## 3 Analysis of Temporal and Spatial Distribution Characteristics of Landslide Surge  
### Analysis of Head Wave Velocity  
The surge waves generated by the landslide are mostly low-frequency waves, and the experimental process is hampered by a variety of external factors, so it is necessary to carry \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factors** & **MLS1** & **MLS2** & **MLS3** & **MLS4** & **MLS5** \\ \hline Water depth (m) & 1.38 & 1.38 & 1.38 & 1.38 & 1.38 \\ Volume (m\({}^{3}\)) & 0.50 & 1.00 & 3.00 & 4.00 & 5.65 \\ Width of landslide (m) & 4.00 & 4.00 & 4.00 & 4.00 & 4.00 \\ Thickness of landslide (m) & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 \\ Length of landslide (m) & 0.63 & 1.25 & 3.75 & 5.00 & 7.06 \\ Velocity of landslide (m/s) & 5.83 & 5.83 & 5.83 & 5.83 & 5.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test program. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Testing Point** & \begin{tabular}{c} **Cross-Sectional** \\ **Area (m\({}^{2}\))** \\ \end{tabular} & \begin{tabular}{c} **Water Depth** \\ **(m)** \\ \end{tabular} & \
\begin{tabular}{c} **Diversion** \\ **(Yes/No)** \\ \end{tabular} &
\begin{tabular}{c} **River Course** \\ **Curvature** \\ \end{tabular} \\ \hline h01 & 2.79 & 1.27 & No & 27.03 \\ h02 & 4.54 & 1.25 & Yes & 12.58 \\ h03 & 2.29 & 1.25 & No & 27.28 \\ h04 & 2.79 & 1.33 & No & 4.37 \\ h05 & 2.72 & 1.31 & No & 8.26 \\ h06 & 2.80 & 1.35 & No & 31.96 \\ h07 & 3.08 & 1.24 & No & 1.73 \\ h08 & 2.83 & 1.28 & No & 84.58 \\ h09 & 1.69 & 0.79 & No & 7.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: River course characteristic parameters at nine testing points. Figure 2: Layout of wave gauges. out low-pass filtering on the wave height curve. In order to study the influence of river course characteristics on wave velocity, the test data with volume of 1.00 m\({}^{3}\) are analyzed; the time of occurrence of the head wave is shown in Figure 3. An analysis of Figure 3. shows that the relationship between the time of head wave occurrence and the distance change of the nine testing points along the river is close to a straight line. This finding is consistent with the traditional wave theory that the wave velocity does not change when the wave propagation medium is stable. However, at testing point h09, which is located in the end of the curved area, there is a phenomenon of lag in the time of the head wave occurrence. The path of the wave propagation changes due to the curved area, thus increasing the distance that the head wave propagates from testing point h08 to h09. The propagation distance is more than 3 m spacing, set when arranging the testing point, so the head wave velocity still does not change during the propagation of the wave. The relationship between the time of head wave occurrence and the distance from the landslide follows the formula \(t=as+b\). Solving for the parameters of the fitting curve \(a\), \(b\), the formula fits the relationship between \(t\) and \(s\), so the reciprocal of \(a\) is the wave velocity studied, which is 2.62 m/s for this case. In order to investigate whether the head wave velocity changes under different volumes, the fitting curve of the time of head wave occurrence was calculated. It refers to five groups of tests, as shown in Figure 4. The five groups of tests in the graph have a high degree of overlap in the time of head wave occurrence at each testing point, indicating that the volume has no effect on the wave velocity of the landslide surge. As a result, the wave velocity curves of each group of tests were fitted to obtain the values of the fitted curves of each group of tests, \(a\) and \(b\). The maximum value of \(b\) is 0.06, which is close to 0; it is in consistent with the predetermined location of the initial testing point where the head wave occurs at the testing point h01. The wave velocity of each group of tests can be obtained after taking the reciprocal of the parameter \(a\), and the wave velocity ranges between 2.54 m/s and 2.66 m/s.