A Novel Time-frequency Representation Method: The Generalized W Transform

The time-frequency representation (TFR) of seismic data is an effective technology for the detection of hydrocarbon reservoirs. To obtain the TFR of a seismic trace, a mathematical transform tool must be used to perform the decomposition of the seismic trace. This paper introduces an effective time-frequency decomposition method: the generalized W transform (GWT). We prove that the GWT is not a strictly reversible mathematical transform. The numerical experiment of a simulated seismic trace shows that the reconstruction relative error of inverse GWT could reach up to 20%. Nevertheless, the time-frequency spectrum obtained from its forward transform is particularly suitable for identifying oil and gas reservoirs. The presented GWT has three advantages: (1) Its time-frequency spectrum has a high temporal resolution even at low frequencies; (2) The spectral centroid corresponds to the peak frequency of the wavelet; (3) It eliminates the singularity of the original W transform (WT) at the peak frequency of the waveform. Compared with the wavelet transform and the S transform, the generalized W transform can more accurately characterize reservoirs. A real data example illustrates that the GWT provides better TFR performance and can more effectively identify hydrocarbon reservoirs.