Velocity analysis by iterative profile migration

Geophysics ◽  
1989 ◽  
Vol 54 (6) ◽  
pp. 718-729 ◽  
Author(s):  
Kamal Al‐Yahya
Keyword(s):  
Initial Velocity ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Prestack Migration ◽  
Subsequent Step ◽  
One Step ◽  
Velocity Variations ◽  
And Migration

In conventional seismic processing, velocity analysis is performed by using the normal moveout (NMO) equation which is based on the assumption of flat, horizontal reflectors. Imaging by migration (either before or after stack) is done normally in a subsequent step using these velocities. In this paper, velocity analysis and imaging are combined in one step, and migration itself is used as a velocity indicator. Because, unlike NMO, migration can be formulated for any velocity function, migration‐based velocity analysis methods are capable of handling arbitrary structures, i.e., those with lateral velocity variations. In the proposed scheme, each shot gather (profile) is migrated with an initial depth‐velocity model. Profile migration is implemented in the (x, ω) domain, but the actual implementation of profile migration is not critical, as long as it is not done in a spatial‐wavenumber domain, which would preclude handling of lateral velocity variations. After migration with an initial velocity model, the velocity error is estimated, and the initial velocity model is updated; the process is repeated until convergence is achieved. The velocity analysis is based on the principle that after prestack migration with the correct velocity model, an image in a common‐receiver gather (CRG) is aligned horizontally regardless of structure. The deviation from horizontal alignment is therefore a measure of the error in velocity. If the migration velocity is lower than the velocity of the medium, events curve upward, whereas if the migration velocity is higher than the velocity of the medium, events curve downward.

Migration velocity analysis: Accounting for the effects of lateral velocity variations

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 164-175 ◽  
Author(s):  
Hans J. Tieman
Keyword(s):  
Migration Velocity ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Traveltime Inversion ◽  
Long Wavelength ◽  
Migration Velocity Analysis ◽  
Unstable Process ◽  
Velocity Variations ◽  
Iterative Procedures ◽  
Migration Analysis

The most common migration velocity analysis algorithms, iterative profile migration, focusing analysis, and stack power analysis are based on restrictive subsurface assumptions that may cause the methods to break down in the presence of lateral velocity variations. Typically, the subsurface is assumed to have either a constant velocity, or at most, a depth variable velocity. Recent innovations include the use of traveltime inversion philosophy to invert migration measurements of the curvature as a function of offset exhibited by an event following migration. Traveltime inversion makes few assumptions regarding the subsurface, but is a rather unstable process. Thus, an important question is, “Under what conditions do the traditional methods break down and make the use of traveltime inversion methods mandatory?” Marrying the common migration analysis with tomography results in a set of equations that, while useful for generating updates from migration measurements, are too complex for answering the above question. However, by restricting the subsurface to low relief structures and assuming small angle wave propagation, these updating equations can be approximated by forms that are identical to the traditional updating equations, except for a factor that is dependent upon the magnitude, position, and spatial wavelength of potential lateral velocity variations. These simpler equations indicate that even relatively long wavelength anomalies can cause updates to point in the wrong direction and iterative procedures to diverge, and under certain conditions, cause the accuracy of these updates to decrease dramatically.

Tau migration and velocity analysis: Theory and synthetic examples

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1331-1339 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Time Domain ◽  
Synthetic Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Surface Velocity ◽  
Velocity Analysis ◽  
Near Surface ◽  
Prestack Migration ◽  
Interval Velocity ◽  
Migration Velocity Analysis

Prestack migration velocity analysis in the time domain reduces the velocity‐depth ambiguity usually hampering the performance of prestack depth‐migration velocity analysis. In prestack τ migration velocity analysis, we keep the interval velocity model and the output images in vertical time. This allows us to avoid placing reflectors at erroneous depths during the velocity analysis process and, thus, avoid slowing down its convergence to the true velocity model. Using a 1D velocity update scheme, the prestack τ migration velocity analysis performed well on synthetic data from a model with a complex near‐surface velocity. Accurate velocity information and images were obtained using this time‐domain method. Problems occurred only in resolving a thin layer where the low resolution and fold of the synthetic data made it practically impossible to estimate velocity accurately in this layer. This 1D approach also provided us reasonable results for synthetic data from the Marmousi model. Despite the complexity of this model, the τ domain implementation of the prestack migration velocity analysis converged to a generally reasonable result, which includes properly imaging the elusive top‐of‐the‐reservoir layer.

scholarly journals Using constraints to address the instabilities of automated prestack velocity analysis

Geophysics ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 404-419 ◽  
Author(s):  
Christof Stork ◽  
Robert W. Clayton
Keyword(s):  
Initial Velocity ◽  
Variable Interval ◽  
Velocity Model ◽  
Velocity Fields ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Interval Velocity ◽  
Additional Information ◽  
Analysis Methods ◽  
Automated Methods

Generalized prestack velocity analysis methods that use an automated approach to resolve laterally variable interval velocity fields are beset by a series of problems. The problem of resolving lateral velocity variations has inherent complications that prevent automated methods from being robust enough to be applied routinely to data from a variety of geologic provinces. The use of automated prestack velocity analysis methods will not eliminate the step of carefully producing an initial velocity model derived from regional geologic information and an interpretation of a conventionally processed section. For the methods to regularly produce useful additional information, the unique characteristics of each application must be input into the prestack velocity analysis with the use of inversion constraints. These constraints serve either to adapt the generalized prestack velocity analysis to a focused objective in a particular area or to provide iterative, interpretational tools that help the user produce a velocity model.

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.

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.

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