Overview of modeling approaches to the SR

Modeling the SR aims to compute the resonance spectrum and the parameters of the modes from given physical inputs. Historically, five main approaches have developed, which form a spectrum from analytical estimate to fully numerical simulation.

(a) The analytical model of a uniform cavity (normal modes) assumes an ideally symmetric spherical cavity and gives a closed-form solution — a fast estimate of the eigenfrequencies and the shape of the spectra. (b) The 2-D telegraph equation (TDTE) solves the propagation of ELF waves over the spherical surface for an arbitrary source-observer configuration. (c) FDTD (finite differences in the time domain) computes the fields on a global grid and naturally includes inhomogeneities. (d) FEM (the finite element method) works in the frequency domain and allows a 3D inhomogeneous cavity. (e) TLM (transmission line matrix) models the cavity by a network of equivalent transmission lines.

The key difference between the methods is the trade-off between speed, accuracy and the ability to capture inhomogeneities (day-night asymmetry, conductivity profile). The analytical model is the fastest but the crudest; FDTD and FEM are computationally demanding, but faithful.