Polynomial chaos expansions for coupled mode amplitude and phase uncertainty in the presence of oceanographic uncertainty

Abstract

Polynomial chaos (PC) techniques have recently been introduced to the field of underwater acoustics for modeling the nonlinear transfer of probabilistic measures of the propagation environment into measures of acoustic propagation uncertainty [Finette, J. Acoust. Soc. Am. 117, 997–1000 (2005)]. Recently we have proposed and implemented a PC method for modeling this process for coupled mode propagation through internal waves (IWs) [LePage, J. Acoust. Soc. Am. 118, 1903–1904 (2005)]. While showing promise, the approach was implemented for a single empirical orthogonal function (EOF) component of the IW field only and was derived for small PC coefficients. In this paper the restriction of small coefficients is removed for the first two terms of the PC expansion, and results for uncertainty caused by more than one uncorrelated EOF component are also presented. [Work supported by ONR.]