Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study
In this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inv...
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/6/837 |
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| author | Denis Byzov Petr Martyshko |
| author_facet | Denis Byzov Petr Martyshko |
| author_sort | Denis Byzov |
| collection | DOAJ |
| description | In this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inversion (creating density models of the Earth’s crust) has been developed. The algorithm can accept either regular or irregular polyhedron discretization for density model creation. The models are approximated with dense irregular grids, elements of which are polyhedrons. When performing gravity data inversion, we face three problems: topography with large amplitude, the sphericity of the planet, and a long computation time because of the large amount of data. In our previous works, we have already considered those problems separately but without explaining the details of the computation of the closed-form solution for a polyhedron. In this paper, we present for the first time a performance-effective numerical method for the inversion of gravity data based on topography. The method is based on closed-form expression for the gravity field of a spherical density model of the Earth’s crust with the upper topography layer, and provides great accuracy and speed of calculation. There are no restrictions on the model’s geometry or gravity data grid. As a case study, a spherical density model of the Earth’s crust of the Urals is created. |
| first_indexed | 2024-04-24T18:02:27Z |
| format | Article |
| id | doaj.art-481c405bf2404c678278c4ddae027ead |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T18:02:27Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-481c405bf2404c678278c4ddae027ead2024-03-27T13:53:03ZengMDPI AGMathematics2227-73902024-03-0112683710.3390/math12060837Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case StudyDenis Byzov0Petr Martyshko1Bulashevich Institute of Geophysics, UB RAS, 620016 Yekaterinburg, RussiaBulashevich Institute of Geophysics, UB RAS, 620016 Yekaterinburg, RussiaIn this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inversion (creating density models of the Earth’s crust) has been developed. The algorithm can accept either regular or irregular polyhedron discretization for density model creation. The models are approximated with dense irregular grids, elements of which are polyhedrons. When performing gravity data inversion, we face three problems: topography with large amplitude, the sphericity of the planet, and a long computation time because of the large amount of data. In our previous works, we have already considered those problems separately but without explaining the details of the computation of the closed-form solution for a polyhedron. In this paper, we present for the first time a performance-effective numerical method for the inversion of gravity data based on topography. The method is based on closed-form expression for the gravity field of a spherical density model of the Earth’s crust with the upper topography layer, and provides great accuracy and speed of calculation. There are no restrictions on the model’s geometry or gravity data grid. As a case study, a spherical density model of the Earth’s crust of the Urals is created.https://www.mdpi.com/2227-7390/12/6/837gravity data inversionspherical density model of Earth’s crust with the upper topography layergravitational field of a polyhedron |
| spellingShingle | Denis Byzov Petr Martyshko Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study Mathematics gravity data inversion spherical density model of Earth’s crust with the upper topography layer gravitational field of a polyhedron |
| title | Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study |
| title_full | Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study |
| title_fullStr | Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study |
| title_full_unstemmed | Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study |
| title_short | Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study |
| title_sort | three dimensional modeling and inversion of gravity data based on topography urals case study |
| topic | gravity data inversion spherical density model of Earth’s crust with the upper topography layer gravitational field of a polyhedron |
| url | https://www.mdpi.com/2227-7390/12/6/837 |
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