1. An apparatus for extracting slowness dispersion characteristics of one or more sonic wave forms in broadband acoustic waves received by an array of two or more sensors comprising: means for digitizing the sonic wave forms to form discrete time wave forms and converting the discrete time wave forms into frequency domain wave forms; means for dividing a processing band of the frequency domain wave forms into frequency sub-bands and for each sub-band; approximating a family of candidate dispersion curves for multiple modes; parameterizing each of the family of approximated candidate dispersion curves by phase and group slowness; forming a frequency dependent over-complete dictionary of basis elements, each corresponding to a pair of phase and group slownesses, and spanning a range of values thereof; forming multiple measurement vectors from the frequency domain data; implementing a sparse Bayesian learning (SBL) algorithm on the multiple measurement vectors with a block sparse signal model by: estimating a mode spectrum amplitude with a Bayesian approach; estimating a mode spectrum variance, noise variance and other model parameters with a maximum likelihood estimation; optionally utilizing spectrum correlation patterns of multiple modes; pruning mode candidates by comparing the estimated mode parameters with a threshold; iterating between the Bayesian approach and the maximum likelihood estimation until convergence according to a criterion; outputting the phase and group slowness and the mode spectrum amplitude for the given sub-band; and means for generating a final dispersion curve over the processing frequency band.