Geometrically Derived Ray-Theory Results and Direct Verification of the Pekeris Solution for Unbounded Constant-Gradient Media

This paper directly verifies the Pekeris solution to the point-source Helmholtz equation for an unbounded constant-gradient medium using only elementary vector calculus. Self-contained geometrical derivations of ray-theory results for such a medium are presented: (1) ray-path location and travel tim...

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Bibliographic Details
Published in:IEEE journal of oceanic engineering 2012-04, Vol.37 (2), p.244-254
Main Author: Barnard, T. E.
Format: Article
Language:English
Subjects:
Angles (geometry)
Calculus
Derivation
Equations
Equivalence
Geometry
Linear sound-speed profile
Marine
Mathematical analysis
point-source Helmholtz equation
Position (location)
Position measurement
ray theory
Receivers
Sea surface
Surface waves
unbounded constant-gradient medium
Wave fronts
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Summary:This paper directly verifies the Pekeris solution to the point-source Helmholtz equation for an unbounded constant-gradient medium using only elementary vector calculus. Self-contained geometrical derivations of ray-theory results for such a medium are presented: (1) ray-path location and travel time as a function of source location, ray start angle, and ray angle; (2) the wavefront equation as a function of source location and travel time; (3) the wavefront location and ray angle along a ray as a function of source location, ray start angle, and travel time; and (4) source angle and receiver angle as a function of source location and receiver location. A short mathematical derivation gives the travel time between two points for a given source location and a given receiver location. In some cases, the form of the results seems to be simpler than that of the equivalent results previously given in the literature.
ISSN:0364-9059
1558-1691
DOI:10.1109/JOE.2012.2188161