Generalized nonhyperbolic moveout approximation

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. U9-U18 ◽  
Author(s):  
Sergey Fomel ◽  
Alexey Stovas
Keyword(s):  
Functional Form ◽  
Velocity Analysis ◽  
Numerical Examples ◽  
Time Migration ◽  
Analytical Approximations ◽  
Offset Time ◽  
Zero Offset ◽  
Two Parameters

Reflection moveout approximations are commonly used for velocity analysis, stacking, and time migration. A novel functional form for approximating the moveout of reflection traveltimes at large offsets is introduced. In comparison with the classic hyperbolic approximation, which uses only two parameters (zero-offset time and moveout velocity), this form involves five parameters that can be determined, in a known medium, from zero-offset computations and from tracing one nonzero-offset ray. It is called a generalized approximation because it reduces to some known three-parameter forms with a particular choice of coefficients. By testing the accuracy of the proposed approximation with analytical and numerical examples, the new approximation is shown to bring an improvement in accuracy of several orders of magnitude compared to known analytical approximations, which makes it as good as exact for many practical purposes.

Analyzing operators of 3-D imaging software with impulse responses

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1079-1092 ◽  
Author(s):  
William A. Schneider
Keyword(s):  
Impulse Response ◽  
Imaging Techniques ◽  
Velocity Model ◽  
Impulse Responses ◽  
Step Size ◽  
Data Set ◽  
Time Migration ◽  
Offset Time ◽  
Zero Offset ◽  
Algorithm Implementation

No processing step changes seismic data more than 3-D imaging. Imaging techniques such as 3-D migration and dip moveout (DMO) generally change the position, amplitude, and phase of reflections as they are converted into reflector images. Migration and DMO may be formulated in many different ways, and various algorithms are available for implementing each formulation. These algorithms all make physical approximations, causing imaging software to vary with algorithm choice. Imaging software also varies because of additional implementation approximations, such as those that trade accuracy for efficiency. Imaging fidelity, then, generally depends upon algorithm, implementation, specific software parameters (such as aperture, antialias filter settings, and downward‐continuation step size), specific acquisition parameters (such as nominal x- and y-direction trace spacings and wavelet frequency range), and, of course, the velocity model. Successfully imaging the target usually requires using appropriate imaging software, parameters, and velocities. Impulse responses provide an easy way to quantitatively understand the operators of imaging software and then predict how specific imaging software will perform with the chosen parameters. (An impulse response is the image computed from a data set containing only one nonzero trace and one arrival on that trace.) I have developed equations for true‐amplitude impulse responses of 3-D prestack time migration, 3-D zero‐offset time migration, 3-D exploding‐reflector time migration, and DMO. I use these theoretical impulse responses to analyze the operators of actual imaging software for a given choice of software parameters, acquisition parameters, and velocity model. The procedure is simple: compute impulse responses of some software; estimate position, amplitude, and phase of the impulse‐response events; and plot these against the theoretical values. The method is easy to use and has proven beneficial for analyzing general imaging software and for parameter evaluation with specific imaging software.

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.

Reply by the authors to Arthur E. Barnes

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1944-1946
Author(s):  
M. Tygel ◽  
J. Schleicher ◽  
P. Hubral
Keyword(s):  
Destructive Interference ◽  
Depth Migration ◽  
Time Migration ◽  
Pulse Distortion ◽  
Nmo Correction ◽  
Important Processing ◽  
Offset Time ◽  
Zero Offset ◽  
Seismic Reflections ◽  
Processing Steps

We highly appreciate the useful remarks of Dr. Barnes relating our work to well‐known practical seismic processing effects. This is of particular interest as normal‐moveout (NMO) correction and post‐stack time migration are still two very important processing steps. Most exploration geophysicists know about the significance of pulse distortions known as “NM0 stretch” and “frequency shifting due to zero‐offset time migration.” As a result of the discussion of Dr. Barnes, it should now be possible to better appreciate the importance of our very general formulas (27) describing the pulse distortion of seismic reflections from an arbitrarily curved subsurface reflector when subjected to a prestack depth migration in 3‐D laterally inhomogeneous media. This discussion thus relates in particular to such important questions as how to correctly sample signals in the time or depth domain in order to avoid spatial aliasing, or how to stack seismic data without loss of information due to destructive interference of wavelets of different lengths.

3D generalized nonhyperboloidal moveout approximation

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. C49-C59 ◽  
Author(s):  
Yanadet Sripanich ◽  
Sergey Fomel ◽  
Alexey Stovas ◽  
Qi Hao
Keyword(s):  
Time Domain ◽  
Functional Form ◽  
Seismic Imaging ◽  
High Accuracy ◽  
Velocity Analysis ◽  
Zero Offset ◽  
Independent Parameters

Moveout approximations are commonly used in velocity analysis and time-domain seismic imaging. We revisit the previously proposed generalized nonhyperbolic moveout approximation and develop its extension to the 3D multiazimuth case. The advantages of the generalized moveout approximation are its high accuracy and its ability to reduce to several other known approximations with particular choices of parameters. The proposed 3D functional form involves 17 independent parameters instead of five as in the 2D case. These parameters can be defined by zero-offset traveltime attributes and four additional far-offset rays. In our tests, the proposed approximation achieves significantly higher accuracy than previously proposed 3D approximations.

Velocity continuation and the anatomy of residual prestack time migration

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1650-1661 ◽  
Author(s):  
Sergey Fomel
Keyword(s):  
Continuous Process ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Image Transformation ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Seismic Image ◽  
Spectral Algorithms ◽  
Prestack Time Migration ◽  
Zero Offset

Velocity continuation is an imaginary continuous process of seismic image transformation in the postmigration domain. It generalizes the concepts of residual and cascaded migrations. Understanding the laws of velocity continuation is crucially important for a successful application of time‐migration velocity analysis. These laws predict the changes in the geometry and intensity of reflection events on migrated images with the change of the migration velocity. In this paper, I derive kinematic and dynamic laws for the case of prestack residual migration from simple geometric principles. The main theoretical result is a decomposition of prestack velocity continuation into three different components corresponding to residual normal moveout, residual dip moveout, and residual zero‐offset migration. I analyze the contribution and properties of each of the three components separately. This theory forms the basis for constructing efficient finite‐difference and spectral algorithms for time‐migration velocity analysis.

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.

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.

Description of a scanless method of stacking velocity analysis

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1596-1606 ◽  
Author(s):  
Hans J. Tieman
Keyword(s):  
Empirical Studies ◽  
Real Data ◽  
Velocity Variation ◽  
Velocity Analysis ◽  
Velocity Control ◽  
Lateral Velocity ◽  
Interval Velocity ◽  
Offset Time ◽  
Zero Offset ◽  
Traditional Approaches

Stacking velocities can be directly estimated from seismic data without recourse to a multivelocity stack and subsequent search techniques that many current procedures use. This is done as follows: (1) apply NMO to the data (over a window, for a particular common midpoint) using initial estimates for zero offset time and velocity; (2) produce two stacks by summing the data over offset after applying different weighting functions; (3) cross correlate the two stacks; and (4) translate the lag into velocity and time updates. The procedure is iterated until convergence has occurred. Referred to as ARAMVEL (U.S. Patent No. 4,813,027), the method is best implemented as an interactive continuous velocity analysis. Although very simple, both empirical studies and theoretical analysis have shown that it determines velocities more accurately than more traditional approaches based on a scan approach. Convergence is fast, with only one or two iterations usually necessary. The method is robust, as only approximate information is necessary initially. Results with real data show that the method can economically give the detailed velocity control necessary for processing data from areas with considerable lateral velocity variation, as well as provide traveltime information that can be used for sophisticated inversion into interval velocity and depth.

Sign in / Sign up

Export Citation Format

Share Document