Symbolic solution of a multilayer ocean waveguide problem with arbitrary depth dependent ambient density and sound speed profiles
Young, Charles Joseph
Ziomek, Lawrence J.
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The main purpose of this thesis was to obtain the symbolic solution of a multilayer (four fluid media) ocean waveguide problem. The waveguide was assumed to have depthdependent ambient density and sound speed profiles in all fluid media, and arbitrarily shaped boundaries between all fluid media. A system of 28 equations in 17 unknowns was generated by satisfying all of the boundary conditions (including the boundary condition at the source) in cylindrical coordinates. The problem was set up as a weighted least squares problem for symbolic solution by the computer program Mathematica, Due to software and hardware constraints, a symbolic solution for the most general case was not obtained. However, by making all of the boundaries plane, parallel boundaries, two cases were successfully programmed, yielding symbolic solutions which were verified by comparison to previously known results.
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