An analytical approach to migration velocity analysis

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

A new velocity analysis method has been developed and is tested on the Marmousi data. This method characterizes a velocity distribution by the macro model and uses an analytical formula to update velocity. Our formula estimates the update in velocity by computing a derivative function of imaged depths with respect to parameters that characterize a velocity model in a general background medium context. When the medium has strongly lateral velocity variations, this formula is more accurate than conventional ones based on hyperbolic residual moveout. The test results show our velocity analysis method to be superior for complex media such as in the Marmousi model.

One of the most serious problems in anisotropic velocity analysis is the trade-off between anisotropy and lateral heterogeneity, especially if velocity varies on a scale smaller than the maximum offset. We have developed a P-wave MVA (migration velocity analysis) algorithm for transversely isotropic (TI) models that include layers with small-scale lateral heterogeneity. Each layer is described by constant Thomsen parameters e and δ and the symmetry-direction velocity V0 that varies as a quadratic function of the distance along the layer boundaries. For tilted TI media (TTI), the symmetry axis is taken orthogonal to the reflectors. We analyzed the influence of lateral heterogeneity on image gathers obtained after prestack depth migration and found that quadratic lateral velocity variation in the overburden can significantly distort the moveout of the target reflection. Consequently, medium parameters beneath the heterogeneous layer(s) are estimated with substantial error, even when borehole information (e.g., check shots or sonic logs) is available. Because residual moveout in the image gathers is highly sensitive to lateral heterogeneity in the overburden, our algorithm simultaneously inverts for the interval parameters of all layers. Synthetic tests for models with a gently dipping overburden demonstrate that if the vertical profile of the symmetry-direction velocity V0 is known at one location, the algorithm can reconstruct the other relevant parameters of TI models. The proposed approach helps increase the robustness of anisotropic velocity model-building and enhance image quality in the presence of small-scale lateral heterogeneity in the overburden.

Wide‐aperture, prestack depth migration requires application of challenging and time‐consuming velocity analysis and depth focusing, collectively referred to here as depth focusing. We present an approach to depth focusing using (1) a detailed starting velocity model obtained by a 1‐D transformation of the first‐arrival times, followed iteratively by (2) interactive analysis of the common‐image gathers, (3) computation of coherency attributes of the wavefield in the depth domain, and (4) 2‐D traveltime tomography to update the background velocity model. We employ two interactive method of migration velocities refinement. In the first method (similar to the common‐midpoint velocity spectrum approach), residual velocity updates are picked directly from the common‐image gathers. In another method (analogous to the common velocity stacks), we pick the velocity updates from the areas of maximum coherency in depth sections that are migrated using rescaled traveltime maps. Both types of migration velocity picks, optionally combined with the first arrivals, are inputs for a 2‐D traveltime inversion scheme that uses either the infinite‐frequency or a finite‐bandwidth approximation. This flexible and versatile depth focusing approach is implemented for several prestack depth migration algorithms and illustrated on an application to a real, ultrashallow seismic data set. The technique resolves overburden velocity variations and facilitates reliable high‐resolution reflection imaging of a paleochannel that was the target of the study.

Residual moveout (RMO) can have a severe impact on seismic amplitude-variation-with-offset (AVO) analysis. It is, therefore, common practice to quality control and correct the processed seismic data for RMO before AVO analysis. However, a complicating factor is that AVO effects and tuning may result in up- or down-dipping events that are easily mistaken for events with RMO, e.g., AVO Class 2p response. Flattening these events will lead to an incorrect AVO estimation. We present a new Bayesian joint RMO and AVO inversion to estimate the RMO time shifts and the AVO intercept and gradient. The joint inversion corrects the seismic data based on the RMO and AVO prior models rather than explicitly assuming that the data should be flattened. The prior models will typically guide toward flat gathers but will also allow for up- and down-dipping events when these are possible within the prior model. The method is illustrated on synthetic and real seismic data. For cases wherein flat events are correct, the results are similar to sequential methods with RMO correction before AVO analysis, but in situations wherein dipping seismic reflectors may be misinterpreted as events with RMO, the joint inversion provides better results by evaluating RMO and AVO simultaneously. The inversion results include the posterior covariance matrix, which represents uncertainties for the AVO intercept and gradient, the RMO time shifts, and the correlations between these at all samples. The uncertainty of the RMO time shift varies within seismic gathers and depends on the seismic quality and how clear and well determined the seismic events are. The uncertainty of the RMO is lower for clear and continuous events but increases in the zones with weaker and noisy events. The uncertainty of the RMO time shifts has a low impact on the uncertainty of the AVO intercept but increases the uncertainty of the AVO gradient significantly.

Through the use of iterative turning‐ray tomography followed by wave‐equation datuming (or tomo‐datuming) and prestack depth migration, we generate accurate prestack images of seismic data in overthrust areas containing both highly variable near‐surface velocities and rough topography. In tomo‐datuming, we downward continue shot records from the topography to a horizontal datum using velocities estimated from tomography. Turning‐ray tomography often provides a more accurate near‐surface velocity model than that from refraction statics. The main advantage of tomo‐datuming over tomo‐statics (tomography plus static corrections) or refraction statics is that instead of applying a vertical time‐shift to the data, tomo‐datuming propagates the recorded wavefield to the new datum. We find that tomo‐datuming better reconstructs diffractions and reflections, subsequently providing better images after migration. In the datuming process, we use a recursive finite‐difference (FD) scheme to extrapolate wavefield without applying the imaging condition, such that lateral velocity variations can be handled properly and approximations in traveltime calculations associated with the raypath distortions near the surface for migration are avoided. We follow the downward continuation step with a conventional Kirchhoff prestack depth migration. This results in better images than those migrated from the topography using the conventional Kirchhoff method with traveltime calculation in the complicated near surface. Since FD datuming is only applied to the shallow part of the section, its cost is much less than the whole volume FD migration. This is attractive because (1) prestack depth migration usually is used iteratively to build a velocity model, so both efficiency and accuracy are important factors to be considered; and (2) tomo‐datuming can improve the signal‐to‐noise (S/N) ratio of prestack gathers, leading to more accurate migration velocity analysis and better images after depth migration. Case studies with synthetic and field data examples show that tomo‐datuming is especially helpful when strong lateral velocity variations are present below the topography.

An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.

Prestack time migration can still be a suitable alternative to image complex structures with moderate lateral velocity variations and it is less sensitive to the knowledge of the migration-velocity model than prestack depth migration.

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.

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.

We consider a case where a 3D depth migration has been performed in the local angle domain (LAD) using rich-azimuth seismic data (e.g., conventional land surveys). The subsurface geologic model is characterized by considerable azimuthally anisotropic velocity variations. The background velocity field used for the migration can consist of azimuthally independent, e.g., vertical transverse isotropy, and/or azimuthally dependent (e.g., orthorhombic), velocity layers. The resulting 3D full-azimuth reflection angle gathers generated by the LAD migration represent in situ high-resolution amplitude preserved reflectivities associated with opening angles between incident and reflected slowness vectors in the specular directions. Residual moveouts (RMOs) automatically picked on these 3D image gathers along major horizons can indicate considerable residual periodic azimuthal variations. This situation is typical in depth imaging applied to unconventional shale plays, where the background velocity model doesn’t yet account for the aligned stress/fracture systems that exist in some of the target layers. We use the azimuthally dependent, phase-angle RMOs to update the interval parameters of the background model, accounting for the azimuthal anisotropy effect. Until now, this problem was mainly treated in the unmigrated time-offset domain, which is limited in describing the actual in situ changes of the velocity field with azimuths. The subsurface full-azimuth phase-angle domain RMOs provide better physical parameters to analyze the in situ azimuthal variations of the anisotropic media. Our method is grounded in a newly derived generalized Dix-based theory, where locally the background and updated models are assumed to be 1D anisotropic velocity models. At each lateral location, the orthorhombic axis x3 points in the vertical direction across all layers, but the azimuthal orientations of the orthorhombic layers change from layer to layer. An effective model for such a layered structure (background or updated) is represented by a single layer with a vertical time identical to that of the whole package, effective fast and slow normal moveout (NMO) velocities, and an effective azimuthal orientation of the slow NMO velocity. Our approach begins with computation of these effective parameters for the background model and conversion of the high-resolution RMOs into a dense set of updated, effective, azimuthally dependent NMO velocities, which are then converted into three effective parameters of the updated model. Next, we apply a generalized Dix-based inversion approach to estimate the local NMO parameters for each updated layer. Finally, we convert the local parameters into interval azimuthally varying anisotropic model parameters (e.g., TTI, orthorhombic, or tilted orthorhombic) within each layer. The 1D Dix-based approach presented in this work should not be considered an alternative to more accurate 3D global inversion approaches, such as global anisotropic tomography. However, the proposed method can be effectively used for moderately laterally varying models, and some of the principal physical rules derived for the 1D model can be further used to improve the formulation and geophysical constraints applied to 3D global inversion methods.

Summary As for the areas of rugged surface and complex subsurface, conventional pre-stack depth migration velocity analysis would adjust the rugged surface to final datum on which to update and iterate velocity. This paper proposes a method of tomographic velocity inversion on rugged surface, which is the improvement of conventional travel-time tomographic method. This method could update velocity from rugged surface and need not statics correction in prestack data. Through this method, we can improve the precision and efficiency of velocity analysis. This paper introduces the method to acquire angle-domain common imaging gathers (ADCIGs) on rugged surface Gaussian beam migration method on which to perform the tomographic velocity analysis. The tests to model data and field data prove the method to be correct and effective.

Reflection tomography and interval velocity analysis (IVA) is applied to a 2D seismic line in the Surat Basin - an area where the primary goal is achieving reliable depth conversion of low relief structures, in the presence of near surface velocity anomalies and subtle lateral velocity gradients.The technique, using commercially available velocity analysis and Pre-Stack-Depth-Migration (PSDM) software, represents a potential solution to problems which have challenged previous workers. We demonstrate reflection tomography can resolve shallow velocity anomalies by using as input the moveout errors of deeper horizons from an initial pass of PSDM. Significantly, reflection energy from the near-surface layer is not required to resolve its velocity. When the shallow velocity model is determined, the interval velocity analysis of subsequent layers becomes stable and a more refined velocity model may be constructed. Several iterations of PSDM and reflection tomography are generally required before running a final pass of PSDM. The example seismic line contains three wells which are used to judge the quality of the final depth migration.The results demonstrate that it is possible to extract accurate lateral velocity information inherent in high fold CMP gathers from land data containing shallow velocity anomalies or residual static errors. A lateral velocity gradient causing an apparent pull up of 26 metres between Wells B and C is successfully resolved. The example demonstrates the predicted formation tops of Well C would have been accurate to around +/- 5m if reflection tomography and interval velocity analysis had been applied in place of a regional velocity function derived from nearby well data.

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.