Time-shift imaging condition in seismic migration |

In order to understand the angle-domain mapping, we consider a simple synthetic in which we model common-image gathers corresponding to incidence at a particular angle. The experiment is depicted in Figure 15 for time-shift imaging, and in Figure 16 for space-shift imaging. For this experiment, the sampling parameters are the following: km, km, and s.

A reflection event at a single angle of incidence maps in common-image gathers as a line of a given slope. The left panels in Figures 15 and 16 show cases, corresponding to angles of , and . Since we want to analyze how such events map to angle, we subsample each line to selected samples lining-up at the correct slope.

The middle panels in Figures 15 and 16 show the data in the left panels after slant-stacking in or panels, respectively. Each individual sample from the common-image gathers maps in a line of a different slope intersecting in a point. For example, normal incidence in a time-shift gather maps at the migration velocity km/s (Figure 15 top row, middle panel), and normal incidence in a space-shift gather maps at slant-stack parameter .

The right panels in Figures 15 and 16 show the data from the middle panels after mapping to angle using equations (23) and (20), respectively. All lines from the slant-stack panels map into curves that intersect at the angle of incidence.

We note that all curves for the time-shift angle-gathers have zero curvature at normal incidence. Therefore, the resolution of the time-shift mapping around normal incidence is lower than the corresponding space-shift resolution. However, the storage and computational cost of time-shift imaging is smaller than the cost of equivalent space-shift imaging. The choice of the appropriate imaging condition depends on the imaging objective and on the trade-off between the cost and the desired resolution.

ttest
Image-gather formation using time-shift imaging.
Each row depicts an event at
(top),
(middle), and
(bottom).
Three columns correspond to
subsampled time-shift gathers (left),
slant-stacked gathers (middle), and
angle-gathers (right).
Figure 15. |
---|

htest
Image-gather formation using space-shift imaging.
Each row depicts an event at
(top),
(middle), and
(bottom).
Three columns correspond to
subsampled space-shift gathers (left),
slant-stacked gathers (middle), and
angle-gathers (right).
Figure 16. |
---|

Time-shift imaging condition in seismic migration |

2007-04-08