Hypothesis testing for geoacoustic environmental models using likelihood ratio

Abstract

A generalized likelihood ratio test is developed for testing acoustic environmental models with an application to parameter inversion using an acoustic propagation code. The signal-to-noise ratio in acoustic measurements proves to limit the details on geoacoustic environments that can be determined by matched field processing methods. A hypothesis test serves in Monte Carlo simulations as a tool to determine minimal signal levels for the bottom parameter inversion. The term “hierarchy of models” is used for denoting a sequence of models in which each particular model contains all previous ones. For determining the model order and its parameters, a combined parameter estimation and multiple sequential test is proposed. Given the observed data, how many parameters should be included in the model? The last question is important for the order selection in hierarchies of models with an increasing number of parameters. Multiple sequential hypotheses testing provides a procedure to determine the model order in a statistically justified way. Monte Carlo simulations show the behavior of the test for selecting a model order as a function of the signal-to-noise (SNR) ratio. The test is applied to broadband data measured using a vertical array near the island of Elba in the Mediterranean Sea and compared with Akaike’s Information Criterion.