Perturbation theory in depth and range-dependent environments
This dissertation starts with the following problem. If one uses the parabolic approximation of the wave equation, the user is required to provide initial data or a starting field. Although it is well known that the correct starting field involves normal modes, alternative approaches are often used because they are more readily computed.^ In the following a matrix equation is derived using the perturbation approach which governs the special combination of normal modes that gives the starting field.^ Further, a methodology is developed which allows the closeness of two starting fields to be measured. This methodology is demonstrated using several contemporary starting fields.^ In addition, efficient methods for solving the matrix equation which governs the normal modes are explored. These methods involve finding the $-$1/4 power of a matrix which is generated from the fast Fourier transform of one of the coefficients of the partial differential equation. ^
Elmer Richard Robinson,
"Perturbation theory in depth and range-dependent environments"
Dissertations and Master's Theses (Campus Access).