Generalized W Transform and Its Application in Gas-Bearing Reservoir Characterization

The W transform (WT), employing a Gaussian window with non-stationary dominant frequency weight, is suitable for reservoir description with high time resolution at low-frequency band. In this letter, we generalize the WT through designing a novel frequency-varying Gaussian standard deviation with a two-parameter multivariate composite exponential form of the dominant frequency, namely generalized WT (GWT), which can avoid the singularity of WT caused by the non-differentiability of its standard deviation at the dominant frequency, thus obtaining a smoother and more flexible window. Compared with the S-transform (ST) and WT, the proposed method provides a better time-frequency (TF) representation performance. The analysis results of simulated seismic trace and field seismic data illustrate that the GWT can effectively characterize gas-bearing reservoirs.