Derivation of the Paraxial Ray Equations in Three Conformal Representations

Abstract: Acoustic rays can be described by null geodesics of a pseudo-Riemannian manifold. This allows for the immediate generalization of paraxial ray systems via geodesic deviation. The technique has appeared in the literature for the past decade and has been used by the author in the development of dynamic ray trace codes. The techniques involved are powerful but abstract and frequently unfamiliar in the field of acoustics. This brief paper derives the complete paraxial system for the case of acoustics in the presence of an inhomogeneous isotopic time independent media described by a sound speed profile c(x,y,z). The derivation is performed for three distinct conformal representations of the acoustic metric.