Analytical Models of the Physical Fields of the Earth in Regional Version with Ellipticity

On the Uniqueness of the Solution to the Inverse Problem of Determining the Diffusion Coefficient of the Magnetic Field Necessary for Constructing Analytical Models of the Magnetic Field of Mercury

“…For the specified field component, regional S-approximations were constructed: the components of the magnetic induction vector were represented as the sum of simple and double layers, distributed over two or more spheres. In this case, a structural-parametric approach was used: for each of the carriers its own solution vector was determined [8]. In all cases, systems of linear algebraic equations (SLAEs), to which the solution to the inverse problem of restoring the magnetic field of Mercury was reduced, were solved using the Cholesky regularization method and the improved block method for solving SLAEs (for details, see [8]).…”

“…In this case, a structural-parametric approach was used: for each of the carriers its own solution vector was determined [8]. In all cases, systems of linear algebraic equations (SLAEs), to which the solution to the inverse problem of restoring the magnetic field of Mercury was reduced, were solved using the Cholesky regularization method and the improved block method for solving SLAEs (for details, see [8]). At the same time, we assumed that Mercury is a ball of radius R 0 = 2439 km.…”

“…At the same time, we note that there are two options for modeling the surface of the planet: in the form of a plane or in the form of a sphere. The first option corresponds to local S-approximations, and the second, which is used in this work, corresponds to regional ones (see works [7,8]).…”

On Finding the Analytical Continuation of the Magnetic Field of Mars From Satellite Data Using a Combined Approach

“…Принимая во внимание изложенное, мы хотели бы протестировать на данных о магнитном поле Марса (и, возможно, усовершенствовать) предложенную нами ранее для Земли аппроксимационную конструкцию [Stepanova, Shchepetilov, Mikhailov, 2022], в которой явно или неявно присутствует время.…”