scholarly journals Velocity analysis based on minimum entropy

Geophysics ◽  
1984 ◽  
Vol 49 (12) ◽  
pp. 2132-2142 ◽  
Author(s):  
D. De Vries ◽  
A. J. Berkhout
Keyword(s):  
Velocity Estimation ◽  
Resolving Power ◽  
Velocity Analysis ◽  
Minimum Entropy ◽  
Estimation Techniques ◽  
Velocity Error ◽  
Seismic Resolution ◽  
Velocity Information ◽  
Zero Offset

Seismic resolution is determined by the sparsity of reflection events together with the dispersion of the wavelets representing those events. In this paper, minimum entropy (ME) norms are introduced as a measure of spatial resolving power. It is shown that the lateral dispersion of inverted diffractor responses (inverted spatial wavelets) increases with increasing velocity error. Using this property, minimum entropy velocity analysis (MEVA) is proposed to extract velocity information from diffraction energy. MEVA can be successfully applied to zero‐offset (including poststack) data and common‐offset data with a sufficient amount of diffraction energy. In addition, MEVA can be used as an alternative to existing CMP velocity estimation techniques.

Wave-equation migration velocity analysis by focusing diffractions and reflections

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U19-U27 ◽  
Author(s):  
Paul C. Sava ◽  
Biondo Biondi ◽  
John Etgen
Keyword(s):  
Wave Equation ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Interval Velocity ◽  
Migration Velocity Analysis ◽  
Inversion Procedure ◽  
Velocity Information ◽  
Zero Offset

We propose a method for estimating interval velocity using the kinematic information in defocused diffractions and reflections. We extract velocity information from defocused migrated events by analyzing their residual focusing in physical space (depth and midpoint) using prestack residual migration. The results of this residual-focusing analysis are fed to a linearized inversion procedure that produces interval velocity updates. Our inversion procedure uses a wavefield-continuation operator linking perturbations of interval velocities to perturbations of migrated images, based on the principles of wave-equation migration velocity analysis introduced in recent years. We measure the accuracy of the migration velocity using a diffraction-focusing criterion instead of the criterion of flatness of migrated common-image gathers that is commonly used in migration velocity analysis. This new criterion enables us to extract velocity information from events that would be challenging to use with conventional velocity analysis methods; thus, our method is a powerful complement to those conventional techniques. We demonstrate the effectiveness of the proposed methodology using two examples. In the first example, we estimate interval velocity above a rugose salt top interface by using only the information contained in defocused diffracted and reflected events present in zero-offset data. By comparing the results of full prestack depth migration before and after the velocity updating, we confirm that our analysis of the diffracted events improves the velocity model. In the second example, we estimate the migration velocity function for a 2D, zero-offset, ground-penetrating radar data set. Depth migration after the velocity estimation improves the continuity of reflectors while focusing the diffracted energy.

Migration velocity analysis by wave‐field extrapolation

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1664-1674 ◽  
Author(s):  
Oz Yilmaz ◽  
Ron Chambers
Keyword(s):  
Wave Field ◽  
Seismic Signal ◽  
Velocity Estimation ◽  
Resolving Power ◽  
Mapping Procedure ◽  
Migration Velocity Analysis ◽  
Simple Mapping ◽  
Velocity Information ◽  
Zero Offset ◽  
And Migration

Velocity information is essential to both common midpoint (CMP) stacking and migration. CMP stacking provides the basis for conventional velocity estimation techniques in that, for a number of trial velocities, the stack response of a CMP gather is computed and displayed in the form of a velocity table. An alternative approach to velocity estimation makes use of the basic ingredients of migration—downward extrapolation and imaging of seismic wave fields. The procedure involves migration of a CMP gather with a number of trial velocities and collection of the zero‐offset information, again in the form of a velocity table. Operating on a CMP gather, the migration‐based approach produces results similar to those of the conventional method. Analyses of synthetic CMP gathers using both methods show essentially equivalent treatments of seismic signal, and similar dependence of accuracy and resolving power on recording geometry. We have extended the migration‐based approach to include more than one CMP gather in each analysis. This extension allows proper treatment of dipping events and yields velocity information that is more appropriate for use in migration. By using the intermediate wave field at each step of downward extrapolation, we need only do a single constant‐velocity migration of the unstacked data followed by a simple mapping procedure in order to recover the velocity information.

Selective-correlation velocity analysis

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. U11-U19 ◽  
Author(s):  
Ken Larner ◽  
Valmore Celis
Keyword(s):  
Time Domain ◽  
Random Noise ◽  
Computational Cost ◽  
Threshold Value ◽  
Resolving Power ◽  
Velocity Analysis ◽  
Reflection Time ◽  
Offset Time ◽  
Zero Offset ◽  
Velocity Spectra

Increased resolution in computed velocity spectra aids in distinguishing between neighboring primary events from reflectors with conflicting dip and in identifying primaries in the presence of multiples. The transformation from the offset and reflection-time domain to the stacking-velocity and zero-offset-time domain can be achieved using any of several coherence measures based on crosscorrelations among traces in a common-midpoint (CMP) gather or a common-image gather (CIG). Use of just selected subsets of crosscorrelations rather than all possible ones in a gather can improve both the reliability and resolution of velocity analysis. In selective-correlation velocity analysis, we include in the summation only crosscorrelations for those pairs of traces with relative differential moveout of reflections exceeding a chosen threshold value. Comparisons of performance on CMP gathers, both synthetic and field-data, show that selective-correlation velocity analysis considerably enhances the resolving power of velocity spectra over that of conventional crosscorrelation sum (normalized or unnormalized) in the presence of closely interfering reflections, statics distortions, and random noise, at no sacrifice in quality of results, and does so at computational cost comparable to that for conventional velocity analysis.

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.

Focusing analysis of seismic data with peg‐leg multiples

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 177-182
Author(s):  
Einar Maeland
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Velocity Estimation ◽  
Time Shift ◽  
Data Set ◽  
Seismic Migration ◽  
Imaging Condition ◽  
Multilayered Medium ◽  
Velocity Information ◽  
Zero Offset

Seismic migration with an erroneous velocity field produces an “image” that must be interpreted to obtain reliable velocity information. Inclusion of multiples in common‐shot data makes velocity estimation more difficult. Zero‐offset migration, based on the exploding reflector model, can be used to identify peg‐leg multiples by application of an extra time shift in the imaging condition. The time and the corresponding position when reflected energy focuses must be detected by inspection of the migrated data set. Formulas are derived and the method is tested on synthetic data from a multilayered medium.

Accuracy study of velocity estimation in 3-D layered models

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1567-1574
Author(s):  
Valery Sorin
Keyword(s):  
Three Dimensional ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Apparent Velocity ◽  
Velocity Anisotropy ◽  
Strike Direction ◽  
Accuracy Study ◽  
Layer Velocity ◽  
Structure Geometry ◽  
Zero Offset

Velocity estimation is examined in 3-D layered structures formed by plane and curved interfaces. The applied technique of coherency inversion tests the layer velocity through the repeating sequence of ray migration/coherency measurement. The reconstructed velocity‐depth model fits zero‐offset reflection times and maximizes semblance on input common midpoint (CMP) gathers. The correctness of layer velocity analysis disregarding the three‐dimensionality of the structures is under consideration. Using the 2-D coherency inversion technique, velocity is correctly determined in the upper layer of the examined structures. Two‐dimensional analysis in the deeper layer gives biased velocity estimates. The errors in the 2-D velocity estimates vary with the profile azimuth and appear in the form of the apparent velocity anisotropy. The inaccuracy of 2-D velocity estimation is analytically considered for the profile oriented along the refractor strike direction. The derived equation relates the velocity error to structure geometry and to the velocity contrast above and below the refractor. Three‐dimensional velocity analysis in the examined structures reveals that the layer velocity resolution is affected by the refractor shape. Below the convex refractor the velocity resolution deteriorates compared with that below the plane.

Numeric implementation of wave-equation migration velocity analysis operators

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE145-VE159 ◽  
Author(s):  
Paul Sava ◽  
Ioan Vlad
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Image Optimization ◽  
Migration Velocity Analysis ◽  
Zero Offset ◽  
Wavefield Extrapolation

Wave-equation migration velocity analysis (MVA) is a technique similar to wave-equation tomography because it is designed to update velocity models using information derived from full seismic wavefields. On the other hand, wave-equation MVA is similar to conventional, traveltime-based MVA because it derives the information used for model updates from properties of migrated images, e.g., focusing and moveout. The main motivation for using wave-equation MVA is derived from its consistency with the corresponding wave-equation migration, which makes this technique robust and capable of handling multipathing characterizing media with large and sharp velocity contrasts. The wave-equation MVA operators are constructed using linearizations of conventional wavefield extrapolation operators, assuming small perturbations relative to the background velocity model. Similar to typical wavefield extrapolation operators, the wave-equation MVA operators can be implemented in the mixed space-wavenumber domain using approximations of differentorders of accuracy. As for wave-equation migration, wave-equation MVA can be formulated in different imaging frameworks, depending on the type of data used and image optimization criteria. Examples of imaging frameworks correspond to zero-offset migration (designed for imaging based on focusing properties of the image), survey-sinking migration (designed for imaging based on moveout analysis using narrow-azimuth data), and shot-record migration (also designed for imaging based on moveout analysis, but using wide-azimuth data). The wave-equation MVA operators formulated for the various imaging frameworks are similar because they share elements derived from linearizations of the single square-root equation. Such operators represent the core of iterative velocity estimation based on diffraction focusing or semblance analysis, and their applicability in practice requires efficient and accurate implementation. This tutorial concentrates strictly on the numeric implementation of those operators and not on their use for iterative migration velocity analysis.

Some aspects of interval velocity analysis using 3-D depth‐migrated gathers

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 261-266 ◽  
Author(s):  
Moshe Reshef
Keyword(s):  
Velocity Estimation ◽  
Velocity Analysis ◽  
Estimation Techniques ◽  
Interval Velocity

Analysis of depth‐migrated gathers is the basis of most interval velocity estimation techniques. These gathers, known as common image gathers (CIGs), should consist of flat events when the velocity used for the migration is correct (Faye and Jeannot, 1986; Al‐Yahya, 1989). As a result of this assumption, interval velocity analysis has become a procedure of flattening events in CIGs.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspects

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1202-1212 ◽  
Author(s):  
Hervé Chauris ◽  
Mark S. Noble ◽  
Gilles Lambaré ◽  
Pascal Podvin
Keyword(s):  
Cost Function ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Paraxial Ray ◽  
The Cost

We present a new method based on migration velocity analysis (MVA) to estimate 2‐D velocity models from seismic reflection data with no assumption on reflector geometry or the background velocity field. Classical approaches using picking on common image gathers (CIGs) must consider continuous events over the whole panel. This interpretive step may be difficult—particularly for applications on real data sets. We propose to overcome the limiting factor by considering locally coherent events. A locally coherent event can be defined whenever the imaged reflectivity locally shows lateral coherency at some location in the image cube. In the prestack depth‐migrated volume obtained for an a priori velocity model, locally coherent events are picked automatically, without interpretation, and are characterized by their positions and slopes (tangent to the event). Even a single locally coherent event has information on the unknown velocity model, carried by the value of the slope measured in the CIG. The velocity is estimated by minimizing these slopes. We first introduce the cost function and explain its physical meaning. The theoretical developments lead to two equivalent expressions of the cost function: one formulated in the depth‐migrated domain on locally coherent events in CIGs and the other in the time domain. We thus establish direct links between different methods devoted to velocity estimation: migration velocity analysis using locally coherent events and slope tomography. We finally explain how to compute the gradient of the cost function using paraxial ray tracing to update the velocity model. Our method provides smooth, inverted velocity models consistent with Kirchhoff‐type migration schemes and requires neither the introduction of interfaces nor the interpretation of continuous events. As for most automatic velocity analysis methods, careful preprocessing must be applied to remove coherent noise such as multiples.

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.

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