Abstract:

Mode models of sound propagation in layered media begin with a search for modes in the complex wave-number plane, followed by computation of the vertical mode functions and mode superposition. Sound propagation modelers would like to search for modes ever more efficiently and thoroughly. The search amounts to the mathematical problem of finding the roots (zeros) of a complex-valued function---a problem that defies definitive solution. Rather than reducing the numerical test for modes (roots) to a single characteristic equation, singular value decomposition (SVD) can be used to test when the global matrix describing the propagation of plane waves through the layered media is singular, which is an equivalent condition for a mode. The advantages of this approach are that it is numerical stable, it automatically gives the vertical mode functions (although un-normalized), it can detect duct and interface modes at any depth, and it can identify and resolve close-mode pairs (double roots) and their antisymmetric mode functions occurring in weakly coupled sound channels.