Migration Velocity Analysis with Reflected and Transmitted Waves

Chauris, Hervé; Lameloise, Charles-Antoine; Donno, Daniela

doi:10.3997/2214-4609.20130936

Cited by 7 publications

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“…Reflectivity is usually estimated from data. Here, we first define the data as a function of the extended reflectivity (Symes ; Chauris, Lameloise and Donno ). The extended model allows preserving the same dimensions in the data space and in the model space.…”

Section: Migration Velocity Analysismentioning

confidence: 99%

“…The shapes of events in CIGs for an incorrect velocity can be predicted by ray theory (Chauris et al . ; Mulder ). By setting γ as the ratio between migration velocity and modelling velocity and z 0 as the true reflector depth, the shapes associated with reflected waves for incorrect migration velocities are given by:

z = γ \sqrt{z_{0}^{2} + \frac{{∥ boldh ∥}^{2}}{1 - γ^{2}}} .

…”

Section: Migration Velocity Analysismentioning

confidence: 99%

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Improving the gradient of the image‐domain objective function using quantitative migration for a more robust migration velocity analysis

Lameloise

Chauris

Noble

2014

Geophysical Prospecting

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International audienceMigration velocity analysis aims at determining the background velocity model. Classical artefacts, such as migration smiles, are observed on subsurface offset common image gathers, due to spatial and frequency data limitations. We analyse their impact on the differential semblance functional and on its gradient with respect to the model. In particular, the differential semblance functional is not necessarily minimum at the expected value. Tapers are classically applied on common image gathers to partly reduce these artefacts. Here, we first observe that the migrated image can be defined as the first gradient of an objective function formulated in the data-domain. For an automatic and more robust formulation, we introduce a weight in the original data-domain objective function. The weight is determined such that the Hessian resembles a Dirac function. In that way, we extend quantitative migration to the subsurface-offset domain. This is an automatic way to compensate for illumination. We analyse the modified scheme on a very simple 2D case and on a more complex velocity model to show how migration velocity analysis becomes more robust

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Section: Migration Velocity Analysismentioning

confidence: 99%

z = γ \sqrt{z_{0}^{2} + \frac{{∥ boldh ∥}^{2}}{1 - γ^{2}}} .

…”

Section: Migration Velocity Analysismentioning

confidence: 99%

Improving the gradient of the image‐domain objective function using quantitative migration for a more robust migration velocity analysis

Lameloise

Chauris

Noble

2014

Geophysical Prospecting

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“…Otherwise, we end up with smiles concaved upward or downward depending on the migration velocity being high or low, respectively. Moreover, the transmitted events in ODCIGs can also be a measure of accuracy in a velocity model (Chauris et al, 2013;Shen, 2013). Their behavior is of course different than the reflected ones.…”

Section: Introductionmentioning

confidence: 99%

Common-image gathers using the excitation amplitude imaging condition

Kalita

Alkhalifah

2016

GEOPHYSICS

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Common-image gathers (CIGs) are extensively used in migration velocity analysis. Any defocused events in the subsurface offset domain or equivalently nonflat events in angle-domain CIGs are accounted for revising the migration velocities. However, CIGs from wave-equation methods such as reverse time migration are often expensive to compute, especially in 3D. Using the excitation amplitude imaging condition that simplifies the forward-propagated source wavefield, we have managed to extract extended images for space and time lags in conjunction with prestack reverse time migration. The extended images tend to be cleaner, and the memory cost/disk storage is extensively reduced because we do not need to store the source wavefield. In addition, by avoiding the crosscorrelation calculation, we reduce the computational cost. These features are demonstrated on a linear vðzÞ model, a twolayer velocity model, and the Marmousi model.

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Imaging moveout in acoustic factorized orthorhombic media

Galtung,

Stovas

2024

Geophysical Journal International

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Summary In velocity model building using full waveform inversion, diving waves are a source of the low-frequency information needed to update the low- to intermediate wavenumber components in the velocity model. Because full waveform inversion is a highly non-linear optimization problem attempting to fit the information from the whole wavefield, it is prone to get stuck in local minimums and experience cycle skipping if the initial model does not contain accurate enough information about the low-wavenumbers to constrain the kinematics. Such initial velocity models will typically be estimated using alternative inversion methods that only apply information from parts of the wavefield in the forward modelling and recorded data. In migration velocity analysis, the unfocusing of the image, caused by inconsistency in the kinematics of reflected waves, is measured and is used to update the velocity model by applying differential semblance optimization. The same concept is applicable when using information from diving waves. For diving waves, little is known about the focusing behaviour, also known as imaging moveout, especially in the presence of azimuthal anisotropy, such as orthorhombic anisotropy, which is a good approximation for volcanic plains and sedimentary basins. Obtaining more knowledge about the focusing behaviour of diving waves for this type of anisotropy may help when choosing parameters to invert during inversion that yield a low trade-off between the parameters. Here, we derive approximate series-based equations describing the imaging moveout of diving qP-waves in acoustic factorized orthorhombic anisotropic media. Due to the complexity of the analytical solutions for diving wave properties in such models, we find a vertical transverse isotropic type of simplification that manages to conserve the curvature and horizontal velocity of the diving qP-wave. The accuracy of the simplified expressions is compared to the exact form and found to yield small errors. To verify the validity of the derived equations for imaging moveout, we compare the generated surfaces with images containing the shape of the unfocusing obtained using reverse time migration, showing a good fit. Of the anisotropic parameters defining the acoustic factorized orthorhombic model, the ε1 and ε2 parameters have the largest influence on the shape of the surface. The anelliptical parameters are shown only to induce minimal changes. Our method to obtain the series expressions describing the imaging moveout in the acoustic factorized orthorhombic model is also applicable to higher symmetry special cases of orthorhombic anisotropy by setting appropriate conditions. Here, this is demonstrated by additionally finding an approximate series expression describing the imaging moveout in acoustic factorized vertical transversely isotropic media, yielding a good match with the image obtained from reverse time migration.

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Migration Velocity Analysis with Reflected and Transmitted Waves

Cited by 7 publications

References 0 publications

Improving the gradient of the image‐domain objective function using quantitative migration for a more robust migration velocity analysis

Improving the gradient of the image‐domain objective function using quantitative migration for a more robust migration velocity analysis

Common-image gathers using the excitation amplitude imaging condition

Imaging moveout in acoustic factorized orthorhombic media

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