Velocity-independent normal moveout correction based on multiscale dynamic time warping

Seismic data processing is essential in hydrocarbon exploration, with normal moveout (NMO) correction being a pivotal step in enhancing seismic signal quality. However, conventional NMO correction often suffers from the stretch effect, which distorts seismic reflections and degrades data quality, especially in long-offset data. This study addresses the issue by analyzing synthetic models and proposing a nonhyperbolic stretch-free NMO correction technique. The proposed method significantly improves seismic data quality by preserving up to 90% of the original amplitude, maintaining frequency content stability at 30 Hz, and achieving a high reduction of stretch-related distortions. Compared to conventional NMO, our technique results in clearer seismic gathers, enhanced temporal resolution, and more accurate velocity models. These improvements have substantial implications for high-resolution subsurface imaging and precise reservoir characterization.This work offers a robust and computationally efficient solution to a longstanding limitation in seismic processing, advancing the reliability of exploration in geologically complex environments.

Two-way traveltime (TWT) is one of the most important seismic attributes for reservoir characterization. Erroneous analysis of TWT can lead to incorrect estimates of velocity models resulting in improper structural interpretation of the subsurface. TWT analysis starts with the most fundamental step of seismic data processing, namely, normal moveout (NMO) correction. NMO correction is generally performed in the offset-time (X-t) domain, by fitting a hyperbolic curve to the observed traveltimes corresponding to each reflection event. The commonly used NMO equation is valid for small offsets and does not consider anisotropy — an effect commonly observed in fractured media. The performance of NMO correction depends on the quality of data in the prestack domain and the underlying geology. In the plane wave (τ-p) domain, the estimation of layer parameters can be done using an exact equation for delay-time free from the approximation errors present in the X-t domain. In this domain, a layer stripping approach can also be used to account for the presence of multiple anisotropic and isotropic layers.

Summary Numerical and physical modelling studies have been used to investigate the accuracy and limitations of the small-offset P-wave NMO velocity estimation in transversely isotropic media. An expression for the P-wave small-offset NMO velocity for a single horizontal reflector in a vertically transversely isotropic layer has been previously obtained: V nmo =+ αδ 0 12 where αο and δ respectively represent the vertical P-wave velocity and the P-wave critical anisotropy at oblique angles. The above equation is presented as being exact and valid for any degree of anisotropy and has been used in estimating the small-off set NMO velocity in the offshore Zaire seismic data acquired by Unocal in West Africa. The accuracy of this expression is subject t o practical testing in this paper. A one-layer horizontal model was used to carry out the numerical modelling studies. A computer program which calculates Pwave NMO velocities in transversely isotropic media was used. This program uses the exact equations for the phase and ray velocities in generating velocity functions to be used in ray tracing; it is known to give accurate results. Using the publishe d elastic parameters for anisotropic rocks, the small-offset NMO velocities are computed and results are compared with values obtained using the above expression. The degree of anisotropy varied from very weak to strong and contrasting velocity function s (positive and negative δ) were used in numerical modelling simulations. Phenolite materials with contrasting velocity functions were used to simulate transversely isotropic media with vertical axis of symmetry in physical modelling tests. Experimental reflection data were collected and velocity analysis was conducted for small-offset tr aces, and the NMO velocity determined by the maximum stack response. The elastic parameters αο and δ of the Phenolite materials were recovered by an anisotropic inversion technique. These parameters were used to estimate the small-offset P-wave NMO velocity in Phenolite with the above expression and also with our computer program. The NMO velocities obtained from these two methods were compared to that obtained from velocity analysis of the experimental seismic data. These comparisons enabled the validity of the above expressio n to yield accurate P-wave NMO velocity, in the limit of small offset, to be tested. Numerical and physical modelling results indicate that the accuracy of the small-offset P-wave NMO equation depends on the nature and degree of the anisotropy encountered in a given area, and is not valid for all degrees of P-wave anisotropy. The sma lloffset NMO (stacking) velocity from horizontal reflectors is known to influence the effects of vertical transverse isotropy on normal moveout (NMO), dip moveout (DMO) corrections and time migration. Determination of the correct small-offset P-wave NMO velocity is essential for obtaining accurate seismic images, and subsequently correct interpretations.

The normal moveout correction(NMO) is an important step in seismic data processing.After the digital NMO correction,the events with large ratio of offset and reflection depth have the phenomenon of stretch and distortion.NMO mute causes the loss of effective data with large ratio of offset and reflection depth.Conclusions can be drawn through theoretical calculation.If the events are overlapped,they have the maximum stretch value.After the correction,the events having the appearance of distortion and the number will be increased.Otherwise,the events will show a fat wave shape,the dominant frequency will decrease,the frequency band will be narrow and the amplitude larger.Therefore,it's significant to study the non-stretch correction method.With the method,the signal-noise ratio and resolution of seismic data can be improved.Using the spectrum based moveout method,the information of large offset and effective stacking times increase.The events will be more continuous and become easier to recognize and trace.This method is suitable for marine seismic data processing.

A prestack time migration is presented that is simple, efficient, and provides detailed velocity information. It is based on Kirchhoff prestack time migration and can be applied to both 2-D and 3-D data. The method is divided into two steps: the first is a gathering process that forms common scatterpoint (CSP) gathers; the second is a focusing process that applies a simplified Kirchhoff migration on the CSP gathers, and consists of scaling, filtering, normal moveout (NMO) correction, and stacking. A key concept of the method is a reformulation of the double square‐root equation (of source‐scatterpoint‐receiver traveltimes) into a single square root. The single square root uses an equivalent offset that is the surface distance from the scatterpoint to a colocated source and receiver. Input samples are mapped into offset bins of a CSP gather, without time shifting, to an offset defined by the equivalent offset. The single square‐root reformulation gathers scattered energy to hyperbolic paths on the appropriate CSP gathers. A CSP gather is similar to a common midpoint (CMP) gather as both are focused by NMO and stacking. However, the CSP stack is a complete Kirchhoff prestack migrated section, whereas the CMP stack still requires poststack migration. In addition, the CSP gather has higher fold in the offset bins and a much larger offset range due to the gathering of all input traces within the migration aperture. The new method gains computational efficiency by delaying the Kirchhoff computations until after the CSP gather has been formed. The high fold and large offsets of the CSP gather enables precise focusing of the velocity semblance and accurate velocity analysis. Our algorithm is formulated in the space‐time domain, which enables prestack migration velocity analysis to be performed at selected locations and permits prestack migration of a 3-D volume into an arbitrarily located 2-D line.

Deep-learning-based methods have been successfully applied to seismic data random noise attenuation. Among them, the supervised deep-learning-based methods dominate the unsupervised ones. The supervised methods need accurate noise-free data as training labels. However, the field seismic data cannot meet this requirement. To circumvent it, some researchers utilized realistic-looking synthetic data or denoised results via conventional methods as labels. The former ones encounter the problem of weak generalization ability because it requires the same distribution of test and training data. The latter ones encounter the issue of insufficient denoising ability because its denoising ability is difficult to significantly exceed the conventional methods which were used to generate labels. To avoid preparing noise-free labels, we propose a novel deep learning framework for attenuating random noise of prestack seismic data in an unsupervised manner. The prestack seismic data, such as common-reflection-point (CRP) gathers and common-midpoint (CMP) gathers after normal moveout (NMO) correction, have high self-similarity. It is because their events are coherent in the time–space domain and approximately horizontal from shallow to deep layers. The generator convolutional neural network (GCN) first learns self-similar features before any learning. The useful signals are more self-similar than random noise, which is incoherent and randomly distributed. Therefore, the GCN extracts features of useful signals before random noise. We select the specific training iteration and adopt the early stopping strategy to suppress random noise. Both synthetic and field prestack seismic data examples demonstrate the validity of our methods.

Summary Transversely isotropic with vertical symmetry axis (VTI) is a practical assumption for wave propagation environment in many 2D seismic data, due to its acceptable accuracy and limited number of input parameters. Explicit VTI traveltime approximations are commonly used in many seismic data processing and inversion algorithms. In this study we propose a new traveltime approximation for P-wave propagation in VTI media that is more accurate than the previously reported most accurate approximations. We compare its accuracy, and show that it can outperform other three-parameter approximations in velocity analysis and normal moveout correction.

Moveout correction for irregular topography has been a longstanding challenge in processing seismic exploration data. Irregular topography usually results in large moveout among traces, a low signal-to-noise ratio (S/N), and difficulty in modeling near-surface velocities. Conventional normal moveout (NMO) corrections and elevation static methods are imprecise and tend to introduce significant errors for large offsets. Over the past two decades, several multiparameter time corrections and stacking techniques to reduce noise and improve resolution have been proposed in place of the classic NMO and common-midpoint stack. These include the common-reflection-surface (CRS), common-offset CRS, nonhyperbolic CRS, implicit CRS, multifocusing (MF), irregular surface MF (IS-MF), spherical MF (SMF), and common-offset MF methods. Various CRS-type operators that consider the top-surface topography have been proposed. For MF-type operators, only IS-MF can be applied directly to the irregular topography with no elevation statics required. In this study, we have developed a new MF formulation, modifying the SMF method to consider nonzero elevations of sources and receivers and we corrected moveout of nonplanar data directly without prior elevation static corrections. The proposed extension combines the sensitivity to spherical reflectors of SMF with the applicability of the IS-MF method to irregular topography. We investigated the behavior of the new operator using a physical model data set and compared the results with those from the conventional IS-MF method. The results revealed that the new operator is more robust over a wide range of source and receiver elevations and has advantages on strongly curved interfaces. We also confirmed the potential of the proposed approach by comparing stacking results for a real-land data set with a low S/N.

This article presents the pre-stack attenuation of multiple noises from a 2-D land seismic survey acquired on the Iraq-Kuwait border in southern Iraq. The processing workflow is performed using the Geovation software from CGG that employs a de-aliased High-Resolution Radon with a non-iterative process for seismic reflection data. First, we apply noise attenuation, surface deconvolution (predictive), and normal move-out (NMO) correction, which is executed using the root-mean-square velocity (RMS velocity) to flatten the primary event, and the Common Mid-Point gathers (CMP gathers) are converted into the Radon domain using a least-squares-parabolic Radon transform. Several tests are performed on some parameters to predict the multiple events using a High-Resolution de-aliased multiple attenuation (RAMUR) algorithm aimed to attenuate multiple events. RAMUR algorithms compute a model of primary and multiple events based on data decomposition into user-defined parabolas and are performed using a high-resolution, de-aliased least-squares method. The Radon transforms separate primary reflection and multiple reflection events in the (τ-q) domain based on move-out differences between primary and multiple events, which are characterized as events with slower velocity. Reflection events relating to parabolas with a higher curvature are counted as multiples, whereas events with smaller are counted as primary events. The RAMUR algorithms subtract the model of multiples from the input gathers. The workflow effectively attenuates reflection-based generated multiples events, which improves the overall seismic response after imaging, and enhances correlation with well information.

Two component ocean bottom cable (2C OBC) data are often affected by substantial noise. The noise is probably caused by shear wave energy registered on the vertical geophone. It exhibits random properties in common shot domain but coherent properties in common receiver domain. This phenomenon is observed in most OBC surveys worldwide, and the noise level can be very substantial. Typically, there is a substantial move out difference between the noise and the signal, i.e., reflected PP waves, allowing use of velocity filtering for noise suppression. Velocity of sound in water can be used as a quite universal parameter for normal moveout (NMO) correction before the velocity filtering. The NMO correction substantially simplifies design of the velocity filter. Efficiency of the proposed approach is illustrated using real 2C OBC data.

Velocity picking is to pick several peaks on seismic semblance image (stacking energy) that is very important in seismic data processing. In time-velocity semblance image, these chosen peaks are representing the relation of stacking velocity and time. In this study, we apply simulated annealing (SA) on seismic velocity picking problem and use two constraints in the energy function of SA algorithm for searching a best peak point combination. After obtaining the best polyline, we use the picking result to perform further seismic data processing including normal move-out (NMO) correction and common midpoint stacking. This method automates the velocity picking procedure with short period of time and improves the further seismic data interpretation.

The double‐square‐root (DSR) equation used in pre‐stack migration is formulated in terms of velocity‐dependent and velocity‐independent terms. The velocity‐dependent term is shown to be the hyperbolic normal moveout (NMO) correction, whereas the velocity‐independent term is related to the recording geometry only. This separation of the velocity‐dependent term offers a means of applying vertical corrections to an initial migration velocity field. Using this concept, procedures are described both for velocity determination and for achieving improved structural imaging.This decoupling is accurate both for constant‐velocity media and for media whose velocity varies as a function of depth. In media whose velocity varies as a function of both space and depth, a procedure is described for building velocity models through common‐image gather (CIG) stacking following prestack depth migration (PSDM) and time conversion (TC). This so‐called PSDM‐TC stack procedure provides a means of (a) incorporating both vertical and lateral velocity updates into an initial velocity model, (b) obtaining improved structural imaging by using a non‐optimal velocity model for the prestack depth migration, and (c) updating velocity by flattening CIGs and maximizing stack energy. The procedure can be applied to both P‐P wave and P‐SV wave migration.

The high-density acquisition technique can improve subsurface imaging accuracy. However, it increases production cost rapidly and limits the wide application in practice. To solve this issue, the high productivity blending acquisition technology has emerged as a promising way to significantly increase the efficiency of seismic acquisition and reduce production cost. The great challenge of the blending acquisition technology lies in the severe interference noise of simultaneous sources. Therefore, the success of the blending acquisition technology relies heavily on the effectiveness of separating effective energy from the blended noise. We propose a blended noise suppression approach by using a hybrid median filter, normal moveout (NMO), and complex curvelet transform (CCT) approach. First, median filter is applied to original data after NMO correction. Second, the CCT-based thresholding denoising method is used to extract the remained effective energy from the data after median filtering to get the preliminary de-blended result. Next, the updated data are obtained by subtracting the pseudo-de-blended data of the de-blended result from the original data, and the process iterates. Last, the final de-blended result is obtained by adding the retrieved energy at each iteration until the signal-to-noise ratio satisfies the desired level. We demonstrate the effectiveness of the proposed approach on simulated synthetic and field data examples.

The Sao Francisco Basin is a polycyclic Proterozoic basin that represents an interesting challenge to geophysical research considering your complexity and small amount of data. In the 90s, the Sao Francisco sedimentary basin area was a target of a huge hydrocarbon exploratory campaign, sponsored by PETROBRAS .S.A, that include a series of reflection seismic data acquisition (Programa Sismico de Santana, April 1994). Some of those reflections seismic lines were acquired by GETA/UFBA with ANP (National Agency of Petroleum). The present work aimed to processing the seismic line 0027-RL-1932 in Sao Francisco Basin, using the techniques of seismic method, in order to obtain seismic sections that provide subsurface structures information to the interpreter. The processing Involves different stages organized in a seismic processing flowchart, among which include: geometry, static correction, amplitude correction, deconvolution, velocity analysis, normal moveout correction (NMO), stacking and migration.

Marine seismic data is often missing near offset information due to separation between the source and receiver cables. To solve this problem, a convolutional neural network is trained on synthetic seismic data to reconstruct the near offset gap. The synthetic data is created using a two‐dimensional finite difference method within a heterogeneous velocity model. These synthetics are generated with a source‐over‐receiver acquisition geometry so that they contain complete near offset data. The convolutional neural network is then trained on input‐target synthetic pairs where the inputs are common midpoint gathers with the near offset section removed, and the targets are the same gathers with the near offset section retained. Following training, the robustness of the method is investigated with regards to common midpoint data sorting, normal moveout correction and changes in the velocity model. It is found that training on common midpoint‐sorted data results in 2.8 times lower error than training on shot gathers, that normal moveout correction of the training data makes no significant difference in error levels, and that the model can reconstruct realistic near offsets on synthetic data generated 10 km away within the heterogeneous velocity model. In field data testing, first a dataset with source‐over‐cable acquisition geometry from the Barents Sea is used to compare the reconstructed wavefields to ground truth values. Although the reconstructed amplitudes require minor scaling to match the true values, predictions on this dataset yield 2.5 times lower near offset reconstruction error compared to a simple Radon transform interpolation method. Furthermore, amplitude versus offset gradient and intercept sections from the Barents Sea dataset are estimated with half the error when including the convolutional neural network‐predicted near offset data, compared to only using the conventionally‐acquirable portion of the data (beyond 112.5 m of offset). In a secondary field data test, a conventional northern North Sea dataset is used to demonstrate how the method may be applied in practice. Here, the convolutional neural network generates more realistic predictions than the Radon method, and the gradient and intercept sections calculated using the convolutional neural network‐predicted traces have higher signal‐to‐noise ratios than the sections calculated using only the original data. The combination of high‐quality synthetic training data and interpolation in the common midpoint domain enables near offset reconstruction at significant depth (1 s of two‐way traveltime or more), which is demonstrated in both synthetic and field examples.