Butterworth Dip Filters
, by Dave Hale and Jon F. Claerbout
Dip filters enable a geophysicist to discriminate between various seismic events on the basis of apparent dip. The
frequency-wavenumber (w, k) domain seems an attractive domain to perform dip filtering, because it permits the
application of an arbitrary transfer function of dip. Seismic applications of dip filtering, however, seldom require the
flexibility offered by the (w, k) domain; and one may be willing to sacrifice this flexibility to obtain features
now possible with (w, k) domain filters, but readily available with time-space (t-x) domain filters. Examples are
(1) time and space variability,
(2) flexible treatment of computational grid boundaries
(3) an efficient, recursive implementation.
We decribe a (t, x) domain dip filtering method with these features.
In the derivation of a (t, x) domain filter, we first discuss (t, k) and (w, x) domain dip filters. While not fully possessing
the advantages of a (t, x) domain dilter, these filters are an attractive combination of two very efficient and commonly
available processes: (1) one-dimensional Butterworth filtering and (2) one-dimentsional Fourier transforms. We then derive (t, x)
domain approximations to these filters which have the features noted above.
STANFORD