The multiscale Fourier transform

Locci-Lopez, Daniel (School of Geosciences, University of Louisiana at Lafayette) | Zhang, Rui (School of Geosciences, University of Louisiana at Lafayette) | Oyem, Arnold (Department of Earth and Atmospheric Sciences, University of Houston) | Castagna, John (Department of Earth and Atmospheric Sciences, University of Houston)

OnePetro 

Summary Multi-resolution spectral decomposition methods such as the S-transform and the Continuous Wavelet Transform, are known to distort spectral attributes such as peak frequency. We introduce a spectral decomposition approach via a multi-scale Fourier Transform that utilizes a frequency-dependent temporal window to achieve any desired combination of temporal and frequency resolution. We investigate a specific frequency-dependent window that focusses the analysis on the full-width at half-maximum of a frequency-dependent Gaussian function. The resulting time-frequency analysis has significantly improved timeresolution relative to the S-transform. This is demonstrated on real seismic data in the Permian Basin.