On Constructing Analytical Models of the Magnetic Field of Mercury from Satellite Data

A new method is proposed for analytical description of the magnetic field of Mercury from the data of satellite missions based on the local and regional versions of the linear integral representation method. The inverse problem on finding the sources of the field is reduced to solving ill-conditioned systems of linear algebraic equations with an approximately given right-hand side. The charts of the isolines of the z-component of the magnetic induction vector in the Cartesian coordinate system rigidly connected with the planet, as well as the regional S-approximation of the field radial component are plotted. The results of the mathematical experiment on analytic continuation of the magnetic field towards the sources are presented.