Wavelet display of dispersion in concrete using Paul and Morlet wavelets

Non-destructive inspection of concrete presents significant difficulties because of the presence of material inhomogeneities on a number of different scales. Many practitioners of ultrasonic testing view wave dispersion as noise when performing ultrasonic tests. However, significant information is present in the dispersion characteristics. Measurement of dispersion has the potential to separate the effects of inhomogeneities and damage because of differences in length scales. Wavelet decomposition makes it possible to measure dispersion using standard non-destructive testing equipment and a single receiving transducer. In this study two complex wavelet functions, the Paul and Morlet, are investigated. Unlike the Morlet wavelet, the Paul wavelet satisfies the admissibility conditions for a wavelet function with very few restrictions on the adjustment of wavelet parameters. The Paul wavelet may even be used to reproduce the Morlet wavelet scalograms. However, as a result of the broad admissibility, the Paul wavelet can also be adjusted for any required time-frequency resolution. The Paul wavelet can thus be `tuned' for a particular application to provide an optimal compromise between time and frequency resolution. Such tuning will be shown to be useful in the visualization of the dispersion due to damage in concrete.