Regularization in slope tomography

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE39-VE47 ◽  
Author(s):  
Jessé C. Costa ◽  
Francisco J. da Silva ◽  
Ellen N. Gomes ◽  
Jörg Schleicher ◽  
Luiz André Melo ◽  
...  
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Synthetic Data ◽  
Velocity Model ◽  
Model Estimation ◽  
Distinct Effect ◽  
Additional Information ◽  
Numerical Tests ◽  
Reflection Angle ◽  
Velocity Model Building

Seismic imaging in depth is limited by the accuracy of velocity model estimation. Slope tomography uses the slowness components and traveltimes of picked reflection or diffraction events for velocity model building. The unavoidable data incompleteness requires additional information to assure stability to inversion. One natural constraint for ray-based tomography is a smooth velocity model. We propose a new, reflection-angle-based kind of smoothness constraint as regularization in slope tomography and have compared its effects to three other, more conventional constraints. The effects of these constraints were evaluated through angle-domain common-image gathers, computed with wave-equation migration using the estimated velocity model. We found that the smoothness constraints have a distinct effect on the velocity model but a weaker effect on the migrated data. In numerical tests on synthetic data, the new constraint leads to geologically more consistent models.

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.

Velocity model building by semblance maximization of modulated-shot gathers

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. U67-U73 ◽  
Author(s):  
Robert Soubaras ◽  
Bruno Gratacos
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Model ◽  
Multiscale Approach ◽  
Nonlinear Inversion ◽  
Velocity Models ◽  
Velocity Model Building ◽  
Frequency Maximum ◽  
The Cost ◽  
Starting Model

In recent years, wave-equation migration has greatly enhanced imaging in complex velocity models. However, velocity model building is still dependent on ray-theory approximations. We propose a full wave-equation methodology for velocity model building based on the nonlinear inversion of a semblance criterion with respect to the velocity field. A newly described type of migration, called the modulated-shot migration, is used to obtain the necessary gathers, which are indexed in surface angle. The semblance of these gathers, after spatial averaging, is used as the cost function. This methodology is shown to successfully image the Marmousi model and the subsalt part of the Sigsbee model, especially in terms of focusing, which is as good as with the true model, but also in terms of depthing which is enhanced compared with the initial model. Realistic constraints are used in terms of minimum frequency, maximum offset, and crudeness of the starting model. A key point in the success of this methodology is the multiscale approach wherein the iterations are started on a coarse scale, and ended at a finer scale.

3D angle gathers from reverse time migration

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. S77-S92 ◽  
Author(s):  
Sheng Xu ◽  
Yu Zhang ◽  
Bing Tang
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Model ◽  
Azimuth Angle ◽  
Three Dimensions ◽  
Practical Implementation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Reflection Angle

Common-image gathers are an important output of prestack depth migration. They provide information needed for velocity model building and amplitude and phase information for subsurface attribute interpretation. Conventionally, common-image gathers are computed using Kirchhoff migration on common-offset/azimuth data volumes. When geologic structures are complex and strong contrasts exist in the velocity model, the complicated wave behaviors will create migration artifacts in the image gathers. As long as the gather output traces are indexed by any surface attribute, such as source location, receiver location, or surface plane-wave direction, they suffer from the migration artifacts caused by multiple raypaths. These problems have been addressed in a significant amount of work, resulting in common-image gathers computed in the reflection angle domain, whose traces are indexed by the subsurface reflection angle and/or the subsurface azimuth angle. Most of these efforts have concentrated on Kirchhoff and one-way wave-equation migration methods. For reverse time migration, subsurface angle gathers can be produced using the same approach as that used for one-way wave-equation migration. However, these approaches need to be revisited when producing high-quality subsurface angle gathers in three dimensions (reflection angle/azimuth angle), especially for wide-azimuth data. We have developed a method for obtaining 3D subsurface reflection angle/azimuth angle common-image gathers specifically for the amplitude-preserved reverse time migration. The method builds image gathers with a high-dimensional convolution of wavefields in the wavenumber domain. We have found a windowed antileakage Fourier transform method that leads to an efficient and practical implementation. This approach has generated high-resolution angle-domain gathers on synthetic 2.5D data and 3D wide-azimuth real data.

Onshore wave-equation depth imaging and velocity model building

2010 ◽  
Vol 29 (11) ◽  
pp. 1386-1392 ◽  
Author(s):  
Joe Higginbotham ◽  
Morgan Brown ◽  
Cosmin Macesanu ◽  
Oscar Ramirez
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Model ◽  
Depth Imaging ◽  
Velocity Model Building

scholarly journals A transversely isotropic medium with a tilted symmetry axis normal to the reflector

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. A19-A24 ◽  
Author(s):  
Tariq Alkhalifah ◽  
Paul Sava
Keyword(s):  
Closed Form ◽  
Model Building ◽  
Incidence Angle ◽  
Transversely Isotropic ◽  
Velocity Model ◽  
Reflection Angle ◽  
Velocity Model Building ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Zero Offset

The computational tools for imaging in transversely isotropic media with tilted axes of symmetry (TTI) are complex and in most cases do not have an explicit closed-form representation. Developing such tools for a TTI medium with tilt constrained to be normal to the reflector dip (DTI) reduces their complexity and allows for closed-form representations. The homogeneous-case zero-offset migration in such a medium can be performed using an isotropic operator scaled by the velocity of the medium in the tilt direction. For the nonzero-offset case, the reflection angle is always equal to the incidence angle, and thus, the velocities for the source and receiver waves at the reflection point are equal and explicitly dependent on the reflection angle. This fact allows for the development of explicit representations for angle decomposition as well as moveout formulas for analysis of extended images obtained by wave-equation migration. Although setting the tilt normal to the reflector dip may not be valid everywhere (i.e., on salt flanks), it can be used in the process of velocity model building, in which such constrains are useful and typically are used.

Velocity model building in complex settings: combining the strengths of Tomography and Wave‐Equation PreSDM

2008 ◽  
Author(s):  
François Audebert ◽  
Pierre Jousselin ◽  
Bertrand Duquet ◽  
Kaveh Dehghan ◽  
Yves Le Stunff
Keyword(s):  
Wave Equation ◽  
Model Building ◽  
Velocity Model ◽  
Velocity Model Building ◽  
Complex Settings
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