## 1. Introduction

[2] The study of electromagnetic scattering by buried obstacles has attracted much attention for many years. Especially when the scatterer is located beneath the ground, the theoretical analyses can have numerous practical applications. *Howard* [1972] determined the field developed by a subterranean cylinder under external excitation. *Carin et al.* [2002] implement an algorithm to reconstruct material profiles of dielectric objects buried in a lossy Earth using transmitters and receivers placed in the air. Also, *Cui et al.* [2001] present the main issues concerning microwave subsurface sensing and provide examples relevant to the sensing of land mines.

[3] Another popular topic that pertains more to geophysics than to electromagnetics is the effect of the ionosphere on wireless terrestrial communications. At low operating frequencies the ionosphere behaves like a good conductor and therefore a waveguide is formed between it and the conducting Earth's surface [*Pappert*, 1989]. The models describing the propagation of electromagnetic waves inside this structure have been reviewed by *Cummer* [2000], while the presence of an ionized column into the aforementioned waveguide is investigated in [*Wait*, 1991]. Moreover, the radiation of a dipole between Earth and ionosphere is treated by *Barrick* [1999] with use of simplified boundary conditions.

[4] The ionosphere possesses an interesting property not extensively examined in the above references: its height varies during the transition from day to night (dusk) and vice versa (dawn) [*Uberall and Seaborn*, 1982; *Surana and Williams*, 2003]. This height variation could be seen as a natural scanner for the substrate because the ridge of the ionosphere is moving as time goes by. In particular, an image of the ionospheric discontinuity is created inside the conducting ground and could provide information about subterranean inhomogeneities. The coupling between sliding ionosphere and subterranean formations is examined in this work. The motivation is similar to that of *Nam et al.* [2007] where the magnetotelluric method is investigated.

[5] In the present study a two-dimensional, double-layered plane model is considered and an abrupt variation in ionospheric altitude is assumed. A cylindrical formation is buried inside the lossy Earth and scatters the field produced by a dipole source located between the two layers: air, ground. As the longitudinal dimensions are infinite, a study for the two-layered, parallel-plate waveguide is carried out in the first place. After the derivation of the guiding condition, the propagation constants are determined and the orthogonality of the supported modes is proved (section 3).

[6] The Green's function of the problem (for subterranean sources) is essential to proceed further to the solution. The term indicating the influence of the horizontal layers is obtained with use of spectral integrals satisfying the Helmholtz equation. The other term of the Green's function (expressing the effect of the ridge) is found by implementing the mode matching technique along the step discontinuity plane [*Mahmoud and Real*, 1975]. The elements of the constant vector of the linear system are rapidly converging spectral integrals, while the singular part of the Green's function is taken to be common for both sides of the discontinuity. The mode matching technique is utilized for the incident field as well but in this case the direct evaluation of the integrals is not possible (due to the position of the source) and thus residue theorem is employed instead (section 4).

[7] The scattering by the buried cylinder is treated with use of the method of auxiliary sources (MAS) [*Leviatan et al.*, 1983; *Uberall et al.*, 1987] which is usually applied for two adjacent regions. The scatterer itself is considered as the one region and all the remaining area as the other. The Green's function for the ridged ionosphere accompanied by ground with finite conductivity, is essential to implement the method for the cylindrical scatterer formation. To this end, a point matching technique is applied for the manipulation of the boundary conditions (section 5).

[8] Numerical results are presented concerning the scattered field measured by a receiver stationed on the Earth's surface. The measurements are taken periodically and correspond to different positions of the ionospheric discontinuity. In many cases the detection of the obstacle is possible and its location is revealed by the local maxima or minima of the curves. Several conclusions are drawn related to the behavior of the scattering field distribution for different observation points, operating frequencies, radii and conductances of the scatterer (section 6).