Dispersion and repopulation of the Heard–Ascension modes.

The modal spectrum of the PE field (MOSPEF) along the horizontally refracted ray path to model the Heard–Ascension Island propagation is used. First, the travel‐time error imposed by the PE approximation is discussed, and an analytic formula for travel‐time error is given to clarify the validity of the PE application. Second, the modal repopulation caused by mode coupling at the transition from the surface duct to the deep SOFAR duct is estimated. Finally, modal dispersion effects, including modal arrival time spreading and the modal pulse elongation within the transmitted bandwidth, are calculated based upon a second‐order Taylor expansion of the MOSPEF phase. By using a finite‐difference technique instead of Fourier decomposition of the transmitted spectrum, only three frequencies (56.99, 57.00, and 57.01 Hz) are needed to characterize the dispersion. [This work was supported by ONR and NOAA.]