This paper presents detailed numerical comparisons between propagation losses as calculated by ray theory and by mode theory. Both theories are based on the bilinear surface-duct model. In the image-interference region, the theories give almost identical results, the accuracy of the mode solution being limited at very close ranges by the number of modes treated. As many as 40 modes are considered. Comparison with experimental data at 530 and 1030 cps indicates that the mode theory is definitely superior to ray theory in regions where ray theory predicts shadow zones and caustics. The nature of the mode solution is examined in detail. The manner in which the mode theory produces the image-interference pattern is controlled by the detailed amplitude and phase characteristics of a large number of modes and is not readily interpreted as the interference between a direct and a surface-reflected acoustic path.
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Pedersen et al. (1965) studied this question.