Common Midpoint Gather 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.

Inverse Scattering Series Internal Multiple Attenuation in the Common-Midpoint Domain

Internal multiple prediction remains a high-priority problem in seismic data processing, such as subsurface imaging and quantitative amplitude analysis and inversion, particularly in the common-midpoint (CMP) gathers, which contain multicoverage reflection information of the subsurface. Internal multiples, generated by unknown reflectors in complex environments, can be reconstructed with certain combinations of seismic reflection events using the inverse scattering series internal multiple prediction algorithm, which is usually applied to shot records in source–receiver coordinates. The computational overhead is one of the major challenges limiting the strength of the multidimensional implementation of the prediction algorithm, even in the coupled plane-wave domain. In this paper, we first comprehensively review the plane-wave domain inverse scattering series internal multiple prediction algorithm, and we propose a new scheme of achieving 2D multiple attenuation using a 1.5D prediction algorithm in the CMP domain, which significantly reduces the computational burden. Moreover, we quantify the difference in behavior of the 1.5D prediction algorithm for the shot/receiver and the CMP gathers on tilted strata. Numerical analysis of prediction errors shows that the 1.5D algorithm is more capable of handling dipping generators in the CMP domain than in the shot/receiver gathers, and it is able to predict the accredited traveltimes of internal multiples caused by dipping reflectors with small inclinations. For more complex cases with large inclination, using the 1.5D prediction algorithm, internal multiple predictions fail both in the CMP domain and in the shot/receiver gathers, which require the full 2D prediction algorithm. To attenuate internal multiples in the CMP gathers generated by large-dipping strata, a modified version is proposed based on the full 2D plane-wave domain internal multiple prediction algorithm. The results show that the traveltimes of internal multiples caused by dipping generators seen in the simple benchmark example are correctly predicted in the CMP domain using the modified 2D prediction algorithm.

Optimal transmit apodization for the maximization of lag-one coherence with applications to aberration delay estimation

Phase aberration is one of the major sources of image degradation in medical ultrasound imaging. One of the earliest and simplest techniques to correct for phase aberration involves nearest-neighbor cross correlation to estimate delays between neighboring receive channels and the compensation of aberration delays in a delay-and-sum beamformer. The main challenge is that neighboring receive channels may not have sufficient signal correlation to accurately estimate the aberration delays. Although algorithms such as the translating transmit aperture or the common midpoint gather are designed to perfectly maximize signal correlations between received signals, these algorithms require the use of different transmit apertures for each received signal. Instead, this work proposes the use of a single globally-applicable transmit apodization function that optimizes the lag-one coherence based on the van Cittert–Zernike theorem. For the application to phase aberration correction, it is shown across 20 different zero-mean Gaussian-random aberrators that the proposed optimal apodization function reduces the estimation error in the aberration delay profile from 22.85% to 15.72%.

Stochastic velocity modeling for assessment of imaging uncertainty during seismic migration: Application to salt bodies

Variations in the migration velocity model directly affect the position of the imaged reflectors in the subsurface, leading to structural imaging uncertainties. These uncertainties are not explicitly addressed when trying to deterministically build an adequate velocity model. This paper presents a new stochastic geology-controlled velocity modeling method that handles the possible presence of a salt weld. This permits the generation of a large set of geologic scenarios and associated velocity models. Each model is used to remigrate the seismic data. Then, a statistical analysis of the resulting seismic images is performed to quantify the local variability of the seismic responses. The approach is applied to the imaging of salt diapirs in an iterative scheme (migrate, pick, and update). The results indicate that similar to stacking common-midpoint gathers, the statistical analysis preferentially preserves recurrent features from one image to another. In particular, this analysis permits the distinction between the connected and detached diapirs without prior knowledge about their connectivity, highlighting the potential of the method to resolve important aspects of the basin and reservoir architecture. More generally, it provides quantitative information on the parts of the seismic image most sensitive to migration velocity variations, which opens an interesting perspective to quantitative interpretation uncertainty assessment. Finally, the presented application also suggests that it is possible to significantly improve the quality of the generated seismic images by sampling many possible geologic scenarios.

Reduction of normal-moveout stretch using nonstationary scaling transformation in time-frequency domain

The normal-moveout (NMO) stretch causes decrease in the dominant frequency of seismic wavelet after conventional NMO correction and severely damages the quality of the stacked data for shallower reflectors at far offsets. Muting, which is commonly used to handle this problem, reduces seismic fold and negatively affects results of the amplitude-variation-with-offset analysis within the stretched area. We found a novel approach to reduce the stretching phenomenon through compensating the lost frequencies by increasing the dominant frequency of the seismic wavelet before applying the NMO correction. The added so-called compensated frequencies are defined according to the difference between the dominant frequency of the original seismic wavelet and the assumed stretched wavelet after the NMO correction. The corresponding procedure considers frequency content of each time sample along each trace in the time-frequency domain using the Gabor transform. As such, the dominant frequency of the seismic wavelets is increased in a nonstationary manner. Performance of our method is evaluated by applying it on the synthetic and field data examples. The obtained results suggest that this approach provides common-midpoint (CMP) gathers with reduced stretching effect, with the potential to be considered as another alternative for nonstretch NMO correction. However, it should be noted that the presented method resolves neither the problem of intersecting events nor the multiples in the CMP gather. This method also cannot handle highly contaminated noise data and does not contribute in removing multiples during the frequency compensation process.

Analysis of subsurface velocity using CMP gathers picked up by unshielded GPR system: results from an experimental NAPL contaminated test site

Adequate knowledge of velocity is required for accurate data imaging and depth conversion, as well as for quantifying the distribution of soil water content. Without complementary borehole information in the form of dielectric permittivity and/or porosity logs along the profile, it is currently impossible to reliably estimate the high-frequency electromagnetic velocity distribution in the probed subsurface region. Here, we present a new method for calculating the precise subsurface velocity structure from ground penetrating radar (GPR) reflection data that does not require boreholes or log data. This study investigates the ability of the pulse_EKKO PRO GPR system to predict a vertical profile for the possible velocity estimation of a layered and contaminated geophysical test site in Hangzhou, China. All data were acquired and saved on the GPR system in various files (projects) before analysis using GPR software to obtain approximated velocity modelling using common midpoint (CMP) gathers. Using the velocity spectrum analysis, a vertical profile of the interval velocities can be derived from each CMP gather. The findings of this study indicate that the proposed method is effective and sustainable. Furthermore, owing to the efficacy of the method in terms of field effort and computational complexity, it can easily be expanded to 3D GPR velocity exploration, increasing its importance in comparison to standard offset-based techniques for estimating velocity using GPR.

Distributed aberration correction in diagnostic ultrasound by time-delay computation from sound speed estimates using common midpoint gathers

We describe a method of distributed aberration correction from local sound speed estimates of tissue. In this case, compensated beamforming delays are computed using the eikonal equation to account for refracted paths of the ultrasound waves based on an estimation of the local sound speed of the tissue. Signals acquired from a multistatic synthetic aperture sequence are used for image reconstruction in order to refocus the ultrasound beam at every image point without re-transmission. We estimate sound speed using the common midpoint gathers (CMGs) of the synthetic aperture signals, which have high signal coherence that can be used for accurate time measurements. These time measurements are used in overlapping ray paths traced onto a discrete grid to solve an inverse ultrasound computed tomography problem. We separately utilize absolute delay measurements at each depth (to capture axial variations) together with differential time-delays between CMG gathers (to capture lateral variations). For generalized sound speed reconstruction, we balance the contributions of both terms with regularization. In simulations, local sound speed was reconstructed with an rmse of 5.3 m/s in four-layered media and 6.0 m/s in focal lesions. In multilayer propanol/agar phantoms, local sound speed was reconstructed with an rmse of 5.0 m/s.

Full wave seismic exploration technology

Reflected wave seismology has the following defects: the acquisition design is based on the assumption of layered media, the signal processing suppresses weak signals such as diffracted wave and scattered wave, and the seismic wave band after the image processing is narrow. They limit the full utilization of broadband raw data. The concept of full wave seismic exploration is redefined based on the idea of balanced utilization of reflected wave, diffracted wave and scattered wave information, its characteristics and adaptive conditions are clarified. A set of key technologies suitable for full wave seismic exploration are put forward. During seismic acquisition period, it is necessary to adopt multi geometry, i.e. embed small bin, small offset and small channel interval data in conventional geometry. By discretizing of common midpoint (CMP) gathers, small offset with high coverage, the weak signals such as diffracted wave and scattered wave in the raw seismic data can be enhanced. During seismic processing, the signal and noise in the original seismic data need to be redefined at first. The effective signals of seismic data are enhanced through merging of multi-geometry data. By means of differential application of data with different bin sizes and different arrangement modes, different regimes of seismic waves can be effectively decomposed and imaged separately. During seismic interpretation stage, making the most of the full wave seismic data, and adopting well-seismic calibration on multi-scale and multi-dimension, the seismic attributes in multi-regimes and multi-domains are interpreted to reveal interior information of complex lithology bodies and improve the lateral resolution of non-layered reservoirs.

Data-driven reflection imaging based on seismic interferometry

In conventional land seismic exploration, shallow seismic reflections with low fold are usually contaminated by noise and most conventional acquisition geometries struggle to produce sufficient near-offset fold to process shallow seismic reflections based on the velocity model. Deep seismic reflections tend to occur as weak events due to seismic wave absorption and attenuation. To enhance the shallow and deep seismic reflections, we have developed a data-driven reflection imaging method based on seismic interferometry of cross-coherence type, which first retrieves coherent reflections by cross-coherence of full wavefields with zero-offset reflections and then achieves imaging results with high quality by summing all of the crosscorrelations of full wavefields with coherent reflections in a common-midpoint gather. The novel purely data-driven method does not require any velocity information and can flatten noisy interfering reflection events with no waveform distortions. The focusing effects, which represent the stack of all the seismic reflection events, increase the fold of weak seismic reflections and further significantly improve the signal-to-noise ratio of imaging results. In comparison with data-driven reflection imaging methods based on seismic interferometry of crosscorrelation type, our results illustrate that the data-driven reflection imaging method based on seismic interferometry of cross-coherence type can automatically compress the band-limited source signature and make full use of background noise to broaden the bandwidth of reflection signals for achieving imaging results with a higher resolution.

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.

Wavelet estimation and nonstretching NMO correction

Normal-moveout (NMO) correction is an important step applied to common-midpoint (CMP) gathers for subsequent stacking. However, conventional NMO correction methods often suffer from the problem of NMO stretching, which nonlinearly increases with offsets and decreases with zero-offset traveltime. The NMO stretching can be quantified by frequency distortion, so stretching is confined mainly to large offsets and shallow times. To solve this problem, we have proposed a wavelet-based method with the following four steps. First, we estimate a wavelet from the CMP gather by using the NMO stretching appearing in the conventional NMO correction. Second, we deconvolve the original CMP gather based on the estimated wavelet. This step of removing the wavelet from the CMP gather is helpful for the next steps of NMO velocity scan and NMO correction. Third, we apply an improved NMO correction to the deconvolved CMP gather and obtain flattened reflectivities. Finally, we convolve the flattened and deconvolved gather with the estimated wavelet back to obtain an NMO-corrected gather without stretching artifacts. In our method, by using a deconvolved CMP gather, we are able to calculate a high-resolution semblance velocity spectrum that benefits from the NMO velocity picking. In addition, applying the NMO correction to the deconvolved CMP gather, instead of the original gather, is helpful in reducing the NMO stretching related to the wavelet distortion. Tests on synthetic and field data find that our new NMO correction method can estimate an accurate seismic wavelet and obtain an NMO-corrected gather without NMO stretching. Reducing the NMO stretching can significantly improve the resolution of shallow layers at far offsets and preserve the spectral bandwidth.

Multiple attenuation based on connected-component analysis and high-resolution parabolic Radon transform

Multiple attenuation is an important issue in seismic exploration. The high-resolution parabolic Radon transform (RT) is a widely used multiple attenuation method for the advantages of simple principle and low computational cost. In the Radon domain, however, the curvatures of primaries and multiples are difficult to focus on, sometimes even close to or overlap with each other, which makes their separation faces great difficulties, and ultimately leads to multiple leakages existing in the attenuation results. To eliminate the multiple leakages caused by the high-resolution parabolic RT, we propose a new multiple-attenuation method that combines the high-resolution parabolic RT with the connected-component analysis. The high-resolution parabolic RT is used to obtain the estimated multiples in the input data. Based on the estimated multiples, the connected-component analysis can fully use the continuity of multiples in the input data to eliminate the multiple leakages. The industrial model data are validated by both the proposed and the high-resolution parabolic RT methods. Comparing their attenuation results, we conclude that not only does the proposed method achieve better performance even under complex geological structures, it is also suitable for common-midpoint gathers before normal moveout.

Resolution-Oriented Weighted Stacking Algorithm

In this paper, we proposed a weighted stacking algorithm for obtaining high-resolution data and constructed an optimization objective function using the similarity of the stacked amplitude spectrum and constant (amplitude spectrum of impulse function). The optimization problem is solved to obtain the stacking weights involved in the common midpoint (CMP) gathers by using the alternating iterative method of gradient descent and subgradient descent. Then, the weighted stacking is performed to obtain resolution-enhanced data. A traditional post-stack deconvolution algorithm decomposes the data and performs frequency-weighted recombination, which alters the original frequency composition. Furthermore, most existing methods require wavelet estimation, which may be inaccurate. The amplitude-spectrum shape of CMP gather controls the resolution-enhanced data using the proposed method, which is a stacking scheme that does not require wavelet estimation. On the other hand, our proposed stacking algorithm can handle data containing white noise, and we introduce a penalty term to avoid the mutual offset between the effective signals caused by negative weight, which improves the stacked signal-to-noise ratio. Applications to synthetic and field seismic datasets demonstrate that data stacked using the proposed method have higher resolution and can be more easily interpretated compared to the traditional equal-weight stacking.

High-resolution seismic velocity analysis by sign-based weighted semblance

Building an accurate velocity model plays a vital role in routine seismic imaging workflows. Normal-moveout (NMO)-based seismic velocity analysis is a popular method for making the velocity models. However, traditional velocity analysis methodologies are not generally capable of handling amplitude variations across moveout curves, specifically polarity reversals caused by amplitude-variation-with-offset (AVO) anomalies. I have developed an NMO-based velocity analysis approach that circumvents this shortcoming by modifying the conventional semblance (CS) function to include polarity and amplitude correction terms computed using correlation coefficients of seismic traces in the velocity analysis scanning window with a reference trace. Thus, the proposed method workflow is suitable for any class of AVO effects. The approach is evaluated with four synthetic data examples of different conditions and field data consisting of a common-midpoint gather. Lateral resolution enhancement using the proposed method workflow is evaluated by comparison between the results from the workflow and the results obtained by the application of CS and three semblance-based velocity analysis algorithms developed to circumvent the challenges associated with amplitude variations across moveout curves, caused by seismic attenuation and class II AVO anomalies. According to the obtained results, the proposed method is superior to all of the presented workflows in handling such anomalies.

Near Surface Velocity Estimation Using GPR Data: Investigations by Numerical Simulation, and Experimental Approach with AVO Response

The velocity of near-surface materials is one of the most important for Ground-Penetrating Radar (GPR). In the study, we evaluate the options for determining the GPR velocity to measure the accuracy of velocity approximations from the acquired GPR data at an experimental site in Hangzhou, China. A vertical profile of interval velocities can be estimated from each common mid-point (CMP) gather using velocity spectrum analysis. Firstly, GPR data are acquired and analyzed using the popular method of hyperbola fitting which generated surprisingly high subsurface signal velocity estimates while, for the same profile, the Amplitude variation with offset (AVO) analysis of the GPR data (using the same hyperbola fitting method) generate a more reasonable subsurface signal velocity estimate. Several necessary processing steps are applied both for CMP and AVO analysis. Furthermore, experimental analysis is conducted on the same test site to get velocities of samples based on dielectric constant measurement during the drilling process. Synthetic velocities generated by AVO analysis are validated by the experimental velocities which confirmed the suitability of velocity interpretations.

Inversion-based non-stationary normal moveout correction along with prestack high-resolution processing

Seismic wave propagated in viscoelastic media always suffers from amplitude attenuation and velocity dispersion. It not only reduces seismic resolution, but also affects the quality of traditional stationary normal moveout (NMO) correction by distorting wavelets. To address both issues of attenuation and the wavelet stretch simultaneously, we present a non-stationary NMO correction method along with prestack high-resolution processing. Instead of invariant wavelets, spatiotemporal variant wavelets are adopted via an inversion scheme for implementing NMO correction and removing the attenuation effect. In the inversion, two goal-oriented constraints including the temporal sparsity and horizontal coherence of prestack reflectivity are combined into a structural sparsity constraint to impose on the data misfit between the synthetic non-stationary common-midpoint (CMP) gather and the observed one. Both constraints approximately represented by a convex l2,1 norm limit the optimal solution to structural sparsest reflectivity, contributing to construct the flattened corrected gather with invariant wavelets. Synthetic and field data examples illustrate performances of the inversion-based non-stationary NMO correction. Moreover, we compared the corrected gathers obtained by the improved approach with those by the traditional and inversion-based stationary NMO correction approaches, and took the gabor spectrum as a quality control. The proposed method produces more flatten events without stretch and gives consistent frequency components, thus improving prestack seismic resolution.

Pre-stack Q estimation based on inverse spectral decomposition

The quality factor can quantitatively measure the attenuation of seismic waves, and it can compensate for seismic wave amplitude attenuation and correct the phase distortion. The traditional Q extraction method uses the post-stack seismic data to extract the Q-factor. Due to the low-pass filtering effect of the stacked seismic data, the obtained quality factor may be inaccurate. A method of estimating the quality factor using pre-stack common midpoint (CMP) gather data is proposed in this paper. In this method, inversion spectrum decomposition (ISD) and shaping regularization are introduced to obtain the Q-factor. During the process, we obtained the average-Q through inversion and finally obtained the internal-Q by using the average-Q. The numerical simulation and field data application show that the Q obtained using this method can accurately identify the oil-bearing area. Then, the Q is applied to the inverse Q-filter and produces seismic data with a high resolution and a high signal-to-noise ratio.

Application of Velocity Analysis Picking for 2D Seismic Data Processing in West An-Najaf Are

In the current study, 2D seismic data in west An-Najaf (WN-36 line) were received after many steps of processing by Oil Exploration Company in 2018. Surface Consistent Amplitude Compensation (SCAC) was applied on the seismic data. The processing sequence in our study started by sorting data in a common mid-point (CMP) gather, in order to apply the velocity analysis using Interactive Velocity Analysis Application (INVA) with Omega system. Semblance of velocity was prepared to preform normal move-out (NMO) vs. Time. Accurate root mean square velocity (VRMS) was selected, which was controlled by flatness of the primary events. The resultant seismic velocity section for the study area shows that the velocity analysis became smother and provided an accurate seismic section.

Automatic velocity picking from semblances with a new deep-learning regression strategy: Comparison with a classification approach

The physical basis, parameterization, and assumptions involved in root-mean-square (rms) velocity estimation have not significantly changed since they were first developed. However, these three aspects are all good targets for novel application of the recent emergence of machine learning (ML). Therefore, it is useful at this time to provide a tutorial overview of two state-of-the-art ML implementations; we have designed and evaluated classification and regression neural networks for the extraction of apparent rms velocity trajectories from semblance data. Both networks share a similar end-to-end trainable structure, except for the final layer. In the classification network, the velocity picking is performed by finding the largest amplitude trajectory through all velocity bins. The regression network, on the other hand, applies a differentiable soft-argmax function that converts the feature maps directly to apparent rms velocity values as functions of traveltime. Relative confidence maps can also be estimated from both neural networks. A large number of synthetic models with horizontal layers are created, and common-midpoint gathers are simulated from those models as training samples. Transfer learning is applied to fine-tune the networks with a small number of samples for testing with synthetic and field data from more complicated (2D) models. Tests using synthetic data show that the regression and classification networks can give reasonable velocity predictions from semblances, but the regression network gives higher accuracy.

Improving prestack time migration by least-squares equivalent offset method

Time migration is an important tool to provide a subsurface image because it is faster and less sensitive to velocity errors than depth migration. However, a reliable and focused time migration image is achievable only with well-determined time-migration velocities. As an alternative of prestack time migration, equivalent offset migration (EOM) provides intermediate common scatterpoint (CSP) gathers that have higher fold and larger offset range than common midpoint (CMP) gathers, which enables precise focusing of the velocity semblance and accurate velocity analysis. However, direct implementation of EOM might introduce coherent mapping noise, which smears the velocity spectra and decreases the resolution of the final stacked image. We reformulate the EOM as a linear operator that maps CMP gathers to CSP gathers and then propose least-squares equivalent offset migration (LS-EOM) method that inverts for optimal CSP gathers by minimising the misfit between simulated and observed CMP gathers. Compared with the EOM method, LS-EOM provides noise-free CSP gathers, leading to better focusing of the velocity semblance and higher resolution of the final stacked image. Both synthetic and field data tests demonstrate the effectiveness of our proposed method.