Velocity analysis after migration

Normal moveout (NMO) correction is one of the common steps of seismic data processing. Conventional NMO correction is generally based on a velocity function, but velocity analysis is considered time consuming and labor intensive. Moreover, the field seismic data observed in complex areas can have a low signal-to-noise ratio, resulting in inaccurate picked velocity parameters and poor NMO correction. Conventional NMO correction has stretching issues, most significantly in shallow and large-offset areas. To address these problems, a new multiscale dynamic time-warping (MSD) algorithm for velocity-independent stretch-free NMO correction is investigated. This algorithm has higher accuracy and stronger noise resistance, as our comparisons with other applications of dynamic time warping show. In our algorithm, the original seismic data are decomposed into multiple morphological scales (using mathematical morphology theory), and alignment errors are calculated separately at each scale, followed by further adaptive weighted summation. Accumulation and backtracking operations based on alignment errors produce time-shift sequences for automatic flattening of the gathers. The effectiveness of the presented approach is tested on synthetic and field data. The results determine that compared with traditional velocity-based NMO correction methods, our method can accurately flatten seismic gathers without the NMO stretch and is robust to strong noise.

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.

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.

Overburden (shallow) anomalies such as channels, sink holes, or karst features pose challenges for seismic time imaging, resulting in an obscured image below the anomalies i.e. pull-ups or push-downs. These anomalies can propagate down to the reservoir masking the image and create structural uncertainties. These relatively small scale (< 1 – 2 km) overburden anomalies cannot be resolved with conventional depth imaging usually, based on migration velocity analysis and residual move out (RMO) minimization only. This paper proposes the application of dip-constrained tomography, in combination with RMO tomography to help resolve these shallow anomalies. Although the method has been widely used elsewhere e.g. in offshore Brazil and North Sea (Chen et al., 2012, Guillaume et al., 2013, Carotti et al., 2015 and Hollingworth et al., 2015), this is the first time it has been applied in a carbonate oilfield in offshore Abu Dhabi. An accurate velocity model is required for seismic depth imaging. The velocity model is optimized using a tomographic technique which is a non-linear optimization process with relevant constraints imposed. The data are migrated using an initial velocity model and common image gathers are obtained. RMO is defined in a cost function and non-linear tomography finds a velocity model minimizing the cost function. An additional structural constraint in the form of an offset-dependent dip constraint is introduced in the cost function for minimizing the misfit between the offset-dependent dip of the events and the expected dip. Dip-constrained tomography was able to obtain a high resolution velocity model in the overburden and provided a robust seismic image essentially free of pull-up and push-down effects in the reservoir. The structural uncertainty in the reservoir was subsequently reduced. Inverting the dip term together with RMO term can potentially correct image distortions e.g. pull-ups and push-downs and focus the image simultaneously. The refined subsurface image can help optimize the reservoir model with less structure uncertainty and can enhance the production profile by providing more flexibility in well design and planning. The methodology was applied on a pilot area which gave quite encouraging results and leads to extend the pre-stack depth imaging to a full-field application.

An integrated procedure for migration velocity analysis in complex structures of thrust belts

Prestack depth migration (PSDM) heavily depends on the accuracy of the migration velocity model. Reflection tomography on the base of common-image gathers (CIGs) is an important tool to build such models in depth domain. Unlike the conventional offset domain PSDM, angle domain PSDM can avoid migration artifacts when the velocity models are complex. It is easier to build the back-projection matrix for tomography according to the residual moveout (RMO) on the angle domain common image gathers (ADCIGs). In this abstract, we propose a novel nonlinear post-migration tomography approach to build velocity model using ADCIGs. The picked angle domain RMO is converted to prestack domain as invariants for data-fitting and model updating in the tomography iteration. Synthetic example proves the validity of this approach.

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.

In the mountainous terrain of west China, seismic data quality may be very poor due to severe statics problem and heavy noise especially in presence of complicated surface topography and complex subsurface structures. Moreover the complexity of subsurface structures maks the wave field much more complicated and the velocity distribution laterally varies significantly. Under this unfavorable context, it is very challenging to build a reasonable velocity model for the pre-stack depth migration to delineate the explicit structure contact relationship under complex geological settings. Here one enhanced velocity model building solution is presented. We innovatively make use of diving wave refraction tomography to build shallow velocity model and high-resolution reflection tomography to update the whole velocity model especially deep data. By tightly constraining the seismically derived velocity with available well control, one reliable velocity model can eventually obtained. After that we performed the pre-stack Kirchhoff depth migration and achieved geologically reasonable depth imaging results to help the geologists better understand the complex subsurface structures. This project is the first application of diving wave tomography on land seismic data in China. Its success has provided one robust and effective velocity model building solution and has significant meaning to other complex depth imaging land projects in China.

The occurrence of gas hydrate has been inferred from the presence of Bottom-Simulating Reflectors (BSRs) along the western continental margin of India. In this paper, we assess the spatial and vertical distribution of gas hydrates by analyzing the interval velocities and Amplitude Versus Offset (AVO) responses obtained from multi-channel seismics (MCSs). The hydrate cements the grains of the host sediment, thereby increasing its velocity, whereas the free gas below the base of hydrate stability zone decreases the interval velocity. Conventionally, velocities are obtained from the semblance analysis on the Common Mid-Point (CMP) gathers. Here, we used wave-equation datuming to remove the effect of the water column before the velocity analysis. We show that the interval velocities obtained in this fashion are more stable than those computed from the conventional semblance analysis. The initial velocity model thus obtained is updated using the tomographic velocity analysis to account for lateral heterogeneity. The resultant interval velocity model shows large lateral velocity variations in the hydrate layer and some low velocity zones associated with free gas at the location of structural traps. The reflection from the base of the gas layer is also visible in the stacked seismic data. Vertical variation in hydrate distribution is assessed by analyzing the AVO response at selected locations. AVO analysis is carried out after applying true amplitude processing. The average amplitudes of BSRs are almost constant with offset, suggesting a fluid expulsion model for hydrate formation. In such a model, the hydrate concentrations are gradational with maxima occurring at the base of hydrate stability zone.

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.

The tomography algorithm presented will generate an optimum velocity model for time migration. The velocity model is computed to flatten every sample on every common image gather. It is constrained to be smooth and bounded, and uses the correct relationship between residual curvature and velocity perturbations. This avoids the inconsistency of vertical updating which updates the velocity in a different manner from how the velocity is used for imaging. The resulting interval velocity model satisfies all available information and is shown to contain valid high resolution features. As a consequence, the updated velocity model gives an improved seismic image.

The Guando field is in an area of rough topography and complex geology. In order to better site wells in such fields it is of value to have a sound understanding of this geological complexity. Obtaining a satisfactory seismic image to enable such interpretation requires pre-stack imaging. The geological complexity is such that post stack imaging fails due to the failure of the common mid point assumption. Is it sufficient to perform pre-stack time migration or is it necessary to perform pre-stack depth migration? In this instance both have been performed on this field and results for each of them will be shown. The basic theory of both pre-stack time and pre-stack depth migration will be described without using mathematics. Model data will then be used to illustrate the shortcomings of pre-stack time migration using a model of similar geological complexity to the Guando field. Both pre-stack migrations require a velocity field. These differ and the manner of their derivation also differs. Velocity model building for both techniques will be described. Particular emphasis will be placed on the use of tomographic and scanning techniques for pre-stack depth migration. Examples will be shown of the velocity models from both migrations. It will be shown that the pre-stack depth migration velocity model is also a valuable interpretation asset. Data from both migrations will be shown. These will demonstrate the superiority of the pre-stack depth migrated data and the reasons why it is superior.

The idea of path-integral imaging is to sum over the migrated images obtained for a set of migration velocity models. Velocities where common-image gathers align horizontally are stationary, thus favoring these images in the overall stack. The overall image forms with no knowledge of the true velocity model. However, the velocity information associated with the final image can be determined in the process. By executing the path-integral imaging twice and weighting one of the stacks with the velocity value, the stationary velocities that produce the final image can then be extracted by a division of the two images. The velocity extraction, interpolation, and smoothing can be done fully automatically, without the need for human interpretation or other intervention. A numerical example demonstrated that quantitative information about the migration velocity model can be determined by double path-integral migration. The so-obtained velocity model can then be used as a starting model for subsequent velocity analysis tools like migration velocity analysis or tomographic methods.

This study introduces a Common Offset (CO) extension of the Common Reflection Surface (CRS) method to address seismic imaging challenges in complex geological settings and with noisy data. This CO-CRS approach aims to enhance the signal-to-noise ratio and overcome the limitations of conventional preconditioning techniques that rely on accurate parameterization. Building upon established work on zero-offset CRS (ZO-CRS), the CO method generates regularized prestack data suitable for both time- and depth-domain processing by interpolating missing offsets using a local hyperbolic approximation. Ultimately, this study utilizes CO-CRS for enhanced velocity analysis and data preconditioning prior to performing prestack time migration (PSTM). In this study, the CO-CRS is then used for velocity analysis and prestack time migration. The results show that prestack CO-CRS data yield improved time-migrated seismic images, and we suggest extending the application to the depth domain. To achieve a reliable velocity model for imaging, recursive seismic inversion (RSI) is applied to derive the velocity model using the PSTM stack and a velocity interval time, based on CRS semblance velocity analysis. Furthermore, the prestack depth migration (PSDM) is then tested. The depth-imaging results are reliable, and it can be concluded that combining the benefits of the CRS noise-reduction feature with more accurate velocity analysis and prestack migration can provide enhanced capabilities.

ABSTRACTLeast‐squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long‐scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single‐scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey‐sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey‐sinking (depth‐oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning‐based (surface‐oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth‐oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton‐like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model‐based data fitting.