Ocean acoustic inversion with estimation of a posteriori probability distributions

Inversion methods are applied in ocean acoustics to infer parameters which characterize the environment. The objective of this paper is to provide such estimates, and means of evaluating the inherent uncertainty of the parameter estimates. In a Bayesian approach, the result of inversion is the a posteriori probability density for the estimated parameters, from which all information such as mean, higher moments, and marginal distributions can be extracted. These are multidimensional integrals of the a posteriori probability density, which are complicated to evaluate for many parameters. Various sampling options are examined and it is suggested that “importance sampling” based on a directed Monte Carlo method, such as genetic algorithms, is the preferred method. The formulation of likelihood functions and maximum-likelihood objective functions for multifrequency data on a vertical array is discussed. A priori information about the parameters may be used in the formulation. Shallow-water acoustic data obtained at several frequencies using a vertical array is used to illustrate the applicability of the technique.