Description of a scanless method of stacking velocity analysis

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1596-1606 ◽  
Author(s):  
Hans J. Tieman

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.

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1118-1127 ◽  
Author(s):  
Dimitri Bevc ◽  
James L. Black ◽  
Gopal Palacharla

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.


Geophysics ◽  
1982 ◽  
Vol 47 (6) ◽  
pp. 884-897 ◽  
Author(s):  
Walter S. Lynn ◽  
Jon F. Claerbout

In areas of large lateral variations in velocity, stacking velocities computed on the basis of hyperbolic moveout can differ substantially from the actual root mean square (rms) velocities. This paper addresses the problem of obtaining rms or migration velocities from stacking velocities in such areas. The first‐order difference between the stacking and the vertical rms velocities due to lateral variations in velocity are shown to be related to the second lateral derivative of the rms slowness [Formula: see text]. Approximations leading to this relation are straight raypaths and that the vertical rms slowness to a given interface can be expressed as a second‐order Taylor series expansion in the midpoint direction. Under these approximations, the effect of the first lateral derivative of the slowness on the traveltime is negligible. The linearization of the equation relating the stacking and true velocities results in a set of equations whose inversion is unstable. Stability is achieved, however, by adding a nonphysical fourth derivative term which affects only the higher spatial wavenumbers, those beyond the lateral resolution of the lateral derivative method (LDM). Thus, given the stacking velocities and the zero‐offset traveltime to a given event as a function of midpoint, the LDM provides an estimate of the true vertical rms velocity to that event with a lateral resolution of about two mute zones or cable lengths. The LDM is applicable when lateral variations of velocity greater than 2 percent occur over the mute zone. At variations of 30 percent or greater, the internal assumptions of the LDM begin to break down. Synthetic models designed to test the LDM when the different assumptions are violated show that, in all cases, the results are not seriously affected. A test of the LDM on field data having a lateral velocity variation caused by sea floor topography gives a result which is supported by depth migration.


Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. U87-U96 ◽  
Author(s):  
Mamoru Takanashi ◽  
Ilya Tsvankin

One of the most serious problems in anisotropic velocity analysis is the trade-off between anisotropy and lateral heterogeneity, especially if velocity varies on a scale smaller than the maximum offset. We have developed a P-wave MVA (migration velocity analysis) algorithm for transversely isotropic (TI) models that include layers with small-scale lateral heterogeneity. Each layer is described by constant Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-direction velocity [Formula: see text] that varies as a quadratic function of the distance along the layer boundaries. For tilted TI media (TTI), the symmetry axis is taken orthogonal to the reflectors. We analyzed the influence of lateral heterogeneity on image gathers obtained after prestack depth migration and found that quadratic lateral velocity variation in the overburden can significantly distort the moveout of the target reflection. Consequently, medium parameters beneath the heterogeneous layer(s) are estimated with substantial error, even when borehole information (e.g., check shots or sonic logs) is available. Because residual moveout in the image gathers is highly sensitive to lateral heterogeneity in the overburden, our algorithm simultaneously inverts for the interval parameters of all layers. Synthetic tests for models with a gently dipping overburden demonstrate that if the vertical profile of the symmetry-direction velocity [Formula: see text] is known at one location, the algorithm can reconstruct the other relevant parameters of TI models. The proposed approach helps increase the robustness of anisotropic velocity model-building and enhance image quality in the presence of small-scale lateral heterogeneity in the overburden.


Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1846-1858 ◽  
Author(s):  
Claudio Bagaini ◽  
Umberto Spagnolini

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.


Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U19-U27 ◽  
Author(s):  
Paul C. Sava ◽  
Biondo Biondi ◽  
John Etgen

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.


Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. U9-U18 ◽  
Author(s):  
Sergey Fomel ◽  
Alexey Stovas

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.


1989 ◽  
Vol 20 (2) ◽  
pp. 301
Author(s):  
P.D. Grant

The Puffin Field is located within the Vulcan Sub-basin of the Timor sea, off the Northwest Coast of Australia. It lies within the offshore exploration permit AC/P2, operated by BHP Petroleum and its co-venturers. It is situated on the Ashmore Platform, an old Triassic horst which is normal faulted against the Swan Graben, a major Mesozoic depocentre and the regional source area. Three wells were drilled in the 1970's. Puffin-1 and Puffin-3 encountered oil in "FIT" tests from within the Maastrichtian 100 ft sand, and Puffin-2 flowed over 4000 barrels of oil per day from a slightly younger 4 m sand. On examination of the results of the Puffin wells, it was evident that there were severe velocity anomalies and differing oil water contacts in the Puffin field. The top of the 100 ft reservoir sand is at 2031.4 m subsea in Puffin-1, 2045 m subsea at Puffin-2 and 2074 m subsea at Puffin-3. The two way times to these events were 1392 ms, 1328 ms and 1398 ms respectively. The interpreted oil water contacts in Puffin-1 and Puffin-3 were 2033 and 2077 ms subsea respectively with no contact seen at Puffin-2. In an attempt to resolve these anomalies the AC/P2 joint venture undertook a detailed seismic reprocessing project of the 1980 data with special emphasis on detailed velocity analysis. This 1987 reprocessing effort involved two passes of velocity filtering and velocity analysis at every 600 m. Velocity analyses were picked on a horizon-consistent basis, such that variations in interval velocity for key horizons could be established for later use in depth conversion. Although sceptical in using stacking functions as the input velocities to depth conversion, they were used, as no viable alternative was feasible. Data quality was reliable to the top of the Palaeocene Calcilutite, and six horizons were picked with their respective velocities to this level. Analysis of the data indicated that the two major units exhibiting interval velocity variation were the Pliocene "low velocity layer" and the Eocene carbonates. Using the smoothed stacking velocity down to the Top Palaeocene Calcilutite the three wells tied the depth conversion with an accuracy of 0.5%. Below this horizon two constant interval velocities were used from well data as the quality of the seismic pick were not as reliable. To verify this model BHPP also undertook a "layer-cake" velocity approach which, although confirming the anomalous zones, could not be used laterally away from the three wells, which unfortunately all lay in a straight line. Two wells, Puffin-4 and Parry-1 were drilled in 1988 to test the resultant interpretation. The wells intersected the Top Palaeocene Calcilutite within 1% of prognosis at Puffin-4 and within 2.2% of prognosis at Parry-1, therefore confirming the stacking velocity model used in depth conversion. However, both wells came in deep to prognosis at the deeper, objective level as a result, in the case of Puffin-4, of being on the downthrown side of a small fault, and at Parry-1 due to a thickening of the Paleocene section and seismic mispicking of the Top Palaeocene Calcilutite. Had the mispick at Parry-1 been avoided then the tie would have been less than 1.0%. Both these mis-interpretations were made in the part of the section where the quality of seismic was poorest. These two results suggest that even though the depth conversion to the Top Paleocene Calcilutite is accurate to within 1%, the magnitude of the velocity variation is larger than the magnitude of the independent depth closure. The Puffin Field requires both better quality seismic below the Base Palaeocene Calcilutite, or the means to resolve the lateral extent and possible thickness of a 4 m sand away from Puffin-2. Until such a method of obtaining either better quality seismic to the objective level, or to be able to define the seismic resolution of the differing sand bodies of a minimum size of 4 m, the Puffin Field will remain a Geophysical enigma.


Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 604-609 ◽  
Author(s):  
Alexander Mihai Popovici ◽  
James A. Sethian

Recently, fast marching methods (FMM) beyond first order have been developed for producing rapid solutions to the eikonal equation. In this paper, we present imaging results for 3‐D prestack Kirchhoff migration using traveltimes computed using the first‐order and second‐order FMM on several 3‐D prestack synthetic and real data sets. The second order traveltimes produce a much better image of the structure. Moreover, insufficiently sampled first order traveltimes can introduce consistent errors in the common reflection point gathers that affect velocity analysis. First‐order traveltimes tend to be smaller than analytic traveltimes, which in turn affects the migration velocity analysis, falsely indicating that the interval velocity was too low.


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