Modified S transform for time-frequency analysis of borehole flexural waves dispersion

Abstract

Guided wave propagation usually exhibits dispersive behaviour. The time-varying spectral components of dispersive waves have been characterized effectively using the time-frequency approach; the short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are commonly used for this purpose. However, the resulting energy distributions suffer from poor resolution related to the uncertainty principle, and this complicates the allocation of energy to individual propagation modes especially when the dispersion curves of these modes are close to each other in the time-frequency domain (in which case the separation becomes a challenge). Therefore there is a need for high resolution time-frequency techniques. To meet this challenge we introduce a modified version of the S transform, a method which combines the advantage of the STFT and CWT but with greater resolution. An adaptive algorithm is presented which identifies frequency regions of interest related to different energy modes, and employs the modified S transform to a dispersion curve model to extract the proportional energy distribution of a specific mode from a multimode dispersive wave signal. The effectiveness of this approach is demonstrated on dispersive flexural waves obtained from an acoustic borehole logging tool.