Conditioning bounds for traveltime tomography in layered media
This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in thi...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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IOP Publishing
2013
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| Online Access: | http://hdl.handle.net/1721.1/80872 https://orcid.org/0000-0001-7052-5097 |
| _version_ | 1811090140692480000 |
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| author | Baek, Hyoung Su Demanet, Laurent |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Baek, Hyoung Su Demanet, Laurent |
| author_sort | Baek, Hyoung Su |
| collection | MIT |
| description | This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that traveltimes of reflected rays do not contain enough information to recover the medium in a well-posed manner, regardless of the discretization. The counterpart of the Abel transform in the case of reflected rays is a Fredholm kernel of the first kind, which is shown to have singular values that decay at least root exponentially. Kinematically equivalent media are characterized in terms of a sequence of matching moments. This severe conditioning issue comes on top of the well-known rearrangement ambiguity due to low-velocity zones. Numerical experiments in an ideal scenario show that a waveform-based model inversion code fits data accurately while converging to the wrong wave speed profile. |
| first_indexed | 2024-09-23T14:34:48Z |
| format | Article |
| id | mit-1721.1/80872 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:34:48Z |
| publishDate | 2013 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/808722022-10-01T21:45:05Z Conditioning bounds for traveltime tomography in layered media Baek, Hyoung Su Demanet, Laurent Massachusetts Institute of Technology. Department of Mathematics Baek, Hyoung Su Demanet, Laurent This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that traveltimes of reflected rays do not contain enough information to recover the medium in a well-posed manner, regardless of the discretization. The counterpart of the Abel transform in the case of reflected rays is a Fredholm kernel of the first kind, which is shown to have singular values that decay at least root exponentially. Kinematically equivalent media are characterized in terms of a sequence of matching moments. This severe conditioning issue comes on top of the well-known rearrangement ambiguity due to low-velocity zones. Numerical experiments in an ideal scenario show that a waveform-based model inversion code fits data accurately while converging to the wrong wave speed profile. Alfred P. Sloan Foundation National Science Foundation (U.S.) 2013-09-23T17:15:31Z 2013-09-23T17:15:31Z 2012-04 2012-02 Article http://purl.org/eprint/type/JournalArticle 0266-5611 1361-6420 http://hdl.handle.net/1721.1/80872 Baek, H, and L Demanet. “Conditioning bounds for traveltime tomography in layered media.” Inverse Problems 28, no. 5 (May 1, 2012): 055008. https://orcid.org/0000-0001-7052-5097 en_US http://dx.doi.org/10.1088/0266-5611/28/5/055008 Inverse Problems Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf IOP Publishing MIT web domain |
| spellingShingle | Baek, Hyoung Su Demanet, Laurent Conditioning bounds for traveltime tomography in layered media |
| title | Conditioning bounds for traveltime tomography in layered media |
| title_full | Conditioning bounds for traveltime tomography in layered media |
| title_fullStr | Conditioning bounds for traveltime tomography in layered media |
| title_full_unstemmed | Conditioning bounds for traveltime tomography in layered media |
| title_short | Conditioning bounds for traveltime tomography in layered media |
| title_sort | conditioning bounds for traveltime tomography in layered media |
| url | http://hdl.handle.net/1721.1/80872 https://orcid.org/0000-0001-7052-5097 |
| work_keys_str_mv | AT baekhyoungsu conditioningboundsfortraveltimetomographyinlayeredmedia AT demanetlaurent conditioningboundsfortraveltimetomographyinlayeredmedia |