A strategy for computing seismic attributes on depth-migrated data using time-shift gathers

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. O37-O46
Author(s):  
Mark Roberts
Keyword(s):  
Interpolation Method ◽  
Seismic Attributes ◽  
Depth Image ◽  
Time Shift ◽  
Lateral Velocity ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Velocity Variations ◽  
Made In

Assumptions made during postprocessing can be as important as those made during migration. Prestack depth migration (PSDM) is often used due to its ability to handle lateral velocity variations and dipping events. However, most postprocessing flows still use a simple 1D “depth-to-time” vertical stretch, violating the very assumptions that led us to use PSDM. Postprocessing workflows based on time-shift depth image gathers allow for postprocessing flows that make no further approximations other than those made in migration. For cases in which time-shift gathers are not computed during migration, they can be approximated by use of the “exploding-reflector” model or through an orthogonal shift and interpolation method.

Overthrust imaging with tomo‐datuming: A case study

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Xianhuai Zhu ◽  
Burke G. Angstman ◽  
David P. Sixta
Keyword(s):  
Velocity Model ◽  
Surface Velocity ◽  
Time Shift ◽  
Lateral Velocity ◽  
Prestack Depth Migration ◽  
Near Surface ◽  
Depth Migration ◽  
Static Corrections ◽  
Velocity Variations ◽  
Kirchhoff Method

Through the use of iterative turning‐ray tomography followed by wave‐equation datuming (or tomo‐datuming) and prestack depth migration, we generate accurate prestack images of seismic data in overthrust areas containing both highly variable near‐surface velocities and rough topography. In tomo‐datuming, we downward continue shot records from the topography to a horizontal datum using velocities estimated from tomography. Turning‐ray tomography often provides a more accurate near‐surface velocity model than that from refraction statics. The main advantage of tomo‐datuming over tomo‐statics (tomography plus static corrections) or refraction statics is that instead of applying a vertical time‐shift to the data, tomo‐datuming propagates the recorded wavefield to the new datum. We find that tomo‐datuming better reconstructs diffractions and reflections, subsequently providing better images after migration. In the datuming process, we use a recursive finite‐difference (FD) scheme to extrapolate wavefield without applying the imaging condition, such that lateral velocity variations can be handled properly and approximations in traveltime calculations associated with the raypath distortions near the surface for migration are avoided. We follow the downward continuation step with a conventional Kirchhoff prestack depth migration. This results in better images than those migrated from the topography using the conventional Kirchhoff method with traveltime calculation in the complicated near surface. Since FD datuming is only applied to the shallow part of the section, its cost is much less than the whole volume FD migration. This is attractive because (1) prestack depth migration usually is used iteratively to build a velocity model, so both efficiency and accuracy are important factors to be considered; and (2) tomo‐datuming can improve the signal‐to‐noise (S/N) ratio of prestack gathers, leading to more accurate migration velocity analysis and better images after depth migration. Case studies with synthetic and field data examples show that tomo‐datuming is especially helpful when strong lateral velocity variations are present below the topography.

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.

scholarly journals Depth Imaging Sub-salt Structures: A Case Study in the Midyan Peninsula (Red Sea)

GeoArabia ◽  
1999 ◽  
Vol 4 (4) ◽  
pp. 445-464 ◽  
Author(s):  
Denis Mougenot ◽  
Amir A. Al-Shakhis
Keyword(s):  
Red Sea ◽  
Structural Model ◽  
Oil And Gas ◽  
Imaging Techniques ◽  
Depth Image ◽  
Lateral Velocity ◽  
Seismic Line ◽  
Depth Imaging ◽  
Depth Migration ◽  
Velocity Variations

ABSTRACT In the Midyan Peninsula (onshore northern Red Sea, Saudi Arabia), the current prospective oil and gas exploration targets are sub-salt structures. In this region, conventional time-migrated seismic sections are distorted due to the presence of salt diapirs, faults, and related lateral velocity variations. As demonstrated in other sub-salt prospects (North Sea, Gulf of Suez, and Gulf of Mexico), pre-stack depth migration can remove these distortions and accurately focus the structural image. Depth migration, however, requires a model which includes both lateral and vertical velocity variations to compensate for ray bending. Building such a velocity model is an iterative process which involves integration of various time/depth processing and interpretation skills. A 2-D seismic line, crossing various extensional structures in the dip direction, is used to illustrate these depth-imaging techniques. At the location of the sub-salt prospect, the depth image is improved and the lateral position of the main fault is shifted by 345 meters. The resulting structural model has refined the target definition and well position. This imaging approach is compared with the different steps of the seismic processing/interpretation flow.

Offset‐domain pseudoscreen prestack depth migration

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1895-1902 ◽  
Author(s):  
Shengwen Jin ◽  
Charles C. Mosher ◽  
Ru‐Shan Wu
Keyword(s):  
Heterogeneous Media ◽  
Fourier Transforms ◽  
Data Migration ◽  
Computationally Efficient ◽  
Lateral Velocity ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Narrow Angle ◽  
Domain Phase ◽  
Wavefield Extrapolation

The double square root equation for laterally varying media in midpoint‐offset coordinates provides a convenient framework for developing efficient 3‐D prestack wave‐equation depth migrations with screen propagators. Offset‐domain pseudoscreen prestack depth migration downward continues the source and receiver wavefields simultaneously in midpoint‐offset coordinates. Wavefield extrapolation is performed with a wavenumber‐domain phase shift in a constant background medium followed by a phase correction in the space domain that accommodates smooth lateral velocity variations. An extra wide‐angle compensation term is also applied to enhance steep dips in the presence of strong velocity contrasts. The algorithm is implemented using fast Fourier transforms and tri‐diagonal matrix solvers, resulting in a computationally efficient implementation. Combined with the common‐azimuth approximation, 3‐D pseudoscreen migration provides a fast wavefield extrapolation for 3‐D marine streamer data. Migration of the 2‐D Marmousi model shows that offset domain pseudoscreen migration provides a significant improvement over first‐arrival Kirchhoff migration for steeply dipping events in strong contrast heterogeneous media. For the 3‐D SEG‐EAGE C3 Narrow Angle synthetic dataset, image quality from offset‐domain pseudoscreen migration is comparable to shot‐record finite‐difference migration results, but with computation times more than 100 times faster for full aperture imaging of the same data volume.

Seismic depth migration with the Dirac equation

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 925-933 ◽  
Author(s):  
Ketil Hokstad ◽  
Rune Mittet
Keyword(s):  
Dirac Equation ◽  
Taylor Series ◽  
Rapid Expansion ◽  
Difference Operators ◽  
Square Root ◽  
Exact Linearization ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Spatial Derivatives ◽  
Velocity Variations

We demonstrate the applicability of the Dirac equation in seismic wavefield extrapolation by presenting a new explicit one‐way prestack depth migration scheme. The method is in principle accurate up to 90° from the vertical, and it tolerates lateral velocity variations. This is achieved by performing the extrapolation step of migration with the Dirac equation, implemented in the space‐frequency domain. The Dirac equation is an exact linearization of the square‐root wave equation and is equivalent to keeping infinitely many terms in a Taylor series or continued‐fraction expansion of the square‐root operator. An important property of the new method is that the local velocity and the spatial derivatives decouple in separate terms within the extrapolation operator. Therefore, we do not need to precompute and store large tables of convolutional extrapolator coefficients depending on velocity. The main drawback of the explicit scheme is that evanescent energy must be removed at each depth step to obtain numerical stability. We have tested two numerical implementations of the migration scheme. In the first implementation, we perform depth stepping using the Taylor series approximation and compute spatial derivatives with high‐order finite difference operators. In the second implementation, we perform depth stepping with the Rapid expansion method and numerical differentiation with the pseudospectral method. The imaging condition is a generalization of Claerbout’s U / D principle. For both implementations, the impulse response is accurate up to 80° from the vertical. Using synthetic data from a simple fault model, we test the depth migration scheme in the presence of lateral velocity variations. The results show that the proposed migration scheme images dipping reflectors and the fault plane in the correct positions.

Analytic synthetic seismograms for depth migration testing

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 697-700
Author(s):  
Samuel H. Gray ◽  
Chester A. Jacewitz ◽  
Michael E. Epton
Keyword(s):  
Velocity Field ◽  
Acoustic Velocity ◽  
Synthetic Seismograms ◽  
Lateral Velocity ◽  
Seismic Migration ◽  
Depth Migration ◽  
Circular Arcs ◽  
Velocity Variations ◽  
Migration Testing ◽  
Speed And Accuracy

By using the fact that raypaths in a linear acoustic velocity field are circular arcs, we analytically generate a number of distinct nontrivial synthetic seismograms. The seismograms yield accurate traveltimes from reflection events, but they do not give reflection amplitudes. The seismograms are useful for testing seismic migration programs for both speed and accuracy, in settings where lateral velocity variations can be arbitrarily high and dipping reflectors arbitrarily steep. Two specific examples are presented as illustrations.

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.

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.

Hybrid migration: A cost‐effective 3-D depth‐imaging technique

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 568-576 ◽  
Author(s):  
Young C. Kim ◽  
Worth B. Hurt, ◽  
Louis J. Maher ◽  
Patrick J. Starich
Keyword(s):  
Model Building ◽  
Cost Effective ◽  
Velocity Model ◽  
Depth Image ◽  
Hybrid Technique ◽  
Prestack Depth Migration ◽  
Depth Imaging ◽  
Depth Migration ◽  
Time Migration ◽  
Prestack Time Migration

The transformation of surface seismic data into a subsurface image can be separated into two components—focusing and positioning. Focusing is associated with ensuring the data from different offsets are contributing constructively to the same event. Positioning involves the transformation of the focused events into a depth image consistent with a given velocity model. In prestack depth migration, both of these operations are achieved simultaneously; however, for 3-D data, the cost is significant. Prestack time migration is much more economical and focuses events well even in the presence of moderate velocity variations, but suffers from mispositioning problems. Hybrid migration is a cost‐effective depth‐imaging approach that uses prestack time migration for focusing; inverse migration for the removal of positioning errors; and poststack depth migration for proper positioning. When lateral velocity changes are moderate, the hybrid technique can generate a depth image that is consistent with a velocity field. For very complex structures that require prestack depth migration, the results of the hybrid technique can be used to create a starting velocity model, thereby reducing the number of iterations for velocity model building.

Seismic depth imaging with the Gabor transform

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. S91-S97 ◽  
Author(s):  
Yongwang Ma ◽  
Gary F. Margrave
Keyword(s):  
Fourier Transform ◽  
Phase Shift ◽  
Gabor Transform ◽  
Positioning Error ◽  
Lateral Velocity ◽  
Data Set ◽  
Depth Migration ◽  
Velocity Variations ◽  
Spatial Positioning ◽  
Wavefield Extrapolation

Wavefield extrapolation in depth, a vital component of wave-equation depth migration, is accomplished by repeatedly applying a mathematical operator that propagates the wavefield across a single depth step, thus creating a depth marching scheme. The phase-shift method of wavefield extrapolation is fast and stable; however, it can be cumbersome to adapt to lateral velocity variations. We address the extension of phase-shift extrapolation to lateral velocity variations by using a spatial Gabor transform instead of the normal Fourier transform. The Gabor transform, also known as the windowed Fourier transform, is applied to the lateral spatial coordinates as a windowed discrete Fourier transform where the entire set of windows is required to sum to unity. Within each window, a split-step Fourier phase shift is applied. The most novel element of our algorithm is an adaptive partitioning scheme that relates window width to lateral velocity gradient such that the estimated spatial positioning error is bounded below a threshold. The spatial positioning error is estimated by comparing the Gabor method to its mathematical limit, called the locally homogeneous approximation — a frequency-wavenumber-dependent phase shift that changes according to the local velocity at each position. The assumption of local homogeneity means this position-error estimate may not hold strictly for large scattering angles in strongly heterogeneous media. The performance of our algorithm is illustrated with imaging results from prestack depth migration of the Marmousi data set. With respect to a comparable space-frequency domain imaging method, the proposed method improves images while requiring roughly 50% more computing time.

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