On the travel time tomography problem in 3D
Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect...
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Gespeichert in:
| Autor*in: |
Klibanov, Michael V. [verfasserIn] |
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| Format: |
Artikel |
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| Erschienen: |
2019 |
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| Anmerkung: |
© 2019 Walter de Gruyter GmbH, Berlin/Boston |
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| Übergeordnetes Werk: |
Enthalten in: Journal of inverse and ill-posed problems - De Gruyter, 1993, 27(2019), 4 vom: 16. Juli, Seite 591-607 |
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| Übergeordnetes Werk: |
volume:27 ; year:2019 ; number:4 ; day:16 ; month:07 ; pages:591-607 |
| Links: |
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| DOI / URN: |
10.1515/jiip-2019-0036 |
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OLC2141745497 |
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| 520 | |a Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator. | ||
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10.1515/jiip-2019-0036 doi (DE-627)OLC2141745497 (DE-B1597)jiip-2019-0036-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Klibanov, Michael V. verfasserin aut On the travel time tomography problem in 3D 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2019 Walter de Gruyter GmbH, Berlin/Boston Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator. Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 27(2019), 4 vom: 16. Juli, Seite 591-607 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:27 year:2019 number:4 day:16 month:07 pages:591-607 https://doi.org/10.1515/jiip-2019-0036 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 27 2019 4 16 07 591-607 |
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10.1515/jiip-2019-0036 doi (DE-627)OLC2141745497 (DE-B1597)jiip-2019-0036-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Klibanov, Michael V. verfasserin aut On the travel time tomography problem in 3D 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2019 Walter de Gruyter GmbH, Berlin/Boston Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator. Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 27(2019), 4 vom: 16. Juli, Seite 591-607 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:27 year:2019 number:4 day:16 month:07 pages:591-607 https://doi.org/10.1515/jiip-2019-0036 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 27 2019 4 16 07 591-607 |
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10.1515/jiip-2019-0036 doi (DE-627)OLC2141745497 (DE-B1597)jiip-2019-0036-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Klibanov, Michael V. verfasserin aut On the travel time tomography problem in 3D 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2019 Walter de Gruyter GmbH, Berlin/Boston Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator. Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 27(2019), 4 vom: 16. Juli, Seite 591-607 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:27 year:2019 number:4 day:16 month:07 pages:591-607 https://doi.org/10.1515/jiip-2019-0036 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 27 2019 4 16 07 591-607 |
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Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator. © 2019 Walter de Gruyter GmbH, Berlin/Boston |
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Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator. © 2019 Walter de Gruyter GmbH, Berlin/Boston |
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Abstract Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables are used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator. © 2019 Walter de Gruyter GmbH, Berlin/Boston |
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