Аннотация:A new technique for simultaneous construction of the ``gravity'' and ``magnetic'' images of Mercury from satellite data based on the regional version of the S approximation is proposed. The mathematical statement of the inverse problem of finding the images of a planet from the data on the potential fields recorded at different instants with different degrees of accuracy is reduced to solving ill-conditioned systems of linear algebraic equations (SLAE) with approximate right-hand sides. Based on the analytical approximations of the mercury magnetic and gravity fields determined from the solution of the ill-conditioned SLAE, the distributions of the equivalent 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 continued analytically to the field sources are presented.
