Inversion of electrical conductivity data with Tikhonov regularization approach: some considerations
Electromagnetic induction measurements, which are generally used to determine lateral variations of apparent electrical conductivity, can provide quantitative estimates of the subsurface conductivity at different depths. Quantitative inference about the Earth's interior from e...
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| Format: | Article |
| Language: | English |
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Istituto Nazionale di Geofisica e Vulcanologia (INGV)
2003-06-01
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| Series: | Annals of Geophysics |
| Subjects: | |
| Online Access: | http://www.annalsofgeophysics.eu/index.php/annals/article/view/3427 |
| _version_ | 1818345067517050880 |
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| author | C. Manzi E. Bonomi G. P. Deidda |
| author_facet | C. Manzi E. Bonomi G. P. Deidda |
| author_sort | C. Manzi |
| collection | DOAJ |
| description | Electromagnetic induction measurements, which are generally used to determine lateral variations of apparent electrical conductivity, can provide quantitative estimates of the subsurface conductivity at different depths. Quantitative inference about the Earth's interior from experimental data is, however, an ill-posed problem. Using the generalised McNeill's theory for the EM38 ground conductivity meter, we generated synthetic apparent conductivity curves (input data vector) simulating measurements at different heights above the soil surface. The electrical conductivity profile (the Earth model) was then estimated solving a least squares problem with Tikhonov regularization optimised with a projected conjugate gradient algorithm. Although the Tikhonov approach improves the conditioning of the resulting linear system, profile reconstruction can be surprisingly far from the desired true one. On the contrary, the projected conjugate gradient provided the best solution without any explicit regularization ( a= 0) of the objective function of the least squares problem. Also, if the initial guess belongs to the image of the system matrix, Im(A), we found that it provides a unique solution in the same subspace Im(A). |
| first_indexed | 2024-12-13T16:56:29Z |
| format | Article |
| id | doaj.art-a81954ab4d004ff3919c4b2c6cb29ceb |
| institution | Directory Open Access Journal |
| issn | 1593-5213 2037-416X |
| language | English |
| last_indexed | 2024-12-13T16:56:29Z |
| publishDate | 2003-06-01 |
| publisher | Istituto Nazionale di Geofisica e Vulcanologia (INGV) |
| record_format | Article |
| series | Annals of Geophysics |
| spelling | doaj.art-a81954ab4d004ff3919c4b2c6cb29ceb2022-12-21T23:37:54ZengIstituto Nazionale di Geofisica e Vulcanologia (INGV)Annals of Geophysics1593-52132037-416X2003-06-0146310.4401/ag-3427Inversion of electrical conductivity data with Tikhonov regularization approach: some considerationsC. ManziE. BonomiG. P. DeiddaElectromagnetic induction measurements, which are generally used to determine lateral variations of apparent electrical conductivity, can provide quantitative estimates of the subsurface conductivity at different depths. Quantitative inference about the Earth's interior from experimental data is, however, an ill-posed problem. Using the generalised McNeill's theory for the EM38 ground conductivity meter, we generated synthetic apparent conductivity curves (input data vector) simulating measurements at different heights above the soil surface. The electrical conductivity profile (the Earth model) was then estimated solving a least squares problem with Tikhonov regularization optimised with a projected conjugate gradient algorithm. Although the Tikhonov approach improves the conditioning of the resulting linear system, profile reconstruction can be surprisingly far from the desired true one. On the contrary, the projected conjugate gradient provided the best solution without any explicit regularization ( a= 0) of the objective function of the least squares problem. Also, if the initial guess belongs to the image of the system matrix, Im(A), we found that it provides a unique solution in the same subspace Im(A).http://www.annalsofgeophysics.eu/index.php/annals/article/view/3427inverse problemsTikhonov regularizationprojected conjugate gradienthigh-frequency electromagnetics |
| spellingShingle | C. Manzi E. Bonomi G. P. Deidda Inversion of electrical conductivity data with Tikhonov regularization approach: some considerations Annals of Geophysics inverse problems Tikhonov regularization projected conjugate gradient high-frequency electromagnetics |
| title | Inversion of electrical conductivity data with Tikhonov regularization approach: some considerations |
| title_full | Inversion of electrical conductivity data with Tikhonov regularization approach: some considerations |
| title_fullStr | Inversion of electrical conductivity data with Tikhonov regularization approach: some considerations |
| title_full_unstemmed | Inversion of electrical conductivity data with Tikhonov regularization approach: some considerations |
| title_short | Inversion of electrical conductivity data with Tikhonov regularization approach: some considerations |
| title_sort | inversion of electrical conductivity data with tikhonov regularization approach some considerations |
| topic | inverse problems Tikhonov regularization projected conjugate gradient high-frequency electromagnetics |
| url | http://www.annalsofgeophysics.eu/index.php/annals/article/view/3427 |
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