Determination of phase spectrum using harmonic wavelet transform

The dispersive phase velocity of a wave propagating through a system is an important parameter and carries valuable information in non-destructive tests related to multi-layered systems such as a soil site. The dispersive phase velocity of a wave can be estimated using the phase spectrum, which is easily evaluated through the cross power spectrum. However, the phase spectrum as obtained using the cross power spectrum is sensitive to background noise, which always exists in the field. This causes difficulties in the determination of the dispersive phase velocities. In this paper, a new method to evaluate the phase spectrum using the harmonic wavelet transform is proposed. The introduced method can successfully remove background noise effects. To evaluate the validity of this method, numerical simulations of multi-layered systems were performed. Phase spectra determined by the suggested method were found to be in good agreement with the actual phase spectra under conditions characterized by heavy background noise. This shows the potential of the proposed method.