Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information
The paper discusses theoretical aspects of solving the nonlinear inverse problem of gravimetry with uncertainty of a priori information. The a priori information is described by fuzzy sets. Special-purpose geophysical problem with uncertain a priori information is transformed into a multi-objective...
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | Russisch |
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S. Subbotin Institute of Geophysics of the NAS of Ukraine
2015
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| Online Zugang: | https://journals.uran.ua/geofizicheskiy/article/view/111148 |
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| Назва журналу: | Geofizicheskiy Zhurnal |
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Geofizicheskiy Zhurnal| _version_ | 1856543152274407424 |
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| author | Kishman-Lavanova, T. |
| author_facet | Kishman-Lavanova, T. |
| author_sort | Kishman-Lavanova, T. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-10-07T11:38:43Z |
| description | The paper discusses theoretical aspects of solving the nonlinear inverse problem of gravimetry with uncertainty of a priori information. The a priori information is described by fuzzy sets. Special-purpose geophysical problem with uncertain a priori information is transformed into a multi-objective optimization problem. One of the criteria is the membership function of a fuzzy set of possible solutions. Solution of the problem is a set of Pareto-optimal solutions, which is constructed in the parametric space applying a three-step search algorithm. The advantage of the proposed method is that it provides a possibility of including the wide range of non-probabilistic a priori information in the inversion procedure and can be applied to the solution of highly nonlinear problems. This reduces the number of direct computing problems by selective modeling of sample points in the parametric space.A test example has been given of the algorithm applied to the inverse problem of gravimetry for a single contact surface. |
| first_indexed | 2025-07-17T11:05:28Z |
| format | Article |
| id | journalsuranua-geofizicheskiy-article-111148 |
| institution | Geofizicheskiy Zhurnal |
| language | Russian |
| last_indexed | 2025-07-17T11:05:28Z |
| publishDate | 2015 |
| publisher | S. Subbotin Institute of Geophysics of the NAS of Ukraine |
| record_format | ojs |
| spelling | journalsuranua-geofizicheskiy-article-1111482020-10-07T11:38:43Z Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information Kishman-Lavanova, T. inverse problem of gravimetry indeterminate a priori information Pareto-optimal solution The paper discusses theoretical aspects of solving the nonlinear inverse problem of gravimetry with uncertainty of a priori information. The a priori information is described by fuzzy sets. Special-purpose geophysical problem with uncertain a priori information is transformed into a multi-objective optimization problem. One of the criteria is the membership function of a fuzzy set of possible solutions. Solution of the problem is a set of Pareto-optimal solutions, which is constructed in the parametric space applying a three-step search algorithm. The advantage of the proposed method is that it provides a possibility of including the wide range of non-probabilistic a priori information in the inversion procedure and can be applied to the solution of highly nonlinear problems. This reduces the number of direct computing problems by selective modeling of sample points in the parametric space.A test example has been given of the algorithm applied to the inverse problem of gravimetry for a single contact surface. S. Subbotin Institute of Geophysics of the NAS of Ukraine 2015-10-01 Article Article application/pdf https://journals.uran.ua/geofizicheskiy/article/view/111148 10.24028/gzh.0203-3100.v37i5.2015.111148 Geofizicheskiy Zhurnal; Vol. 37 No. 5 (2015); 93-103 Геофизический журнал; Том 37 № 5 (2015); 93-103 Геофізичний журнал; Том 37 № 5 (2015); 93-103 2524-1052 0203-3100 ru https://journals.uran.ua/geofizicheskiy/article/view/111148/106017 Copyright (c) 2020 Geofizicheskiy Zhurnal https://creativecommons.org/licenses/by/4.0 |
| spellingShingle | inverse problem of gravimetry indeterminate a priori information Pareto-optimal solution Kishman-Lavanova, T. Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information |
| title | Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information |
| title_full | Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information |
| title_fullStr | Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information |
| title_full_unstemmed | Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information |
| title_short | Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information |
| title_sort | pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information |
| topic | inverse problem of gravimetry indeterminate a priori information Pareto-optimal solution |
| topic_facet | inverse problem of gravimetry indeterminate a priori information Pareto-optimal solution |
| url | https://journals.uran.ua/geofizicheskiy/article/view/111148 |
| work_keys_str_mv | AT kishmanlavanovat paretooptimalsolutionsoftheinverseproblemofgravimetrywithindeterminateaprioriinformation |