An Improved Unscale S-Transform in Frequency Domain

The time-frequency analysis methods are powerful tools in seismic interpretation and bright spot identification. The S-transform (ST), as a hybrid of the short-time Fourier transform (STFT) and continuous wavelet transform (CWT), can achieve progressive time-frequency resolution. However, limited by its linear-frequency-dependent term, the ST obtains a deviated frequency distribution. By removing this term, the frequency form of unscaled ST (FUST), as a variation of the ST, is proposed to preserve the reliable frequency distribution. The fly in the ointment is that the FUST decreases the temporal resolution of the low-frequency components, which may not be suitable for seismic reflection interpretation and reservoir location. In addition, the ST cannot tailor the time-frequency resolution for particular applications. To solve these problems, a simple and effective method is proposed by substituting the basis of the FUST. The proposed method can obtain the desired time resolution by adjusting two adjustable parameters. The corresponding inverse transform is also derived to guarantee its energy conservation and inevitable property. Numerical experiments and real data examples show better performance of the proposed method in improving temporal resolution and reservoir location over the ST and FUST.