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Acoustic rays can be described by null geodesics of a pseudo-Riemannianmanifold. This allows for the immediate generalization of paraxial ray systemsvia geodesic deviation. The technique has appeared in the literature for thepast decade and has been used by the author in the development of dynamic raytrace codes. The techniques involved are powerful but abstract and frequentlyunfamiliar in the field of acoustics. This brief paper derives the completeparaxial system for the case of acoustics in the presence of an inhomogeneousisotopic time independent media described by a sound speed profile c(x,y,z).The derivation is performed for three distinct conformal representations of theacoustic metric.

Derivation of the Paraxial Ray Equations in Three Conformal Representations