Modified S-Transform in time-frequency analysis of seismic data and its application



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The S-Transform (ST) is a frequency-dependent spectral decomposition method that truly localizes spectra in time and frequency. However, it exhibits poor temporal resolution at low frequencies, which can result in inaccurate localization of spectral anomalies and obscure features that have geological meanings. While prior literature developed various modified S-Transforms, called the Generalized ST, (GST) to tailor analyzing windows for particular applications, they do not specifically address the particular shortcoming as noted above. To improve the ST’s temporal resolution at low frequencies, this dissertation develops a new modification to the ST. The proposed algorithm (termed MST) replaces frequency in the ST’s normalized Gaussian window with a linear function of frequency. Through optimizing two constants in the linear frequency function, the modified window shortens its width and sharpens its waveform to improve time resolution at low frequencies without degrading frequency resolution while retaining the ST’s time and frequency resolution at higher frequencies. Further, the MST also conserves energy and preserves the spectral properties of the ST. Comparison analyses of synthetic and real seismic data using the ST, CWT, MST and GSTs show that the MST successfully accomplishes the above. By using optimized coefficients in its linear frequency function, the MST can be useful in hydrocarbon detection and geological interpretation.



S-transform, Modified S-transform, Spectral decomposition, Time-frequency analysis, Time resolution, Frequency resolution, Spectral localization, Hydrocarbon indication