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

Abstract

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.