Image Summation in Shallow-Water Sound Propagation

Abstract

Shallow-water sound propagation is often described in terms of normal mode theory in which the sound field is given as the sum of normal modes. Much less work has been done on the counterpart of this theory—image theory—probably because of the formidable task of summing the many images required. In this paper such image sums were obtained with a digital computer, and sets of transmission curves were obtained for various frequencies and water depths. For ease of computation, the reflection coefficient was first taken to be independent of angle; when compared with field data, the computed curves were found to fall off too fast with range. Better agreement was had under the more realistic assumption of unity reflection coefficient within the critical angle and zero beyond. Comparison with measured transmission runs selected at random in widely separated areas show that the agreement with the field data is often good. Yet there are many instances of wide divergence between the predicted and observed transmission that must be the result of the over-simplified bottom conditions necessarily assumed in the theory. The prediction problem in short-range shallow-water sound transmission is still essentially unsolved.