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

Abstract

Dip filtering is a necessary part of accurate frequency‐space domain migration, so design and application of reliable and efficient filters are of practical as well as theoretical importance. Frequency‐space domain dip filters are implemented using Butterworth and Chebyshev algorithms. By transforming the product terms of the filter transfer function into summations, a cascaded (serial) Butterworth or Chebyshev dip filter can be made parallel, which improves computational efficiency. For a given order of filter, the cost of the Butterworth and Chebyshev filters is the same. However, the Chebyshev filter has a sharper transition zone than that of a Butterworth filter with the same order, which makes it more effective for phase compensation than a Butterworth filter, but at the expense of some wavenumber‐dependent amplitude ripples. Both implementations have been incorporated into 3-D one‐way frequency‐space depth migration for evanescent energy removal and for phase compensation of splitting errors; a single filter achieves both goals.