Thematic Set: Velocity model building with wave equation migration: the importance of wide azimuth input, versatile tomography, and migration velocity analysis

First Break ◽  
2010 ◽  
Vol 28 (1728) ◽  
Author(s):  
F. Audebert ◽  
P. Jousselin ◽  
B. Duquet ◽  
J. Sirgue
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Model Building ◽  
Migration Velocity Analysis ◽  
And Migration

Target-oriented wavefield tomography using synthesized Born data

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB191-WB207 ◽  
Author(s):  
Yaxun Tang ◽  
Biondo Biondi
Keyword(s):  
Model Building ◽  
Signal To Noise Ratio ◽  
Synthetic Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Model Building ◽  
Migration Velocity Analysis ◽  
New Strategy ◽  
Modeling Strategy

We present a new strategy for efficient wave-equation migration-velocity analysis in complex geological settings. The proposed strategy has two main steps: simulating a new data set using an initial unfocused image and performing wavefield-based tomography using this data set. We demonstrated that the new data set can be synthesized by using generalized Born wavefield modeling for a specific target region where velocities are inaccurate. We also showed that the new data set can be much smaller than the original one because of the target-oriented modeling strategy, but it contains necessary velocity information for successful velocity analysis. These interesting features make this new data set suitable for target-oriented, fast and interactive velocity model-building. We demonstrate the performance of our method on both a synthetic data set and a field data set acquired from the Gulf of Mexico, where we update the subsalt velocity in a target-oriented fashion and obtain a subsalt image with improved continuities, signal-to-noise ratio and flattened angle-domain common-image gathers.

The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. S241-S249 ◽  
Author(s):  
Xiao-Bi Xie ◽  
Hui Yang
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Data Sets ◽  
Velocity Analysis ◽  
Depth Migration ◽  
Sensitivity Kernel ◽  
Migration Velocity Analysis ◽  
Tomography Method

We have derived a broadband sensitivity kernel that relates the residual moveout (RMO) in prestack depth migration (PSDM) to velocity perturbations in the migration-velocity model. We have compared the kernel with the RMO directly measured from the migration image. The consistency between the sensitivity kernel and the measured sensitivity map validates the theory and the numerical implementation. Based on this broadband sensitivity kernel, we propose a new tomography method for migration-velocity analysis and updating — specifically, for the shot-record PSDM and shot-index common-image gather. As a result, time-consuming angle-domain analysis is not required. We use a fast one-way propagator and multiple forward scattering and single backscattering approximations to calculate the sensitivity kernel. Using synthetic data sets, we can successfully invert velocity perturbations from the migration RMO. This wave-equation-based method naturally incorporates the wave phenomena and is best teamed with the wave-equation migration method for velocity analysis. In addition, the new method maintains the simplicity of the ray-based velocity analysis method, with the more accurate sensitivity kernels replacing the rays.

scholarly journals Automatic wave-equation migration velocity analysis by focusing subsurface virtual sources

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. U1-U8 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Real Data ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Data Set ◽  
Migration Velocity Analysis ◽  
Band Limited

Macro-velocity model building is important for subsequent prestack depth migration and full-waveform inversion. Wave-equation migration velocity analysis uses the band-limited waveform to invert for velocity. Normally, inversion would be implemented by focusing the subsurface offset common-image gathers. We reexamine this concept with a different perspective: In the subsurface offset domain, using extended Born modeling, the recorded data can be considered as invariant with respect to the perturbation of the position of the virtual sources and velocity at the same time. A linear system connecting the perturbation of the position of those virtual sources and velocity is derived and solved subsequently by the conjugate gradient method. In theory, the perturbation of the position of the virtual sources is given by the Rytov approximation. Thus, compared with the Born approximation, it relaxes the dependency on amplitude and makes the proposed method more applicable for real data. We determined the effectiveness of the approach by applying the proposed method on isotropic and anisotropic vertical transverse isotropic synthetic data. A real data set example verifies the robustness of the proposed method.

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.

Efficient 3D velocity modeling building using joint inline and crossline plane-wave wave-equation migration velocity analyses

2020 ◽  
Author(s):  
Xuejian Liu ◽  
Lianjie Huang ◽  
Zongcai Feng ◽  
George El-kaseeh ◽  
Robert Will ◽  
...  
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Model Building ◽  
Velocity Model ◽  
Migration Velocity ◽  
Inversion Method ◽  
Data Interpolation ◽  
Image Domain ◽  
Velocity Model Building ◽  
3D Velocity Model

Summary Wave-equation migration velocity analysis (WEMVA) is an image-domain inversion method for velocity model building. Automatic plane-wave WEMVA (PWEMVA) calculates the moveouts of plane-wave common-image gathers (CIGs) by searching a best-fitting parabola with semblance analysis and back-projects residual CIG moveouts into wavefield wavepaths with a reflection tomographic kernel. However, 3D PWEMVA is very computationally expensive because 3D reflection tomographic inversion requires at least five 3D reverse-time migrations per iteration and stores two types of source wavefields at model boundaries. We develop a joint inline and crossline PWEMVA method for efficient 3D velocity model building. We alternatively implement the inline and crossline PWEMVAs with a constraint for each other, in which we iteratively construct the 3D velocity model update through 1D spline interpolation of 2D gradients. The inline and crossline joint inversion is practical since PWEMVA only inverts for low-wavenumber velocity perturbations along wavepaths, and the method can take less than one per cent of the computational cost of full 3D PWEMVA. To construct unaliased plane-waves for our joint inline and crossline PWEMVA, we develop a 3D data interpolation method in the frequency-wavenumber (FK) domain to recover regularly and randomly missing traces. The method minimizes the misfit on sufficiently localized data subsets with iterative optimal step-lengths and a gradient preconditioner that iteratively selects dominant dips along different azimuths. In numerical experiments, we use a 3D synthetic seismic dataset and a land 3D field seismic dataset acquired at the Farnsworth CO2-EOR [Enhanced Oil Recovery] field to demonstrate the efficacy of our velocity model building and data interpolation methods.

Linearized wave-equation migration velocity analysis by image warping

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. S35-S46 ◽  
Author(s):  
Francesco Perrone ◽  
Paul Sava ◽  
Clara Andreoletti ◽  
Nicola Bienati
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Migration Velocity ◽  
Background Model ◽  
Data Migration ◽  
Physical Parameters ◽  
Model Parameters ◽  
Single Shot ◽  
Velocity Analysis ◽  
Migration Velocity Analysis

Seismic imaging produces images of contrasts in physical parameters in the subsurface, e.g., velocity or impedance. To build such images, a background model describing the wave kinematics in the earth is necessary. In practice, the structural image and background velocity model are unknown and have to be estimated from the acquired data. Migration velocity analysis deals with estimation of the background model in the framework of seismic migration and relies on two main elements: data redundancy and invariance of the structures with respect to different seismic experiments. Because all the experiments probe the same model, the reflectors must be invariant in suitable domains (e.g., shots or reflection angle); the semblance principle is the tool used to measure the invariance of a set of multiple images. We measure the similarity of the structural features between pairs of single-shot migrated images obtained from adjacent experiments. By using the estimated warping vector field between two migrated images, we construct an image perturbation which describes the difference in reflectivity observed by two shots. We derive an expression for the image perturbation that drives a migration velocity analysis procedure based on a linearization of the wave-equation with respect to the model parameters. Synthetic 2D examples show promising results in retrieving errors in the velocity model. This methodology can be directly applied to 3D.

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 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.

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