In this thesis we derive the convergence order of a regularized error functional for reconstructing faults from boundary measurements of displacement fields. The convergence was proved to occur as the regularization parameter converges to zero but the convergence order was unknown. This functional is used to solve an inverse problem related to a half-space linear elasticity model. We first discuss this related model and review some basic properties of this functional and then we derive the convergence order for small regularization parameters. This study is a first, but essential, step toward analyzing the convergence order of related numerical methods. The reconstruction method of faults studied in this thesis was built from a model for real-world faults between tectonic plates that occur in nature. This model was first proposed by geophysicists and was later analyzed by mathematicians who were interested in building efficient numerical methods with proof of convergence.
| Identifer | oai:union.ndltd.org:wpi.edu/oai:digitalcommons.wpi.edu:etd-theses-2378 |
| Date | 17 May 2020 |
| Creators | Jiang, Yulong |
| Contributors | Darko Volkov, Advisor |
| Publisher | Digital WPI |
| Source Sets | Worcester Polytechnic Institute |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Masters Theses (All Theses, All Years) |
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