Parallel Butterworth and Chebyshev dip filters with applications to 3-D seismic migration

Dip filtering is a necessary part of accurate frequency-space domain migrat ion, so design and application of reliable and efficient filters are of pra ctical as well as theoretical importance. Frequency-space domain dip filter s are implemented using Butterworth and Chebyshev algorithms. By transformi ng the product terms of the filter transfer function into summations, a cas caded (serial) Butterworth or Chebyshev dip filter can be made parallel, wh ich improves computational efficiency For a given order of filter, the cost of the Butterworth and Chebyshev filters is the same. However, the Chebysh ev filter has a sharper transition zone than that of a Butterworth filter w ith the same order, which makes it more effective for phase compensation th an a Butterworth filter, but at the expense of some wavenumber-dependent am plitude ripples. Both implementations have been incorporated into 3-D one-w ay frequency-space depth migration for evanescent energy removal and for ph ase compensation of splitting errors; a single filter achieves both goals.