Time spreading of a target echo from a short pulse in a waveguide

Abstract

The normal mode approach has proven very useful for calculating reverberation in a shallow water waveguide. Generally the calculation is done as a function of range r, then the time dependence t is obtained via t = 2r/c, where c is some average sound speed. This assumes that all the multipath returns from a particular scattering point arrive at the same time. A better time dependence can be obtained by using mode group velocities [D. Ellis, J. Acoust. Soc. Am. 97, 2804–2814 (1995)]. For reverberation from a uniform bottom this only has a small effect compared to the simple approach. However, for a compact scattering feature or target, the time spreading for a short pulse can be quite significant. Analytical results for an isospeed waveguide have been previously obtained using an energy flux approach. Here, a model using modal group velocities is used to calculate the time dependence of an echo from a target or compact reverberation feature. The mode approach extends to a general sound speed profile. One can convolve the impulse response with the amplitude envelope of the transmitted pulse to obtain the echo time decay. [Work supported by Mount Allison University, and US Office of Naval Research.]