Wavelet transforms in surface wave analysis

Surface wave based seismic techniques, like the spectral analysis of surface waves (SASW), have been primarily used in modulus profiling of layered systems, like soils and pavements. Typical analysis involves generation of the dispersion curves using the spectral analysis and backcalculation of the profile, or in cases where a large number of receivers are used, the analysis is conducted through data presentation in the frequency-wave number domain. Wavelet transforms have significant advantages over a typical spectral analysis, since the data can be presented, as a function of both time and frequency, in terms of wavelet maps. Several applications and advantages of the wavelet transforms are presented. The first application deals with the use of harmonic wavelet transform (HWT) in generation of the surface wave dispersion curve. The advantages of the wavelet approach include more stable phase velocity calculations than using the traditional phase unwrapping, and simultaneous calculation of phase and group velocities. The second application deals with detection and characterization of cavities and objects buried in the ground using continuous wavelet transforms (CWT). Finally, use of wavelet transforms in characterization of layer interfaces, with respect to layer dipping and abrupt interface changes is illustrated.