Poststack migration of P-SV seismic data

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1127-1135 ◽  
Author(s):  
Mark P. Harrison ◽  
Robert R. Stewart
Keyword(s):  
Phase Shift ◽  
Inhomogeneous Medium ◽  
Seismic Data ◽  
Migration Velocity ◽  
Velocity Function ◽  
Zero Offset ◽  
Migration Velocities

The exploding‐reflector model is only satisfied for zero‐offset P-SV data when [Formula: see text] is depth‐invariant. P-SV diffractions in a vertically‐inhomogeneous medium are approximately hyperbolic, and an expression for their migration velocity is derived. The resulting migration velocities are 6–11 percent less than the corresponding P-SV rms velocities. Migration of DMO‐corrected synthetic P-SV stacked data, using a conventional phase‐shift algorithm and the derived migration velocities, is found to adequately collapse diffractions, whereas migration using the rms velocity function gives significant overmigration.

Seismic constant‐velocity remigration

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 589-597 ◽  
Author(s):  
Jörg Schleicher ◽  
Peter Hubral ◽  
German Höcht ◽  
Frank Liptow
Keyword(s):  
Constant Velocity ◽  
Wave Equations ◽  
Single Point ◽  
Velocity Model ◽  
Migration Velocity ◽  
Body Waves ◽  
Reflection Point ◽  
Ray Trajectories ◽  
Zero Offset ◽  
Migration Velocities

When a seismic common midpoint (CMP) stack or zero‐offset (ZO) section is depth or time migrated with different (constant) migration velocities, different reflector images of the subsurface are obtained. If the migration velocity is changed continuously, the (kinematically) migrated image of a single point on the reflector, constructed for one particular seismic ZO reflection signal, moves along a circle at depth, which we call the Thales circle. It degenerates to a vertical line for a nondipping event. For all other dips, the dislocation as a function of migration velocity depends on the reflector dip. In particular for reflectors with dips larger than 45°, the reflection point moves upward for increasing velocity. The corresponding curves in a Time‐migrated section are parabolas. These formulas will provide the seismic interpreter with a better understanding of where a reflector image might move when the velocity model is changed. Moreover, in that case, the reflector image as a whole behaves to some extent like an ensemble of body waves, which we therefore call remigration image waves. In the same way as physical waves propagate as a function of time, these image waves propagate as a function of migration velocity. Different migrated images can thus be considered as snapshots of image waves at different instants of migration velocity. By some simple plane‐wave considerations, image‐wave equations can be derived that describe the propagation of image waves as a function of the migration velocity. The Thales circles and parabolas then turn out to be the characteristics or ray trajectories for these image‐wave equations.

Velocity estimation by image-focusing analysis

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. U49-U60 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
New York ◽  
Seismic Data ◽  
Field Data ◽  
Velocity Estimation ◽  
Data Set ◽  
Velocity Function ◽  
Curvature Correction ◽  
Velocity Information ◽  
Zero Offset ◽  
Inherent Ambiguity

Migration velocity can be estimated from seismic data by analyzing, focusing, and defocusing of residual-migrated images. The accuracy of these velocity estimates is limited by the inherent ambiguity between velocity and reflector curvature. However, velocity resolution improves when reflectors with different curvatures are present. Image focusing is measured by evaluating coherency across structural dips, in addition to coherency across aperture/azimuth angles. The inherent ambiguity between velocity and reflector curvature is directly tackled by introducing a curvature correction into the computation of the semblance functional that estimates image coherency. The resulting velocity estimator provides velocity estimates that are (1) unbiased by reflector curvature and (2) consistent with the velocity information that is routinely obtained by measuring coherency over aperture/azimuth angles. Applications to a 2D synthetic prestack data set and a 2D field prestack data set confirm that the proposed method provides consistent and unbiased velocity information. They also suggest that velocity estimates based on the new image-focusing semblance may be more robust and have higher resolution than estimates based on conventional semblance functionals. Applying the proposed method to zero-offset field data recorded in New York Harbor yields a velocity function that is consistent with available geologic information and clearly improves the focusing of the reflectors.

Migration velocity analysis with the Kirchhoff integral

Geophysics ◽  
1991 ◽  
Vol 56 (3) ◽  
pp. 365-370 ◽  
Author(s):  
Y. C. Kim ◽  
R. Gonzalez
Keyword(s):  
Maximum Amplitude ◽  
Migration Velocity ◽  
Downward Continuation ◽  
Velocity Analysis ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Prestack Time Migration ◽  
Zero Offset ◽  
Kirchhoff Integral ◽  
Migration Velocities

To obtain accurate migration velocities, we must estimate the velocity at migrated depth points. Wavefront focusing analysis with downward continuation yields the rms velocity at migrated depth points; however, the large amount of computation required for downward continuation limits use of this approach for routine processing. The purpose of this paper is to present an implementation of the Kirchhoff integral which makes the wavefront focusing analysis practical for time‐migration velocity analysis. Downward continuation focuses the wavefront to the zero offset at the depth controlled by the velocity used for the continuation. The migration velocity is then determined from the depth where the focused wavefront attains the maximum amplitude. The flexibility of the Kirchhoff integral allows us to compute only the zero‐offset trace at each depth point and lets us avoid most of the computation for the downward continuation of unstacked data. Furthermore, since the velocity is obtained from the location where the focused wavefront shows the maximum amplitude, prestack time migration with the velocity from this technique produces the maximum amplitude for the subsurface reflector.

scholarly journals Study on the Velocity Analysis Method of Low SNR Seismic Data

2021 ◽  
Vol 11 (1) ◽  
pp. 78
Author(s):  
Jianbo He ◽  
Zhenyu Wang ◽  
Mingdong Zhang
Keyword(s):  
Seismic Data ◽  
Fresnel Zone ◽  
Signal To Noise Ratio ◽  
Normal Wave ◽  
Curvature Radius ◽  
Velocity Spectrum ◽  
Velocity Analysis ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Zero Offset

When the signal to noise ratio of seismic data is very low, velocity spectrum focusing will be poor., the velocity model obtained by conventional velocity analysis methods is not accurate enough, which results in inaccurate migration. For the low signal noise ratio (SNR) data, this paper proposes to use partial Common Reflection Surface (CRS) stack to build CRS gathers, making full use of all of the reflection information of the first Fresnel zone, and improves the signal to noise ratio of pre-stack gathers by increasing the number of folds. In consideration of the CRS parameters of the zero-offset rays emitted angle and normal wave front curvature radius are searched on zero offset profile, we use ellipse evolving stacking to improve the zero offset section quality, in order to improve the reliability of CRS parameters. After CRS gathers are obtained, we use principal component analysis (PCA) approach to do velocity analysis, which improves the noise immunity of velocity analysis. Models and actual data results demonstrate the effectiveness of this method.

Migration of seismic data by phase shift plus interpolation

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 124-131 ◽  
Author(s):  
Jeno Gazdag ◽  
Piero Sguazzero
Keyword(s):  
Phase Shift ◽  
Wave Field ◽  
Seismic Data ◽  
Three Dimensional ◽  
Reference Wave ◽  
Second Step ◽  
Lateral Velocity ◽  
Wave Fields ◽  
Shift Method ◽  
Phase Shift Method

Under the horizontally layered velocity assumption, migration is defined by a set of independent ordinary differential equations in the wavenumber‐frequency domain. The wave components are extrapolated downward by rotating their phases. This paper shows that one can generalize the concepts of the phase‐shift method to media having lateral velocity variations. The wave extrapolation procedure consists of two steps. In the first step, the wave field is extrapolated by the phase‐shift method using ℓ laterally uniform velocity fields. The intermediate result is ℓ reference wave fields. In the second step, the actual wave field is computed by interpolation from the reference wave fields. The phase shift plus interpolation (PSPI) method is unconditionally stable and lends itself conveniently to migration of three‐dimensional data. The performance of the methods is demonstrated on synthetic examples. The PSPI migration results are then compared with those obtained from a finite‐difference method.

2-D continuation operators and their applications

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1846-1858 ◽  
Author(s):  
Claudio Bagaini ◽  
Umberto Spagnolini
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Integral Form ◽  
Amplitude Distribution ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Seismic Data Processing ◽  
Analysis Method ◽  
Standard Tool ◽  
Zero Offset

Continuation to zero offset [better known as dip moveout (DMO)] is a standard tool for seismic data processing. In this paper, the concept of DMO is extended by introducing a set of operators: the continuation operators. These operators, which are implemented in integral form with a defined amplitude distribution, perform the mapping between common shot or common offset gathers for a given velocity model. The application of the shot continuation operator for dip‐independent velocity analysis allows a direct implementation in the acquisition domain by exploiting the comparison between real data and data continued in the shot domain. Shot and offset continuation allow the restoration of missing shot or missing offset by using a velocity model provided by common shot velocity analysis or another dip‐independent velocity analysis method.

Transformation to zero offset for mode‐converted waves

Geophysics ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 474-477 ◽  
Author(s):  
Mohammed Alfaraj ◽  
Ken Larner
Keyword(s):  
Seismic Data ◽  
Constant Velocity ◽  
Reflection Point ◽  
P Waves ◽  
S Waves ◽  
Nmo Correction ◽  
Converted Waves ◽  
Zero Offset ◽  
Correct Data

The transformation to zero offset (TZO) of prestack seismic data for a constant‐velocity medium is well understood and is readily implemented when dealing with either P‐waves or S‐waves. TZO is achieved by inserting a dip moveout (DMO) process to correct data for the influence of dip, either before or after normal moveout (NMO) correction (Hale, 1984; Forel and Gardner, 1988). The TZO process transforms prestack seismic data in such a way that common‐midpoint (CMP) gathers are closer to being common reflection point gathers after the transformation.

Plumes: Response of time migration to lateral velocity variation

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1118-1127 ◽  
Author(s):  
Dimitri Bevc ◽  
James L. Black ◽  
Gopal Palacharla
Keyword(s):  
Impulse Response ◽  
Synthetic Data ◽  
Migration Velocity ◽  
Velocity Variation ◽  
Velocity Dependence ◽  
Geometrical Construction ◽  
Lateral Velocity ◽  
Time Migration ◽  
Offset Time ◽  
Zero Offset

We analyze how time migration mispositions events in the presence of lateral velocity variation by examining the impulse response of depth modeling followed by time migration. By examining this impulse response, we lay the groundwork for the development of a remedial migration operator that links time and depth migration. A simple theory by Black and Brzostowski predicted that the response of zero‐offset time migration to a point diffractor in a v(x, z) medium would be a distinctive, cusp‐shaped curve called a plume. We have constructed these plumes by migrating synthetic data using several time‐migration methods. We have also computed the shape of the plumes by two geometrical construction methods. These two geometrical methods compare well and explain the observed migration results. The plume response is strongly influenced by migration velocity. We have studied this dependency by migrating synthetic data with different velocities. The observed velocity dependence is confirmed by geometrical construction. A simple first‐order theory qualitatively explains the behavior of zero‐offset time migration, but a more complete understanding of migration velocity dependence in a v(x, z) medium requires a higher order finite‐offset theory.

Accurate depth migration by a generalized phase‐shift method

Geophysics ◽  
1987 ◽  
Vol 52 (8) ◽  
pp. 1074-1084 ◽  
Author(s):  
Dan Kosloff ◽  
David Kessler
Keyword(s):  
Phase Shift ◽  
Velocity Structure ◽  
Shift Method ◽  
Depth Migration ◽  
Integration Techniques ◽  
Matrix Diagonalization ◽  
Offset Time ◽  
Zero Offset ◽  
Spatially Variant ◽  
Phase Shift Method

A new depth migration method derived in the space‐frequency domain is based on a generalized phase‐shift method for the downward continuation of surface data. For a laterally variable velocity structure, the Fourier spatial components are no longer eigenvectors of the wave equation, and therefore a rigorous application of the phase‐shift method would seem to require finding the eigenvectors by a matrix diagonalization at every depth step. However, a recently derived expansion technique enables phase‐shift accuracy to be obtained without resorting to a costly matrix diagonalization. The new technique is applied to the migration of zero‐offset time sections. As with the laterally uniform velocity case, the evanescent components of the solution need to be isolated and eliminated, in this case by the application of a spatially variant high‐cut filter. Tests performed on the new method show that it is more accurate and efficient than standard integration techniques such as the Runge‐Kutta method or the Taylor method.

Linear‐transform techniques for processing shear‐wave anisotropy in four‐component seismic data

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 240-256 ◽  
Author(s):  
Xiang‐Yang Li ◽  
Stuart Crampin
Keyword(s):  
Time Series ◽  
Shear Wave ◽  
Seismic Data ◽  
Shear Waves ◽  
Shear Wave Splitting ◽  
Data Set ◽  
Reflection Data ◽  
Wave Splitting ◽  
Linear Transform ◽  
Zero Offset

Most published techniques for analyzing shear‐wave splitting tend to be computing intensive, and make assumptions, such as the orthogonality of the two split shear waves, which are not necessarily correct. We present a fast linear‐transform technique for analyzing shear‐wave splitting in four‐component (two sources/ two receivers) seismic data, which is flexible and widely applicable. We transform the four‐component data by simple linear transforms so that the complicated shear‐wave motion is linearized in a wide variety of circumstances. This allows various attributes to be measured, including the polarizations of faster split shear waves and the time delays between faster and slower split shear waves, as well as allowing the time series of the faster and slower split shear waves to be separated deterministically. In addition, with minimal assumptions, the geophone orientations can be estimated for zero‐offset verticle seismic profiles (VSPs), and the polarizations of the slower split shear waves can be measured for offset VSPs. The time series of the split shear‐waves can be separated before stack for reflection surveys. The technique has been successfully applied to a number of field VSPs and reflection data sets. Applications to a zero‐offset VSP, an offset VSP, and a reflection data set will be presented to illustrate the technique.

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