Numerical methods for gravity inversion, synthetic aperture radar, and travel-time tomography
"Inverse problems have many applications. In this thesis, we focus on designing and implementing numerical methods for three inverse problems: gravity inversion, synthetic aperture radar, and travel-time tomography. We present extensive numerical examples to demonstrate that these algorithms are stable and efficient. In Chapter 2, low-rank approximation is incorporated into a local level-set method for gravity inversion. This change helps to reduce the computational time of the mismatch gravity force term on the boundary, and reduces the computational complexity from O(N3 ) to O(N2 ) in 2D and from O(N5 ) to O(N4 ) in 3D. Many numerical results show that the locations of unknown objects are accurately captured by this low-rank level-set method. In Chapter 3, both the wave equation and Radon transform are carried out as an approach to the synthetic aperture radar problem. The wave-equation-based method includes harmonic extension at terminal time, solving the wave equation backward using a perfectly matched layer, and Neumann iteration. These two methods provide comparable results and help to prove that a curved flight path is no better than a straight one. In Chapter 4, we implement the finite element method as a penalization-regularization-operator splitting method for travel-time tomography based on the eikonal equation. Both the travel time and slowness are recovered with this algorithm in both 2D and 3D. Finally, Chapter 5 contains our conclusions."--Page ii.
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- In Collections
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Electronic Theses & Dissertations
- Copyright Status
- In Copyright
- Material Type
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Theses
- Authors
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Gao, Qinfeng
- Thesis Advisors
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Qian, Jianliang
- Committee Members
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Cheng, Yingda
Chiu, Chichia
Tang, Moxun
Zhou, Zhengfang
- Date
- 2017
- Subjects
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Tomography--Mathematical models
Inverse problems (Differential equations)--Numerical solutions
Gravity--Mathematical models
Inverse synthetic aperture radar
Mathematical models
- Program of Study
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Applied Mathematics - Doctor of Philosophy
- Degree Level
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Doctoral
- Language
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English
- Pages
- viii, 78 pages
- ISBN
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9781369746150
1369746156
- Embargo End Date
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Indefinite
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