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.

3-D prestack depth migration by wavefield extrapolation methods

2003 ◽  
Vol 2003 (2) ◽  
pp. 1-4
Author(s):  
James Sun ◽  
Carl Notfors ◽  
Zhang Yu ◽  
Gray Sam ◽  
Young Jerry
Keyword(s):  
Extrapolation Methods ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Wavefield Extrapolation

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.

Optimum split-step Fourier 3D depth migration: Developments and practical aspects

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S167-S175 ◽  
Author(s):  
Jianfeng Zhang ◽  
Linong Liu
Keyword(s):  
Finite Difference ◽  
Heterogeneous Media ◽  
Fourier Transforms ◽  
Computational Cost ◽  
Fourier Method ◽  
Approximate Algorithm ◽  
Wide Angle ◽  
Data Set ◽  
Depth Migration ◽  
Varying Coefficients

We present an efficient scheme for depth extrapolation of wide-angle 3D wavefields in laterally heterogeneous media. The scheme improves the so-called optimum split-step Fourier method by introducing a frequency-independent cascaded operator with spatially varying coefficients. The developments improve the approximation of the optimum split-step Fourier cascaded operator to the exact phase-shift operator of a varying velocity in the presence of strong lateral velocity variations, and they naturally lead to frequency-dependent varying-step depth extrapolations that reduce computational cost significantly. The resulting scheme can be implemented alternatively in spatial and wavenumber domains using fast Fourier transforms (FFTs). The accuracy of the first-order approximate algorithm is similar to that of the second-order optimum split-step Fourier method in modeling wide-angle propagation through strong, laterally varying media. Similar to the optimum split-step Fourier method, the scheme is superior to methods such as the generalized screen and Fourier finite difference. We demonstrate the scheme’s accuracy by comparing it with 3D two-way finite-difference modeling. Comparisons with the 3D prestack Kirchhoff depth migration of a real 3D data set demonstrate the practical application of the proposed method.

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.

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.

Multicomponent prestack depth migration by scalar wavefield extrapolation

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1886-1894 ◽  
Author(s):  
Anning Hou ◽  
Kurt J. Marfurt
Keyword(s):  
Wave Equation ◽  
Single Shot ◽  
Complex Structures ◽  
Scalar Wave ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Polarization Filtering ◽  
Polarity Reversals ◽  
Wavefield Extrapolation ◽  
Propagation Velocities

We present a new multicomponent prestack depth migration methodology based on successive application of conventional scalar wave equation migration. We do not separate the data into PP‐ and PS‐waves; rather, we migrate each x‐, y‐, and z‐component of the data using both P and S propagation velocities, followed by polarization filtering in the depth domain. By generating intermediate images in the depth domain, we can account for polarity reversals of the PS reflection for all dips. Since the polarization angles are calculated from the data, it is straightforward to accommodate anisotropic effects (quasi‐P and quasi‐S) into multicomponent migration. The multicomponent migration results in our synthetic examples demonstrate that even for a single shot gather, we can obtain clean PP‐ and PS‐wave images over complex structures and resolve the problem of PS‐wave polarity reversals.

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.

True amplitude corrections for a narrow-angle one-way elastic wave equation

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. T19-T26 ◽  
Author(s):  
D. A. Angus
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Energy Flux ◽  
Wave Equations ◽  
Heterogeneous Media ◽  
Leading Order ◽  
Computationally Efficient ◽  
Elastic Wave Equation ◽  
Narrow Angle ◽  
Correction Terms

Wavefield extrapolators using one-way wave equations are computationally efficient methods for accurate traveltime modeling in laterally heterogeneous media, and have been used extensively in many seismic forward modeling and migration problems. However, most leading-order, one-way wave equations do not simulate waveform amplitudes accurately and this is primarily because energy flux is not accounted for correctly. I review the derivation of a leading-order, narrow-angle, one-way elastic wave equation for 3D media. I derive correction terms that enable energy-flux normalization and introduce a new higher-order, narrow-angle, one-way elastic wave extrapolator. By implementing these correction terms, the new true amplitude wave extrapolator allows accurate amplitude estimates in the presence of strong gradients. I present numerical examples for 1D velocity transition models to show that (1) the leading-order, narrow-angle propagator accurately models traveltimes, but overestimates transmitted- or primary-wave amplitudes and (2) the new amplitude corrected narrow-angle propagator accurately models both the traveltimes and amplitudes of all forward-traveling waves.

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