Abstract
Several theoretical results linking ray and normal-mode quantities are derived by assuming Wentzel–Kramers–Brillouin (WKB) solutions for the depth dependence of the acoustic field in both water and bottom. Some of the results are not new but are extended here to the general case of reflection from a structured, lossy bottom: (1) Mode and ray cycle distances are equal if the ray cycle distance includes the beam displacement on reflection; (2) cycle distance is simply related to the normalization of the normal modes; (3) mode attenuation per cycle is equal to bottom loss per bounce of the equivalent ray; (4) a complete normal-mode solution for water may be obtained from the plane-wave reflection coefficient with no further knowledge of the bottom; and (5) the WKB solution for the bottom is equivalent to a calculation assuming interfering geometric ray paths.
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