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In Jedlicka, 1989, I introduced a velocity analysis using stochastic normal
moveout (SMOC).
Let us briefly review the basics. A sampling interval is chosen
in the sloth domain, but instead of a sum along hyperbolas, a sum is
made from all amplitudes lying between adjacent hyperbolas. In other
words a histogram is created (Figure ). This operation is
equivalent to the filtering of -space with a boxcar filter
over the sloth domain.
A spectrum of the triangular filter
| |
(11) |

has lower sidelobes than the spectrum of the boxcar
filter and therefore it causes less overlapping
(Figure ).
Furthermore it
can be viewed as an approximation
to a Gaussian. This is the initial idea of Francis Muir that led to the
concept of SMOC.
From Figure b we can see that the
truncation effect is strongly attenuated.
For comparison, a velocity analysis panel shown in Figure c was
filtered over the sloth domain;
the result should be equivalent to the velocity stack produced with SMOC.
However, the result shown in Figure a is not so clean. This
comparison shows the advantage of using SMOC over the filtering in the sloth
domain.
The length of the filter should not be chosen to be too small, otherwise the
truncation effect is not attenuated (Figure c). Choosing the
length of the filter to be too big leads to a fuzzy appearance of the velocity
analysis panel.

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Stanford Exploration Project

1/13/1998