Time Difference Raytrace Method For Ranging And Sound Channel Probing

A method for time delay ranging in the deep sound channel is outlined here. The method is based on modeling sound channel SSP by an N-layer model. The parameters of the model are reference sound speed
C_{o}
. layer thickness
\Delta
Z and sound speed gradient vector
\underline{g}
. For ranging purposes, it is only necessary to determine the composite parameter(
\Delta C/\Delta R
). As shown, this can be done by differential ray trace or by using two distinct bearing angles. Another alternative is to use an analytical profile and to differentiate axial range with respect to the vertical arrival angle
\phi
. The same methodology is proposed to solve the inverse problem, namely the gradient set is obtained from
N
independent observations of the phase gradient parameter(
\Delta C/\Delta R
). The explicit transformation of SSP to phase gradient for an axial configuration of sources and receivers for the layered model is outlined. A simple transposition method is discussed to obtain an off-axis configuration of source/receiver allocations. All the results presented here have been restricted to ray trajectories having a single upper and single lower rapath loop. This propagation mode is generally associated with first convergence zone ranges, that is to say ranges of the order of 50km.