Microlocal analysis with applications to seismic inverse problems
Abstract/Contents
- Abstract
- This thesis considers the travel time tomography problem for elastic media, particularly in the transversely isotropic setting. A pseudo-linearization argument reduces the problem to the microlocal analysis of certain operators, bringing the problem in line with certain problems in X-ray tomography and boundary rigidity studied by de Hoop, Stefanov, Uhlmann, Vasy, et al.. In this thesis, we will consider two versions of the travel time tomography problem, with the two versions using different kinds of assumptions, thus leading to the usage of different kinds of mathematical analysis. The analysis involves asking whether we can provide parametrices for certain classes of operators that are not quite elliptic. In one version of the problem, we show recovery under "global" assumptions using an operator calculus first developed by Boutet de Monvel used to provide parametrices for parabolic operators, while in the second version of the problem, we localize the problem by adding an artificial boundary; the analysis then concerns finding parametrices to certain classes of non-elliptic scattering pseudodifferential operators.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Zou, Yuzhou |
|---|---|
| Degree supervisor | Vasy, András |
| Thesis advisor | Vasy, András |
| Thesis advisor | Luk, Jonathan, (Professor) |
| Thesis advisor | Mazzeo, Rafe |
| Degree committee member | Luk, Jonathan, (Professor) |
| Degree committee member | Mazzeo, Rafe |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Yuzhou Zou. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/tp697xc0955 |
Access conditions
- Copyright
- © 2021 by Yuzhou Zou
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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