Geophysical research: article

I.E. Stepanova 1 A.M. Salnikov 1,2 T.V. Gudkova 1 A.V. Batov 1,2 A.V. Shchepetilov 3
1 Sсhmidt Institute of Physics of the Earth of the Russian Academy of Sciences 2 Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences 3 Lomonosov Moscow State University,
Journal: Geophysical research
Tome: 24
Number: 2
Year: 2023
Pages: 58-83
UDK: 550.8, 523.43
DOI: 10.21455/gr2023.2-4
Full text
Keywords: regularization method, analytical continuation, time-dependent integral representation
Аnnotation: Using a combined approach, analytical models of the magnetic field of Mars are constructed based on satellite data measured by the MAG magnetometer of the American MAVEN mission in the landing area of the Zhurong rover of the Chinese Tianwen-1 mission. A new method for interpreting Mars remote sensing data is described, which includes the construction of regional modified S-approximations taking into account ellipticity (for an ellipsoid of revolution) and local (flat) approximations of a non-stationary field, which is the solution of some parabolic-type equation with constant coefficients. The main provisions of the method of linear integral representations are developed as applied to time-dependent differential operators, which is of fundamental importance in solving many inverse problems of mathematical geophysics. The time-dependent magnetic field of Mars has been studied in the Cartesian coordinate system, so far only a local version of a new technique for solving inverse problems of magnetic exploration has been developed due to the complexity of the problem of analytical description of a non-stationary field on a global scale. The results of a mathematical experiment on the analytical continuation of the magnetic field of Mars from the orbit towards the sources are presented. The new technique is based on the construction of a modified S-approximation in the regional version for a given set of observation points in three-dimensional space and given initial approximations to unknown weight functions. According to the found distribution of sources equivalent in external magnetic field on the surface of several generalized spheres, the approximated field is analytically continued into a certain region of three- dimensional space. In this case, the value of the solution quality index is calculated, which is the ratio of the Euclidean norm of the difference between the theoretical values of the field and the values obtained as a result of the approximation, to the norm of the field itself. The weight functions are changed in accordance with the rule defined by the researcher, the process is repeated until the required accuracy is achieved. The calculated values of the magnetic field in a certain region of three-dimensional space are taken as the initial and boundary values of the time-dependent vector function, which is the solution of a three-dimensional homogeneous (or inhomogeneous) parabolic equation. For such a vector-function, a variational problem is posed, within the framework of the local version of the method of integral representations in three-dimensional space with time dependence, to find the sources of masses. The sources can be distributed either on a family of planes of three-dimensional space, if the initial-boundary value problem for the heat equation is considered, or on some discrete network of points, if it is assumed that the vector function is a solution of a parabolic type equation in the entire space.
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