Very-low-frequency (VLF) electromagnetic waves (3–30 kHz) are stable and attenuated, suitable for various applications in submarine communication and earthquake prediction. Very-low-frequency electromagnetic waves usually propagate in atmospheric waveguides formed between the anisotropic ionosphere at low to medium heights and the earth. However, the electromagnetic parameters of the anisotropic ionosphere at low to medium heights are very complex, making it difficult to accurately calculate and analyze the scattering characteristics of very-low-frequency electromagnetic waves. This article divides the mid to low altitude anisotropic ionosphere into fine layers, and establishes a more accurate transmission model for ultra-low-frequency electromagnetic waves in the layered structure of ionization layers by deriving the anisotropy/transmission matrix of each layer. In the comparative verification, we calculated the field strength of 17 kHz VLF electromagnetic waves within a transmission distance range of 500–1600 km based on the proposed method and compared it with statistical data collected from actual communication experiments and theoretical calculation results based on traditional ITU-R P.372-11. The results show that compared with the theoretical results based on ITU-R P.372-11, the method proposed in this paper fully considers the vertical height non-uniformity of the ionosphere, and its calculated results are more consistent with actual measurement data, with higher accuracy. Our work provides excellent guidance for the development of precise models for the propagation and prediction of extremely low-frequency electromagnetic waves, as well as a good idea for the accurate calculation of VLF electromagnetic scattering within 500–1500 km.

Short-wave communication, operating within the frequency range of 3–30 MHz, is extensively employed for long-distance communication because of its extended propagation range and robustness. The ionosphere undergoes complex transformations when influenced by the geomagnetic field, evolving into an uneven and anisotropic electromagnetic medium. This complex property makes the transmission of electromagnetic fields within the ionosphere extremely complex, posing significant challenges for accurately evaluating electromagnetic scattering phenomena. To address the aforementioned challenges, this paper proposes a new method for calculating short-wave ionospheric scattering based on a complex anisotropic multilayer medium transmission matrix. Firstly, by utilizing the characteristic changes of ionospheric electron density with height, the ionization layer is divided into multiple horizontal thin layers, each with an approximately uniform electron density, forming a multilayer horizontal anisotropic structure. Subsequently, the scattering characteristics of electromagnetic waves in the ionosphere were calculated using the transmission matrix approach. The results calculated using this method are consistent with actual measurement values and superior to traditional short-wave ionospheric transmission calculation methods.