by Chong, Cheung-Yu = 開放球腔中波動之二分量理論 / 莊翔宇. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 84-87). / Text in English; abstracts in English and Chinese. / by Chong, Cheung-Yu = Kai fang qiu qiang zhong bo dong zhi er fen liang li lun / Zhuang Xiangyu. / Abstract --- p.i / Acknowledgments --- p.iii / Contents --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Open Cavities and Quasinormal Modes --- p.1 / Chapter 1.2 --- Completeness of Quasinormal Modes --- p.3 / Chapter 1.3 --- Objective and Outline of this Thesis --- p.5 / Chapter 2 --- Waves in One-Dimensional Open Cavities I: Completeness --- p.6 / Chapter 2.1 --- Quasinormal Modes of One-Dimensional Open Cavities --- p.6 / Chapter 2.2 --- Green's Function Formalism --- p.7 / Chapter 2.2.1 --- Construction of the Green's Function --- p.8 / Chapter 2.2.2 --- Conditions for Completeness --- p.9 / Chapter 2.2.3 --- Quasinormal Mode Expansion of the Green's Function --- p.10 / Chapter 2.3 --- Two-Component Formalism --- p.11 / Chapter 2.3.1 --- Overcompleteness --- p.11 / Chapter 2.3.2 --- Two-Component Expansion --- p.11 / Chapter 2.3.3 --- Linear Space Structure --- p.13 / Chapter 3 --- Waves in One-Dimensional Open Cavities II: Time-Independent Problems --- p.16 / Chapter 3.1 --- Perturbation Theory --- p.16 / Chapter 3.1.1 --- Formalism I: Green's Function Formalism --- p.17 / Chapter 3.1.2 --- Formalism II: Two-Component Formalism --- p.20 / Chapter 3.2 --- Diagonalization Method --- p.23 / Chapter 3.2.1 --- Formalism I: One-Component Expansion --- p.24 / Chapter 3.2.2 --- Formalism II: Green's Function Formalism --- p.25 / Chapter 3.2.3 --- Formalism III: Two-Component Formalism --- p.28 / Chapter 3.2.4 --- Numerical Example --- p.29 / Chapter 4 --- Waves in Open Spherical Cavities I: Completeness --- p.34 / Chapter 4.1 --- Quasinormal Modes of Open Spherical Cavities --- p.34 / Chapter 4.2 --- Green's Function Formalism --- p.36 / Chapter 4.2.1 --- Construction of the Green's Function --- p.37 / Chapter 4.2.2 --- Conditions for Completeness --- p.37 / Chapter 4.2.3 --- Quasinormal Mode Expansion of the Green's Function --- p.38 / Chapter 4.3 --- Two-Component Formalism --- p.39 / Chapter 4.3.1 --- Evolution Formula --- p.40 / Chapter 4.3.2 --- Two-Component Expansion --- p.48 / Chapter 4.3.3 --- Outgoing-Wave Boundary Condition --- p.49 / Chapter 4.3.4 --- Numerical Example --- p.51 / Chapter 4.3.5 --- Linear Space Structure --- p.52 / Chapter 5 --- Waves in Open Spherical Cavities II: Time-Independent Prob- lems --- p.57 / Chapter 5.1 --- Perturbation Theory --- p.57 / Chapter 5.1.1 --- Formalism I: Green's Function Formalism --- p.57 / Chapter 5.1.2 --- Formalism II: Two-Component Formalism --- p.60 / Chapter 5.2 --- Diagonalization Method --- p.61 / Chapter 5.2.1 --- Formalism I: One-Component Expansion --- p.61 / Chapter 5.2.2 --- Formalism II: Green's Function Formalism --- p.63 / Chapter 5.2.3 --- Formalism III: Two-Component Formalism --- p.64 / Chapter 5.2.4 --- Numerical Example --- p.65 / Chapter 6 --- Numerical Evolution of Outgoing Waves in Open Spherical Cav- ities --- p.73 / Chapter 6.1 --- Formulation of the Problem --- p.74 / Chapter 6.2 --- Derivation of the Boundary Condition --- p.75 / Chapter 6.3 --- Boundary Condition without High Derivatives --- p.76 / Chapter 6.4 --- Numerical results --- p.78 / Chapter 6.5 --- Discussion --- p.79 / Chapter 7 --- Conclusion --- p.82 / Chapter 7.1 --- Summary of Our Work --- p.82 / Chapter 7.2 --- Future Developments --- p.83 / Bibliography --- p.84

Sound propagation in a waveguide is greatly dependent on the acoustic properties of the boundaries. The effect of these properties can be described by a bottom reflection coefficient RB, and surface reflection coefficient RS. Two methods for estimating reflection coefficients are used in this research. The first, the ratio method, is based on the variations of the Green's function with depth utilizing the ratio of the wavenumber spectra at two depths. The second, the pole method, is based on the wavenumbers of the modal peaks in the spectrum at a particular depth. A method to invert for sound speed and density is also examined. Estimates of RB and RS based on synthetic data by the ratio method were very close to their predicted values, especially for higher frequencies and longer apertures. The pole method returned less precise estimates though with longer apertures, the estimates were better. Using experimental data, results of the pole method as well a geoacoustic inversion technique based on them were mixed. The ratio method was used to estimate RS based on the actual data and returned results close to the predicted phase of p. / by Alexander Conrad. / Vita. / Thesis (M.S.C.S.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.