Prestack residual migration in the frequency domain

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 634-640 ◽  
Author(s):  
Paul C. Sava
Keyword(s):  
Migration Velocity ◽  
Accurate Estimate ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Traveltime Tomography ◽  
Interval Velocity ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Velocity Changes ◽  
Wavefield Extrapolation

Prestack Stolt residual migration can be applied to seismic images that are depth migrated using wavefield extrapolation techniques. This method has significant advantages over other methods that estimate interval velocity functions for depth migration. It is more accurate than methods that are based on focusing the stack of migrated images by a residual NMO operation, so it provides a more accurate estimate of the correct migration velocities. Also, it is conceptually simpler and easier to implement than traveltime tomography methods. Although the theory is developed assuming constant velocity, the method can be used for depth‐migrated images produced with smoothly varying velocity models, since the residually migrated images depend only on the ratio of the reference and updated velocities. This method closely resembles Stolt‐stretch techniques, so it inherits the Stolt method's speed and convenience. The main applications of this method are in migration velocity analysis (MVA), where it can be used to investigate the effects of gross velocity changes on the migrated image, and as a tool for residual image enhancement used by more sophisticated MVA methods, e.g., wave‐equation migration velocity analysis.

Wave-equation migration velocity analysis by focusing diffractions and reflections

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U19-U27 ◽  
Author(s):  
Paul C. Sava ◽  
Biondo Biondi ◽  
John Etgen
Keyword(s):  
Wave Equation ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Interval Velocity ◽  
Migration Velocity Analysis ◽  
Inversion Procedure ◽  
Velocity Information ◽  
Zero Offset

We propose a method for estimating interval velocity using the kinematic information in defocused diffractions and reflections. We extract velocity information from defocused migrated events by analyzing their residual focusing in physical space (depth and midpoint) using prestack residual migration. The results of this residual-focusing analysis are fed to a linearized inversion procedure that produces interval velocity updates. Our inversion procedure uses a wavefield-continuation operator linking perturbations of interval velocities to perturbations of migrated images, based on the principles of wave-equation migration velocity analysis introduced in recent years. We measure the accuracy of the migration velocity using a diffraction-focusing criterion instead of the criterion of flatness of migrated common-image gathers that is commonly used in migration velocity analysis. This new criterion enables us to extract velocity information from events that would be challenging to use with conventional velocity analysis methods; thus, our method is a powerful complement to those conventional techniques. We demonstrate the effectiveness of the proposed methodology using two examples. In the first example, we estimate interval velocity above a rugose salt top interface by using only the information contained in defocused diffracted and reflected events present in zero-offset data. By comparing the results of full prestack depth migration before and after the velocity updating, we confirm that our analysis of the diffracted events improves the velocity model. In the second example, we estimate the migration velocity function for a 2D, zero-offset, ground-penetrating radar data set. Depth migration after the velocity estimation improves the continuity of reflectors while focusing the diffracted energy.

CRP-based seismic migration velocity analysis

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. U21-U28 ◽  
Author(s):  
Weihong Fei ◽  
George A. McMechan
Keyword(s):  
Velocity Model ◽  
Migration Velocity ◽  
Data Sets ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Interval Velocity ◽  
Model Parameterization ◽  
Migration Velocity Analysis ◽  
Local Interval

A new migration velocity analysis is developed by combining the speed of parsimonious prestack depth migration with velocity adjustments estimated within and across common-reflection-point (CRP) gathers. The proposed approach is much more efficient than conventional tomographic velocity analysis because only the traces that contribute to a series of CRP gathers are depth migrated at each iteration. The local interval-velocity adjustments for each CRP are obtained by maximizing the stack amplitude over the predicted (nonhyperbolic) moveout in each CRP gather; this does not involve retracing rays. At every iteration, the velocity in each pixel is updated by averaging over all the predicted velocity updates. Finally, CRP positions and orientations are updated by parsimonious migration, and rays are retraced to define new CRP gathers for the next iteration; this ensures internal consistency between the updated velocity model and the CRP gather. Because the algorithm has a gridded-model parameterization, no explicit representation or fitting of reflectors is involved. Strong lateral-velocity variations, such as those found at salt flanks, can be handled. Application to synthetic and field data sets show that the proposed algorithm works effectively and efficiently.

Fast model-based migration velocity analysis and reflector shape estimation

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. U9-U17 ◽  
Author(s):  
Weihong Fei ◽  
George A. McMechan
Keyword(s):  
Computation Time ◽  
Migration Velocity ◽  
Velocity Variation ◽  
Velocity Analysis ◽  
Shape Estimation ◽  
Reflection Point ◽  
Data Set ◽  
Depth Migration ◽  
Interval Velocity ◽  
Migration Velocity Analysis

Migration velocity analysis can be made more efficient by preselecting the traces that contribute to a series of common-reflection-point (CRP) gathers and migrating only those traces. The data traces that contribute to a CRP for one reflection point on one layer are defined in a two-step procedure. First, poststack parsimonious Kirchhoff depth migration of zero-offset (or stacked) traces defines approximate reflector positions and orientations. Then, ray tracing from the reflection points for nonzero reflection angles defines the source and receiver locations of the data traces in the CRP gather. These traces are then prestack depth migrated, and the interval velocity model adjustment is obtained by fitting the velocity that maximizes the stack amplitude over the predicted (nonhyperbolic) moveout. A small number (2–3) of iterations converge to a 2D model of layer shape and interval velocity. Further efficiency is obtained by implementing layer stripping. The computation time is greatly reduced by combining parsimonious migration with processing only the salient portions of the whole seismic data set. The algorithm can handle lateral velocity variation within each layer as well as constant velocity. The computation time of the proposed algorithm is of the same order as that of the standard rms velocity scan method, but it does not have the inherent assumptions of the velocity scan method and is faster than current iterative prestack depth migration velocity analysis methods for typical field data.

Numeric implementation of wave-equation migration velocity analysis operators

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE145-VE159 ◽  
Author(s):  
Paul Sava ◽  
Ioan Vlad
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Image Optimization ◽  
Migration Velocity Analysis ◽  
Zero Offset ◽  
Wavefield Extrapolation

Wave-equation migration velocity analysis (MVA) is a technique similar to wave-equation tomography because it is designed to update velocity models using information derived from full seismic wavefields. On the other hand, wave-equation MVA is similar to conventional, traveltime-based MVA because it derives the information used for model updates from properties of migrated images, e.g., focusing and moveout. The main motivation for using wave-equation MVA is derived from its consistency with the corresponding wave-equation migration, which makes this technique robust and capable of handling multipathing characterizing media with large and sharp velocity contrasts. The wave-equation MVA operators are constructed using linearizations of conventional wavefield extrapolation operators, assuming small perturbations relative to the background velocity model. Similar to typical wavefield extrapolation operators, the wave-equation MVA operators can be implemented in the mixed space-wavenumber domain using approximations of differentorders of accuracy. As for wave-equation migration, wave-equation MVA can be formulated in different imaging frameworks, depending on the type of data used and image optimization criteria. Examples of imaging frameworks correspond to zero-offset migration (designed for imaging based on focusing properties of the image), survey-sinking migration (designed for imaging based on moveout analysis using narrow-azimuth data), and shot-record migration (also designed for imaging based on moveout analysis, but using wide-azimuth data). The wave-equation MVA operators formulated for the various imaging frameworks are similar because they share elements derived from linearizations of the single square-root equation. Such operators represent the core of iterative velocity estimation based on diffraction focusing or semblance analysis, and their applicability in practice requires efficient and accurate implementation. This tutorial concentrates strictly on the numeric implementation of those operators and not on their use for iterative migration velocity analysis.

Migration velocity analysis using traveltime wavefield tomography

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. U73-U85 ◽  
Author(s):  
Saleh M. Al-Saleh ◽  
Jianwu Jiao
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Migration Velocity ◽  
Equation Modeling ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Traveltime Tomography ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Complex Structural

We introduce an integrated wave-equation technique for migration velocity analysis (MVA) that consists of three steps: (1) forming the extended data, (2) approximating the correct transmitted wavefield, and (3) using wavefield tomography to update the velocity model. In the first step, the crosscorrelation imaging condition is relaxed to produce other nonzero-lag common image gathers (CIG) that, combined, form a common image cube (CIC). Slicing the CIC at different crosscorrelation lags forms a series of CIGs. Flattened events will occur in the CIGs at a lag other than the zero-lag when an incorrect velocity model is used in the migration. In the second step, for each event on the CIG, we pick the focusing depth and crosscorrelation lag at which it is flattest. We then model a Green’s function by seeding a source at the focusing depth using one-way wave equation modeling, then shift the modeled wavefield with the focusing crosscorrelation lag. This process is repeated for the other primary events at different lateral and vertical positions. The result is a set of modeled data whose wavefield approximates the wavefield that would have been generated if the correct velocity model had been used to simulate these gathers. We then apply wavefield tomography on these data-driven modeled data to update the velocity model. Our inversion scheme is based on wave-equation traveltime tomography that can update the velocity model in the presence of large velocity errors and a complex environment. Tests on synthetic and real 2D seismic data confirm the method’s effectiveness in building velocity models in complex structural areas that have large lateral velocity variations.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspects

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1202-1212 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Cost Function ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray ◽  
The Cost

We present a new method based on migration velocity analysis (MVA) to estimate 2‐D velocity models from seismic reflection data with no assumption on reflector geometry or the background velocity field. Classical approaches using picking on common image gathers (CIGs) must consider continuous events over the whole panel. This interpretive step may be difficult—particularly for applications on real data sets. We propose to overcome the limiting factor by considering locally coherent events. A locally coherent event can be defined whenever the imaged reflectivity locally shows lateral coherency at some location in the image cube. In the prestack depth‐migrated volume obtained for an a priori velocity model, locally coherent events are picked automatically, without interpretation, and are characterized by their positions and slopes (tangent to the event). Even a single locally coherent event has information on the unknown velocity model, carried by the value of the slope measured in the CIG. The velocity is estimated by minimizing these slopes. We first introduce the cost function and explain its physical meaning. The theoretical developments lead to two equivalent expressions of the cost function: one formulated in the depth‐migrated domain on locally coherent events in CIGs and the other in the time domain. We thus establish direct links between different methods devoted to velocity estimation: migration velocity analysis using locally coherent events and slope tomography. We finally explain how to compute the gradient of the cost function using paraxial ray tracing to update the velocity model. Our method provides smooth, inverted velocity models consistent with Kirchhoff‐type migration schemes and requires neither the introduction of interfaces nor the interpretation of continuous events. As for most automatic velocity analysis methods, careful preprocessing must be applied to remove coherent noise such as multiples.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

Prestack depth migration of an Alberta Foothills data set—The Husky experience

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 392-398 ◽  
Author(s):  
W.-J. Wu ◽  
L. Lines ◽  
A. Burton ◽  
H.-X. Lu ◽  
J. Zhu ◽  
...  
Keyword(s):  
Velocity Analysis ◽  
Reverse Time ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Geological Interpretation ◽  
Prestack Migration ◽  
Velocity Models ◽  
Depth Images ◽  
Migration Velocity Analysis

We produce depth images for an Alberta Foothills line by iteratively using a number of migration and velocity analysis techniques. In imaging steeply dipping layers of a foothills data set, it is apparent that thrust belt geology can violate the conventional assumptions of elevation datum corrections and common midpoint (CMP) stacking. To circumvent these problems, we use migration from topography in which we perform prestack depth migration on the data using correct source and receiver elevations. Migration from topography produces enhanced images of steep shallow reflectors when compared to conventional processing. In addition to migration from topography, we couple prestack depth migration with the continuous adjustment of velocity depth models. A number of criteria are used in doing this. These criteria require that our velocity estimates produce a focused image and that migrated depths in common image gathers be independent of source‐receiver offset. Velocity models are estimated by a series of iterative and interpretive steps involving prestack migration velocity analysis and structural interpretation. Overlays of velocity models on depth migrations should generally show consistency between velocity boundaries and reflection depths. Our preferred seismic depth section has been produced by using prestack reverse‐time depth migration coupled with careful geological interpretation.

Depth‐migration velocity analysis

1991 ◽  
Author(s):  
M. Turhan Taner ◽  
Richard W. Postma ◽  
Lee Lu ◽  
Edip Baysal
Keyword(s):  
Migration Velocity ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Migration Velocity Analysis

Seismic imaging and velocity analysis for an Alberta Foothills seismic survey

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 721-732 ◽  
Author(s):  
Lanlan Yan ◽  
Larry R. Lines
Keyword(s):  
Seismic Imaging ◽  
Migration Velocity ◽  
Surface Velocity ◽  
Seismic Survey ◽  
Velocity Analysis ◽  
Prestack Depth Migration ◽  
Near Surface ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Imaging Results

Seismic imaging of complex structures from the western Canadian Foothills can be achieved by applying the closely coupled processes of velocity analysis and depth migration. For the purposes of defining these structures in the Shaw Basing area of western Alberta, we performed a series of tests on both synthetic and real data to find optimum imaging procedures for handling large topographic relief, near‐surface velocity variations, and the complex structural geology of steeply dipping formations. To better understand the seismic processing problems, we constructed a typical foothills geological model that included thrust faults and duplex structures, computed the model responses, and then compared the performance of different migration algorithms, including the explicit finite difference (f-x) and Kirchhoff integral methods. When the correct velocity was used in the migration tests, the f-x method was the most effective in migration from topography. In cases where the velocity model was not assumed known, we determined a macrovelocity model by performing migration/velocity analysis by using smiles and frowns in common image gathers and by using depth‐focusing analysis. In applying depth imaging to the seismic survey from the Shaw Basing area, we found that imaging problems were caused partly by near‐surface velocity problems, which were not anticipated in the modeling study. Several comparisons of different migration approaches for these data indicated that prestack depth migration from topography provided the best imaging results when near‐surface velocity information was incorporated. Through iterative and interpretive migration/velocity analysis, we built a macrovelocity model for the final prestack depth migration.

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