LTE for Railways (LTE-R) is a next-generation communication network dedicated to railway services, enabling high-speed, reliable, and intelligent communications to ensure safety and efficiency for rail passengers. The wireless channel between the train and the ground is a key challenge in network design and optimization. The high-speed train (HST) and its surrounding scenarios bring nonstationarity and unique radio propagation characteristics to the HST channel. A comprehensive and in-depth analysis of channel characteristics is the basis of channel modeling. In this paper, based on the measurement-validation ray tracing (RT) simulator, the quasi-stationary intervals are presented first to reasonably quantify channel statistical parameters. Next, the time-varying multidimensional spectra of the channels in three typical HST scenarios are shown, including the power delay profile (PDP), the arrival/departure angular spectrum, and the Doppler spectrum. Moreover, the corresponding channel characteristic parameters are extracted, such as the root-mean-square (RMS) delay spread, angular spread, and Doppler spread. Based on multidimensional channel characteristic analysis, combined with multipath geometric parameters provided by RT, we extract significant scatterers and mine key physical factors that affect radio propagation in HST scenarios. This work lays a solid foundation for accurate time-varying HST channel modeling.