On the measurement of modal group time delays in the deep ocean

Abstract

The modal description of sound propagation in deep ocean environments is considered. Recently published inversion algorithms have assumed that modal group time delays can be measured. Such a measurement is straightforward to make if either: (1) the modal group arrival of interest is resolved in time; or (2) the wave field is sampled on a dense vertical array which spans much of the water column, thereby enabling the orthogonality of the modes to be exploited. In order to temporally resolve modal group arrivals using measurements made on a single hydrophone, the frequency bandwidth must: (a) be sufficiently broad that the temporal separation between successive modal arrivals exceeds the reciprocal bandwidth; and (b) be sufficiently narrow that, across the band, the group slownesses of neighboring mode numbers do not overlap. To satisfy both conditions [(a) and (b)] the ratio of the range to the center frequency must be large. Unlike ray arrivals, modal group arrivals broaden as range increases due to dispersive spreading. To minimize dispersive spreading so that accurate group delay time estimates can be obtained, the ratio of range to center frequency should be kept small. Thus the requirements for temporally resolving modal group arrivals conflict with the conditions that minimize dispersive spreading. Numerical results are presented which give quantitative estimates of which combinations of range, center frequency, bandwidth, and mode number produce conditions which are favorable for temporally resolving modal group arrivals in six regions of the deep ocean at mid and low latitudes. These results suggest that it is extremely difficult to find conditions which allow modal group arrivals to be temporally resolved and simultaneously allow group delay times to be measured with sufficient accuracy to be useful for tomography. The situation is further complicated by internal waves which appear to cause mode coupling and significant broadening of modal group arrivals at frequencies above approximately 50 Hz. The combined effects of dispersive spreading and internal wave-induced mode coupling suggest that, without employing mode filtering techniques, modal group time delay-based inversion schemes in the deep ocean do not appear to be promising.