The linear canonical W-transform

Abstract

The time–frequency spectrogram of seismic data is commonly used as an attribute in the analysis and interpretation of nonstationary seismic signals. To improve the capability of the W transform to analyze nonstationary data, we introduce the linear canonical W transform by implementing an affine matrix along with scaling parameters to generate highly-resolved and energy-concentrated time–frequency spectra. More features of nonstationary signals can be explored in the time–linear canonical frequency domain by transforming the time–frequency plane, which makes the algorithm more applicable to seismic signals. For the completeness of the linear canonical W transform, we also propose the inverse linear canonical W transform to extend its applications. Examples of synthetic and field seismic data show that a highly-resolved and energy-concentrated time–frequency spectrogram can be estimated with the linear canonical W transform at negligible additional computational burden. In addition, the proposed algorithm is promising for several seismic data processing and interpretation techniques, such as reservoir characterization and thin layer identification, etc.