Migration velocity analysis: Theory and an iterative algorithm

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 142-153 ◽  
Author(s):  
Zhenyue Liu ◽  
Norman Bleistein
Keyword(s):  
Synthetic Data ◽  
Quantitative Relationship ◽  
Migration Velocity ◽  
Data Migration ◽  
Iteration Algorithm ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
The Difference ◽  
And Migration

Imaging complex structures inside the earth requires reasonable velocities that can be provided by applying prestack depth migration to multichannel seismic data. Migration velocity analysis is based on the principle that the images in the migrated data will be distorted when an erroneous velocity is used, and the difference of the imaged depths (residual moveout) at a common image gather is a measure of the error in the velocity. The imaging equations that we derive from Snell’s law describe a general, quantitative relationship between migration images and migration velocity. Based on the imaging equations, we analyze properties of common‐image gathers and derive analytical formulas to represent residual moveout in some cases. These formulas show what factors affect the sensitivity of velocity analysis, which is useful to assess errors involved in velocity estimates. In addition, we develop a simple‐iteration algorithm to correct the layer velocities from residual moveout. The algorithm presented here is applicable to a medium that consists of constant‐velocity layers separated by arbitrary smooth interfaces. Some computer implementations are presented for both synthetic data and physical‐tank data. They demonstrate the effectiveness of our velocity analysis approach.

An analytical approach to migration velocity analysis

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1238-1249 ◽  
Author(s):  
Zhenyue Liu
Keyword(s):  
Synthetic Data ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Curvature Analysis ◽  
Derivative Function ◽  
Migration Velocity Analysis ◽  
Residual Curvature

Prestack depth migration provides a powerful tool for velocity analysis in complex media. Both prominent approaches to velocity analysis—depth‐focusing analysis and residual‐curvature analysis, rely on approximate formulas to update velocity. Generally, these formulas are derived under the assumptions of horizontal reflector, lateral velocity homogeneity, or small offset. Therefore, the conventional methods for updating velocity lack accuracy and computational efficiency when velocity has large, lateral variations. Here, based on ray theory, I find the analytic representation for the derivative of imaged depths with respect to migration velocity. This derivative function characterizes a general relationship between residual moveout and residual velocity. Using the derivative function and the perturbation method, I derive a new formula to update velocity from residual moveout. In the derivation, I impose no limitation on offset, dip, or velocity distribution. Consequently, I revise the residual‐curvature‐analysis method for velocity estimation in the postmigrated domain. Furthermore, my formula provides sensitivity and error estimation for migration‐based velocity analysis, which is helpful in quantifying the reliability of the estimated velocity. The theory and methodology in this paper have been tested on synthetic data (including the Marmousi data).

The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. S241-S249 ◽  
Author(s):  
Xiao-Bi Xie ◽  
Hui Yang
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Data Sets ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Sensitivity Kernel ◽  
Migration Velocity Analysis ◽  
Tomography Method

We have derived a broadband sensitivity kernel that relates the residual moveout (RMO) in prestack depth migration (PSDM) to velocity perturbations in the migration-velocity model. We have compared the kernel with the RMO directly measured from the migration image. The consistency between the sensitivity kernel and the measured sensitivity map validates the theory and the numerical implementation. Based on this broadband sensitivity kernel, we propose a new tomography method for migration-velocity analysis and updating — specifically, for the shot-record PSDM and shot-index common-image gather. As a result, time-consuming angle-domain analysis is not required. We use a fast one-way propagator and multiple forward scattering and single backscattering approximations to calculate the sensitivity kernel. Using synthetic data sets, we can successfully invert velocity perturbations from the migration RMO. This wave-equation-based method naturally incorporates the wave phenomena and is best teamed with the wave-equation migration method for velocity analysis. In addition, the new method maintains the simplicity of the ray-based velocity analysis method, with the more accurate sensitivity kernels replacing the rays.

3D common-reflection-point-based seismic migration velocity analysis

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. S161-S167 ◽  
Author(s):  
Weihong Fei ◽  
George A. McMechan
Keyword(s):  
Synthetic Data ◽  
Computation Time ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reflection Point ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Spatial Coordinates

Three-dimensional prestack depth migration and depth residual picking in common-image gathers (CIGs) are the most time-consuming parts of 3D migration velocity analysis. Most migration-based velocity analysis algorithms need spatial coordinates of reflection points and CIG depth residuals at different offsets (or angles) to provide updated velocity information. We propose a new algorithm that can analyze 3D velocity quickly and accurately. Spatial coordinates and orientations of reflection points are provided by a 3D prestack parsimonious depth migration; the migration involves only the time samples picked from the salient reflection events on one 3D common-offset volume. Ray tracing from the reflection points to the surface provides a common-reflection-point (CRP) gather for each reflection point. Predicted (nonhyperbolic) moveouts for local velocity perturbations, based on maximizing the stacked amplitude, give the estimated velocity updates for each CRP gather. Then the velocity update for each voxel in the velocity model is obtained by averaging over all predicted velocity updates for that voxel. Prior model constraints may be used to stabilize velocity updating. Compared with other migration velocity analyses, the traveltime picking is limited to only one common-offset volume (and needs to be done only once); there is no need for intensive 3D prestack depth migration. Hence, the computation time is orders of magnitude less than other migration-based velocity analyses. A 3D synthetic data test shows the algorithm works effectively and efficiently.

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

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.

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.

scholarly journals Smiles and frowns in migration/velocity analysis

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1200-1209 ◽  
Author(s):  
Jinming Zhu ◽  
Larry Lines ◽  
Sam Gray
Keyword(s):  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Migration Velocity Analysis

Reliable seismic depth migrations require an accurate input velocity model. Inaccurate velocity estimates will distort point diffractors into smiles or frowns on a depth section. For both poststack and prestack migrated sections, high velocities cause deep smiles while low velocities cause shallow frowns on migrated gathers. However, for prestack images in the offset domain, high velocities cause deep frowns while low velocities cause shallow smiles. If the velocity is correct, there will be no variation in the depth migration as a function of offset and no smiles or frowns in the offset domain. We explain migration responses both mathematically and graphically and thereby provide the basis for depth migration velocity analysis.

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