Airy functions and the Recursive Ray Acoustics Algorithm

Abstract

Two main problems are analyzed and discussed in this thesis. First, a detailed derivation of the exact solution for the inhomogeneous Helmholtz equation for a free-space propagation problem when the square of the index of refraction is a linear function of depth and the input is an omnidirectional point source is performed and discussed. The exact solution is in terms of Airy and Bairy functions. Second, the accuracy of the Recursive Ray Acoustics (RRA) Algorithm was tested by generating test cases using a sound-speed profile with the square of the index of refraction a linear function of depth. The acoustic pressure (amplitude and phase) calculations obtained from the RRA Algorithm were then compared to the exact "Airy function" solution. Computer simulation results indicate that both solutions are in good agreement.