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The basic idea in building a steering filter is to create a filter
that destroys a given slope p. Further, we would like to
keep differences of the bandwidth response
for filters oriented at different
slopes to a minimum. We can achieve both these goals by constructing
a triangle centered at the appropriate slope (Figure 6.)
Every grid
cell center which the triangle passes through is assigned a negative value
proportional to the height of the triangle at that location.
The wider the triangle base, the less precise, and more Gaussianlike
our smoother becomes, Figure 7. By decreasing the sum
of the coefficients (with a hard limit of 1 to ensure filter stability
when applying polynomial division Claerbout (1976)), we can spread information
larger distances.
steering
Figure 6 A finitedifference star for a monoplane rejection filter.
The left column contains a `1'. The right column contains
samples off a triangle.
The desired
slope is represented by p, the smaller w the more precise
the dip smoothed, and the larger h the bigger the
area the smoother acts on.

 
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Stanford Exploration Project
4/20/1999