Joint inversion of the reflectivity and the velocity model

Geophysics ◽  
2021 ◽  
pp. 1-68
Author(s):  
Alejandro Cabrales-Vargas ◽  
Rahul Sarkar ◽  
Biondo L. Biondi ◽  
Robert G. Clapp
Keyword(s):  
Wave Equation ◽  
Field Data ◽  
Joint Inversion ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Migration Velocity ◽  
Background Model ◽  
Seismic Events ◽  
Velocity Analysis ◽  
Migration Velocity Analysis

During linearized waveform inversion, the presence of small inaccuracies in the background subsurface model can lead to unfocused seismic events in the final image. The effect on the amplitude can mislead the interpretation. We present a joint inversion scheme in the model domain of the reflectivity and the background velocity model. The idea is to unify the inversion of the background and the reflectivity model into a single framework instead of treating them as decoupled problems. We show that with this method, we can obtain a better estimate of the reflectivity than that obtained with conventional linearized waveform inversion. Conversely, the background model is improved by the joint inversion with the reflectivity in comparison with wave-equation migration velocity analysis. We perform tests on 2D synthetics and 3D field data that demonstrate both benefits.

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.

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.

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.

Residual migration‐velocity analysis in the plane‐wave domain

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1258-1269 ◽  
Author(s):  
Junru Jiao ◽  
Paul L. Stoffa ◽  
Mrinal K. Sen ◽  
Roustam K. Seifoullaev
Keyword(s):  
Plane Wave ◽  
Field Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
New Method ◽  
Velocity Analysis ◽  
Top Down ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Interval Velocities

Over the last few years, migration‐velocity analysis methods have been developed for 2‐D and 3‐D models by extending the assumptions and approximations used for rms velocity models. Computational requirements for these analyses have increased dramatically because top‐down layer‐stripping migration is needed to derive interval velocities directly instead of using rms velocities and then converting into interval velocities. We establish exact equations for 1‐D and 2‐D residual velocity analysis in the depth‐plane‐wave domain and use these in an iterative and interactive migration velocity analysis program. The new method updates interval velocities directly in a top‐down residual‐difference correction for all layers after prestack depth migration instead of top‐down layer‐stripping migration followed by residual analysis. This makes the new method a suitable tool for migration velocity analysis, especially for 3‐D surveys. We test the method on synthetic and field data. The field data results show that a reasonable velocity model is obtained and most common image gathers are correctly imaged using no more than four iterations.

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.

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