Research on VLF Ionospheric Propagation Method Based on the Dynamic Stratification Transmission Matrix

To address the poor computational efficiency of traditional fixed-stratification methods in very low frequency (VLF) ionospheric propagation modeling, this paper proposes a dynamic stratification algorithm. First, filtering optimization is applied to the electron density, and dynamic adaptive stratification is implemented in the vertical direction. By establishing a nonlinear mapping relationship between the electron density gradient and the stratification thickness, the algorithm integrates dynamic ionospheric stratification with a hybrid regularization algorithm for the transmission matrix. Specifically, Singular Value Decomposition (SVD) and dynamic truncation techniques are employed to process the transmission matrix, effectively resolving the numerical ill-posedness in regions with abrupt ionospheric changes. This enables high-precision calculation of reflection coefficients in the 3–30 kHz frequency band. By tuning parameters such as the reference stratification thickness and adjustment factors, an optimized stratification model and an algorithm quality evaluation coefficient are obtained. The simulation results demonstrate that, compared with fixed stratification, the proposed algorithm achieves an average relative error of 4.7% for the reflection coefficient in the VLF range while improving computational efficiency by more than 50%. This provides a promising approach for efficient and high-precision prediction of VLF wave propagation.