Prestack depth migration by symmetric nonstationary phase shift

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 594-603 ◽  
Author(s):  
Robert J. Ferguson ◽  
Gary F. Margrave
Keyword(s):  
Phase Shift ◽  
Symmetric Operator ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Velocity Model ◽  
Computational Effort ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Zero Offset

A new depth migration method suitable for heterogeneous media is presented. The well‐known phase shift plus interpolation (PSPI) method and the recently introduced nonstationary phase‐shift (NSPS) method are combined into a single symmetric operator with improved accuracy and stability and with similar computational effort. For prestack depth migration, the symmetric operator is used in a recursive wavefield extrapolation to compute incident and reflected wavefields at any desired depth, and the ratio of the incident and reflected wavefields at a particular depth is used to estimate seismic reflectivity. When the velocity model is made piecewise constant laterally, the symmetric extrapolation operator can be computed efficiently using ordinary phase‐shift extrapolation for a series of reference velocities and appropriate spatial windowing. Migration of the Marmousi synthetic data set by symmetric nonstationary phase shift (SNPS) provides an image that compares favorably with an image of the zero‐offset reflectivity derived from the Marmousi velocity model.

Sensitivity of prestack depth migration to the velocity model

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 873-882 ◽  
Author(s):  
Roelof Jan Versteeg
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Model Space ◽  
Velocity Model ◽  
Depth Image ◽  
Necessary Condition ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Model Determination

To get a correct earth image from seismic data acquired over complex structures it is essential to use prestack depth migration. A necessary condition for obtaining a correct image is that the prestack depth migration is done with an accurate velocity model. In cases where we need to use prestack depth migration determination of such a model using conventional methods does not give satisfactory results. Thus, new iterative methods for velocity model determination have been developed. The convergence of these methods can be accelerated by defining constraints on the model in such a way that the method only looks for those components of the true earth velocity field that influence the migrated image. In order to determine these components, the sensitivity of the prestack depth migration result to the velocity model is examined using a complex synthetic data set (the Marmousi data set) for which the exact model is known. The images obtained with increasingly smoothed versions of the true model are compared, and it is shown that the minimal spatial wavelength that needs to be in the model to obtain an accurate depth image from the data set is of the order of 200 m. The model space that has to be examined to find an accurate velocity model from complex seismic data can thus be constrained. This will increase the speed and probability of convergence of iterative velocity model determination methods.

Integrated prestack depth migration of vertical seismic profile and surface seismic data from the Rocky Mountain Foothills of southern Alberta, Canada

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1782-1791 ◽  
Author(s):  
M. Graziella Kirtland Grech ◽  
Don C. Lawton ◽  
Scott Cheadle
Keyword(s):  
Seismic Data ◽  
Rocky Mountain ◽  
Velocity Model ◽  
Seismic Profile ◽  
Vertical Seismic Profile ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Southern Alberta ◽  
Vsp Data

We have developed an anisotropic prestack depth migration code that can migrate either vertical seismic profile (VSP) or surface seismic data. We use this migration code in a new method for integrated VSP and surface seismic depth imaging. Instead of splicing the VSP image into the section derived from surface seismic data, we use the same migration algorithm and a single velocity model to migrate both data sets to a common output grid. We then scale and sum the two images to yield one integrated depth‐migrated section. After testing this method on synthetic surface seismic and VSP data, we applied it to field data from a 2D surface seismic line and a multioffset VSP from the Rocky Mountain Foothills of southern Alberta, Canada. Our results show that the resulting integrated image exhibits significant improvement over that obtained from (a) the migration of either data set alone or (b) the conventional splicing approach. The integrated image uses the broader frequency bandwidth of the VSP data to provide higher vertical resolution than the migration of the surface seismic data. The integrated image also shows enhanced structural detail, since no part of the surface seismic section is eliminated, and good event continuity through the use of a single migration–velocity model, obtained by an integrated interpretation of borehole and surface seismic data. This enhanced migrated image enabled us to perform a more robust interpretation with good well ties.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

Unified imaging of multichannel seismic data: Combining traveltime inversion and prestack depth migration

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE269-VE280 ◽  
Author(s):  
Priyank Jaiswal ◽  
Colin A. Zelt
Keyword(s):  
Seismic Data ◽  
Joint Inversion ◽  
Velocity Model ◽  
Depth Image ◽  
Prestack Depth Migration ◽  
Traveltime Inversion ◽  
Depth Migration ◽  
Interval Velocity ◽  
Wide Aperture ◽  
Zero Offset

Imaging 2D multichannel land seismic data can be accomplished effectively by a combination of traveltime inversion and prestack depth migration (PSDM), referred to as unified imaging. Unified imaging begins by inverting the direct-arrival times to estimate a velocity model that is used in static corrections and stacking velocity analysis. The interval velocity model (from stacking velocities) is used for PSDM. The stacked data and the PSDM image are interpreted for common horizons, and the corresponding wide-aperture reflections are identified in the shot gathers. Using the interval velocity model, the stack interpretations are inverted as zero-offset reflections to constrain the corresponding interfaces in depth; the interval velocity model remains stationary. We define a coefficient of congruence [Formula: see text] that measures the discrepancy between horizons from the PSDM image andtheir counterparts from the zero-offset inversion. A value of unity for [Formula: see text] implies that the interpreted and inverted horizons are consistent to within the interpretational uncertainties, and the unified imaging is said to have converged. For [Formula: see text] greater than unity, the interval velocity model and the horizon depths are updated by jointly inverting the direct arrivals with the zero-offset and wide-aperture reflections. The updated interval velocity model is used again for both PSDM and a zero-offset inversion. Interpretations of the new PSDM image are the updated horizon depths. The unified imaging is applied to seismic data from the Naga Thrust and Fold Belt in India. Wide-aperture and zero-offset data from three geologically significant horizons are used. Three runs of joint inversion and PSDM are required in a cyclic manner for [Formula: see text] to converge to unity. A joint interpretation of the final velocity model and depth image reveals the presence of a triangle zone that could be promising for exploration.

Nonlinear 3D tomographic least-squares inversion of residual moveout in Kirchhoff prestack-depth-migration common-image gathers

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE13-VE23 ◽  
Author(s):  
Frank Adler ◽  
Reda Baina ◽  
Mohamed Amine Soudani ◽  
Pierre Cardon ◽  
Jean-Baptiste Richard
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Velocity Model ◽  
Migration Velocity ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Layer Velocity ◽  
Map Migration

Velocity-model estimation with seismic reflection tomography is a nonlinear inverse problem. We present a new method for solving the nonlinear tomographic inverse problem using 3D prestack-depth-migrated reflections as the input data, i.e., our method requires that prestack depth migration (PSDM) be performed before tomography. The method is applicable to any type of seismic data acquisition that permits seismic imaging with Kirchhoff PSDM. A fundamental concept of the method is that we dissociate the possibly incorrect initial migration velocity model from the tomographic velocity model. We take the initial migration velocity model and the residual moveout in the associated PSDM common-image gathers as the reference data. This allows us to consider the migrated depth of the initial PSDM as the invariant observation for the tomographic inverse problem. We can therefore formulate the inverse problem within the general framework of inverse theory as a nonlinear least-squares data fitting between observed and modeled migrated depth. The modeled migrated depth is calculated by ray tracing in the tomographic model, followed by a finite-offset map migration in the initial migration model. The inverse problem is solved iteratively with a Gauss-Newton algorithm. We applied the method to a North Sea data set to build an anisotropic layer velocity model.

Anisotropic parsimonious prestack depth migration

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. S25-S36 ◽  
Author(s):  
Ernesto V. Oropeza ◽  
George A. McMechan
Keyword(s):  
Model Building ◽  
Computing Time ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Velocity Model ◽  
P Wave ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Tti Media ◽  
Map Migration

An efficient Kirchhoff-style prestack depth migration, called “parsimonious” migration, was developed a decade ago for isotropic 2D and 3D media by using measured slownesses to reduce the amount of ray tracing by orders of magnitude. It is conceptually similar to “map” migration, but its implementation has some differences. We have extended this approach to 2D tilted transversely isotropic (TTI) media and illustrated it with synthetic P-wave data. Although the framework of isotropic parsimonious may be retained, the extension to TTI media requires redevelopment of each of the numerical components, calculation of the phase and group velocity for TTI media, development of a new two-point anisotropic ray tracer, and substitution of an initial-angle isotropic shooting ray-trace algorithm for an anisotropic one. The model parameterization consists of Thomsen’s parameters ([Formula: see text], [Formula: see text], [Formula: see text]) and the tilt angle of the symmetry axis of the TI medium. The parsimonious anisotropic migration algorithm is successfully applied to synthetic data from a TTI version of the Marmousi2 model. The quality of the image improves by weighting the impulse response by the calculation of the anisotropic Fresnel radius. The accuracy and speed of this migration makes it useful for anisotropic velocity model building. The elapsed computing time for 101 shots for the Marmousi2 TTI model is 35 s per shot (each with 501 traces) in 32 Opteron cores.

Ultrashallow depth imaging of a channel stratigraphy with first-arrival traveltime inversion and prestack depth migration: A case history from Bull Creek, Oklahoma

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. B87-B96 ◽  
Author(s):  
Ammanuel Fesseha Woldearegay ◽  
Priyank Jaiswal ◽  
Alexander R. Simms ◽  
Hanna Alexander ◽  
Leland C. Bement ◽  
...  
Keyword(s):  
Velocity Model ◽  
Depth Image ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Imaging ◽  
Traveltime Inversion ◽  
Time Processing ◽  
Depth Migration ◽  
First Arrival ◽  
Bull Creek

Depth imaging in ultrashallow ([Formula: see text]) environments presents twofold challenge: (1) coda available for depth migration is very limited; and (2) conventional time processing with limited coda generally fails to estimate reliable velocity models for depth migration. We studied the combining of first-arrival traveltime inversion and prestack depth migration (PSDM) for depth imaging of ultrashallow paleochannel stratigraphy associated with the Bull Creek drainage system, Oklahoma. Restricted by a limited number of geophones (24) we acquired data for inversion and migration through two coincident profiles. The first profile for inversion has a wider survey-aperture (115-m maximum shot-receiver spacing) and consequently sparse CMP spacing (2.5 m), whereas the second profile for PSDM has denser CMP spacing (1 m) and consequently a narrower survey aperture (46-m maximum shot-receiver spacing). We also found that the velocity model from traveltime inversion of the wider-aperture data set is more preferable for depth-migration than the velocity model from time processing of the denser data set. The preferred depth image showed three episodes of incision whose chronological order is resolved through radio-carbon dating of terrace sediments. Results suggested that even with limited geophones, depth imaging of ultrashallow targets can be achieved by combining first-arrival traveltime inversion and PSDM through coincident wide- and narrow-aperture acquisitions.

Depth image focusing in traveltime map‐based wide‐angle migration

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1903-1912 ◽  
Author(s):  
Igor B. Morozov ◽  
Alan Levander
Keyword(s):  
Velocity Model ◽  
Depth Image ◽  
Velocity Spectrum ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Arrival Times ◽  
Depth Migration ◽  
Traveltime Tomography ◽  
Interactive Analysis ◽  
The Common

Wide‐aperture, prestack depth migration requires application of challenging and time‐consuming velocity analysis and depth focusing, collectively referred to here as depth focusing. We present an approach to depth focusing using (1) a detailed starting velocity model obtained by a 1‐D transformation of the first‐arrival times, followed iteratively by (2) interactive analysis of the common‐image gathers, (3) computation of coherency attributes of the wavefield in the depth domain, and (4) 2‐D traveltime tomography to update the background velocity model. We employ two interactive method of migration velocities refinement. In the first method (similar to the common‐midpoint velocity spectrum approach), residual velocity updates are picked directly from the common‐image gathers. In another method (analogous to the common velocity stacks), we pick the velocity updates from the areas of maximum coherency in depth sections that are migrated using rescaled traveltime maps. Both types of migration velocity picks, optionally combined with the first arrivals, are inputs for a 2‐D traveltime inversion scheme that uses either the infinite‐frequency or a finite‐bandwidth approximation. This flexible and versatile depth focusing approach is implemented for several prestack depth migration algorithms and illustrated on an application to a real, ultrashallow seismic data set. The technique resolves overburden velocity variations and facilitates reliable high‐resolution reflection imaging of a paleochannel that was the target of the study.

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.

Kinematic interpretation in the prestack depth‐migrated domain

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1226-1237 ◽  
Author(s):  
Irina Apostoiu‐Marin ◽  
Andreas Ehinger
Keyword(s):  
Signal To Noise Ratio ◽  
Velocity Model ◽  
Point Of View ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Velocity Models ◽  
Time Domain Data ◽  
And Migration ◽  
Point To Point ◽  
Homogeneous Media

Prestack depth migration can be used in the velocity model estimation process if one succeeds in interpreting depth events obtained with erroneous velocity models. The interpretational difficulty arises from the fact that migration with erroneous velocity does not yield the geologically correct reflector geometries and that individual migrated images suffer from poor signal‐to‐noise ratio. Moreover, migrated events may be of considerable complexity and thus hard to identify. In this paper, we examine the influence of wrong velocity models on the output of prestack depth migration in the case of straight reflector and point diffractor data in homogeneous media. To avoid obscuring migration results by artifacts (“smiles”), we use a geometrical technique for modeling and migration yielding a point‐to‐point map from time‐domain data to depth‐domain data. We discover that strong deformation of migrated events may occur even in situations of simple structures and small velocity errors. From a kinematical point of view, we compare the results of common‐shot and common‐offset migration. and we find that common‐offset migration with erroneous velocity models yields less severe image distortion than common‐shot migration. However, for any kind of migration, it is important to use the entire cube of migrated data to consistently interpret in the prestack depth‐migrated domain.

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