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.

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.

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.

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.

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).

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.

Migration velocity analysis in factorized VTI media

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 708-718 ◽  
Author(s):  
Debashish Sarkar ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Velocity Gradient ◽  
Migration Velocity ◽  
P Wave ◽  
Velocity Analysis ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Wave Migration ◽  
Vti Media

One of the main challenges in anisotropic velocity analysis and imaging is simultaneous estimation of velocity gradients and anisotropic parameters from reflection data. Approximating the subsurface by a factorized VTI (transversely isotropic with a vertical symmetry axis) medium provides a convenient way of building vertically and laterally heterogeneous anisotropic models for prestack depthmigration. The algorithm for P‐wave migration velocity analysis (MVA) introduced here is designed for models composed of factorized VTI layers or blocks with constant vertical and lateral gradients in the vertical velocity VP0. The anisotropic MVA method is implemented as an iterative two‐step procedure that includes prestack depth migration (imaging step) followed by an update of the medium parameters (velocity‐analysis step). The residual moveout of the migrated events, which is minimized during the parameter updates, is described by a nonhyperbolic equation whose coefficients are determined by 2D semblance scanning. For piecewise‐factorized VTI media without significant dips in the overburden, the residual moveout of P‐wave events in image gathers is governed by four effective quantities in each block: (1) the normal‐moveout velocity Vnmo at a certain point within the block, (2) the vertical velocity gradient kz, (3) the combination kx[Formula: see text] of the lateral velocity gradient kx and the anisotropic parameter δ, and (4) the anellipticity parameter η. We show that all four parameters can be estimated from the residual moveout for at least two reflectors within a block sufficiently separated in depth. Inversion for the parameter η also requires using either long‐spread data (with the maximum offset‐to‐depth ratio no less than two) from horizontal interfaces or reflections from dipping interfaces. To find the depth scale of the section and build a model for prestack depth migration using the MVA results, the vertical velocity VP0 needs to be specified for at least a single point in each block. When no borehole information about VP0 is available, a well‐focused image can often be obtained by assuming that the vertical‐velocity field is continuous across layer boundaries. A synthetic test for a three‐layer model with a syncline structure confirms the accuracy of our MVA algorithm in estimating the interval parameters Vnmo, kz, kx, and η and illustrates the influence of errors in the vertical velocity on the image quality.

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: 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.

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