Butterworth dip filters

Abstract

Dip filters enable a geophysicist to discriminate between various seismic events on the basis of apparent dip. The frequency‐wavenumber (ω, 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 (ω, k) domain; one may often be willing to sacrifice this flexibility to obtain features not possible with (ω, k) domain filters, but readily available with timespace (t, x) domain filters. Examples are (1) time and space variability, (2) flexible treatment of computational grid boundaries, and (3) an efficient, recursive implementation. We describe 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 (ω, x) domain dip filters. While not fully possessing the advantages of a (t, x) domain filter, these filters are an attractive combination of two very efficient and commonly available processes: (1) one‐dimensional Butterworth filtering and (2) one‐dimensional Fourier transforms. We then derive (t, x) domain approximations to these filters which have the features noted above.