Variations of mode amplitudes in a range-dependent waveguide

The ray method of calculating the mode amplitudes is used to analyze the sound fields in deep-water acoustic waveguides with two types of inhomogeneities of the refractive index: (i) weak inhomogeneities that cause small perturbations of ray trajectories and (ii) strong inhomogeneities with large spatial scales. Simple analytical relations are derived for describing the variations of the mode structure of the sound field in the presence of the aforementioned inhomogeneities. A new criterion defining the validity of the adiabatic approximation is formulated. To illustrate and test the results obtained, a numerical simulation of the sound fields is performed on the basis of the parabolic equation method.