Broadband dispersion extraction of borehole acoustic modes via sparse Bayesian learning

This paper considers broadband extraction of multiple strong/weak borehole acoustic modes in acoustic array waveforms by processing the data from multiple frequency points. We first formulate it as basis selection in a multiple measurement vector (MMV) model with varying overcomplete dictionaries and then, propose a generalized sparse Bayesian learning (SBL) method for the application-specified MMV model. The SBL method results in an iterative, hyperparameter-free algorithm to estimate the mode spectrum and update prior parameters. Specifically, the iteration can be implemented in either the fixed-point or expectation-maximization mechanism. Numerical validation with synthetic and field datasets confirms the effectiveness of the proposed method and its advantages over the narrowband (modified matrix pencil) approach.