2‐D wavepath migration

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1528-1537 ◽  
Author(s):  
H. Sun ◽  
G. T. Schuster
Keyword(s):  
Fresnel Zone ◽  
Complex Structure ◽  
Computation Time ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Kirchhoff Migration ◽  
Time Sample ◽  
Grid Points ◽  
Computationally Intensive ◽  
Single Trace

Prestack Kirchhoff migration (KM) is computationally intensive for iterative velocity analysis. This is partly because each time sample in a trace must be smeared along a quasi‐ellipsoid in the model. As a less costly alternative, we use the stationary phase approximation to the KM integral so that the time sample is smeared along a small Fresnel zone portion of the quasi‐ellipsoid. This is equivalent to smearing the time samples in a trace over a 1.5‐D fat ray (i.e., wavepath), so we call this “wavepath migration” (WM). This compares to standard KM, which smears the energy in a trace along a 3‐D volume of quasi‐concentric ellipsoids. In principle, single trace migration with WM has a computational count of [Formula: see text] compared to KM, which has a computational count of [Formula: see text], where N is the number of grid points along one side of a cubic velocity model. Our results with poststack data show that WM produces an image that in some places contains fewer migration artifacts and is about as well resolved as the KM image. For a 2‐D poststack migration example, the computation time of WM is less than one‐third that of KM. Our results with prestack data show that WM images contain fewer migration artifacts and can define the complex structure more accurately. It is also shown that WM can be significantly faster than KM if a slant stack technique is used in the migration. The drawback with WM is that it is sometimes less robust than KM because of its sensitivity to errors in estimating the incidence angles of the reflections.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

Parsimonious 2D prestack Kirchhoff depth migration

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1043-1051 ◽  
Author(s):  
Biaolong Hua ◽  
George A. McMechan
Keyword(s):  
Fresnel Zone ◽  
Computation Time ◽  
Structural Features ◽  
Common Source ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Migration Velocity Analysis ◽  
Reflector Surface ◽  
Kirchhoff Depth Migration ◽  
Ray Parameter

The efficiency of prestack Kirchhoff depth migration is much improved by using ray parameter information measured from prestack common‐source and common‐receiver gathers. Ray tracing is performed only back along the emitted and emergent wave directions, and so is much reduced. The position of the intersection of the source and receiver rays is adjusted to satisfy the image time condition. The imaged amplitudes are spread along the local reflector surface only within the first Fresnel zone. There is no need to build traveltime tables before migration because the traveltime calculation is embedded into the migration. To further reduce the computation time, the input data are decimated by applying an amplitude threshold before the estimation of ray parameters, and only peak and trough points on each trace are searched for ray parameters. Numerical results show that the proposed implementation is typically 50–80 times faster than traditional Kirchhoff migration for synthetic 2D prestack data. The migration speed improvement is obtained at the expense of some reduction in migration quality; the optimal compromise is implemented by the choice of migration parameters. The main uses of the algorithm will be to get a fast first look at the main structural features and for iterative migration velocity analysis.

Kirchhoff migration and velocity analysis for converted and nonconverted waves in anisotropic media

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 265-276 ◽  
Author(s):  
Arcangelo G. Sena ◽  
M. Nafi Toksöz
Keyword(s):  
Anisotropic Media ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Converted Wave ◽  
Anisotropic Models ◽  
Kirchhoff Migration ◽  
Analysis Technique ◽  
Analysis Scheme ◽  
Isotropic Media ◽  
And Migration

We develop asymptotic expressions and outline a procedure to perform Kirchhoff migration in anisotropic media. This technique is based on a new Green’s tensor representation for azimuthally isotropic media obtained by using analytical forms for the ray amplitudes and traveltimes. Since in real applications the usage of general anisotropy in a migration scheme will be limited by the availability and reliability of the velocity model considered, we also develop a new anisotropic velocity analysis scheme to generate realistic anisotropic models for migration in azimuthally isotropic media for nonconverted and converted qP-qSV waves. This velocity analysis technique is based on nonhyperbolic traveltime‐offset formulas explicitly given in terms of the five elastic constants of azimuthal isotropy. The imaging technique is applied to nonconverted‐as well as converted‐wave surface seismic data. In both cases the method provides accurate images of the subsurface. Even with a weak to moderate percentage of anisotropy, we show that an isotropic migration algorithm cannot properly image the subsurface. This paper provides new nonconventional techniques for the velocity analysis and migration in anisotropic media and shows the feasibility of exploiting converted and nonconverted waves.

Parsimonious 2‐D poststack Kirchhoff depth migration

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1497-1503 ◽  
Author(s):  
Biao‐Long Hua ◽  
George A. McMechan
Keyword(s):  
Incident Wave ◽  
Input Data ◽  
Fresnel Zone ◽  
Computation Time ◽  
Structural Features ◽  
Seismic Section ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Ray Path ◽  
Kirchhoff Depth Migration

Efficiency of Kirchhoff migration can be much improved by using slope information from the seismic section to estimate the incident wave directions. Ray tracing is performed only back along the incident wave directions and so is much reduced. Unlike in conventional Kirchhoff implementations, there is no need to build traveltime tables, so relatively little memory and input/output use are required. Compression of the input data and restricting the contribution of each time sample to the image to lie within a Fresnel zone of its ray path further reduces the computation time. Synthetic and field data tests show that the new algorithm is about 30 times faster than traditional Kirchhoff migration for 2‐D poststack data. The main structural features may be imaged very quickly at the expense of some details. There is a tradeoff between speed and image quality; the optimal compromise is implemented by the choice of migration parameters.

3D common-reflection-point-based seismic migration velocity analysis

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. S161-S167 ◽  
Author(s):  
Weihong Fei ◽  
George A. McMechan
Keyword(s):  
Synthetic Data ◽  
Computation Time ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reflection Point ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Migration Velocity Analysis ◽  
Spatial Coordinates

Three-dimensional prestack depth migration and depth residual picking in common-image gathers (CIGs) are the most time-consuming parts of 3D migration velocity analysis. Most migration-based velocity analysis algorithms need spatial coordinates of reflection points and CIG depth residuals at different offsets (or angles) to provide updated velocity information. We propose a new algorithm that can analyze 3D velocity quickly and accurately. Spatial coordinates and orientations of reflection points are provided by a 3D prestack parsimonious depth migration; the migration involves only the time samples picked from the salient reflection events on one 3D common-offset volume. Ray tracing from the reflection points to the surface provides a common-reflection-point (CRP) gather for each reflection point. Predicted (nonhyperbolic) moveouts for local velocity perturbations, based on maximizing the stacked amplitude, give the estimated velocity updates for each CRP gather. Then the velocity update for each voxel in the velocity model is obtained by averaging over all predicted velocity updates for that voxel. Prior model constraints may be used to stabilize velocity updating. Compared with other migration velocity analyses, the traveltime picking is limited to only one common-offset volume (and needs to be done only once); there is no need for intensive 3D prestack depth migration. Hence, the computation time is orders of magnitude less than other migration-based velocity analyses. A 3D synthetic data test shows the algorithm works effectively and efficiently.

Finite‐difference calculation of direct‐arrival traveltimes using the eikonal equation

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1270-1274 ◽  
Author(s):  
Le‐Wei Mo ◽  
Jerry M. Harris
Keyword(s):  
Finite Difference ◽  
Ray Tracing ◽  
Finite Differences ◽  
Eikonal Equation ◽  
Velocity Model ◽  
Uniform Grid ◽  
Square Grid ◽  
Kirchhoff Migration ◽  
Difference Calculation

Traveltimes of direct arrivals are obtained by solving the eikonal equation using finite differences. A uniform square grid represents both the velocity model and the traveltime table. Wavefront discontinuities across a velocity interface at postcritical incidence and some insights in direct‐arrival ray tracing are incorporated into the traveltime computation so that the procedure is stable at precritical, critical, and postcritical incidence angles. The traveltimes can be used in Kirchhoff migration, tomography, and NMO corrections that require traveltimes of direct arrivals on a uniform grid.

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.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

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.

Time-migration velocity analysis by image-wave propagation of common-image gathers

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE161-VE171 ◽  
Author(s):  
J. Schleicher ◽  
J. C. Costa ◽  
A. Novais
Keyword(s):  
Wave Propagation ◽  
Seismic Event ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reference Velocity ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Velocity Image ◽  
The Common

Image-wave propagation or velocity continuation describes the variation of the migrated position of a seismic event as a function of migration velocity. Image-wave propagation in the common-image gather (CIG) domain can be combined with residual-moveout analysis for iterative migration velocity analysis (MVA). Velocity continuation of CIGs leads to a detection of those velocities in which events flatten. Although image-wave continuation is based on the assumption of a constant migration velocity, the procedure can be applied in inhomogeneous media. For this purpose, CIGs obtained by migration with an inhomogeneous macrovelocity model are continued starting from a constant reference velocity. The interpretation of continued CIGs, as if they were obtained from residual migrations, leads to a correction formula that translates residual flattening velocities into absolute time-migration velocities. In this way, the migration velocity model can be improved iteratively until a satisfactory result is reached. With a numerical example, we found that MVA with iterative image continuation applied exclusively to selected CIGs can construct a reasonable migration velocity model from scratch, without the need to build an initial model from a previous conventional normal-moveout/dip-moveout velocity analysis.

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