Automatic dispersion extraction using continuous wavelet transform

In this paper we present a novel framework for automatic extraction of dispersion characteristics from acoustic array data. Traditionally high resolution narrow-band array processing techniques such as Prony´s polynomial method and forward backward matrix pencil method have been applied to this problem. Fundamentally these techniques extract the dispersion components frequency by frequency in the wavenumber-frequency transform domain of the array data. The dispersion curves are subsequently extracted by a supervised post processing and labelling of the extracted wavenumber estimates, making such an approach unsuitable for automated processing. Moreover, this frequency domain processing fails to exploit useful time information. In this paper we present a method that addresses both these issues. It consists in taking the continuous wavelet transform (CWT) of the array data and then applying a wide-band array processing technique based on a modified Radon transform on the resulting coefficients to extract the dispersion curve(s). The time information retained in the CWT domain is useful not only for separating the components present but also for extracting group slowness estimates. The latter help in the automated extraction of smooth dispersion curves. In this paper we will introduce this new method referred to as the exponential projected Radon transform (EPRT) in the CWT domain and limit ourselves to the analysis for the case of one dispersive mode. We will apply the method to synthetic and real data sets and compare the performance with existing methods.