An apparatus is provided for extracting slowness dispersion characteristics of sonic wave forms in broadband acoustic waves received by multiple sensors including means to digitize the sonic wave forms to form discrete time wave forms and converting the discrete time wave forms into frequency domain wave forms and means to divide a processing band of the wave forms into frequency sub-bands. For each sub-band approximating a family of candidate dispersion curves for multiple modes, parameterizing each of the curves by phase and group slowness, and forming a frequency dependent over-complete dictionary of basis elements, each corresponding to a pair of phase and group slownesses. In addition, forming multiple measurement vectors from the frequency domain data and implementing a sparse Bayesian learning (SBL) algorithm on the vectors with a block sparse signal model and outputting the results. Also, a means for generating a fmal dispersion curve.