Interpolation methods for the kernel of f-k migration
Zaiming Jiang, John C. Bancroft
The theory of f-k migration tells us that migration of a stacked seismic section in timespace domain can be done by a mapping operation in frequency-wavenumber domain. The mapping operation involves interpolation among samples of the discrete Fourier transform of the stacked section. This process introduces artifacts into the migrated section. In fact, crude interpolation is the main source of artifacts in f-k migration. The first refined interpolation method, the complex sinc method, was introduced in 1981. Another one, Muir's method, was discussed in 1997. There is an implementation of complex sinc interpolation in the CREWES educational software and data release (MATLAB).
This report discusses interpolation methods and related artifacts. The details of implementing complex sinc interpolation and Muir's interpolation include changing the interpolation formulas according to the Fast Fourier Transform algorithm used, employing mathematical limits of functions to prevent computational overflow, and taking periodic boundary extension instead of zero-padding. It is shown that the two interpolation methods perform almost the same in the sense of both migration quality and computational cost.