Approximation of the fast bottom reflection coefficient in the quadruplet expansion of the method of images in a wedge shaped ocean

Abstract

Image theory is an ideal method for calculating the transmission loss in a shallow water (wedge shaped ocean) environment. It can be used in cross-slope, at all frequencies and in transitional cut off regions that are out of bounds to normal mode theories. This thesis had three objectives: 1) convert the existing image theory models called URTEXT and WEDGE into a high level scripting language called MATLAB™ by Math Works, 2) linearize the existing quadruplet expansion program to increase speed, and 3) to incorporate the Arctan approximation of the Rayleigh reflection coefficient into the quadruplet expansion for the fast bottom case. Objective 1 was completed with accurate results. Objective 2 was completed with a factor of 8 increase in speed. Objective 3 incorporated the Arctan approximation of the reflection coefficient for a fast bottom into the quadruplet expansion, but due to the inaccuracy of the reflection coefficient after the second quadruplet, the results were not favorable. It was also discovered that even with the Rayleigh reflection coefficient, the first order approximations made in developing the quadruplet expansion equation (Equation 6-27) are not accurate enough for the fast bottom case.