Kaiser Bessel gridding kernel for seismic data regularization
Akshay Gulati, Robert James Ferguson
The Kaiser Bessel non-uniform Fast Fourier transform (NFFT ) kernel balances accuracy and computational cost, and we present an application of this NFFT for seismic trace interpolation. Application of the Bessel kernel for non-uniform samples is not a new algorithm, but it is an approximation scheme that can be used to calculate an approximate spectrum. In one dimension, computational complexity of Kaiser Bessel NFFT is O(N log N ) which is a dramatic improvement from the O(N 2 ) complexity of the Discrete Fourier transform (DFT), and it is comparable to Fast Fourier transform (F FT). This algorithm can be easily extended to higher dimensions. Least squares is used to refine an approximated spectra followed by simple Inverse Fast Fourier transform ( IFFT). The applicability of the proposed method is examined using synthetic seismic data.