A 3D TLM code for the study of the ELF electromagnetic wave propagation in the Earth's atmosphere

Abstract

The interest in the study of electromagnetic propagation through planetary atmospheres is briefly discussed. Special attention is devoted to extremely-low-frequency fields in the Earth's atmosphere for its global nature and possible applications to climate monitoring studies among others. In the Earth's case, the system can be considered as a spherical electromagnetic shell resonator in which two concentric and large conducting spheres with a radius around 6300 km are separated by a very small distance of around 100 km, the atmosphere height. A numerical solution using the Transmission Line Method is proposed. The classical spherical-coordinate description is easy to use, however, the important difference in the dimensions along the three coordinate directions causes high numerical dispersion in the results. A Cartesian scheme with equal node size for all directions is used to reduce this undesired dispersion. A pre-processing stage is the key point introduced to lessen the resulting high demand of memory and time calculation and make the solution feasible. A parallelized Fortran code together with pre- and post-processing Python programs to ease the user interface are provided with this work. Details on the Fortran code and the Python modules are included both in the paper and the source codes to allow the use and modifications by other researchers interested in electromagnetic propagation through planetary atmospheres. The program allows calculation of the time evolution of the electromagnetic field at any point in the atmosphere. It includes the possibility of considering multiple time-dependent sources and different homogeneous and inhomogeneous conductivity profiles to model different situations. Profiles to study day-night asymmetries or locally perturbed profiles which have been attributed to earthquakes in the literature are implemented, for instance.