2004/02/29 by David Bergman, David R. Bergman
Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Experimental and Theoretical Physics Studies #Quantum Electrodynamics and Casimir Effect #physics.ao-ph
paper · pdf · doi:10.1080/17455030500338638
published as Waves in Random and Complex Media, Vol 15, Issue 4, pages 417-435, 2005 · Original; 40 pages (double spaced), 1 figure Replaced version; 36 pages single spaced, 7 figures. Expanded content; Complete derivation of the equations from the equations of hydrodynamics, introduction of an auxiliary basis for three dimensional wave-front modeling. Typos in text and equations corrected
openalex publication_date 2005/12/01 · arxiv created 2005/12/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
Paraxial ray tracing has gained popularity in seismology and underwater acoustics for modelling the propagation of sound when the medium is stationary and time independent. In this article differential geometry is used to derive a generalized paraxial ray-tracing procedure valid for any fluid media described by a local sound speed and velocity depending arbitrarily on position and time. Geodesic deviation is used to model acoustic beam deformation, and the sectional curvature along a ray to determine convergence and divergence zones in space. The resulting paraxial equations presented here are the most general that can be derived for the acoustic field and apply to any environment including those with time dependence and fluid motion. Applied to layered media the geodesic deviation equation is solved exactly. Some illustrative examples are included.