IMPROVED STOCKWELL TRANSFORM AND ITS APPLICATIONS

Abstract

Time-frequency analysis is a technique for characterizing and manipulating non-stationary signals which comprise of variable frequency content. By looking at the time series of a signal, it becomes visually impossible to know the different frequencies present in it. But spectral decomposition of the signal enables us to identify the different frequencies comprised by the signal at any particular point of time. S-Transform is one such technique used for time-frequency analysis. But a major drawback associated with it is characteristic low time resolution exhibited at lower frequencies. Low time resolution hinders accurate identification of low frequency anomalies and may result in incorrect time-thickness of lithological layers at such frequencies. ‘Improved Stockwell Transform’ technique is proposed which introduces two constants in the normalized Gaussian window function by mapping the frequency as a linear function ‘af+b’. In order to evaluate the proposed scheme, results obtained from the ST and the IST are evaluated and compared using both synthetic and real data. The comparison showed that IST is a superior method than ST, resulting in a better time-frequency resolution. Two applications of IST are proposed: (a) detecting low frequency anomalies in seismic data which are attributed to abnormally high attenuation in a gas-filled reservoir (b) estimating P-wave and S-wave arrival times in a seismogram accurately.