1. A method for extracting slowness dispersion characteristics of one or more signals in broadband acoustic waves received by an array of two or more sensors comprising: dividing a frequency processing band into frequency sub-bands; for each sub-band: approximating a dispersion curve; parameterizing the dispersion curve by phase and group slowness; forming an over-complete dictionary of broadband basis elements indexed by phase and group slowness; reconstructing signals having a sparse representation in the over-complete dictionary of the basis elements by using a regularizing parameter λ; selecting the regularization parameter λ by varying λ over a range and detecting changes in distribution of residuals and selecting an operating λ, where the residual is the difference between the original and the reconstructed signal; performing mode clustering in phase and group slowness domain; and outputting a result including estimates of phase and group slownesses; and using the results to produce the slowness dispersion characteristics.