On the Leontovich boundary condition in geoelectromagnetism

The paper is dedicated to the 70th anniversary of the formulation of the Leontovich impedance boundary condition. This boundary condition is applied in geophysics for sounding of the lithosphere and diagnostics of the magnetosphere by electromagnetic waves. The use of the Leontovich condition is shown to open new possibilities for investigating the anharmonicity of MHD oscillations of the magnetosphere. The differential impedance equation, which is derived with the aid of the Leontovich boundary condition, can prove useful in the investigation of the electroconductivity of the lithosphere by the method of inductive sounding. It is shown within the framework of a simple model that the method of the Leontovich parabolic equation makes it possible to find a correction to the Leontovich boundary condition caused by the fact that, in general, the relation between the horizontal components of an electromagnetic field is not local. It is shown that the anharmonicity of MHD oscillations of the magnetosphere coupled with the nonlocality of the boundary condition on the Earth’s surface can lead to an apparent nonlinearity of the surface impedance calculated in accordance with the classical technique of magnetotelluric sounding.