Constructing a filter

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 Gaussian-like 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 finite-difference 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.