by Terry Kin-chung Lo. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaf 128). / Dedication --- p.i / Acknowledgements --- p.ii / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Outline of Thesis --- p.1 / Chapter 1.2 --- Microstrip to Slotline Transition --- p.3 / Chapter 1.3 --- Finite Difference as a Numerical Method --- p.4 / Chapter Chapter 2 --- The Method of Finite Difference in Time Domain / Chapter 2.1 --- An Introduction and Brief History --- p.1 / Chapter 2.2 --- The Methodology of FDTD --- p.11 / Chapter 2.3 --- The Yee's Algorithm --- p.13 / Chapter 2.4 --- Stability Criterion --- p.19 / Chapter 2.5 --- Interfaces Between Media --- p.21 / Chapter 2.6 --- Lattice Truncation Condition --- p.24 / Chapter 2.7 --- Error Analysis --- p.28 / Chapter 2.8 --- Implementation of Programs --- p.33 / Chapter 2.9 --- Summary --- p.35 / Chapter Chapter 3 --- Absorbing Boundary Conditions / Chapter 3.1 --- Introduction --- p.39 / Chapter 3.2 --- Mur's ABC --- p.40 / Chapter 3.3 --- Liao's ABC --- p.42 / Chapter 3.4 --- Dispersive ABC --- p.45 / Chapter 3.5 --- Comparison between Mur's ABC & Liao's ABC --- p.47 / Chapter 3.6 --- "Comparison among Mur's 1st Order ABC, Liao's ABC & DBC" --- p.51 / Chapter 3.7 --- Summary --- p.55 / Chapter Chapter 4 --- Microstrip-Slotline Transitions / Chapter 4.1 --- Introduction --- p.57 / Chapter 4.2 --- Approach --- p.59 / Chapter 4.3 --- Single Quarter-Wave Microstrip-Slotline Transitions --- p.67 / Chapter 4.4 --- Single Y-Strip-Slotline Transitions --- p.78 / Chapter 4.5 --- Shorted-Stub Y-Strip-Slotline Transitions --- p.88 / Chapter 4.6 --- Y-Strip-180°-Slotline Transitions --- p.96 / Chapter 4.7 --- Y-Strip-Y-Slot Transitions --- p.104 / Chapter 4.8 --- Y-Strip-Open-Stub-Y-Slot Transitions --- p.112 / Chapter 4.9 --- YY-Transitions --- p.120 / Chapter 4.10 --- Summary --- p.127 / Chapter Chapter 5 --- Conclusions & Future Development / Chapter 5.1 --- Conclusions --- p.129 / Chapter 5.2 --- Future Development --- p.131 / Appendix / Fortran 77 Code of Single Quarter-Wave Microstrip-Slotline Transition --- p.132

Zhang Kai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 99-102). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- The Generalized PML Theory --- p.6 / Chapter 1.1.1 --- Background --- p.6 / Chapter 1.1.2 --- Derivation --- p.8 / Chapter 1.1.3 --- Reflection Properties --- p.11 / Chapter 1.2 --- Unified Formulation --- p.12 / Chapter 1.2.1 --- "Face-, Edge- and Corner-PMLs" --- p.12 / Chapter 1.2.2 --- Unified PML Equations in 3D --- p.15 / Chapter 1.2.3 --- Unified PML Equations in 2D --- p.16 / Chapter 1.2.4 --- Examples of PML Formulations --- p.16 / Chapter 1.3 --- Inhomogeneous Initial Conditions --- p.23 / Chapter 2 --- Numerical Analysis of PMLs --- p.25 / Chapter 2.1 --- Continuous PMLs --- p.26 / Chapter 2.1.1 --- PMLs for Wave Equations --- p.27 / Chapter 2.1.2 --- Finite PMLs for Wave Equations --- p.31 / Chapter 2.1.3 --- Berenger's PMLs for Maxwell Equations --- p.33 / Chapter 2.1.4 --- Finite Berenger's PMLs for Maxwell Equations --- p.35 / Chapter 2.1.5 --- PMLs for Acoustic Equations --- p.38 / Chapter 2.1.6 --- Berenger's PMLs for Acoustic Equations --- p.39 / Chapter 2.1.7 --- PMLs for 1-D Hyperbolic Systems --- p.42 / Chapter 2.2 --- Discrete PMLs --- p.44 / Chapter 2.2.1 --- Discrete PMLs for Wave Equations --- p.44 / Chapter 2.2.2 --- Finite Discrete PMLs for Wave Equations --- p.51 / Chapter 2.2.3 --- Discrete Berenger's PMLs for Wave Equations --- p.53 / Chapter 2.2.4 --- Finite Discrete Berenger's PMLs for Wave Equations --- p.56 / Chapter 2.2.5 --- Discrete PMLs for 1-D Hyperbolic Systems --- p.58 / Chapter 2.3 --- Modified Yee schemes for PMLs --- p.59 / Chapter 2.3.1 --- Stability of the Yee Scheme for Wave Equation --- p.61 / Chapter 2.3.2 --- Decay of the Yee Scheme Solution to the Berenger's PMLs --- p.62 / Chapter 2.3.3 --- Stability and Convergence of the Yee Scheme for the Berenger's PMLs --- p.67 / Chapter 2.3.4 --- Decay of the Yee Scheme Solution to the Hagstrom's PMLs --- p.70 / Chapter 2.3.5 --- Stability and Convergence of the Yee Scheme for the Hagstrom's PMLs --- p.75 / Chapter 2.4 --- Modified Lax-Wendroff Scheme for PMLs --- p.80 / Chapter 2.4.1 --- Exponential Decays in Parabolic Equations --- p.80 / Chapter 2.4.2 --- Exponential Decays in Hyperbolic Equations --- p.82 / Chapter 2.4.3 --- Exponential Decays of Modified Lax-Wendroff Solutions --- p.86 / Chapter 3 --- Numerical Simulation --- p.93 / Bibliography --- p.99

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Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 119-124).

Ray theory plays an important role in seismic imaging and velocity model building. Although rays are the high-frequency asymptotic solutions of the wave equation and therefore do not usually capture all details of the wave physics, they provide a convenient and effective tool for a wide range of geophysical applications. Especially, ray theory gives rise to traveltimes. Even though wave-based methods for imaging and model building had attracted significant attentions in recent years, traveltime-based methods are still indispensable and should be further developed for improved accuracy and efficiency. Moreover, there are possibilities for new ray theoretical methods that might address the difficulties faced by conventional traveltime-based approaches. My thesis consists of mainly four parts. In the first part, starting from the linearized eikonal equation, I derive and implement a set of linear operators by upwind finite differences. These operators are not only consistent with fast-marching eikonal solver that I use for traveltime computation but also computationally efficient. They are fundamental elements in the numerical implementations of my other works. Next, I investigate feasibility of using the double-square-root eikonal equation for near surface first-break traveltime tomography. Compared with traditional eikonal-based approach, where the gradient in its adjoint-state tomography neglects information along the shot dimension, my method handles all shots together. I show that the double-square-root eikonal equation can be solved efficiently by a causal discretization scheme. The associated adjoint-state tomography is then realized by linearization and upwind finite-differences. My implementation does not need adjoint state as an intermediate parameter for the gradient and therefore the overall cost for one linearization update is relatively inexpensive. Numerical examples demonstrate stable and fast convergence of the proposed method. Then, I develop a strategy for compressing traveltime tables in Kirchhoff depth migration. The method is based on differentiating the eikonal equation in the source position, which can be easily implemented along with the fast-marching method. The resulting eikonal-based traveltime source-derivative relies on solving a version of the linearized eikonal equation, which is carried out by the upwind finite-differences operator. The source-derivative enables an accurate Hermite interpolation. I also show how the method can be straightforwardly integrated in anti-aliasing and Kirchhoff redatuming. Finally, I revisit the classical problem of time-to-depth conversion. In the presence of lateral velocity variations, the conversion requires recovering geometrical spreading of the image rays. I recast the governing ill-posed problem in an optimization framework and solve it iteratively. Several upwind finite-differences linear operators are combined to implement the algorithm. The major advantage of my optimization-based time-to-depth conversion is its numerical stability. Synthetic and field data examples demonstrate practical applicability of the new approach. / text

In this thesis we present the Stefan problem with two boundary conditions, one constant and one time-dependent. This problem is a classic example of a free boundary problem in partial differential equations, with a free boundary moving in time. Some properties are being proved for the one-dimensional case and the important Stefan condition is also derived. The importance of the maximum principle, and the existence of a unique solution are being discussed. To numerically solve this problem, an analysis when the time t goes to zero is being done. The approximative solutions are shown graphically with proper error estimates.

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Bibliography: leaves 264-267 / 267 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1988

The Barwon Downs Aquifer in south western Victoria has long been recognized to have extensive groundwater resources. It is also an important source of supply in Barwon Water’s drought emergency management plan. An understanding of the aquifer behaviour in relation to its recharge and withdrawal rates is essential for sustainable development. The main aim of this modelling exercise is to evaluate the present groundwater use and estimate the maximum possible extraction from the aquifer without serious consequences, and hence evaluate the groundwater management options and possible augmentation of the Barwon Downs Wellfield.

Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: Wei-Ping Huang Includes bibliographical references (p. 241-260).