Penetration characteristics of VLF wave from atmosphere into lower ionosphere

The factors affecting the reflection and transmission coefficient of the ionosphere have been analyzed. These factors include wave frequency, incident angle, geomagnetic inclination, electron density and collision frequency in the ionosphere. The ionosphere refractive index is also analyzed. The ionosphere above 70 km is considered to be homogeneous and anisotropic, and the reflection and transmission coefficient matrix is calculated using matrix method. Simultaneously the Booker quartic equation is solved to get the refractive index in the ionosphere. The results show that when the wave frequency is higher, it is easier to penetrate into the ionosphere from its bottom boundary and the propagation attenuation in the ionosphere is smaller. TE (traverse electric) wave and TM (traverse magnetic) wave can both penetrate into the ionosphere with a small incident angle, while TE wave can hardly transmit into the ionosphere when the incident angle is large. The transmission coefficient decreases as the geomagnetic inclination increases. TE and TM wave cannot penetrate into the ionosphere at magnetic equator. When the electron collision frequency is higher, it is easier for VLF wave to penetrate into the ionosphere and the attenuation of ordinary wave is weaker, which may be caused by the energy transportation between the waves and the particles. The ordinary (O) wave experiences severer attenuation than extraordinary (X) wave, and X wave is a penetration mode whereas O wave is a non-penetration mode in the ionosphere. All the results indicate that VLF wave with higher frequency is easier to penetrate into the ionosphere and to be recorded by the satellites at high latitude. It is hard for ULF and the lower frequency VLF wave to transmit into the ionosphere directly for the severe reflection and attenuation. It may transmit into the ionosphere with a small incident angle due to the nonlinear effect, for example, the interaction between the waves and the particles or cross modulation, and then propagate along the whistle duct with small attenuation. This work may be a preliminary theoretical exploration for the future calculation on the response of ground based VLF artificial transmitter in the ionosphere and further study on the seismic ionosphere coupling model.