Efficient migration through complex water‐bottom topography

Geophysics ◽  
1993 ◽  
Vol 58 (3) ◽  
pp. 393-398 ◽  
Author(s):  
Walt Lynn ◽  
Scott MacKay ◽  
Craig J. Beasley
Keyword(s):  
Bottom Topography ◽  
Migration Velocity ◽  
The Other ◽  
Lateral Velocity ◽  
Thin Lens ◽  
Simple Modification ◽  
Depth Migration ◽  
Time Migration ◽  
Sediment Interface ◽  
Water Bottom

An efficient means of imaging structures beneath complex water‐bottom topography is obtained using a conventional time‐migration algorithm with a simple modification to the migration‐velocity field. The process consists of two migration steps: one with the migration velocity set to zero below the water bottom and the other with the migration velocity set to zero above the water bottom. Between the two steps the data are vertically time shifted to account for the lateral velocity variations between the water‐sediment interface. The time shifts used are equivalent to the so‐called “thin‐lens” term used in depth‐migration algorithms. Efficiency is obtained by applying the thin‐lens term only once and by using computationally optimized time‐migration algorithms. Results obtained from this technique are nearly identical to more costly wave‐equation, layer‐replacement, and depth‐migration techniques.

Plumes: Response of time migration to lateral velocity variation

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1118-1127 ◽  
Author(s):  
Dimitri Bevc ◽  
James L. Black ◽  
Gopal Palacharla
Keyword(s):  
Impulse Response ◽  
Synthetic Data ◽  
Migration Velocity ◽  
Velocity Variation ◽  
Velocity Dependence ◽  
Geometrical Construction ◽  
Lateral Velocity ◽  
Time Migration ◽  
Offset Time ◽  
Zero Offset

We analyze how time migration mispositions events in the presence of lateral velocity variation by examining the impulse response of depth modeling followed by time migration. By examining this impulse response, we lay the groundwork for the development of a remedial migration operator that links time and depth migration. A simple theory by Black and Brzostowski predicted that the response of zero‐offset time migration to a point diffractor in a v(x, z) medium would be a distinctive, cusp‐shaped curve called a plume. We have constructed these plumes by migrating synthetic data using several time‐migration methods. We have also computed the shape of the plumes by two geometrical construction methods. These two geometrical methods compare well and explain the observed migration results. The plume response is strongly influenced by migration velocity. We have studied this dependency by migrating synthetic data with different velocities. The observed velocity dependence is confirmed by geometrical construction. A simple first‐order theory qualitatively explains the behavior of zero‐offset time migration, but a more complete understanding of migration velocity dependence in a v(x, z) medium requires a higher order finite‐offset theory.

Response by Arthur E. Barnes to the reply by the authors

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1947-1947 ◽  
Author(s):  
Arthur E. Barnes
Keyword(s):  
Lateral Velocity ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Time Migration ◽  
Pulse Distortion ◽  
Velocity Variations ◽  
Zero Offset ◽  
Complex Geology

I appreciate the thoughtful and thorough response given by Tygel et al. They point out that even for a single dipping reflector imaged by a single non‐zero offset raypath, pulse distortion caused by “standard processing” (NM0 correction‐CMP sort‐stack‐time migration) and pulse distortion caused by prestack depth migration are not really the same, because the reflecting point is mispositioned in standard processing. Within a CMP gather, this mispositioning increases with offset, giving rise to “CMP smear.” CMP smear degrades the stack, introducing additional pulse distortion. Where i‐t is significant, and where lateral velocity variations or reflection curvature are large, such as for complex geology, the pulse distortion of standard processing can differ greatly from that of prestack depth migration.

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).

scholarly journals Wave-equation time migration

Geophysics ◽  
2020 ◽  
pp. 1-58
Author(s):  
Sergey Fomel ◽  
Harpreet Kaur
Keyword(s):  
Wave Equation ◽  
Time Domain ◽  
Field Data ◽  
Model Building ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Time Migration ◽  
Expensive Model ◽  
Approximate Equations ◽  
Ray Coordinates

Time migration, as opposed to depth migration, suffers from two well-known shortcomings: (1)approximate equations are used for computing Green’s functions inside the imaging operator; (2) in case of lateral velocity variations, the transformation between the image ray coordinates andthe Cartesian coordinates is undefined in places where the image rays cross. We show that thefirst limitation can be removed entirely by formulating time migration through wave propagationin image-ray coordinates. The proposed approach constructs a time-migrated image without relyingon any kind of traveltime approximation by formulating an appropriate geometrically accurateacoustic wave equation in the time-migration domain. The advantage of this approach is that thepropagation velocity in image-ray coordinates does not require expensive model building and canbe approximated by quantities that are estimated in conventional time-domain processing. Synthetic and field data examples demonstrate the effectiveness of the proposed approach and show that theproposed imaging workflow leads to a significant uplift in terms of image quality and can bridge thegap between time and depth migrations. The image obtained by the proposed algorithm is correctlyfocused and mapped to depth coordinates it is comparable to the image obtained by depth migration.

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.

Evaluation of two‐pass three‐dimensional migration

Geophysics ◽  
1988 ◽  
Vol 53 (1) ◽  
pp. 32-49 ◽  
Author(s):  
John A. Dickinson
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Three Dimensional ◽  
Velocity Variation ◽  
Lateral Velocity ◽  
Data Manipulation ◽  
Depth Migration ◽  
Data Comparison ◽  
Time Migration ◽  
Order Of Magnitude

The theoretically correct way to perform a three‐dimensional (3-D) migration of seismic data requires large amounts of data manipulation on the computer. In order to alleviate this problem, a true, one‐pass 3-D migration is commonly replaced with an approximate technique in which a series of two‐dimensional (2-D) migrations is performed in orthogonal directions. This two‐pass algorithm produces the correct answer when the velocity is constant, both horizontally and vertically. Here I analyze the error due to this algorithm when the velocities vary vertically. The analysis has two parts: first, a theoretical analysis is performed in which a formula for the error is derived; and second, a field data comparison between one‐pass and two‐pass migrations is shown. My conclusion is that two‐pass 3-D migration is, in general, a very good approximation. Its errors are usually small, the exceptions being when both the reflector dip is large (in practice this typically means greater than about 25 to 40 degrees) and the orientation of the reflector is in neither the inline nor the crossline direction. Even then the error is the same order of magnitude as that due to the uncertainty in the migration velocities. These conclusions are still valid when there is lateral velocity variation, as long as this variation is accounted for by trace stretching. The analysis presented here deals with time migration; no claims are made regarding depth migration.

Prestack layer replacement

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1355-1369 ◽  
Author(s):  
Oz Yilmaz ◽  
Darran Lucas
Keyword(s):  
Wave Equation ◽  
Field Data ◽  
Bottom Topography ◽  
Complex Structure ◽  
Integral Solution ◽  
Scalar Wave ◽  
Time Migration ◽  
Replacement Technique ◽  
Kirchhoff Integral ◽  
Water Bottom

We present a method of layer replacement based on the Kirchhoff integral solution to the scalar wave equation. The term “layer replacement” refers to replacing the overburden velocity with the velocity of the substratum, thereby eliminating raypath bendings at the interface between the overburden and the substratum. It is the raypath bendings that induce distortions and disruptions on reflections beneath a complex structure. When implemented before stack, layer replacement provides an opportunity to revise velocity estimates after correcting for the nonhyperbolic moveout on CMP data caused by a complex overburden. As a result, layer replacement also yields an improved unmigrated stack section. Imaging can then be completed by time migration after stack. We demonstrate the layer‐replacement technique on field data with irregular water‐bottom topography.

Systematics of time‐migration errors

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1419-1434 ◽  
Author(s):  
James L. Black ◽  
Matthew A. Brzostowski
Keyword(s):  
General Scheme ◽  
Velocity Variation ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Time Migration ◽  
Simple Rules ◽  
Rules Of Thumb ◽  
Velocity Changes ◽  
Dip Angle ◽  
Depth Of Burial

Even if the correct velocity is used, time migration mispositions events whenever the velocity changes laterally. These errors increase with lateral velocity variation, depth of burial, and dip angle θ. Our analyses of two model types, one with an implicit gradient and one with an explicit gradient, yield simple “rules of thumb” for these errors to first order in the lateral gradient. The x error is [Formula: see text], and the z error is [Formula: see text], where the quantity A = A(x, z) contains the information about depth of burial and magnitude of lateral gradient. These rules can be used to determine when depth migration is needed. Further analysis also shows that the image‐ray correction to time migration is accurate only at small dip. For dipping events, the image‐ray correction must be supplemented by a shift in x of the form [Formula: see text] and a shift in z given by [Formula: see text]. These time‐migration corrections take the same form for both the models we have studied, suggesting a general scheme for correcting time migration, which we call “remedial migration.”

Tomographic velocity analysis and wave-equation depth migration in an overthrust terrain: A case study from the Tuha Basin, China

2018 ◽  
Vol 6 (1) ◽  
pp. T1-T13
Author(s):  
Bin Lyu ◽  
Qin Su ◽  
Kurt J. Marfurt
Keyword(s):  
Wave Equation ◽  
Data Quality ◽  
Model Building ◽  
Velocity Model ◽  
Lateral Velocity ◽  
Near Surface ◽  
Depth Migration ◽  
Time Migration ◽  
Head Waves ◽  
Velocity Variations

Although the structures associated with overthrust terrains form important targets in many basins, accurately imaging remains challenging. Steep dips and strong lateral velocity variations associated with these complex structures require prestack depth migration instead of simpler time migration. The associated rough topography, coupled with older, more indurated, and thus high-velocity rocks near or outcropping at the surface often lead to seismic data that suffer from severe statics problems, strong head waves, and backscattered energy from the shallow section, giving rise to a low signal-to-noise ratio that increases the difficulties in building an accurate velocity model for subsequent depth migration. We applied a multidomain cascaded noise attenuation workflow to suppress much of the linear noise. Strong lateral velocity variations occur not only at depth but near the surface as well, distorting the reflections and degrading all deeper images. Conventional elevation corrections followed by refraction statics methods fail in these areas due to poor data quality and the absence of a continuous refracting surface. Although a seismically derived tomographic solution provides an improved image, constraining the solution to the near-surface depth-domain interval velocities measured along the surface outcrop data provides further improvement. Although a one-way wave-equation migration algorithm accounts for the strong lateral velocity variations and complicated structures at depth, modifying the algorithm to account for lateral variation in illumination caused by the irregular topography significantly improves the image, preserving the subsurface amplitude variations. We believe that our step-by-step workflow of addressing the data quality, velocity model building, and seismic imaging developed for the Tuha Basin of China can be applied to other overthrust plays in other parts of the world.

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