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After performing the residual Stolt migration and converting to the
angle domain,
I am left with
a volume of dimension , where is aperture angle. From
this volume
we need to pick the best as a function of *x* and *z*.
I also have the problem that even with the redefinition of the
residual Stolt migration problem in Equation (7), events
still have some movement at different 's.
For now I will ignore the movement problem on the theory
that as long as we tend towards the correct solution, the best
focusing will tend towards 1 and the amount of
mispositioning at the best focusing will decrease.
For now I took a rather simple approach. I calculated
the semblance for flat events at the different values.
I then picked the best ratio at
each location. I used this field as my data . I used
the maximum semblance at each location as a weighting operator to
give more preference to strong events. I used
a 2-D gradient operator for my regularization operator and solved
the inversion problem defined by the fitting goals,

| |
(8) |

| |

where is the amount of relative smoothing and
is the resulting model.
A better method, and a topic for future work,
would be to calculate the semblance for a range of moveouts and do
a non-linear search for a smooth function.
To test whether the method works I scanned over values from
.95 to 1.05 on the migration result shown
in the center panel of Figure 2.
The left panel of Figure 5
shows the selected ratio, ,
in
fitting goals (8) and the right panel shows a histogram of
the picked values.
Note how we have generally picked the correct value ().

**pick
**

Figure 5 The left plot is the selected value using
fitting goals (8). The right panel is a histogram of the picked
values. Note the peak at approximately .97, the inverse of the velocity scaling.

** Next:** Back projection
** Up:** METHODOLOGY
** Previous:** Residual Stolt migration
Stanford Exploration Project

11/11/2002