A comparison of common‐midpoint, single‐shot, and plane‐wave depth migration

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 1896-1907 ◽  
Author(s):  
P. Temme
Keyword(s):  
Reflection Coefficient ◽  
Finite Difference ◽  
Plane Wave ◽  
Wave Field ◽  
Single Shot ◽  
Imaging Condition ◽  
Depth Migration ◽  
Finite Aperture ◽  
Wave Migration ◽  
Slant Stacking

A comparison of common‐midpoint (CMP), single‐shot, and plane‐wave migration was made for simple two‐dimensional structures such as a syncline and a horizontal reflector with a laterally variable reflection coefficient by using synthetic seismograms. The seismograms were calculated employing the finite‐difference technique. CMP sections were simulated by 18-fold stacking and plane‐wave sections by slant stacking. By applying a finite‐difference scheme, the synthetic wave field was continued downward. The usual imaging condition of CMP migration was extended in order to carry out migration of single‐shot and plane‐wave sections. The reflection coefficient was reconstructed by comparing the migrated wave field with the incident wave field at the reflector. The results are: (1) all three migration techniques succeeded in reconstructing the reflector position; (2) as a consequence of the finite aperture of the geophone spread, only segments of the reflector could be reconstructed by single‐shot and plane‐wave migration; (3) for single‐shot and plane‐wave migration the reflection coefficient could be obtained; and (4) CMP migration may lead to incorrect conclusions regarding the reflection coefficient.

Plane-wave depth migration

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. S261-S272 ◽  
Author(s):  
Paul L. Stoffa ◽  
Mrinal K. Sen ◽  
Roustam K. Seifoullaev ◽  
Reynam C. Pestana ◽  
Jacob T. Fokkema
Keyword(s):  
Phase Space ◽  
Plane Wave ◽  
Plane Waves ◽  
Computation Time ◽  
Depth Migration ◽  
Velocity Modeling ◽  
Natural Domain ◽  
Data Volume ◽  
Wave Migration ◽  
Slant Stacking

We present fast and efficient plane-wave migration methods for densely sampled seismic data in both the source and receiver domains. The methods are based on slant stacking over both shot and receiver positions (or offsets) for all the recorded data. If the data-acquisition geometry permits, both inline and crossline source and receiver positions can be incorporated into a multidimensional phase-velocity space, which is regular even for randomly positioned input data. By noting the maximum time dips present in the shot and receiver gathers and constant-offset sections, the number of plane waves required can be estimated, and this generally results in a reduction of the data volume used for migration. The required traveltime computations for depth imaging are independent for each particular plane-wave component. It thus can be used for either the source or the receiver plane waves during extrapolation in phase space, reducing considerably the computational burden. Since only vertical delay times are required, many traveltime techniques can be employed, and the problems with multipathing and first arrivals are either reduced or eliminated. Further, the plane-wave integrals can be pruned to concentrate the image on selected targets. In this way, the computation time can be further reduced, and the technique lends itself naturally to a velocity-modeling scheme where, for example, horizontal and then steeply dipping events are gradually introduced into the velocity analysis. The migration method also lends itself to imaging in anisotropic media because phase space is the natural domain for such an analysis.

3D plane-wave migration in tilted coordinates: A field data example

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA199-WCA209 ◽  
Author(s):  
Guojian Shan ◽  
Robert Clapp ◽  
Biondo Biondi
Keyword(s):  
Plane Wave ◽  
Field Data ◽  
Synthetic Data ◽  
Data Set ◽  
Wave Source ◽  
Surface Data ◽  
The One ◽  
Wave Migration ◽  
Wavefield Extrapolation ◽  
Slant Stacking

We have extended isotropic plane-wave migration in tilted coordinates to 3D anisotropic media and applied it on a Gulf of Mexico data set. Recorded surface data are transformed to plane-wave data by slant-stack processing in inline and crossline directions. The source plane wave and its corresponding slant-stacked data are extrapolated into the subsurface within a tilted coordinate system whose direction depends on the propagation direction of the plane wave. Images are generated by crosscorrelating these two wavefields. The shot sampling is sparse in the crossline direction, and the source generated by slant stacking is not really a plane-wave source but a phase-encoded source. We have discovered that phase-encoded source migration in tilted coordinates can image steep reflectors, using 2D synthetic data set examples. The field data example shows that 3D plane-wave migration in tilted coordinates can image steeply dipping salt flanks and faults, even though the one-way wave-equation operator is used for wavefield extrapolation.

Improving plane‐wave decomposition and migration

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 195-205 ◽  
Author(s):  
Hans J. Tieman
Keyword(s):  
Plane Wave ◽  
Computer Time ◽  
Lateral Velocity ◽  
High Quality ◽  
Depth Migration ◽  
Wave Data ◽  
Velocity Variations ◽  
And Migration ◽  
The One ◽  
Slant Stacking

Plane‐wave data can be produced by slant stacking common geophone gathers over source locations. Practical difficulties arise with slant stacks over common receiver gathers that do not arise with slant stacks over common‐midpoint gathers. New techniques such as hyperbolic velocity filtering allow the production of high‐quality slant stacks of common‐midpoint data that are relatively free of artifacts. These techniques can not be used on common geophone data because of the less predictive nature of data in this domain. However, unlike plane‐wave data, slant stacks over midpoint gathers cannot be migrated accurately using depth migration. A new transformation that links common‐midpoint slant stacks to common geophone slant stacks allows the use together of optimized methods of slant stacking and accurate depth migration in data processing. Accurate depth migration algorithms are needed to migrate plane‐wave data because of the potentially high angles of propagation exhibited by the data and because of any lateral velocity variations in the subsurface. Splitting the one‐way wave continuation operator into two components (one that is a function of a laterally independent velocity, and a residual term that handles lateral variations in subsurface velocities) results in a good approximation. The first component is applied in the wavenumber domain, the other is applied in the space domain. The approximation is accurate for any angle of propagation in the absence of lateral velocity variations, although with severe lateral velocity variations the accuracy is reduced to 50°. High‐quality plane‐wave data migrated using accurate wave continuation operators results in a high‐quality image of the subsurface. Because of the signal‐to‐noise content of this data the number of sections that need to be migrated can be reduced considerably. This not only saves computer time, more importantly it makes computer‐intensive tasks such as migration velocity analysis based on maximizing stack power more feasible.

Reverse‐time migration of offset vertical seismic profiling data using the excitation‐time imaging condition

Geophysics ◽  
1986 ◽  
Vol 51 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Wen‐Fong Chang ◽  
George A. McMechan
Keyword(s):  
Finite Difference ◽  
Wave Field ◽  
Image Space ◽  
Variable Velocity ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Zero ◽  
Time Migration ◽  
Excitation Time

To apply reverse‐time migration to prestack, finite‐offset data from variable‐velocity media, the standard (time zero) imaging condition must be generalized because each point in the image space has a different image time (or times). This generalization is the excitation‐time imaging condition, in which each point is imaged at the one‐way traveltime from the source to that point. Reverse‐time migration with the excitation‐time imaging condition consists of three elements: (1) computation of the imaging condition; (2) extrapolation of the recorder wave field; and (3) application of the imaging condition. Computation of the imaging condition for each point in the image is done by ray tracing from the source point; this is equivalent to extrapolation of the source wave field through the medium. Extrapolation of the recorded wave field is done by an acoustic finite‐difference algorithm. Imaging is performed at each step of the finite‐difference extrapolation by extracting, from the propagating wave field, the amplitude at each mesh point that is imaged at that time and adding these into the image space at the same spatial locations. The locus of all points imaged at one time step is a wavefront [a constant time (or phase) trajectory]. This prestack migration algorithm is very general. The excitation‐time imaging condition is applicable to all source‐receiver geometries and variable‐velocity media and reduces exactly to the usual time‐zero imaging condition when used with zero‐offset surface data. The algorithm is illustrated by application to both synthetic and real VSP data. The most interesting and potentially useful result in the processing of the synthetic data is imaging of the horizontal fluid interfaces within a reservoir even when the surrounding reservoir boundaries are not well imaged.

Fast frequency‐wavenumber migration for depth‐dependent velocity

Geophysics ◽  
1987 ◽  
Vol 52 (11) ◽  
pp. 1483-1491 ◽  
Author(s):  
G. Müller ◽  
P. Temme
Keyword(s):  
Plane Wave ◽  
Constant Velocity ◽  
Layered Medium ◽  
Data Interpretation ◽  
Single Shot ◽  
Subsurface Structures ◽  
Inverse Fourier Transformation ◽  
Interactive Data ◽  
Wave Migration ◽  
Target Depth

Fast frequency‐wavenumber migration for a constant‐velocity medium is generalized for a medium with depth‐dependent velocity and density. As in the constant‐velocity case, the migrated section is obtained with one inverse Fourier transformation of the modified spectrum of the observed wave field. The migrated section is exact in a preselected focusing depth (in the case of common‐midpoint and plane‐wave migration) or in a preselected focusing point (in the case of single‐shot migration) and in the vicinity of this depth or point. Elsewhere the migrated section is distorted. The method is in essence a constant‐velocity migration with the velocity [Formula: see text] at the target depth [Formula: see text] (not with an average velocity), extended by a phase‐shift operation which takes account of the true velocity‐depth function v(z) between z = 0 and [Formula: see text]. If the focusing depth or point is located in a layer with constant velocity and density, the migrated section is exact throughout the layer (for CMP and plane‐wave migration) or along the segment of the ray from shot to focusing point, running through the layer (for single‐shot migration). Examples are given for the successful migration of the plane‐wave response of a horizontally layered medium at vertical and oblique incidence and for the single‐shot response of a horizontally layered structure with embedded reflector elements. The method appears to be particularly useful for the investigation of subsurface structures with restricted dimensions; because of its speed, interactive data interpretation is possible.

Plane-wave migration in tilted coordinates

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. S185-S194 ◽  
Author(s):  
Guojian Shan ◽  
Biondo Biondi
Keyword(s):  
Plane Wave ◽  
Coordinate System ◽  
Synthetic Data ◽  
Data Set ◽  
Wave Source ◽  
Surface Data ◽  
Migration Method ◽  
Wave Migration ◽  
Wavefield Extrapolation ◽  
Slant Stacking

We have developed a plane-wave migration method that efficiently images steeply dipping reflectors using one-way wavefield extrapolation. The recorded surface data are converted to plane-wave source data by slant stacking. The data set corresponding to each plane-wave source is migrated independently in a tilted coordinate system, with the extrapolation direction determined by the initial propagation direction of the plane wave at the surface. Waves illuminating steeply dipping reflectors, such as overturned waves and waves traveling nearly horizontally, are extrapolated accurately in an appropriate tilted coordinate system because the extrapolation direction is close to the propagation directions for these waves. Two-dimensional impulse responses and synthetic data examples demonstrate that plane-wave migration in tilted coordinates generates high-quality images of steeply dipping reflectors, particularly rugose salt tops and steep salt flanks.

Implicit Finite-Difference Plane Wave Migration in TTI Media

2011 ◽  
Vol 54 (2) ◽  
pp. 254-263
Author(s):  
Li HAN ◽  
Li-Guo HAN ◽  
Xiang-Bo GONG ◽  
Gang-Yi SHAN ◽  
Jie CUI
Keyword(s):  
Finite Difference ◽  
Plane Wave ◽  
Implicit Finite Difference ◽  
Tti Media ◽  
Wave Migration

scholarly journals Deconvolution-type imaging condition effects on shot-profile migration amplitudes

2012 ◽  
Vol 5 (1) ◽  
pp. 05-18
Author(s):  
Flor-A. Vivas-Mejía ◽  
Herling González-Alvarez ◽  
Ligia-E. Jaimes-Osorio ◽  
Nancy Espindola-López
Keyword(s):  
Spectral Density ◽  
Weighting Function ◽  
Synthetic Data ◽  
Velocity Model ◽  
Single Shot ◽  
Lateral Velocity ◽  
Imaging Condition ◽  
Depth Migration ◽  
Reflectivity Function ◽  
Imaging Conditions

Amplitude preservation in Pre-Stack Depth Migration (PSDM) processes that use wavefield extrapolation must be ensured – first, in the operators used to continue the wavefield in time or depth, and second, in the imaging condition used to estimate the reflectivity function. In the later point, the conventional correlation-type imaging condition must be replaced by a deconvolution-type imaging condition. Migration performed in common-shot profile domain obtains the final migrated image as the superposition of images resulting of migrate each shot separately. The amplitude obtained in a point of the migrated image corresponds to the sum of the reflectivities for each shot which has illuminated such point, along the angles determined by the velocity model and the positions of the source and the receiver. The deeper the reflector, the lower the amplitude of the illumination field will be. As result, the correlation-type imaging condition produces images with an unbalanced amplitude decrease with depth. A deconvolution-type imaging condition scales the amplitudes through a correlation, using the weighting function dependent on the spectral density or the illumination of the downgoing wave field. In this article, two possible scaling functions have been used in the case of a single shot. In the case of data with multiple shots, five scaling possibilities are presented with the spectral density or the illumination function. The results of applying these imaging conditions to synthetic data with multiple shots show that the values of the amplitude in the migrated images are influenced by the coverage of the common midpoint, compensating this effect only in one of the imaging conditions described. Numerical experiments with synthetic data generated using Seismic Unix and the Sigsbee2a data are presented, highlighting that in velocity fields with strong vertical and lateral velocity variations, the balance of the amplitudes of the deep reflectors relative to the shallow reflectors is strongly influenced by the imaging condition applied.

Efficient 3D wave-equation migration using virtual planar sources

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. S185-S197 ◽  
Author(s):  
Bertrand Duquet ◽  
Patrick Lailly
Keyword(s):  
Plane Wave ◽  
Velocity Model ◽  
Prestack Depth Migration ◽  
Depth Imaging ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Wave Migration ◽  
Complex Velocity Model ◽  
Full Volume ◽  
Migration Technique

Full-volume seismic imaging is essential for a sound interpretation of structurally complex geologies. Prestack depth imaging is the most appropriate tool for such imaging, but it requires a precise and often complex velocity model. In such situations, 3D Kirchhoff prestack depth migration can be quite expensive. On the other hand, a wavefield approach, although generally tremendously expensive, is not affected by the complexity of the velocity model. We propose an affordable 3-D wavefield prestack depth-migration technique. It is designed for marine surveys for which the source-receiver azimuth is approximately constant. The technique applies a plane-wave migration algorithm to time-shifted data — quite a surprising approach when we realize that marine surveys do not allow the synthesis of genuine plane-wave data. Additionally, the imaging principle has to be modified to give results consistent with shot-record migration. Our technique also produces image gathers that allow an update of the velocity model by means of migration velocity analysis. Results from synthetics and conventional marine data demonstrate the effectiveness of the method.

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