Generalized Paraxial Ray Trace Procedure Derived from Geodesic Deviation

Details Generalized Paraxial Ray Trace Procedure Derived from Geodesic Deviation Generalized Paraxial Ray Trace Procedure Derived from Geodesic Deviation

2004-02-17

arxiv.org/abs/physics/0402082v2

Waves in Random and Complex Media, Vol 15, Issue 4, pages 417-435, 2005

Physics

Atmospheric and Oceanic Physics

Original; 40 pages (double spaced), 1 figure Replaced version; 36 pages single spaced, 7 figures. Expanded content; Complete d

Scientific paper

10.1080/17455030500338638

Paraxial ray tracing procedures have become widely accepted techniques for acoustic models in seismology and underwater acoustics. To date a generic form of these procedures including fluid motion and time dependence has not appeared in the literature. A detailed investigation of the characteristic curves of the equations of hydrodynamics allows for an immediate generalization of the procedure to be extracted from the equation form geodesic deviation. The general paraxial ray trace equations serve as an ideal supplement to ordinary ray tracing in predicting the deformation of acoustic beams in random environments. The general procedure is derived in terms of affine parameterization and in a coordinate time parameterization ideal for application to physical acoustic ray propagation. The formalism is applied to layered media, where the deviation equation reduces to a second order differential equation for a single field with a general solution in terms of a depth integral along the ray path. Some features are illustrated through special cases which lead to exact solutions in terms of either ordinary or special functions.

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