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Next: Caveats in the computation Up: Anisotropic migration velocity analysis Previous: Estimation of the vertical

Estimation of the horizontal and NMO velocities

Since the vertical velocities cannot be estimated from RMO transformations in anisotropic ADCIGs, we computed the semblance values for $\rho_V_H$ and $\rho_V_N$only. Figure [*] illustrates the velocity spectra computed at the image depth for the various ADCIGs illustrated in Figure [*]. The various semblance panels are computed for various aperture angle ranges ($30^{\circ}$, $45^{\circ}$ and $60^{\circ}$). When computing the semblance of a velocity model, the first-order derivatives in equation 5 are computed around that velocity model, not around the one that was used for the migration. The group aperture angles are computed from phase aperture angles using equation 11. The parameterization of the estimated anisotropic parameters is done with the perturbations in the horizontal ($\rho_V_H$) and NMO velocities ($\rho_V_N$). For visualization purposes, Figure [*] illustrates the same semblance panels, but this time, the axes $\rho_V_H$ and $\rho_V_N$have been normalized by the correct perturbations in the anisotropic migration velocities. As a consequence, in Figure [*], the true velocities lie in the center of the semblance panels. Several conclusions can be drawn from Figure [*].

 
Comb-VelSpec-group
Comb-VelSpec-group
Figure 3
Velocity spectra obtained at the image depth when data modeled with a constant anisotropic velocity model (Taylor Sand) have been migrated using: a) a velocity uniformly perturbed by $\rho_V=0.99$, b) a velocity uniformly perturbed by $\rho_V=0.9$, and c) an isotropic velocity with the correct vertical velocity. The various semblance panels are computed for various aperture angle ranges ($30^{\circ}$, $45^{\circ}$ and $60^{\circ}$ from left to right). The parameterization of the estimated anisotropic velocity model is done with the perturbations in the horizontal ($\rho_V_H$) and in the NMO velocity ($\rho_V_N$). The correct perturbation values are: a) $\rho_V_H=0.99$ and $\rho_V_N=0.99$, b) $\rho_V_H=0.9$ and $\rho_V_N=0.9$, and c) $\rho_V_H=0.905$ and $\rho_V_N=1.037$.


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Comb-VelSpec-group_centrd
Comb-VelSpec-group_centrd
Figure 4
Velocity spectra obtained at the image depth when data modeled with a constant anisotropic velocity model (Taylor Sand) have been migrated using: a) a velocity uniformly perturbed by $\rho_V=0.99$, b) a velocity uniformly perturbed by $\rho_V=0.9$, and c) an isotropic velocity with the correct vertical velocity. The various semblance panels are computed for various ranges of aperture angles ($30^{\circ}$, $45^{\circ}$ and $60^{\circ}$ from left to right). The parameterization of the estimated anisotropic velocity model is done with $\rho_V_H$ and $\rho_V_N$ by the correct perturbation values.


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Table 1: Values of $\left(\rho_V_H-1,\rho_V_N-1\right)$ for the maximum semblance velocity model, as a function of the aperture angle range.
Velocity model perturbation Initial perturbation 3c|Range of aperture angles    
    [0,30] [0,45] [0,60]
1 $\%$ uniform perturbation $\left(-1.0\%,-1.0\%
 \right)$ $\left(-3.5\%,+5.0\% \right)$ $\left(-2.5\%,+2.0\% \right)$ $\left(-1.0\%,+0.5\% \right)$
10 $\%$ uniform perturbation $\left(-10.0\%,-10.0\%
 \right)$ $\left(-4.5\%,+7.0\% \right)$ $\left(-3.0\%,+0.0\% \right)$ $\left(-1.5\%,-1.5\% \right)$
Isotropic model with right VV $\left(-9.5\%,+3.7\%
 \right)$ $\left(+1.5\%,-3.5\% \right)$ $\left(-2.0\%,+1.5\% \right)$ $\left(+0.5\%,+0.0\% \right)$


next up previous print clean
Next: Caveats in the computation Up: Anisotropic migration velocity analysis Previous: Estimation of the vertical
Stanford Exploration Project
5/6/2007