Generalized nonhyperbolic moveout approximation |

For a numerical test, we create a one-dimensional velocity model by extracting a depth column out of the anisotropic Marmousi model, created by Alkhalifah (1997a) and shown in Figure 4. We evaluate exact reflection traveltimes by ray tracing (Figure 5). Next, we compare the exact time for different reflection rays with values predicted by different traveltime approximations. As shown in Figure 6, only the proposed generalized approximation is able to predict the true traveltime accurately over the full range of offsets. To define approximation parameters, we used equations 19-21 and 22-23 and the ray with the largest offset as the reference ray.

vz,v,eta
Anisotropic Marmousi
model. (a) Vertical velocity. (b) NMO velocity. (c)
parameter.
Figure 4. |
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vz1
One-dimensional model
extracted from the left column of the anisotropic Marmousi model and
corresponding reflection rays.
Figure 5. |
---|

hynmo,shnmo,atnmo,fsnmo
Exact
moveout from ray tracing in the one-dimensional anisotropic Marmousi
model (dots) and different approximations (solid lines). (a)
Hyperbolic approximation, (b) Shifted hyperbola approximation, (c)
Alkhalifah-Tsvankin approximation, (d) Generalized nonhyperbolic
approximation.
Figure 6. |
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Generalized nonhyperbolic moveout approximation |

2013-07-26