Application of an integrated wave-equation datuming scheme to overthrust data: A case history from the Chinese foothills

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. B153-B165 ◽  
Author(s):  
Kai Yang ◽  
Hong-Ming Zheng ◽  
Li Wang ◽  
Yu-Zhu Liu ◽  
Fan Jiang ◽  
...  
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Western China ◽  
Velocity Variation ◽  
Lateral Velocity ◽  
Near Surface ◽  
Depth Images ◽  
Static Corrections ◽  
Kirchhoff Integral

An integrated wave-equation datuming scheme improves the imaging quality of seismic data from overthrust areas. It can be regarded as integrated because upward-layer replacement is included. In this scheme, data are downward continued to a nonplanar datum (such as the base of the weathering layer), followed by upward continuation from the nonplanar datum to a final planar datum using a one-way extrapolator. When compared with a Kirchhoff integral, this method can deal better with the strong lateral velocity variation within the near surface. After a test on synthetic data, the scheme is applied successfully to real 2D overthrust data acquired in the Qi-Lian foothills, western China. Compared with results using static corrections, integrated wave-equation datuming results lead to better reconstruction of the diffractions and reflections, more reliable migration-velocity analyses, and stronger stack and final depth images.

Wave-equation global datuming based on the double square root operator

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. U35-U43 ◽  
Author(s):  
Wenge Liu ◽  
Bo Zhao ◽  
Hua-wei Zhou ◽  
Zhenhua He ◽  
Hui Liu ◽  
...  
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Square Root ◽  
New Wave ◽  
Lateral Velocity ◽  
Near Surface ◽  
Traditional Procedure ◽  
Wavefield Continuation ◽  
Static Corrections ◽  
Root Operator

Current schemes for removing near-surface effects in seismic data processing use either static corrections or wave-equation datuming (WED). In the presence of rough topography and strong lateral velocity variations in the near surface, the WED scheme is the only option available. However, the traditional procedure of WED downward continues the sources and receivers in different domains. A new wave-equation global-datuming method is based on the double-square-root operator, implementing the wavefield continuation in a single domain following the survey sinking concept. This method has fewer approximations and therefore is more robust and convenient than the traditional WED methods. This method is compared with the traditional methods using a synthetic data example.

Simultaneous estimation of residual static and crossdip corrections

Geophysics ◽  
1979 ◽  
Vol 44 (7) ◽  
pp. 1175-1192 ◽  
Author(s):  
Kenneth L. Larner ◽  
Bruce R. Gibson ◽  
Ron Chambers ◽  
Ralph A. Wiggins
Keyword(s):  
Three Dimensional ◽  
Synthetic Data ◽  
Simultaneous Estimation ◽  
Broad Line ◽  
Near Surface ◽  
Seismic Surveys ◽  
Surface Reflection ◽  
Static Corrections ◽  
Solution Parameters

Seismic surveys on land are frequently conducted along nonlinear survey lines. Familiar examples include crooked lines controlled by existing road networks or by surface typography, lines that are otherwise linear but along which shotpoints occasionally must be offset laterally, and intentionally designed three‐dimensional (3-D) or broad‐line surveys. Departures from linear profiles introduce an element of complexity—crossdip—into the problem of estimating residual near‐surface reflection static time corrections (statics). Crossdip is the component of dip normal to the local profile direction. We have incorporated the effect of crossdip into the system of simultaneous equations that model residual static anomalies. The observed traveltimes of all reflections selected for analysis are represented as linear combinations of source and receiver static anomalies, structural shapes, residual normal moveouts, and crossdip terms. The static time components are taken to be surface‐consistent and independent of reflecting horizon, whereas the other solution parameters are subsurface‐consistent and pertain to specific horizons. Unfortunately, the inclusion of crossdip in the equations increases the degree of nonuniqueness of residual statics solutions. Its inclusion, however, is a necessity wherever horizons having differing crossdips are analyzed simultaneously. Such simultaneous analysis often is the best means for upgrading the reliability of the crosscorrelation estimates (i.e., the traveltime observations) upon which all statics are based. Synthetic‐data examples demonstrate the degree to which crossdip estimates and statics estimates can be separated from one another. Although estimates of crossdips are a useful by‐product, the accuracy of the static corrections is considered of prime importance. When critical crossdip terms are ignored in a statics solution, the quality of the common‐depthpoint (CDP) stacks suffer, as shown in comparison processings of field sections. Moreover, crossdip estimates from 3-D or broad‐line surveys are questionable if crossdip and static corrections are not considered in a unified solution.

Vertical seismic profile migration using the Kirchhoff integral

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 786-799 ◽  
Author(s):  
P. B. Dillon
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Near Field ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Processing Strategies ◽  
Receiver Array ◽  
Vsp Data ◽  
Kirchhoff Integral

Wave‐equation migration can form an accurate image of the subsurface from suitable VSP data. The image’s extent and resolution are determined by the receiver array dimensions and the source location(s). Experiments with synthetic and real data show that the region of reliable image extent is defined by the specular “zone of illumination.” Migration is achieved through wave‐field extrapolation, subject to an imaging procedure. Wave‐field extrapolation is based upon the scalar wave equation and, for VSP data, is conveniently handled by the Kirchhoff integral. The migration of VSP data calls for imaging very close to the borehole, as well as imaging in the far field. This dual requirement is met by retaining the near‐field term of the integral. The complete integral solution is readily controlled by various weighting devices and processing strategies, whose worth is demonstrated on real and synthetic data.

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.

Overthrust imaging with tomo‐datuming: A case study

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Xianhuai Zhu ◽  
Burke G. Angstman ◽  
David P. Sixta
Keyword(s):  
Velocity Model ◽  
Surface Velocity ◽  
Time Shift ◽  
Lateral Velocity ◽  
Prestack Depth Migration ◽  
Near Surface ◽  
Depth Migration ◽  
Static Corrections ◽  
Velocity Variations ◽  
Kirchhoff Method

Through the use of iterative turning‐ray tomography followed by wave‐equation datuming (or tomo‐datuming) and prestack depth migration, we generate accurate prestack images of seismic data in overthrust areas containing both highly variable near‐surface velocities and rough topography. In tomo‐datuming, we downward continue shot records from the topography to a horizontal datum using velocities estimated from tomography. Turning‐ray tomography often provides a more accurate near‐surface velocity model than that from refraction statics. The main advantage of tomo‐datuming over tomo‐statics (tomography plus static corrections) or refraction statics is that instead of applying a vertical time‐shift to the data, tomo‐datuming propagates the recorded wavefield to the new datum. We find that tomo‐datuming better reconstructs diffractions and reflections, subsequently providing better images after migration. In the datuming process, we use a recursive finite‐difference (FD) scheme to extrapolate wavefield without applying the imaging condition, such that lateral velocity variations can be handled properly and approximations in traveltime calculations associated with the raypath distortions near the surface for migration are avoided. We follow the downward continuation step with a conventional Kirchhoff prestack depth migration. This results in better images than those migrated from the topography using the conventional Kirchhoff method with traveltime calculation in the complicated near surface. Since FD datuming is only applied to the shallow part of the section, its cost is much less than the whole volume FD migration. This is attractive because (1) prestack depth migration usually is used iteratively to build a velocity model, so both efficiency and accuracy are important factors to be considered; and (2) tomo‐datuming can improve the signal‐to‐noise (S/N) ratio of prestack gathers, leading to more accurate migration velocity analysis and better images after depth migration. Case studies with synthetic and field data examples show that tomo‐datuming is especially helpful when strong lateral velocity variations are present below the topography.

Reverse time migration from topography

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. S141-S152 ◽  
Author(s):  
Jeffrey Shragge
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Data Acquisition ◽  
Velocity Variation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Acoustic Wave Propagation ◽  
Lateral Velocity ◽  
Near Surface ◽  
Time Migration

Migration of seismic data from topography using methods based on finite-difference (FD) approximation to acoustic wave propagation commonly suffers from a number of imaging drawbacks due to the difficulty of applying FD stencils to irregular computational meshes. Altering the computational geometry from Cartesian to a topographic coordinate system conformal to the data acquisition surface can circumvent many of these issues. The coordinate transformation approach allows for acoustic wave propagation and the crosscorrelation and inverse-scattering imaging conditions to be posed and computed directly in topographic coordinates. Resulting reverse time migration (RTM) images may then be interpolated back to the Cartesian domain using the known inverse mapping. Orthogonal 2D topographic coordinates can be developed using known conformal mapping transforms and serve as the computational mesh for performing migration from topography. Impulse response tests demonstrate the accuracy of the 2D generalized acoustic wave propagation. RTM imaging examples show the efficacy of performing migration from topography directly from the data acquisition surface on topographic meshes and the ability to image complex near-surface structure even in the presence of strong lateral velocity variation.

Efficient simultaneous wave-equation statics and trace regularization by series approximation

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. U19-U28 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Wave Equation ◽  
Gradient Methods ◽  
Synthetic Data ◽  
Real Data ◽  
Three Dimensions ◽  
Velocity Variation ◽  
Acceptable Solution ◽  
Direct Inversion ◽  
Data Inversion ◽  
Series Approximation

To address the problems of irregular trace spacing and statics correction, simultaneous regularization and wave-equation statics (WE statics) are implemented by least-squares inversion. In general, inversion is found to be intractable in three dimensions, so series approximation is made to reduce significantly the number of required integrals. The resulting operator is suitable for direct inversion or for use with gradient methods. Real and synthetic data are used to determine the viability of the inversion. For synthetic data, even for severe velocity variation and topography, inversion converges to an acceptable solution, and aliasing is reduced significantly. Similarly, for real data, inversion is found to return an antialiased, regularized result with WE statics applied.

Datum correction by wave‐equation extrapolation

Geophysics ◽  
1988 ◽  
Vol 53 (10) ◽  
pp. 1311-1322 ◽  
Author(s):  
V. Shtivelman ◽  
A. Canning
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Real Data ◽  
Static Solution ◽  
Velocity Model ◽  
Lateral Velocity ◽  
Static Correction ◽  
Slow Velocity ◽  
Velocity Variations ◽  
Seismic Sections

Seismic sections are usually datum corrected by static shifting. For small differences in elevation and slow velocity variations between the input datum and the output datum, static shifting is a sufficiently accurate datum correction procedure. However, for significant differences in elevations and a more complicated velocity model, the accuracy of the static solution may prove to be insufficient; and a more exact method should be used. In this paper, we study the limitations of the static method of datum correction and develop simple and effective extrapolation schemes based on the wave equation, schemes which lead to more accurate datum correction. The distortions of seismic events caused by static correction are illustrated by a number of simple examples. To reduce the distortions, we propose a number of extrapolation schemes based on the asymptories of the Kirchhoff integral solution of the 2-D scalar wave equation. Application of the extrapolation algorithms to synthetic data shows that they provide accurate datum corrections even for a nonplanar input datum and vertical and lateral velocity variations. The algorithms have been successfully applied to real data.

Migration with the full acoustic wave equation

Geophysics ◽  
1983 ◽  
Vol 48 (6) ◽  
pp. 677-687 ◽  
Author(s):  
Dan D. Kosloff ◽  
Edip Baysal
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Physical Model ◽  
Wave Equations ◽  
Synthetic Data ◽  
Acoustic Wave Equation ◽  
Model Data ◽  
Lateral Velocity ◽  
Alternative Approach

Conventional finite‐difference migration has relied on one‐way wave equations which allow energy to propagate only downward. Although generally reliable, such equations may not give accurate migration when the structures have strong lateral velocity variations or steep dips. The present study examined an alternative approach based on the full acoustic wave equation. The migration algorithm which developed from this equation was tested against synthetic data and against physical model data. The results indicated that such a scheme gives accurate migration for complicated structures.

Prestack processing of land data with complex topography

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1875-1886 ◽  
Author(s):  
Sara Rajasekaran ◽  
George A. McMechan
Keyword(s):  
Wave Equation ◽  
Processing System ◽  
Essential Elements ◽  
Surface Velocity ◽  
Velocity Variation ◽  
Data Set ◽  
Near Surface ◽  
Depth Migration ◽  
Elevation Changes ◽  
Data Extrapolation

A new wave‐equation–based prestack seismic processing system is proposed. This system has only two essential elements; velocity analysis and depth migration. This approach applies truly surface‐consistent statics corrections, regardless of the amount of elevation, change or of near‐surface velocity variation. It uses tomography for estimating the details of shallow velocities and a finite‐difference solution of the two‐way wave‐equation both for computation of image times and for data extrapolation in migration. A field data set that violates most of the assumptions in conventional common midpoint (CMP) processing, because of severe elevation changes and near‐surface velocity variations, is successfully processed. The final depth section reveals a complicated fold‐thrust geometry that was not visible after CMP processing.

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