Slowness dispersion characteristics of multiple possibly interfering signals in broadband acoustic waves as received by an array of two or more sensors are extracted without using a physical model. The problem of dispersion extraction is mapped to the problem of reconstructing signals having a sparse representation in an appropriately chosen over-complete dictionary of basis elements. A sparsity penalized signal reconstruction algorithm is described where the sparsity constraints are implemented by imposing a l1 norm type penalty. The candidate modes that are extracted are consolidated by means of a clustering algorithm to extract phase and group slowness estimates at a number of frequencies which are then used to reconstruct the desired dispersion curves. These estimates can be further refined by building time domain propagators when signals are known to be time compact, such as by using the continuous wavelet transform.