source data. Each deblending method requires some differences between signal and interference (e.g., coherency difference, dip difference). Those differences are controlled by survey parameters. Except for the encoding scheme, there are still many parameters in simultaneous-source survey controlling the coherency difference. Inappropriate survey parameters lead to unsatisfactorily deblending results. Optimizing survey parameters to obtain the best deblending performance requires understanding the influence of survey parameters on deblending performance. To address the influence of simultaneous-source survey parameters, we simulate the blended datasets with different survey parameters (shot interval, shot number, dithering range and source distance). Inversion methods with two well-known constraints (sparsity and rank-reduction constraints) are implemented to separate the blended data. From the deblended results, some preliminary conclusions can be drawn. Large shot interval reduces the coherency of signal, which is bad for deblending. In common receiver gathers, small shot number shortens the coherency difference between signal and interference, making deblending difficult. A large dithering range can improve the interference incoherence, which is easy to be suppressed by coherency-pass constraint. Large source distance reduces the degree of overlap, which can enhance separation. These conclusions can give the guidance of simultaneous-source survey design, which is beneficial for the successful deblending.

Consistent convolution kernel design for missing shots interpolation using an improved U‐net

ABSTRACTDuring seismic data acquisition, receivers with finer trace intervals can be distributed to record seismic signals. The distance between neighbouring shots, on the other hand, can be significant, resulting in regularly missing shots in the common receiver gathers, which may cause significant spatial aliasing and reduce the precision of later seismic imaging. Traditional interpolation algorithms have several issues and limitations for seismic data with spatial aliasing due to prior assumptions and human–computer interactions. As a result, we present a new deep learning method that includes the generation of adaptive training data and the design of a consistent convolution kernel. Deep learning has the ability to characterize seismic data in a nonlinear manner that is ideal for accurate seismic interpolation. Because the common shot gathers and common receiver gathers have similar features due to the spatial reciprocity of Green's function of the wave equation if all shots have the same physical signatures, the common shot gathers with a refined trace interval are adaptively extracted as the training dataset to guarantee the interpolation performance in the common receiver gathers. With regularly subsampled data as input an improved U‐Net is created and trained to match the desired output, that is, the completed data. The trained network can be deployed to the test common receiver gathers to rebuild regularly missing shots. We develop a novel consistent convolution kernel to ensure high accuracy of missing shot reconstruction while accounting for differences between prestack unmigrated seismic data and images. Using numerically subsampled synthetic and field data, the effectiveness and validity of the developed consistent convolution kernel and the upgraded U‐Net with adaptive training data for missing shot interpolation are demonstrated.

An unsupervised learning approach to deblend seismic data from denser shot coverage surveys

SUMMARY The simultaneous source data obtained by simultaneous source acquisition contain crosstalk noise and cannot be directly used in conventional data processing procedures. Therefore, it is necessary to deblend the blended wavefield to obtain the conventionally acquired single-shot recordings. In this study, we propose an iterative inversion method based on the unsupervised deep neural network (UDNN) to deblend the simultaneous source data from a denser shot coverage survey (DSCS). In the common receiver gather (CRG), the coherent effective signals in the blended data of the primary and secondary sources are similar. We exploit the excellent nonlinear optimization capability of the U-net network to extract similar coherent signals from the blended data of the primary and secondary sources by minimizing the total loss function. The proposed UDNN method does not need to use the raw unblended data as label data, which solves the problem of missing label data and is suitable for deblending the simultaneous source data in different work areas with complex underground structures. One synthetic data and one field data examples are used to prove that the proposed method can suppress crosstalk noise and protect weak effective signals effectively, and achieve good effectiveness for the separation of simultaneous source data.

Reflection residual statics estimated using a high-resolution neural network

Performing reflection statics corrections for improving seismic imaging is an important step in land and shallow marine data processing. The reflection residual statics solution is commonly derived from stack power maximization with hyperbolic assumptions that are valid for normal moveout (NMO) correction and stacking. We have developed a deep learning method for deriving surface-consistent reflection residual statics directly from common-shot, common-receiver, or common-midpoint gathers without velocity analysis and NMO correction. To mitigate overfitting and improve generalization ability, we augment training data by using only a few gathers but massive synthetic statics values. Because the magnitude of residual statics is often small, we apply a high-resolution neural network as a backbone to learn detailed features. We also design the head of the neural network to allow multiscale training and multiscale testing, which enables different acquisition geometries for prediction. Training with labeled samples from synthetic or real data has been tested with new real data as prediction inputs. In both cases, residual statics help improve stacked sections. If the NMO assumption is valid, our method produces results comparable to stack power maximization with much less computation time. If the NMO assumption is invalid, our method produces better results than stack power maximization.

Seismic Interferometry in Linear Radon Domain Applying to Noise Passive Data

We explored a new method for noise passive data to retrieve the virtual-source gathers in linear Radon domain. Seismic interferometry based on the cross correlation algorithm can be viewed as cancellation of a common part of a raypath from a physical source to two different receivers, and a stacking operator is then applied to the crosscorrelagram to take advantage of the contributions from all the sources. As the contributions of retrieving the virtual-shot gathers mainly come from the stationary-phase point, limited passive data with the same ray-parameter plays the major role. That is, the interference effects of most of passive data are counteracted through stacking with each other. Seismic interferometry in linear-Radon domain is proposed for selecting traces with the same ray parameters to retrieve the virtual-shot gathers. As the common-receiver gathers are needed by linear-Radon interferometry, a rearranged operator is used to rearrange noise passive data according to the periodicity. In this way, the common-receiver gathers of noise passive data can be obtained. Then, the common-receiver gathers are transformed into linear-Radon domain and the selected-ray range is used for cross correlation, which can save the computation time significantly. That has important practical significance in processing noise passive data.

Deblending of Seismic Data Based on Neural Network Trained in the CSG

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.

Intelligent Seismic Deblending Through Deep Preconditioner

Seismic deblending is an ill-posed inverse problem that involves counteracting the effect of a blending matrix derived from the shots position and firing time. In this letter, we propose a seismic deblending method based on so-called deep preconditioners. A convolutional Autoencoder (AE) is first trained in a patch-wise fashion to learn an effective sparse representation of the common receiver gathers (CRGs) we aim to reconstruct. Then, the decoder branch of the trained AE is used as a nonlinear preconditioner for the deblending problem. Particularly, to avoid the explicit creation of a training dataset, we suggest to use the common shot gathers (CSGs) of the blended dataset itself to train the AE network, as they are not affected by incoherent blending noise. Numerical examples on synthetic and field datasets demonstrate the effectiveness of the proposed method in comparison with significantly comparable techniques: a dictionary-learning based deblending method; an end-to-end deblending convolution neutral network (CNN).

Iterative Deblending of Simultaneous-Source Seismic Data via a Robust Singular Spectrum Analysis Filter

We solve the simultaneous source separation problem by adopting the projected gradient descent (PGD) method to iteratively estimate the data one would acquire via a conventional seismic acquisition. The projection operator is a windowed robust singular spectrum analysis (SSA) filter that suppresses source interferences in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f-x$ </tex-math></inline-formula> (frequency-space) domain. We reformulate the SSA filter as a robust optimization problem solved via a bifactored gradient descent (BFGD) algorithm. Robustness becomes achievable by adopting Tukey’s biweight loss function for the design of the robust SSA filter. The SSA filter requires breaking down common-receiver gathers or common offset gathers into small overlapping windows. The traditional SSA method needs the filter rank as an input parameter, which can vary from window to window. The latter has been a shortcoming for the application of classical SSA filtering to complex seismic data processing. The proposed robust SSA filter is less sensitive to rank-selection, making it appealing for deblending applications that require windowing. Additionally, the robust SSA projection provides an effective attenuation of random source interferences during the initial iterations of the PGD method. Comparing classical and robust SSA filters, we also report an acceleration of the PGD method convergence when we adopt the robust SSA filter. Finally, we provide synthetic and real data examples, and discuss heuristic strategies for parameter selection.

Reverse Time Migration of Vertical Cable Seismic Data to Image Hydrate-Bearing Sediments With High Resolution

Marine vertical cable seismic (VCS) is a promising survey technique for submarine complex structure imaging and reservoir monitoring, which uses vertical arrays of hydrophones deployed near the seafloor to record seismic wavefields in a quiet environment. Recently, we developed a new type of distributed VCS system for exploration and development of natural gas hydrates preserved in shallow sediments under the seafloor. Using this system and air-gun sources, we accomplished a 3D VCS yield data acquisition for gas hydrates exploration in the Shenhu area, South China Sea. In view of the characteristics of VCS geometry, we implement reverse time migration (RTM) on a common receiver gather to obtain high-resolution images of marine sediments. Due to the unique acquisition method, it is asymmetrical for the reflection path between the sources and the receivers in the VCS survey. Therefore, we apply accurate velocity analysis to common scatter point (CSP) gathers generated from common receiver gathers instead of the conventional velocity analysis based on common depth point gathers. RTM with this reliable velocity model results in high-resolution images of submarine hydrate-bearing sediments in deep water conditions. The RTM imaging section clearly shows the bottom simulating reflector (BSR) and also the reflection characteristics of the hydrate-bearing sediments filled with consolidated hydrates. Moreover, its resolution is relative to that of acoustic logging curves from the nearby borehole, and this imaging section is well consistent with the synthetic seismogram trace generated by the logging data. All these results reveal that VCS is a great potential technology for exploration and production of marine natural gas hydrates.

A method for adequate selection of training data sets to reconstruct seismic data using a convolutional U-Net

Deep-learning (DL) methods have recently been introduced for seismic signal processing. Using DL methods, many researchers have adopted these novel techniques in an attempt to construct a DL model for seismic data reconstruction. The performance of DL-based methods depends heavily on what is learned from the training data. We focus on constructing the DL model that well reflect the features of target data sets. The main goal is to integrate DL with an intuitive data analysis approach that compares similar patterns prior to the DL training stage. We have developed a two-sequential method consisting of two stages: (1) analyzing training and target data sets simultaneously for determining the target-informed training set and (2) training the DL model with this training data set to effectively interpolate the seismic data. Here, we introduce the convolutional autoencoder t-distributed stochastic neighbor embedding (CAE t-SNE) analysis that can provide the insight into the results of interpolation through the analysis of training and target data sets prior to DL model training. Our method was tested with synthetic and field data. Dense seismic gathers (e.g., common-shot gathers) were used as a labeled training data set, and relatively sparse seismic gathers (e.g., common-receiver gathers [CRGs]) were reconstructed in both cases. The reconstructed results and signal-to-noise ratios demonstrated that the training data can be efficiently selected using CAE t-SNE analysis, and the spatial aliasing of CRGs was successfully alleviated by the trained DL model with this training data, which contain target features. These results imply that the data analysis for selecting target-informed training set is very important for successful DL interpolation. In addition, our analysis method can also be applied to investigate the similarities between training and target data sets for other DL-based seismic data reconstruction tasks.

Simultaneous‐source deblending using adaptive coherence‐constrained dictionary learning and sparse approximation

ABSTRACTThe dictionary learning and sparse approximation method using the K‐singular value decomposition algorithm rely on the knowledge of the sparsity or noise variance as a constraint when it is used for data denoising. However, the determination of the sparsity or noise variance of seismic data can be tricky and sometimes unknown, especially in seismic field data. Thus, where the cardinality or the noise variance is not known, the intrinsic character of the relative coherence between the removed noise from noisy data and its learned dictionary is instead used as a constraint for the sparse approximation of simultaneous‐source seismic data. The dictionary learning is obtained using a modified orthogonal matching pursuit algorithm which uses coherence as a constraint and is referred to as coherence dictionary learning. The coherence dictionary learning is then adapted to handle the simultaneous‐source seismic data deblending. A blending structure with random time dithering of sequential source shooting is used to guarantee adequate randomness of the noise. Two‐dimensional overlap patches of the noisy data were extracted from the common receiver gather domain to train the dictionary and to determine the sparse representation of the signal. The method is tested on both synthetic and field data, and it shows adequate data recovery. Comparing the result of this method to the matching pursuit algorithm constrained by the signal sparsity and the noise variance reveals that our approach performs better at noise attenuation and yields a reasonable data recovery especially for strong seismic signal.

Full-waveform inversion strategies using common-receiver gathers for ocean-bottom cable data

Full-waveform inversion (FWI), which is among the most powerful seismic data processing techniques for imaging subsurface geological structures, has a huge computational cost in proportion to the number of sources. To increase the speed of FWI, we explored the use of common-receiver gathers (CRGs) as an alternative to common-shot gathers (CSGs) as observed data. This approach has the potential to reduce the computational cost of FWI significantly, particularly for ocean-bottom cable (OBC) acquisition. As we match modelled and observed CSGs in CSG-based FWI, we match observed CRGs with modelled CSGs of switched source–receiver geometry in CRG-based FWI. According to the reciprocity principle, CRG FWI based on the steepest descent or Gauss–Newton method yields the same inverted velocity models as CSG FWI for an identical and known source signature applied over whole source positions. However, when the source wavelet is unknown, and changes from one source position to another, each trace of a CRG contains a different source signature, making it difficult to apply conventional source estimation or source-independent methods to CRG FWI. Therefore, in this study, we proposed inversion strategies for CRG FWI in both the time and frequency domains to deal with errors arising from different source wavelets between CRG traces. Then, we used a synthetic example for the Marmousi-II model and a real data example from the North Sea to demonstrate that our strategies for CRG FWI provide very similar inverted velocity models to those obtained from CSG FWI, at a lower computational cost.

Source deghosting of coarsely sampled common-receiver data using a convolutional neural network

It is well known that source deghosting can best be applied to common-receiver gathers, whereas receiver deghosting can best be applied to common-shot records. The source-ghost wavefield observed in the common-shot domain contains the imprint of the subsurface, which complicates source deghosting in the common-shot domain, in particular when the subsurface is complex. Unfortunately, the alternative, that is, the common-receiver domain, is often coarsely sampled, which complicates source deghosting in this domain as well. To solve the latter issue, we have trained a convolutional neural network to apply source deghosting in this domain. We subsample all shot records with and without the receiver-ghost wavefield to obtain the training data. Due to reciprocity, these training data are a representative data set for source deghosting in the coarse common-receiver domain. We validate the machine-learning approach on simulated data and on field data. The machine-learning approach gives a significant uplift to the simulated data compared to conventional source deghosting. The field-data results confirm that the proposed machine-learning approach can remove the source-ghost wavefield from the coarsely sampled common-receiver gathers.

Deep-learning seismic full-waveform inversion for realistic structural models

Velocity model inversion is one of the most important tasks in seismic exploration. Full-waveform inversion (FWI) can obtain the highest resolution in traditional velocity inversion methods, but it heavily depends on initial models and is computationally expensive. In recent years, a large number of deep-learning (DL)-based velocity model inversion methods have been proposed. One critical component in those DL-based methods is a large training set containing different velocity models. We have developed a method to construct a realistic structural model for the DL network. Our compressional-wave velocity model building method for creating dense-layer/fault/salt body models can automatically construct a large number of models without much human effort, which is very meaningful for DL networks. Moreover, to improve the inversion result on these realistic structural models, instead of only using the common-shot gather, we also extract features from the common-receiver gather as well. Through a large number of realistic structural models, reasonable data acquisition methods, and appropriate network setups, a more generalized result can be obtained through our proposed inversion framework, which has been demonstrated to be effective on the independent testing data set. The results of dense-layer models, fault models, and salt body models that we compared and analyzed demonstrate the reliability of our method and also provide practical guidelines for choosing optimal inversion strategies in realistic situations.

Seismic imaging of S-wave structures of shallow sediments in the East China Sea using OBN multicomponent Scholte-wave data

The shear-wave (S-wave) structures of shallow marine sediments are important for offshore geotechnical studies, deep crustal S-wave imaging, multicomponent seismic exploration, and underwater acoustics studies. We have applied the multicomponent Scholte-wave analysis technique to an active-source shallow marine seismic profile in the East China Sea. Scholte waves have been excited by shots from a 5450 inch3air-gun array and their recordings have been conducted at the seafloor using ocean bottom nodes (OBNs). First, we extract the common-receiver gathers (CRGs) and correct for the time drift simultaneously using a forward and inverse fast Fourier transform resampling algorithm. Three CRGs of seismic sensors are used for Scholte-wave analysis. Raw sensor CRGs are rotated to the inline, crossline, and vertical coordinate system. The rotated tilt and roll angle are directed using the inner electric compass log value, and the shot inline azimuth is estimated using the particle motion method. Then, the velocity spectra are calculated from the inline and vertical components using the phase-shift method. Higher Scholte-wave modes dominate on the horizontal components, whereas the stronger fundamental mode dominates on the vertical components. The multicomponent velocity spectrum stacking method is adopted to produce the final dispersion energy image. Up to four modes of dispersion curves are retrieved within the 1.1–4.3 Hz frequency band. The multimode dispersion curve inversion is constructed for imaging the shallow sediments. The results suggest a low [Formula: see text] of 180–650 m/s and few lateral variations within the top 0.5 km of shallow marine sediments in the East China Sea. This model can provide an important reference for offshore geotechnical investigations, especially for OBN multicomponent seismic exploration data processing. The use of OBNs has high feasibility in [Formula: see text] imaging for shallow marine sediments when combined with the Scholte-wave dispersion-curve inversion.

Inversion‐based deblending using migration operators

ABSTRACTIn this paper, we compare the denoising‐ and inversion‐based deblending methods using Stolt migration operators. We use Stolt operator as a kernel to efficiently compute apex‐shifted hyperbolic Radon transform. Sparsity promoting transforms, such as Radon transform, can focus seismic data into a sparse model to separate signals, remove noise or interpolate missing traces. Therefore, Radon transforms are a suitable tool for either the denoising‐ or the inversion‐based deblending methods. The denoising‐based deblending treats blending interferences as random noise by sorting the data into new gathers, such as common receiver gather. In these gathers, blending interferences exhibit random structures due to the randomization of the source firing times. Alternatively, the inversion‐based deblending treats blending interferences as a signal, and the transform models this signal by incorporating the blending operator to formulate an inversion problem. We compare both methods using a robust inversion algorithm with sparse regularization. Results of synthetic and field data examples show that the inversion‐based deblending can produce more accurate signal separation for highly blended data.

Intelligent Missing Shots’ Reconstruction Using the Spatial Reciprocity of Green’s Function Based on Deep Learning

The trace interval in the common shot and receiver gathers is always inconsistent. The inconsistency affects the final performance of seismic data processing, and the reconstruction methods can enhance the consistency. Unfortunately, most interpolation algorithms are suitable in randomly missing cases, and the difficulty increases sharply in regularly missing cases, especially with big gaps. As deep learning (DL) has a strong self-learning ability in nonlinear characterizations to avoid linear events, sparsity, and low rank assumptions, we introduce DL into missing shots’ reconstruction. The spatial reciprocity of Green’s function is used to provide reasonable training data sets. First, the residual learning networks (ResNets) and the interpolation issue are briefly illustrated. Then, the spatial reciprocity is reviewed and illustrated qualitatively using the common shot and receiver gathers. The similar features in the common shot and receiver gathers guarantee the reasonability to regard the common shot gathers as the training sets and to regard the common receiver gathers as the test sets. The common shot gathers are divided into the training sets to train ResNets and the validation sets to verify the performance of the trained ResNets. Finally, the trained ResNets are used to reconstruct missing shots intelligently in the common receiver gather. Three different data sets are used to prove the validity of the proposed strategy. After reconstruction, the events are more continuous with less serrations and serious frequency wavenumber (FK) aliasing is attenuated effectively. The reconstructed data with a better consistency can improve the accuracy of migration and the final reservoir characterization.

2D Synthetic Emitter Array methodology for improving GPR reflections

Synthetic 1D-arrays of emitters are used in the area of GPR to improve primary reflections that in single-offset profiles show low continuity and amplitude due to the interference of clutter and noise. In this methodology, at each array position along the survey line, a series of single emitter-receiver measurements is performed, keeping the position of the receiver constant and placing consecutively the emitter at the positions of the nodes of the array grid. A definite phase relation between the traces that constitute each common receiver gather is established and used to shift them in time with respect to the reference-offset trace, and the results are averaged. The phase relations are defined in order to superpose constructively the primary reflections, and reduce the random noise and clutter. The 1D synthetic procedure is equivalent to narrowing the transmitted electromagnetic wave-front along the direction of a real 1D array, which reduces the interference produced by reflectors located in formerly illuminated regions of the soil, and directing the field along an emitters-reflector-receiver path that maximizes the amplitude of the primary reflection at the position of the receiver with respect to the other reflections.In this article, a previously developed 1D-array method is extended to 2D-arrays, and the results of the 2D extension are analyzed and compared to the results of the 1D-array, Common-Midpoint and Single Offset techniques. The proposed 2D procedure considers a rectangular, homogeneous geometry for the array and a simple phase-relation between the component traces. In addition to directing the wave-front towards the target, these settings make possible to reduce the width of the wave-front along both axes of the array, which is expected to enhance the 1D results. Since the dimensionality increases in the 2D geometry, the number of traces in the summation grows significantly, which should also improve the final result. As a part of the 2D methodology, a variable that represents the reflection improvement, with respect to the Single Offset method, is defined and optimized as a function of the phase differences between adjacent traces along both directions of the array and the position of the emitters-receiver group along the survey line. A final data-section is generated from the optimal values found in this step. To evaluate the results of these methodologies, two basic types of reflections are analyzed: diffractions produced by small objects and reflections at extensive interfaces. Numerical and laboratory data are considered. The effects of different numbers of emitters and distances between them on the results are investigated, in order to obtain the best result. The 2D method shows noticeable enhancements of the continuity and amplitude of the primary reflection with respect to the other methods.

Fast least-squares reverse time migration of VSP free-surface multiples with dynamic phase-encoding schemes

For vertical seismic profile (VSP), free-surface multiples can provide much wider subsurface illumination when compared with primaries. However, migration of multiple reflections generates not only the desired image of reflection interfaces but also many crosstalk artifacts. Therefore, the least-squares reverse time migration method is used to image the VSP downgoing free-surface multiples (receiver-side ghosts) and iteratively suppress crosstalks, in which full downgoing data (including direct waves) and downgoing multiples are used as sources and observed data, respectively. To reduce the computational cost, we have developed the simultaneous imaging of different common-receiver gathers that are dynamically blended together with iterations through the altered realizations of the phase-encoding function. Relative to the popular encoding function with a combination of random time delays and polarities, only the random polarities can be applied for further increasing the computational efficiency. Synthetic experiments on Sigsbee2B and Pluto1.5 models indicate that the proposed method can effectively eliminate crosstalk artifacts and improve imaging resolution while calculated even more efficiently than reverse time migration of VSP ghosts.