Abstract
A new technique for simultaneous reconstruction of “gravity” and “magnetic” images of Mercury from satellite data based on the regional version of S-approximations is proposed. The mathematical statement of the inverse problem on finding the images of a planet from the data on the potential fields recorded at different times with different accuracy is reduced to solving ill-conditioned systems of linear algebraic equations (LAES) with approximate right-hand sides. Based on the analytical approximations of the Mercury’s magnetic and gravity fields determined from the solution of the ill-conditioned SLAE, the distributions of the equivalen sources on the spheres are determined. The results of the mathematical experiment on constructing the magnetic image of Mercury from the radial component of the magnetic induction vector analytically continued towards the field sources are presented.
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