Frequency response analysis of ground wave signal transverse propagation over three-dimensional mountainous terrain

Aiming at the problem that traditional two-dimensional prediction methods cannot accurately characterize the transverse propagation effects of ground wave signals over three-dimensional mountainous terrain, this paper proposes a three-dimensional finite-difference time-domain (3D-FDTD) method combined with bilinear transform (BT) technology for accurate calculation of ground wave propagation field strength in three-dimensional mountainous terrain. The proposed method features a concise form and excellent numerical stability, and can be easily extended to electromagnetic wave propagation applications in various dispersive media. A typical two-dimensional mountain benchmark case is adopted to verify the correctness of the proposed method by taking the two-dimensional FDTD (2D-FDTD) method as the reference. Furthermore, the frequency response of ground wave signal transverse propagation over three-dimensional mountainous terrain is analyzed. The results show that the influence of three-dimensional mountainous terrain on transverse propagation increases continuously with frequency. In the very low frequency band, the diffraction effect completely dominates the propagation process, and the transverse scattering effect has negligible impact on the overall propagation characteristics of the TM dominant mode. In the low frequency band, the diffraction effect is weakened, while the transverse reflection and scattering effects begin to enhance, and the TM-TE mode conversion effect emerges. In the medium frequency band, reflection, scattering and interference effects dominate the propagation process, and the TM-TE mode conversion efficiency is significantly high. This study reveals the frequency response law of ground wave transverse propagation over three-dimensional mountains, and provides theoretical support for the design and optimization of ground wave communication and timing systems in mountainous environments.