Fast Generalized Fourier Interpolation of Nonstationary Seismic Records

We propose a fast and efficient method for the interpolation of nonstationary seismic data. The method uses the fast generalized Fourier transform FGFT to identify the space-wavenumber evolution of nonstationary spatial signals at each temporal frequency. The nonredundant nature of FGFT renders a big computational advantage to this interpolation method. A least-squares fitting scheme is used next to retrieve the optimal FGFT coefficients representative of the ideal interpolated data. For randomly sampled data on a regular grid, we seek a sparse representation of FGFT coefficients to retrieve the missing samples. A synthetic seismic data example was used to examine the performance of the method.