An improved 3D numerical ray-tracing method for solving the spitze effects based on poeverlein's diagram

The Spitze phenomenon is closely related to the Earth's magnetic field, and characterizes high-frequency (HF) rays propagating in the ionosphere. Specifically, when the reflection conditions are satisfied, HF rays are reflected perpendicular to the Earth's magnetic field. Studying the HF rays reflected from the Spitze region is important to indirectly learn about the ionosphere magnetic properties. The 3D numerical ray-tracing method is a widely used HF rays inversion technique. However, the conventional 3D Haselegrove numerical ray-tracing method can not trace the ordinary rays in the Spitze region back to the ground. Therefore, we improved the conventional ray-tracing method based on Poeverlein's diagram. The improved method can change the ordinary rays' propagation directions when they travel very close to the Spitze reflection point. In this way, the ordinary rays' propagation interruption caused by the Spitze can be eliminated. An example showing the ordinary and extraordinary rays traced by the conventional and improved ray-tracing methods under the quiet ionosphere is provided to validate the improvement. In addition, three disturbed ionospheric backgrounds with large-scale, medium-scale, and small-scale TIDs are designed to simulate various HF rays for further validation. The simulation results show that the Spitze exists in the quiet and disturbed ionosphere, and the improved ray-tracing method can properly solve the Spitze effects on the traced ordinary rays.