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.

Image gathers of SV-waves in homogeneous and factorized VTI media

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. D55-D64 ◽  
Author(s):  
Ramzy M. Al-Zayer ◽  
Ilya Tsvankin
Keyword(s):  
Shear Wave ◽  
Vertical Velocity ◽  
Migration Velocity ◽  
P Wave ◽  
Model Parameters ◽  
Velocity Analysis ◽  
Wave Data ◽  
Migration Velocity Analysis ◽  
Wave Migration ◽  
Vti Media

Reflection moveout of SV-waves in transversely isotropic media with a vertical symmetry axis (VTI media) can provide valuable information about the model parameters and help to overcome the ambiguities in the inversion of P-wave data. Here, to develop a foundation for shear-wave migration velocity analysis, we study SV-wave image gathers obtained after prestack depth migration. The key issue, addressed using both approximate analytic results and Kirchhoff migration of synthetic data, is whether long-spread SV data can constrain the shear-wave vertical velocity [Formula: see text] and the depth scale of VTI models. For homogeneous media, the residual moveout of horizontal SV events on image gathers is close to hyperbolic and depends just on the NMO velocity [Formula: see text] out to offset-to-depth ratios of about 1.7. Because [Formula: see text] differs from [Formula: see text], flattening moderate-spread gathers of SV-waves does not ensure the correct depth of the migrated events. The residual moveout rapidly becomes nonhyperbolic as the offset-to-depth ratio approaches two, with the migrated depths at long offsets strongly influenced by the SV-wave anisotropy parameter σ. Although the combination of [Formula: see text] and σ is sufficient to constrain the vertical velocity [Formula: see text] and reflector depth, the tradeoff between σ and the Thomsen parameter ε on long-spread gathers causes errors in time-to-depth conversion. The residual moveout of dipping SV events is also controlled by the parameters [Formula: see text], σ, and ε, but in the presence of dip, the contributions of both σ and ε are significant even at small offsets. For factorized v(z) VTI media with a constant SV-wave vertical-velocity gradient [Formula: see text], flattening of horizontal events for a range of depths requires the correct NMO velocity at the surface, the gradient [Formula: see text], and, for long offsets, the parameters σ and ε. On the whole, the nonnegligible uncertainty in the estimation of reflector depth from SV-wave moveout highlights the need to combine P- and SV-wave data in migration velocity analysis for VTI media.

Analysis of image gathers in factorized VTI media

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2016-2025 ◽  
Author(s):  
Debashish Sarkar ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Velocity Gradient ◽  
Migration Velocity ◽  
P Wave ◽  
Velocity Variation ◽  
Velocity Analysis ◽  
Lateral Heterogeneity ◽  
Velocity Models ◽  
Isotropic Media ◽  
Vti Media

Because events in image gathers generated after prestack depth migration are sensitive to the velocity field, they are often used in migration velocity analysis for isotropic media. Here, we present an analytic and numerical study of P‐wave image gathers in transversely isotropic media with a vertical symmetry axis (VTI) and establish the conditions for flattening such events and positioning them at the true reflector depth. Application of the weak‐anisotropy approximation leads to concise expressions for reflections in image gathers from homogeneous and factorized v(z) media in terms of the VTI parameters and the vertical velocity gradient kz. Flattening events in image gathers for any reflector dip requires accurate values of the zero‐dip NMO velocity at the surface [Vnmo (z = 0)], the gradient kz, and the anellipticity coefficient η. For a fixed error in Vnmo and kz, the magnitude of residual moveout of events in image gathers decreases with dip, while the moveout caused by an error in η initially increases for moderate dips but then decreases as dips approach 90°. Flat events in image gathers in VTI media, however, do not guarantee the correct depth scale of the model because reflector depth depends on the vertical migration velocity. For factorized v(x, z) media with a linear velocity variation in both the x‐ and z‐directions, the moveout on image gathers is controlled by Vnmo (x = z = 0), kz, η, and a combination of the horizontal velocity gradient kx and the Thomsen parameter δ (specifically, kx[Formula: see text]). If too large a value of any of these four quantities is used in migration, reflections in the image gathers curve downward (i.e., they are undercorrected; the inferred depth increases with offset), while a negative error results in overcorrection. Lateral heterogeneity tends to increase the sensitivity of moveout of events in image gathers to the parameter η, and errors in η may lead to measurable residual moveout of horizontal events in v(x, z) media even for offset‐to‐depth ratios close to unity. These results provide a basis for extending to VTI media conventional velocity analysis methods operating with image gathers. Although P‐wave traveltimes alone cannot be used to separate anisotropy from lateral heterogeneity (i.e., kx is coupled to δ), moveout of events in image gathers does constrain the vertical gradient kz. Hence, it may be possible to build VTI velocity models in depth by supplementing reflection data with minimal a priori information, such as the vertical velocity at the top of the factorized VTI layer.

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.

Depth‐domain velocity analysis in VTI media using surface P-wave data: Is it feasible?

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 897-903 ◽  
Author(s):  
Yves Le Stunff ◽  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Heterogeneous Media ◽  
Wave Reflection ◽  
P Wave ◽  
Model Parameters ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Velocity Models ◽  
Trade Offs ◽  
Vti Media

The main difficulties in anisotropic velocity analysis and inversion using surface seismic data are associated with the multiparameter nature of the problem and inherent trade‐offs between the model parameters. For the most common anisotropic model, transverse isotropy with a vertical symmetry axis (VTI media), P-wave kinematic signatures are controlled by the vertical velocity V0 and the anisotropic parameters ε and δ. However, only two combinations of these parameters—NMO velocity from a horizontal reflector Vnmo(0) and the anellipticity coefficient η—can be determined from P-wave reflection traveltimes if the medium above the reflector is laterally homogeneous. While Vnmo(0) and η are sufficient for time‐domain imaging in VTI media, they cannot be used to resolve the vertical velocity and build velocity models needed for depth migration. Here, we demonstrate that P-wave reflection data can be inverted for all three relevant VTI parameters (V0, ε and δ) if the model contains nonhorizontal intermediate interfaces. Using anisotropic reflection tomography, we carry out parameter estimation for a two‐layer medium with a curved intermediate interface and reconstruct the correct anisotropic depth model. To explain the success of this inversion procedure, we present an analytic study of reflection traveltimes for this model and show that the information about the vertical velocity and reflector depth was contained in the reflected rays which crossed the dipping intermediate interface. The results of this work are especially encouraging because the need for depth imaging (such as prestack depth migration) arises mostly in laterally heterogeneous media. Still, we restricted this study to a relatively simple model and constrained the inversion by assuming that one of the layers is isotropic. In general, although lateral heterogeneity does create a dependence of P-wave reflection traveltimes on the vertical velocity, there is no guarantee that for more complicated models all anisotropic parameters can be resolved in a unique fashion.

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.

Migration velocity analysis for TI media in the presence of quadratic lateral velocity variation

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. U87-U96 ◽  
Author(s):  
Mamoru Takanashi ◽  
Ilya Tsvankin
Keyword(s):  
Migration Velocity ◽  
P Wave ◽  
Velocity Variation ◽  
Small Scale ◽  
Velocity Analysis ◽  
Lateral Heterogeneity ◽  
Lateral Velocity ◽  
Symmetry Direction ◽  
Migration Velocity Analysis ◽  
Ti Media

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 [Formula: see text] and [Formula: see text] and the symmetry-direction velocity [Formula: see text] 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 [Formula: see text] 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.

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

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.

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