A Recipe To Address Time Frequency Non-Uniqueness: A New Tool For Spectral Decomposition

Spectral decomposition is a well-known technique with applications in, but not-limited to, analysing frequency dependant variation of amplitude with respect to time. Over the past few years, numerous algorithms have been developed (and published) to aid precision in spectral decomposition, however, all these methods, suffer from the Gabor’s uncertainty (similar to Heisenberg uncertainty principle, from quantum mechanics) i.e. the frequency and time for a specific amplitude cannot be isolated unambiguously. This has far reaching consequences with respect to seismic interpretation. e.g. after identifying a high amplitude channel in a window of 100ms zone at a specific frequency, locating the extents (vertical & lateral) of the channel within the seismic is still left to the subjective judgement of the interpreter. This introduces significant uncertainty in interpretation of spectral decomposition results. The method discussed in this paper, based on published mathematical foundations (after, Brevdo et. al., 2014, Herrera et.al. 2014, Said Gaci, 2018) aims at dealing with this spectral uncertainty in order to aid improved spectral interpretation.