Normal-mode analysis of underwater-sound propagation with directional sources and receivers

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Abstract
Standard normal-mode analysis of underwater-sound propagation assumes only an omnidirectional point source. Other writers have proposed that, for use in calculations, a virtual line-array of discrete point sources, arranged vertically, can well approximate the directivity pattern, in the vertical plane, of actual sources. It seems better, however, to use an equivalent vertical line array with a continuous distribution of strength and phase. The equations for relating the actual source and the line source are given, and their solution is discussed. Identical methods allow the calculation of reception by a directional receiver. A related topic, use of a vertical array of discrete elements to stimulate or receive a single mode, is also discussed. An illustrative directivity pattern is presented, for an array adjusted to select the first mode in a shallow-water problem.

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