Stability and Statistical Inversion of Travel time Tomography
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914810737721344 |
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| author | Tarikere, Ashwin Zhou, Hanming |
| author_facet | Tarikere, Ashwin Zhou, Hanming |
| contents | In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12544 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability and Statistical Inversion of Travel time Tomography Tarikere, Ashwin Zhou, Hanming Differential Geometry Statistics Theory In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements. |
| title | Stability and Statistical Inversion of Travel time Tomography |
| topic | Differential Geometry Statistics Theory |
| url | https://arxiv.org/abs/2309.12544 |