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.

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.

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.

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.

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.

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 SPATIAL-TEMPORAL ANALYSIS OF SEISMIC WAVE-FIELD FROM THE DISTRIBUTED MINING EXPLOSION

2019 ◽  
Vol 4 (1) ◽  
pp. 141-148
Author(s):  
Sergey Efimov
Keyword(s):  
Wave Field ◽  
Seismic Wave ◽  
Temporal Analysis ◽  
Seismic Signal ◽  
Environmental Risks ◽  
Time Analysis ◽  
Seismic Recording ◽  
Seismic Records ◽  
Seismic Wave Field ◽  
Spatial Temporal Analysis

The article presents a space-time analysis of the seismic wave from a distributed career explosion. The method of direct measurement based on the dynamic model of the wave field is used to form an image of the seismic wave field in the field of quarry explosions. The efficiency of the proposed method is shown by the example of experimental seismic recording processing. The program "Nelumbo" is used to visualize the seismic field, which on the basis of experimental seismic records allows to form an image of the wave field in the space of the hemisphere, the center of which corresponds to the position of the seismometer (registration point). The algorithm of the program "Nelumbo" is based on the Huygens – Fresnel principle and Kirchhoff's theorem. The algorithm of the program allows to allocate from record of a seismic signal frames of a certain duration and to form the image of a wave field in space of a solid angle dimension π. This approach can be used as a tool to analyze the nature of the development of disturbances in the environment and the analysis of environmental risks in the production of blasting.

AN APPROACH TO INVERSE FILTERING OF NEAR‐SURFACE LAYER EFFECTS FROM SEISMIC RECORDS

Geophysics ◽  
1961 ◽  
Vol 26 (6) ◽  
pp. 754-760 ◽  
Author(s):  
Pierre L. Goupillaud
Keyword(s):  
Surface Layer ◽  
Seismic Reflection ◽  
Normal Incidence ◽  
Resolving Power ◽  
Surface Velocity ◽  
Inverse Filtering ◽  
Near Surface ◽  
Seismic Records ◽  
Stratification Variable ◽  
Velocity Information

This paper suggests a scheme for compensating the effects that the near‐surface stratification, variable from spread to spread, produces on both the character and the timing of the seismic traces. For this purpose, accurate near‐surface velocity information is mandatory. This scheme should greatly reduce the correlation difficulties so frequently encountered in many areas. It may also be used to enhance the resolving power of the seismic reflection technique. The approach presented here is based on the rather restrictive assumptions of normal incidence, parallel equispaced plant reflectors, and noiseless conditions.

Large‐scale three‐dimensional seismic models and their interpretive significance

Geophysics ◽  
1990 ◽  
Vol 55 (9) ◽  
pp. 1166-1182 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Finite Difference ◽  
Wave Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Real Data ◽  
The Real ◽  
Need To Evaluate ◽  
Zero Offset ◽  
Seismic Models

Finite‐difference seismic models are commonly set up in 2-D space. Such models must be excited by a line source which leads to different amplitudes than those in the real data commonly generated from a point source. Moreover, there is no provision for any out‐of‐plane events. These problems can be eliminated by using 3-D finite‐difference models. The fundamental strategy in designing efficient 3-D models is to minimize computational work without sacrificing accuracy. This was accomplished by using a (4,2) differencing operator which ensures the accuracy of much larger operators but requires many fewer numerical operations as well as significantly reduced manipulation of data in the computer memory. Such a choice also simplifies the problem of evaluating the wave field near the subsurface boundaries of the model where large operators cannot be used. We also exploited the fact that, unlike the real data, the synthetic data are free from ambient noise; consequently, one can retain sufficient resolution in the results by optimizing the frequency content of the source signal. Further computational efficiency was achieved by using the concept of the exploding reflector which yields zero‐offset seismic sections without the need to evaluate the wave field for individual shot locations. These considerations opened up the possibility of carrying out a complete synthetic 3-D survey on a supercomputer to investigate the seismic response of a large‐scale structure located in Oklahoma. The analysis of results done on a geophysical workstation provides new insight regarding the role of interference and diffraction in the interpretation of seismic data.

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