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A model for the transmission of Alfvén and fast magnetosonic (FMS) modes through the ionosphere to the Earth's surface has been developed. The model is based on comprehensive analytical relations describing the interaction of magnetohydrodynamic (MHD) wave harmonic with a plane-layered system “upper ionosphere – E-layer – atmosphere – Earth”. The E-layer separating the atmosphere and topside ionosphere is supposed to be mimiced by a thin film with anisotropic height-integrate conductances. This simple model allows the isolation of the influence of individual factors on the interaction of Alfvén and FMS waves with the ionosphere, such as ionospheric conductance, wave scale, geomagnetic field inclination, ground conductivity, etc. and provides a more intuitive understanding of the physics of the process. The spatial structure of the multi-component electric and magnetic field formed in the upper ionosphere upon the incidence of either Alfvén or FMS waves has been calculated together with the amplitude of the ground response. To identify the physical nature of ultra low frequency (ULF) waves and to determine relative contributions of different MHD modes into their structure, the method of apparent impedance based on the measured ratio between the simultaneous ionospheric electric and ground magnetic fields has been proposed. The impedances of Alfven and compressional modes are to be essentially distinct. The model may be used as a simple tool for interpreting combined radar-magnetometer observations of the Pc3-5 and Pi2-3 pulsations.