The inverse problem of the gravitational field of planets as a physical problem

A key feature of the new physical method of interpretation of the Earth's gravity field is determination of the sequence of discrete characteristics of density structures - the mass moments with respect to local rectangular coordinate system. Information about these structures is extracted by s...

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Дата:2012
Автори: Tarakanov, Yu. A., Karagios, O. V.
Формат: Стаття
Мова:rus
Опубліковано: Subbotin Institute of Geophysics of the NAS of Ukraine 2012
Онлайн доступ:https://journals.uran.ua/geofizicheskiy/article/view/116576
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Назва журналу:Geofizicheskiy Zhurnal

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Geofizicheskiy Zhurnal
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spelling journalsuranua-geofizicheskiy-article-1165762020-10-07T12:02:45Z The inverse problem of the gravitational field of planets as a physical problem Tarakanov, Yu. A. Karagios, O. V. A key feature of the new physical method of interpretation of the Earth's gravity field is determination of the sequence of discrete characteristics of density structures - the mass moments with respect to local rectangular coordinate system. Information about these structures is extracted by separate portions for which purpose the data on the geometry of the gravitational field is also delivered by certain portions. At first, by solving the inverse problem one determines the mean smoothed geometric figure of the source, the normal density heterogeneity. As a two-dimensional normal heterogeneity, we choose a spherical cap, and as a three-dimensional one - a difference spherical sector and a difference of two spherical sectors. To specify a three-dimensional heterogeneity, one needs knowledge of six moments and six field elements along a great-circle arc. In the present paper we reveal the dependence of the solution to inverse problem of the potential on the number of harmonics K + 1 in Legendre series. The moments are calculated by solving the inverse problem of the potential. In the present paper we reveal the dependence of the solution to inverse problem of the potential on the number of harmonics K + 1 in Legendre series. The highest power K in these series was equal to 180, 16, 8, 4, 2. For the most difficult variant of field interpretation - spherical sectors of the Earth's inner core, the angular radii were equal to 1 °, 5 °, 15 °, 30 °, 90 °. Due to anomalies smoothing because of remoteness of the structures from the Earth's surface, the field of sectors is the same for K equal to 180, 16, 8. Therefore, to solve the inverse problem of the potential for sectors with linear radius equal to 1215 km, it is sufficient to measure only nine harmonics. The errors in computing the moments from six field elements are smaller by a factor of 100 than those found from three field elements. It was previously shown that the errors of the determining the moments of mantle structures by six elements are smaller by a factor of 10. To determine the geometric shape and size of the inner core sectors it is not necessary to launch a race after measurements of a large number of spherical harmonics in models of the Earth's gravity field. Subbotin Institute of Geophysics of the NAS of Ukraine 2012-02-01 Article Article application/pdf https://journals.uran.ua/geofizicheskiy/article/view/116576 10.24028/gzh.0203-3100.v34i1.2012.116576 Geofizicheskiy Zhurnal; Vol. 34 No. 1 (2012); 32-49 Геофизический журнал; Том 34 № 1 (2012); 32-49 Геофізичний журнал; Том 34 № 1 (2012); 32-49 2524-1052 0203-3100 rus https://journals.uran.ua/geofizicheskiy/article/view/116576/110612 Copyright (c) 2020 Geofizicheskiy Zhurnal https://creativecommons.org/licenses/by/4.0
institution Geofizicheskiy Zhurnal
collection OJS
language rus
format Article
author Tarakanov, Yu. A.
Karagios, O. V.
spellingShingle Tarakanov, Yu. A.
Karagios, O. V.
The inverse problem of the gravitational field of planets as a physical problem
author_facet Tarakanov, Yu. A.
Karagios, O. V.
author_sort Tarakanov, Yu. A.
title The inverse problem of the gravitational field of planets as a physical problem
title_short The inverse problem of the gravitational field of planets as a physical problem
title_full The inverse problem of the gravitational field of planets as a physical problem
title_fullStr The inverse problem of the gravitational field of planets as a physical problem
title_full_unstemmed The inverse problem of the gravitational field of planets as a physical problem
title_sort inverse problem of the gravitational field of planets as a physical problem
description A key feature of the new physical method of interpretation of the Earth's gravity field is determination of the sequence of discrete characteristics of density structures - the mass moments with respect to local rectangular coordinate system. Information about these structures is extracted by separate portions for which purpose the data on the geometry of the gravitational field is also delivered by certain portions. At first, by solving the inverse problem one determines the mean smoothed geometric figure of the source, the normal density heterogeneity. As a two-dimensional normal heterogeneity, we choose a spherical cap, and as a three-dimensional one - a difference spherical sector and a difference of two spherical sectors. To specify a three-dimensional heterogeneity, one needs knowledge of six moments and six field elements along a great-circle arc. In the present paper we reveal the dependence of the solution to inverse problem of the potential on the number of harmonics K + 1 in Legendre series. The moments are calculated by solving the inverse problem of the potential. In the present paper we reveal the dependence of the solution to inverse problem of the potential on the number of harmonics K + 1 in Legendre series. The highest power K in these series was equal to 180, 16, 8, 4, 2. For the most difficult variant of field interpretation - spherical sectors of the Earth's inner core, the angular radii were equal to 1 °, 5 °, 15 °, 30 °, 90 °. Due to anomalies smoothing because of remoteness of the structures from the Earth's surface, the field of sectors is the same for K equal to 180, 16, 8. Therefore, to solve the inverse problem of the potential for sectors with linear radius equal to 1215 km, it is sufficient to measure only nine harmonics. The errors in computing the moments from six field elements are smaller by a factor of 100 than those found from three field elements. It was previously shown that the errors of the determining the moments of mantle structures by six elements are smaller by a factor of 10. To determine the geometric shape and size of the inner core sectors it is not necessary to launch a race after measurements of a large number of spherical harmonics in models of the Earth's gravity field.
publisher Subbotin Institute of Geophysics of the NAS of Ukraine
publishDate 2012
url https://journals.uran.ua/geofizicheskiy/article/view/116576
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