The primary purpose of the research presented is to study solar variations in extremely low frequency (ELF) propagation parameters using Schumann resonance (SR) data from our irregular observations carried out in the East Carpathian mountains. The natural electromagnetic ELF fields in the Earth-ionosphere cavity (the global resonator) are strongly dependent on its resonance and propagation properties as well as on the global thunderstorm activity. Thus a determination of the global resonator parameters from Schumann resonances needs information about such signal properties, which depend only on physical conditions of the Earth-ionosphere cavity. To seek such signal properties, we consider the two-dimensional telegraph equation (TDTE) approach for describing propagation of ELF electromagnetic waves in a two-dimensional spherical transmission line model of the Earth-ionosphere cavity. We have set up a model consisting of a network of finite, homogeneous, one-dimensional transmission lines covering the sphere; with the square root dependence of the attenuation rate from frequency as a sufficient model for the study of the solar influence on global properties of the Earth-ionosphere cavity. Using this model, we have constructed useful formulae and algorithms connecting the observed parameters of Schumann resonances with the attenuation rate. This enables us to study the solar influence on the attenuation rate from diurnal observations of the NS-magnetic component of the ELF field measured at one station. As the measurements were carried out during both the minimum and the maximum of the solar cycle 23, we present in the work of Ku$l$ak et al. <2003> evidence for a change in the ELF attenuation rate in the Earth-ionosphere cavity with solar activity.