Exact boundary conditions of the impedance type in inverse problems of magnetotelluric and magnetovariation sounding
© Shuman V.N.
A new scheme of solving multidimentional inverse problems of deep electromagnetic sounding has been presented in the paper, which is based on the exact vector impedance identity and integrated equation of impedances along the "ground-air" boundary. Formulation of the problems follows from the definition of this boundary (the surface of scattering) in the terms of complex vector space for harmonic electromagnetic fields, given upon this surface. It means its description by unitarian (non-Eucledean) space of the second dimensionality, in which scalar product of vectors has been given. In this case exact vector impedance identity produces two independent imaginary tangential vectors which orthogonality and and equality of norms gives two scalar equations, which determine the surface of scattering (W.M. Boerner and O.A. Aboul-Atta, 1975). As a result in contrast to classical approach the "length" or norm of imaginary vectors depending on position of observation site and frequency of the field variations is being used instead of synthesized by tensor impedance or tipper anomalous magnetic field. It is essential that information on distribution of all the components of electromagnetic field, which is registered upon the Earth's surface is being used in this case. Specific features of solving the inverse problem of magnetic variational sounding on the base of integrated impedance equation with only magnetic field variations measurements are being used.