Connection Between the Solutions of the Helmholtz and Parabolic Equations for Sound Propagation
Abstract
Using a conformal mapping technique in a rectangular waveguide, we present an exact integral relation between the solutions of the Helmholtz equation whose sound speed c(x,y) varies as a function of both depth y and range x and the solutions of a parabolic equation whose sound speed varies in the mapped depth coordinate. The relation of the corresponding boundary value problems is also discussed, as well as the use of the parabolic approximation in underwater sound propagation problems. The conformal transformation interrelates the sound speeds of the two equations. Several examples are discussed. When c(x,y) = c(y) is only a function of depth we get the recent result of Polyanskii. Other examples for a general conformal transformation are functions c(x,y) which are sinusoidal in depth and exponentially decrease to a constant in range. Several alternative methods of using these results are also discussed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1976
- Accession Number
- AD1114819
Entities
People
- John A. Desanto