A robust approach to time-to-depth conversion and interval velocity estimation from time migration in the presence of lateral velocity variations |

The field data shown in Figure 17 is from a section of Gulf of Mexico dataset (Claerbout, 1996). We estimate using the method of velocity continuation (Fomel, 2003) and convert it to . Similar to the spiral model, no domain extension is needed. In Figure 18, the Dix-inverted prior model highly resembles the Dix velocity, because the Dix formula only scales the vertical axis from time to depth regardless of horizontal variations. Figure 19 compares the cost before and after five linearization updates, with a m m triangular smoother. In Figure 20, the norm of the cost, , has a rapid decrease to relative %. Figure 21 illustrates the inverted model and interval velocity update.

vdix
(Top) the estimated
time-migration velocity of a section of Gulf of Mexico dataset and
(bottom) the corresponding time-migrated image.
Figure 17. |
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init
(Top) the Dix velocity
converted from in Figure 17 and (bottom) the
Dix-inverted prior model for inversion, overlaid with image rays.
Figure 18. |
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inv
The cost of (top) prior model
() and (bottom) inverted model ().
Figure 19. |
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hist
Convergence history of
the proposed optimization-based time-to-depth conversion.
Figure 20. | |
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dinv
(Top) the inverted model,
overlaid with image rays, and (bottom) its difference from the prior
model in Figure 18.
Figure 21. |
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Next, we map the time-migrated image to depth using and generated during inversion. Spline interpolation (Press et al., 2007) is used during the coordinate mapping. We also migrate the prestack data by Kirchhoff depth migration (Li and Fomel, 2013) (PSDM). Figure 22 compares the time-mapped image and PSDM image of the inverted model. A good agreement between these two images justifies that time-to-depth conversion has effectively unravelled the distorted time coordinate. Figure 23 compares PSDM images of the prior and inverted models. The velocity update in Figure 21 results in not only changes in structural dips (for example at km) but also improved reflector continuity (for example at km). Moreover, the Kirchhoff migration outputs surface offset common-image gathers. We choose two midpoint locations, km and km, and show their common-image gathers in Figure 24. In deeper sections, flat dashed lines are overlaid as references for the flatness of gathers. The two common-image gathers of prior model appear curved in opposite directions. After time-to-depth conversion, both gathers get flattened across the whole offset range, verifying a correct velocity update.

dmig
(Top) the time-migrated image
in Figure 17 is mapped to depth using products of the
time-to-depth conversion. (Bottom) PSDM image using inverted model
in Figure 21.
Figure 22. |
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ddmig0
PSDM images of (top) the
prior model and (bottom) the inverted model. Both images are plotted
for the same central deep part.
Figure 23. |
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cig0
The surface offset
common-image gathers of prior and inverted models.
Figure 24. |
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A robust approach to time-to-depth conversion and interval velocity estimation from time migration in the presence of lateral velocity variations |

2015-03-25