Plane-wave migration in tilted coordinates

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.

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

Geophysics ◽

10.1190/1.3242752 ◽

2009 ◽

Vol 74 (6) ◽

pp. WCA199-WCA209 ◽

Cited By ~ 4

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.

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Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽

10.1190/1.2235616 ◽

2006 ◽

Vol 71 (5) ◽

pp. U67-U76 ◽

Cited By ~ 7

Author(s):

Robert J. Ferguson

Keyword(s):

Least Squares ◽

Seismic Data ◽

Synthetic Data ◽

Real Data ◽

Structural Data ◽

Irregular Sampling ◽

Data Set ◽

Near Surface ◽

Damped Least Squares ◽

Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

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Imaging near-surface heterogeneities by natural migration of backscattered surface waves: Field data test

Geophysics ◽

10.1190/geo2016-0253.1 ◽

2017 ◽

Vol 82 (3) ◽

pp. S197-S205 ◽

Cited By ~ 8

Author(s):

Zhaolun Liu ◽

Abdullah AlTheyab ◽

Sherif M. Hanafy ◽

Gerard Schuster

Keyword(s):

Surface Waves ◽

Field Data ◽

Synthetic Data ◽

Data Sets ◽

Data Set ◽

Near Surface ◽

3D Data ◽

Strong Surface ◽

Migration Method ◽

Recorded Data

We have developed a methodology for detecting the presence of near-surface heterogeneities by naturally migrating backscattered surface waves in controlled-source data. The near-surface heterogeneities must be located within a depth of approximately one-third the dominant wavelength [Formula: see text] of the strong surface-wave arrivals. This natural migration method does not require knowledge of the near-surface phase-velocity distribution because it uses the recorded data to approximate the Green’s functions for migration. Prior to migration, the backscattered data are separated from the original records, and the band-passed filtered data are migrated to give an estimate of the migration image at a depth of approximately one-third [Formula: see text]. Each band-passed data set gives a migration image at a different depth. Results with synthetic data and field data recorded over known faults validate the effectiveness of this method. Migrating the surface waves in recorded 2D and 3D data sets accurately reveals the locations of known faults. The limitation of this method is that it requires a dense array of receivers with a geophone interval less than approximately one-half [Formula: see text].

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Plane-wave depth migration

Geophysics ◽

10.1190/1.2357832 ◽

2006 ◽

Vol 71 (6) ◽

pp. S261-S272 ◽

Cited By ~ 43

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.

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3D prestack plane-wave, full-waveform inversion

Geophysics ◽

10.1190/1.2952623 ◽

2008 ◽

Vol 73 (5) ◽

pp. VE135-VE144 ◽

Cited By ~ 183

Author(s):

Denes Vigh ◽

E. William Starr

Keyword(s):

Plane Wave ◽

Data Acquisition ◽

Time Domain ◽

Waveform Inversion ◽

Back Propagation ◽

Synthetic Data ◽

Full Waveform Inversion ◽

Data Set ◽

Full Waveform ◽

The Time Domain

Prestack depth migration has been used for decades to derive velocity distributions in depth. Numerous tools and methodologies have been developed to reach this goal. Exploration in geologically more complex areas exceeds the abilities of existing methods. New data-acquisition and data-processing methods are required to answer these new challenges effectively. The recently introduced wide-azimuth data acquisition method offers better illumination and noise attenuation as well as an opportunity to more accurately determine velocities for imaging. One of the most advanced tools for depth imaging is full-waveform inversion. Prestack seismic full-waveform inversion is very challenging because of the nonlinearity and nonuniqueness of the solution. Combined with multiple iterations of forward modeling and residual wavefield back propagation, the method is computer intensive, especially for 3D projects. We studied a time-domain, plane-wave implementation of 3D waveform inversion. We found that plane-wave gathers are an attractive input to waveform inversion with dramatically reduced computer run times compared to traditional shot-gather approaches. The study was conducted on two synthetic data sets — Marmousi2 and SMAART Pluto 1.5 — and a field data set. The results showed that a velocity field can be reconstructed well using a multiscale time-domain implementation of waveform inversion. Although the time-domain solution does not take advantage of wavenumber redundancy, the method is feasible on current computer architectures for 3D surveys. The inverted velocity volume produces a quality image for exploration geologists by using numerous iterations of waveform inversion.

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Wave-equation migration velocity analysis using plane-wave common-image gathers

Geophysics ◽

10.1190/geo2016-0653.1 ◽

2017 ◽

Vol 82 (5) ◽

pp. S327-S340 ◽

Cited By ~ 9

Author(s):

Bowen Guo ◽

Gerard T. Schuster

Keyword(s):

Wave Equation ◽

Plane Wave ◽

Computational Cost ◽

Migration Velocity ◽

Memory Storage ◽

Velocity Analysis ◽

Data Set ◽

Image Domain ◽

Migration Velocity Analysis ◽

Wave Migration

Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain, or time-lag common-image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, we have developed a WEMVA method using plane-wave CIGs. Plane-wave CIGs reduce computational cost and memory storage because they are directly calculated from prestack plane-wave migration and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic data sets and a field data set validate the efficiency and effectiveness of this method.

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Reciprocity and double plane-wave migration

Geophysics ◽

10.1190/geo2017-0161.1 ◽

2017 ◽

Vol 82 (6) ◽

pp. S453-S466 ◽

Cited By ~ 6

Author(s):

Zeyu Zhao ◽

Mrinal K. Sen ◽

Paul L. Stoffa

Keyword(s):

Plane Wave ◽

Computational Cost ◽

Seismic Energy ◽

Data Sets ◽

Reciprocity Principle ◽

Data Set ◽

Wave Data ◽

Double Plane ◽

Wave Migration ◽

Ray Parameter

In plane-wave migration techniques, plane-wave data sets with seismic energy in both positive and negative ray-parameter sections are more desirable than those with seismic energy only in either positive or negative ray-parameter sections. Such plane-wave data sets are often referred to as optimal plane-wave data sets because they can be used to illuminate the subsurface from both sides of the targets and, therefore, can produce sharp images. Traditionally, to obtain optimal plane-wave data sets from one-sided gathers generated by marine seismic acquisition geometry, one needs to invoke the reciprocity principle to sort split-spread gathers prior to implementing plane-wave decomposition. We have investigated the applicability of the reciprocity principle in the double plane-wave (DPW) domain. We have developed an easy and efficient merging method that generates optimal plane-wave data sets in the DPW domain using one-sided shot gathers. We call this resultant plane-wave data set the “optimal DPW data set.” We find that an optimal DPW data set transformed from one-sided gathers is a good approximation to a DPW data set transformed from split-spread gathers with the same maximum offset as that of the one-sided gathers. We find that ray-parameter common-image gathers with continuous events in both positive and negative ray-parameter sections can be generated by migrating optimal DPW data sets. This helps migration velocity analysis and improves the subsurface illumination. In addition, we show that the computational cost of DPW migration methods could be reduced with the help of the reciprocity principle. We test our proposed method using a synthetic model to demonstrate its effectiveness.

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Seismic imaging using lateral adaptive windows

Geophysics ◽

10.1190/1.3359799 ◽

2010 ◽

Vol 75 (2) ◽

pp. S73-S79

Author(s):

Ørjan Pedersen ◽

Sverre Brandsberg-Dahl ◽

Bjørn Ursin

Keyword(s):

Seismic Data ◽

Seismic Imaging ◽

Synthetic Data ◽

Real Data ◽

Extrapolation Methods ◽

Depth Migration ◽

Large Velocity ◽

Migration Method ◽

Wavefield Extrapolation ◽

The Impact

One-way wavefield extrapolation methods are used routinely in 3D depth migration algorithms for seismic data. Due to their efficient computer implementations, such one-way methods have become increasingly popular and a wide variety of methods have been introduced. In salt provinces, the migration algorithms must be able to handle large velocity contrasts because the velocities in salt are generally much higher than in the surrounding sediments. This can be a challenge for one-way wavefield extrapolation methods. We present a depth migration method using one-way propagators within lateral windows for handling the large velocity contrasts associated with salt-sediment interfaces. Using adaptive windowing, we can handle large perturbations locally in a similar manner as the beamlet propagator, thus limiting the impact of the errors on the global wavefield. We demonstrate the performance of our method by applying it to synthetic data from the 2D SEG/EAGE [Formula: see text] salt model and an offshore real data example.

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Time-shift imaging condition in seismic migration

Geophysics ◽

10.1190/1.2338824 ◽

2006 ◽

Vol 71 (6) ◽

pp. S209-S217 ◽

Cited By ~ 247

Author(s):

Paul Sava ◽

Sergey Fomel

Keyword(s):

Time Lag ◽

Synthetic Data ◽

Complex Salt ◽

Time Shift ◽

Reverse Time ◽

Data Set ◽

Imaging Condition ◽

Space And Time ◽

Wavefield Extrapolation ◽

Zero Time

Seismic imaging based on single-scattering approximation is in the analysis of the match between the source and receiver wavefields at every image location. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods (Kirchhoff migration) or by differential methods (reverse-time or wavefield extrapolation migration). Different methods can be used to analyze wavefield matching, of which crosscorrelation is a popular option. Implementation of a simple imaging condition requires time crosscorrelation of source and receiver wavefields, followed by extraction of the zero time lag. A generalized imaging condition operates by crosscorrelation in both space and time, followed by image extraction at zero time lag. Images at different spatial crosscorrelation lags are indicators of imaging accuracy and are also used for image-angle decomposition. In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time crosscorrelation. Prestack images are described as functions of time shifts as opposed to space shifts between source and receiver wavefields. This imaging condition is applicable to migration by Kirchhoff, wavefield extrapolation, or reverse-time techniques. The transformation allows construction of common-image gathers presented as functions of either time shift or reflection angle at every location in space. Inaccurate migration velocity is revealed by angle-domain common-image gathers with nonflat events. Computational experiments using a synthetic data set from a complex salt model demonstrate the main features of the method.

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

Geophysics ◽

10.1190/1.1441602 ◽

1984 ◽

Vol 49 (11) ◽

pp. 1896-1907 ◽

Cited By ~ 18

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.

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