Assessing uncertainty in ocean acoustic inverse problems

Abstract

The goal of solving ocean acoustic inverse problems is not just to find a model fitting the data. We can always fit an N-1th order polynomial to N data points, but it does not tell us much about the uniqueness, or limits placed on resolution in the presence of noise. The real goal is to develop more information than just a model that fits the data. For truly linear problems, constraints on the model information and uniqueness are characterized by the null space of the operator which maps the model to the data, the statistics are Gaussian, and the resolution matrices have well-defined meanings. Unfortunately most inverse problems of interest in ocean acoustics are nonlinear. We are faced with methods such as simulated annealing or genetic algorithms, which tell us nothing about the statistics and little about the uniqueness of our model solution, or exhaustive but numerically intensive Monte Carlo analyses. As an alternative we have examined a nonlinear filter, that is an extension of the Kalman and extended Kalman filters. We discuss the background of the ocean acoustic inverse problem for bottom properties, and how it can be addressed by employing an exact nonlinear filter. [Work supported by ONR.]