The Impact of Oceanographic Variability of Sound Propagation in Shallow Water Using Polynomial Chaos Expansions

The acoustic response to propagation through oceanographic uncertainty has been derived using polynomial chaos expansions to the coupled mode equations for propagation in range dependent environments. In this approach the sound speed variability is decomposed into vertical EOF mode shapes for uncorrelated components of the sound speed defect. Horizontally each of these EOFs is assumed to be characterized by a homogeneous random process with an exponential correlation function. Under these approximations it is possible to expand the coupled mode equations using a perturbation approximation for the coupling coefficients, and obtain the resulting polynomial chaos expansion for the coupled modal amplitudes. These results differ from previous work in that the expansion is obtained for the complex modal amplitudes instead of the log modal amplitudes, and that the horizontal statistics are described by a homogeneous random process. Results obtained for the statistics of the acoustic field are compared to Monte Carlo results as a function of the variance of the oceanographic variability and of the order of the truncation of the chaos.