Modal Propagation of High Frequency Electromagnetic Waves in Straight and Curved Tunnels Within the Earth

Abstract

Modal propagation in tunnels within the earth environment is considered for the case of rectangular and circular shaped tunnels excited by high frequency electromagnetic fields. It is shown that when the applied frequency is sufficiently high, simple forms of the modal fields exist for tunnels with rectangular cross section. The dominant modes in a circular tunnel are hybrid balanced modes in the high frequency limit. Closed form expressions for the modal attenuation rates of the dominant modes in rectangular and circular tunnels are derived and assessed against numerical solutions of the modal equations based on constant surface impedance wall assumption. The case of a curved rectangular tunnel is studied using the Airy function representation of the modal fields. Modal propagation constants in curved tunnels for different polarizations are obtained and it is shown that the tunnel curvature can drastically increase the modal attenuation. Numerical results show that the modes having perpendicular electric field to the curved walls suffer higher attenuation than those modes with the electric field parallel to the curved walls.