Wave-equation migration velocity analysis for VTI models

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA59-WA68 ◽  
Author(s):  
Yunyue Li ◽  
Biondo Biondi ◽  
Robert Clapp ◽  
Dave Nichols
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Rock Physics ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Sources Of Information ◽  
Data Set ◽  
Anisotropic Models ◽  
Migration Velocity Analysis ◽  
Power Maximization

Anisotropic models are needed for wave simulation and inversion where a complex geologic environment exists. We extended the theory of wave equation migration velocity analysis to build vertical transverse isotropic models. Because of the ambiguity between depth and [Formula: see text] in the acoustic regime, we assumed [Formula: see text] can be accurately obtained from other sources of information, and inverted for the NMO slowness and the anellipticity parameter [Formula: see text]. We combined the differential semblance optimization objective function with the stacking power maximization to evaluate the focusing of the prestack image in the subsurface-offset domain. To regularize the multiparameter inversion, we built a framework to adapt the geologic and the rock physics information to guide the updates in NMO slowness and [Formula: see text]. This regularization step was crucial to stabilize the inversion and to produce geologically meaningful results. We tested the proposed approach on a synthetic data set and a 2D Gulf of Mexico data set starting with a fairly good initial anisotropic model. The inversion results revealed shallow anomalies collocated in NMO velocity and [Formula: see text] and improved the continuity and the resolution of the final stacked images.

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.

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.

Angle‐domain common‐image gathers for migration velocity analysis by wavefield‐continuation imaging

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1283-1298 ◽  
Author(s):  
Biondo Biondi ◽  
William W. Symes
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Migration Velocity ◽  
Image Point ◽  
Velocity Analysis ◽  
Data Set ◽  
The North ◽  
Migration Velocity Analysis ◽  
Wide Range ◽  
Wavefield Continuation

We analyze the kinematic properties of offset‐domain common image gathers (CIGs) and angle‐domain CIGs (ADCIGs) computed by wavefield‐continuation migration. Our results are valid regardless of whether the CIGs were obtained by using the correct migration velocity. They thus can be used as a theoretical basis for developing migration velocity analysis (MVA) methods that exploit the velocity information contained in ADCIGs. We demonstrate that in an ADCIG cube, the image point lies on the normal to the apparent reflector dip that passes through the point where the source ray intersects the receiver ray. The image‐point position on the normal depends on the velocity error; when the velocity is correct, the image point coincides with the point where the source ray intersects the receiver ray. Starting from this geometric result, we derive an analytical expression for the expected movements of the image points in ADCIGs as functions of the traveltime perturbation caused by velocity errors. By applying this analytical result and assuming stationary raypaths (i.e., small velocity errors), we then derive two expressions for the residual moveout (RMO) function in ADCIGs. We verify our theoretical results and test the accuracy of the proposed RMO functions by analyzing the migration results of a synthetic data set with a wide range of reflector dips. Our kinematic analysis leads also to the development of a new method for computing ADCIGs when significant geological dips cause strong artifacts in the ADCIGs computed by conventional methods. The proposed method is based on the computation of offset‐domain CIGs along the vertical‐offset axis and on the “optimal” combination of these new CIGs with conventional CIGs. We demonstrate the need for and the advantages of the proposed method on a real data set acquired in the North Sea.

scholarly journals Wave-equation migration velocity analysis using plane-wave common-image gathers

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. S327-S340 ◽  
Author(s):  
Bowen Guo ◽  
Gerard T. Schuster
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Computational Cost ◽  
Migration Velocity ◽  
Memory Storage ◽  
Velocity Analysis ◽  
Data Set ◽  
Image Domain ◽  
Migration Velocity Analysis ◽  
Wave Migration

Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain, or time-lag common-image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, we have developed a WEMVA method using plane-wave CIGs. Plane-wave CIGs reduce computational cost and memory storage because they are directly calculated from prestack plane-wave migration and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic data sets and a field data set validate the efficiency and effectiveness of this 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.

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