Formalizing noise field beam correlation techniques for analyzing deep layers

This work takes an information theoretic approach to understanding and characterizing beam correlations within the ambient noise field and discusses the implications for passive seabed geoacoustic estimation, particularly as it applies to deep layers. The passive fathometer [J. Acoust. Soc. Am. 120(3), 1315–1323 (2006)] and head wave correlation analysis [J. Acoust. Soc. Am. 140(1), EL62–EL66] are examples of techniques that use beam correlations and have generated interest given their ability to expose information about geo-acoustic properties as well as the layering structure of the bottom. However, the conditions under which these techniques can operate, what information is actually available, and which multilayer properties can be independently estimated, are open questions. Formal answers come in the form of the Cramér-Rao lower bounds (CRLB), but this requires an exact definition of the probability function for a cross-beamformer output defined in the space of the multilayered bottom properties. Often prior information about a site is available, and this can readily be incorporated to yield the Bayesian CRLB, which allows this approach to be used for experimental design. The theoretical framework for the Bayesian CRLB will be presented along with simulation and measured data examples.