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.

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 Fast 3D migration-velocity analysis by wavefield extrapolation using the prestack exploding-reflector model

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB151-WB167 ◽  
Author(s):  
Claudio Guerra ◽  
Biondo Biondi
Keyword(s):  
Initial Conditions ◽  
Model Space ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Image Space ◽  
Velocity Analysis ◽  
The North ◽  
Migration Velocity Analysis ◽  
Wavefield Extrapolation

In areas of complex geology, migration-velocity estimation should use methods that describe the complexity of wavefield propagation, such as focusing and defocusing, multipathing, and frequency-dependent velocity sensitivity. Migration-velocity analysis by wavefield extrapolation has the ability to address these issues because, in contrast to ray-based methods, it uses wavefields as carriers of information. However, its high cost and lack of flexibility with respect to model parametrization and to target-oriented analysis have prevented its routine industrial use. We overcome those limitations by using new types of wavefields as carriers of information: the image-space generalized wavefields. These wavefields are synthesized from a prestack image computed with wavefield-extrapolation methods, using the prestack exploding-reflector model. Cost of migration-velocity analysis (MVA) by wavefield extrapolation is decreased because only a small number of image-space generalized wavefields are necessary to accurately describe the kinematics of velocity errors and because these wavefields can be easily used in a target-oriented way. Flexibility is naturally incorporated because modeling these wavefields has as the initial conditions selected reflectors, which allow use of a horizon-based parametrization of the model space. In a 3D example of the North Sea, we show that using wavefields synthesized by the prestack exploding-reflector model greatly improves efficiency of MVA by wavefield extrapolation, while yielding a final migration-velocity model that is accurate as evidenced by well focused and structurally reasonable reflectors.

Subsalt velocity estimation by target-oriented wave-equation migration velocity analysis: A 3D field-data example

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. U19-U29 ◽  
Author(s):  
Yaxun Tang ◽  
Biondo Biondi
Keyword(s):  
Wave Equation ◽  
Field Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Data Set ◽  
Generalized Born ◽  
Migration Velocity Analysis ◽  
Recorded Data

We apply target-oriented wave-equation migration velocity analysis to a 3D field data set acquired from the Gulf of Mexico. Instead of using the original surface-recorded data set, we use a new data set synthesized specifically for velocity analysis to update subsalt velocities. The new data set is generated based on an initial unfocused target image and by a novel application of 3D generalized Born wavefield modeling, which correctly preserves velocity kinematics by modeling zero and nonzero subsurface-offset-domain images. The target-oriented inversion strategy drastically reduces the data size and the computation domain for 3D wave-equation migration velocity analysis, greatly improving its efficiency and flexibility. We apply differential semblance optimization (DSO) using the synthesized new data set to optimize subsalt velocities. The updated velocity model significantly improves the continuity of subsalt reflectors and yields flattened angle-domain common-image gathers.

Migration velocity analysis using traveltime wavefield tomography

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. U73-U85 ◽  
Author(s):  
Saleh M. Al-Saleh ◽  
Jianwu Jiao
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Migration Velocity ◽  
Equation Modeling ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Traveltime Tomography ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Complex Structural

We introduce an integrated wave-equation technique for migration velocity analysis (MVA) that consists of three steps: (1) forming the extended data, (2) approximating the correct transmitted wavefield, and (3) using wavefield tomography to update the velocity model. In the first step, the crosscorrelation imaging condition is relaxed to produce other nonzero-lag common image gathers (CIG) that, combined, form a common image cube (CIC). Slicing the CIC at different crosscorrelation lags forms a series of CIGs. Flattened events will occur in the CIGs at a lag other than the zero-lag when an incorrect velocity model is used in the migration. In the second step, for each event on the CIG, we pick the focusing depth and crosscorrelation lag at which it is flattest. We then model a Green’s function by seeding a source at the focusing depth using one-way wave equation modeling, then shift the modeled wavefield with the focusing crosscorrelation lag. This process is repeated for the other primary events at different lateral and vertical positions. The result is a set of modeled data whose wavefield approximates the wavefield that would have been generated if the correct velocity model had been used to simulate these gathers. We then apply wavefield tomography on these data-driven modeled data to update the velocity model. Our inversion scheme is based on wave-equation traveltime tomography that can update the velocity model in the presence of large velocity errors and a complex environment. Tests on synthetic and real 2D seismic data confirm the method’s effectiveness in building velocity models in complex structural areas that have large lateral velocity variations.

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.

Joint PP and PS plane-wave wave-equation migration-velocity analysis

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R507-R525 ◽  
Author(s):  
Zongcai Feng ◽  
Bowen Guo ◽  
Lianjie Huang
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Wave Velocity ◽  
Migration Velocity ◽  
Relative Depth ◽  
Velocity Analysis ◽  
Analysis Method ◽  
S Wave ◽  
Velocity Models ◽  
Migration Velocity Analysis

Conventional joint PP and PS velocity analysis is based on ray tomography. We develop a joint PP and PS wave-equation migration-velocity-analysis method using plane-wave common-image gathers (CIGs) to produce accurate P- and S-wave velocity models. The objective function of our new method consists of three terms: The first and second terms penalize the moveout residuals computed from PP and PS plane-wave CIGs, respectively, and the third term constrains the nonzero relative depth shifts between the PP and PS migration images. The moveout of plane-wave CIGs is automatically picked using a semblance analysis method, and the relative depth shifts between the PP and PS images are automatically computed using dynamic warping or manually picking the depths of certain primary reflectors. The moveout residuals and the relative depth shifts are transformed into weighted image perturbations, and they are then projected into the velocity models to update the P- and S-wave velocity models using the scalar-wave equations and their linearized forms. Numerical tests with synthetic and multicomponent field data demonstrate that our method can simultaneously invert for accurate P- and S-wave velocity models for elastic migration.

Time-lapse wave-equation migration velocity analysis

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. S69-S79 ◽  
Author(s):  
Jeffrey Shragge ◽  
David Lumley
Keyword(s):  
Wave Equation ◽  
Time Lapse ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Earth Model ◽  
Linear Perturbation ◽  
Velocity Analysis ◽  
Approximate Methods ◽  
Migration Velocity Analysis ◽  
Image Difference

Time-lapse (4D) analysis of seismic data acquired at different stages of hydrocarbon production or gas/fluid injection has been very successful at imaging detailed reservoir changes. Conventional time-domain analysis of 4D data sets usually assumes a linear perturbation about a reference baseline earth model. However, this assumption is violated when production/injection significantly alters the subsurface generating large 4D velocity changes, time shifts, and complicated 4D wavefield coda, necessitating a more robust 4D analysis involving prestack wave-equation depth migration and velocity analysis. We address these situations by extending conventional 3D wave-equation migration velocity analysis (WEMVA) based on one-way wave-equations and single-scattering theory to 4D velocity estimation using a “parallel” inversion approach involving parallel solution of two separate inversion problems. Recognizing that the 4D WEMVA strategy requires precomputed baseline/monitor image-difference volumes, we develop an approximate 4D WEMVA technique that replaces these differences with a single weight function derived from the smooth background time-lapse image difference. We demonstrate the usefulness of the parallel and an approximate 4D WEMVA approach using a synthetic time-lapse [Formula: see text] geosequestration experiment that requires inverting for a thin-layer velocity change derived from [Formula: see text] injection in an analogue North Sea reservoir. The parallel 4D WEMVA solutions generate an excellent high-resolution velocity estimates, whereas the approximate methods recover lower-resolution estimates with magnitudes that must be rescaled through a post-inversion gradient line-search.

Migration velocity analysis by double path-integral migration

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA225-WCA231 ◽  
Author(s):  
Jörg Schleicher ◽  
Jessé C. Costa
Keyword(s):  
Path Integral ◽  
Velocity Model ◽  
Migration Velocity ◽  
Quantitative Information ◽  
Velocity Analysis ◽  
Integral Imaging ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Velocity Information ◽  
Starting Model

The idea of path-integral imaging is to sum over the migrated images obtained for a set of migration velocity models. Velocities where common-image gathers align horizontally are stationary, thus favoring these images in the overall stack. The overall image forms with no knowledge of the true velocity model. However, the velocity information associated with the final image can be determined in the process. By executing the path-integral imaging twice and weighting one of the stacks with the velocity value, the stationary velocities that produce the final image can then be extracted by a division of the two images. The velocity extraction, interpola-tion, and smoothing can be done fully automatically, without the need for human interpretation or other intervention. A numerical example demonstrated that quantitative information about the migration velocity model can be determined by double path-integral migration. The so-obtained velocity model can then be used as a starting model for subsequent velocity analysis tools like migration velocity analysis or tomographic methods.

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