Quasi-analytical solutions for 2-D electromagnetic field

Assume now that both the electromagnetic field and the complex conductivity a in a gcoelectrical model are two-dimensional, i.e., they vary only along the directions X and z in some Cartesian system of coordinates, and they are constant in the y direction. In this case, repeating the derivations described above for the 3-D case, wc can obtain the following quasi-analytical expressions for a 2-D electromagnetic field  

These formulae can serve as a new effective quasi-anaJ3d ical tool in the solution of both direct and inverse 2-D electromagnetic problems. Numerical tests demonstrate that these approximations produce a very accurate result for 2-D models (Dmitriev et al., 1999). 

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