Internal symmetry in acoustical ray theory

Abstract

A connection between acoustic ray theory and differential geometry suggests the existence of a local symmetry within ray theory. The local symmetry, in this case conformal symmetry, is reminiscent of that encountered in the study of electromagnetic field theory, or more generally gauge theory. Acousticians can take advantage of this symmetry by choosing a gauge that best suits a given problem. In this paper, the symmetry is discussed in the most general context and the transformations for both ray theory and paraxial ray theory are given. When applied to the paraxial equations this transformation alters the stability parameters of the system. For low dimensional problems in ray theory, such as those including depth and range dependence in the local sound speed, the stability parameters become a property of the medium. Specific applications to layered media are presented and their consequences discussed.