Numerical calculation of electromagnetic waves in an anisotropic multilayered medium

Abstract

An improved matrix method of calculating the solutions of wave equations in a horizontally stratified anisotropic medium is described. An inhomogeneous medium is divided into a number of thin horizontal and homogeneous slabs. The solutions of a differential equation with constant coefficients in each slab are connected by applying the boundary conditions, and the wave fields are given as the power series expansion of wave fields. In calculating the wave fields, a matrix is divided into two matrices for two independent solutions and Gram‐Schmidt orthogonalizing process is applied to prevent numerical swamping. Comparisons are made between this and other full wave methods regarding step size and computer time, and this method is found to be more efficient than the full wave method especially at high frequency wave fields. The magnetoionic modes separated from the resultant wave are shown for a model ionosphere.

The numerical simulation on ionospheric perturbations in electric field before large earthquakes

“…At 10 kHz, the frequency is so high that the ions can be ignored, which means the calculated results must be the same, whether using the VLF model or the ULF model. Figure 4 shows the simulated results at 10 kHz by using Nagano's VLF model (Nagano et al, 1975), which are consistent with the results from our new ULF model. It can be seen that the solid lines (ULF model) totally super- Fig.…”

“…To avoid the numerical swamping resulted from the loss of medium, the orthogonal scale down process developed by Nagano et al (1975) is also used in this study. Because Nagano's code is only used to solve the electromagnetic field of the VLF wave, the matrix M is simplified as expression (6).…”

“…The waves excited by earthquakes are mainly at a ULF band, so the effect of the ion cannot be ignored as that at a VLF band. In this paper, a model considering the effect of ions is constructed based on the VLF wave propagation code of Nagano et al (1975) to study the effects with different backgrounds and variations of the ionospheric ion and electron densities on the electromagnetic field at the topside ionosphere when a ULF wave penetrates from the bottom of the ionosphere. And two earthquakes in equatorial and mid latitudes studied by Zhang et al (2014) are selected to simulate the abnormal characteristic of electromagnetic field change due to different background…”

“…As for the seismo-ionospheric coupling theory, Nagano et al (1975Nagano et al ( , 1993) had constructed a model using the full wave method to study the VLF electromagnetic waves (3-30 kHz) penetrating into the ionosphere. The waves excited by earthquakes are mainly at a ULF band, so the effect of the ion cannot be ignored as that at a VLF band.…”

Estimation of collision frequency in the upper D and E regions from LF wave by means of a rocket experiment.

“…(1) for a whistler mode above an altitude of 90km, we will present a result of the full wave technique which is capable of separating each characteristic mode from the total field (NAGANO et al, 1975). Figure 8 shows the intensity variations of the whistler mode wave calculated by both methods for the ionospheric models which are shown in Figs.…”