## 4 Results and Discussion
### Dynamic Processes Determined by PFH Inversion  
PFH inversion is based on the assumption that a landslide is a block having a constant mass \(m\). With the constant landslide mass, the landslide momentum (\(m\times v\)) can be calculated by integrating the force-time function. As the Taimali landslide first slid toward the northeast, the E-component momentum increased and reached the maximum at the 24 th second (Figure 7a). After that, both the E- and N-component momentums decreased, and the E-component momentum reached zero; subsequently, the landslide turned to the west at the 37 th second (Figure 7b). The time interval between the 1 st and the 37 th seconds (09:31:34-09:32:11) can be considered the first stage of the landslide propagation (Figure 7c).  
Figure 7: Dynamic run-out direction of the Taimali landslide. (**a**) The momentum changes in the eastern direction. Notice that the start time was 09:31:34, which is the 34 th second in Figure 3. (**b**) The momentum changes in the north direction. (**c**) The three landslide propagation stages and the average velocity for each stage.  
The landslide slid toward the west for only a short time, i.e., 17 s, and turned to the east again. The time interval between the 37 th and 54 th seconds (09:32:11-09:32:28) can be considered the second stage of the landslide propagation (Figure 7c). After the 54 th second (09:32:28), the landslide continued toward the east until it stopped. Therefore, the time interval between the 54 th and 174 th seconds (09:32:28-09:34:28) can be considered the third stage of the landslide propagation. The variations of velocity in the E- and N-components did not decrease to zero at the end of landslide propagation. [PERSON] et al. [14] noted that long-period noise might accumulate with linear trends as the force is integrated in the time domain. Meanwhile, the slight fluctuations in the momentums in the third stage were possibly caused by the small landslides around the Taimali landslide. During the third stage, some small landslides might have generated weak seismic signals that affected the inversion results. Besides, the trajectories of the landslide movement could be measured from the post-event satellite images and DEM. The starting point was defined at the deepest point of the landslide source area. There were two obvious topographic turning points on the route of the landslide movement. The turning points could be considered the starting points of the second and third stages. In addition, the centroid of the deposit area in the river channel could be considered the termination point of the landslide. Eventually, the runout distances of each stage and average velocities could be calculated (Table 3).  
[PERSON] et al. [16] performed a waveform inversion using the LFH method for the Taimali landslide. To ensure the equilibrium of forces, the LFH method makes strict assumptions about the force changes during the landslide (unloading/reloading cycles). As a result, the block trajectory deduced by the LFH inversion may not completely correspond to the real terrain, but can only show the overall direction of movement. The PFH method does not confine the force changes during a landslide within certain limits, so a more detailed force-time function can be obtained, which can be used to reflect the correlation between the landslide propagation and the actual terrain. [PERSON] et al. [26] and [PERSON] [27] used a 3D discrete element method to simulate the dynamic processes of the Taimali landslide. The studies both displayed that the landslide moved toward the northeast, which coincides with the results from the PFH inversion method. Besides, [PERSON] [27] reported that the landslide turned to the west at the 40 th second, and the movement velocity exceeded 20 m/s. Although the two numerical simulations did not present the force history of the landslide, the simulated movement direction and velocity were both consistent with the results of the PFH inversion method.