Geophysical Signal Parameterization and Filtering Using the fractional Fourier Transform

The fractional Fourier transform (FrFT) domain operations offer an alternative to the conventional Fourier Transform (FT) in signal processing, especially for seismic data. It is shown that subsurface reflection events in a two-dimensional (time-spatial) seismic data behave like linear chirps for each frequency in the frequency-spatial domain. Since the FrFT kernel is a set of linear chirps, frequency-spatial domain seismic data processing is better suited using the FrFT than the FT. An analytical relationship between linear seismic events and FrFT parameters is derived and illustrated with an example. Seismic data from a field survey is used to show that the FrFT filtering performs better in coherent noise attenuation than the FT.