New techniques for investigating the properties of chaotic ray paths

Abstract

It has been established that acoustic ray paths in a range-dependent ocean environment can exhibit chaotic behavior [Palmer et al., Geophys. Res. Lett. 15, 569–572 (1988)]. The usual techniques for identifying chaotic rays are the examination of Poincaré sections and power spectra of path depth, as well as the observation of exponential sensitivity to initial conditions. These techniques are not always useful, however, and are not directly related to observable signal characteristics. Travel times, ray elevation angle at axis crossings, and upper and lower turning point depths have practical relevance and provide new insights into the character of chaotic rays. Since this effort involved the numerical calculation of ray paths for both the Helmholtz and parabolic equations, procedures were developed for comparing results obtained for the two equations.