## 3 Method
### Selection of \(T_{SP}\) for the Slope Deformation Acceleration  
[PERSON], [PERSON] [23] and others proposed a method using the intersection of the short-term moving average (SMA) and long-term moving average (LMA) of velocity to calculate the onset of acceleration (OOA). The calculation methods for SMA and LMA values are shown in Equation (5). Based on experience [29], when \(\mathrm{n}=3\), this represents the SMA value; when \(\mathrm{n}=7\), this represents the LMA value. When the short-term average velocity curve forms a positive cross (i.e., the short-term average velocity curve rises above and crosses the long-term average velocity curve), it indicates that the slope has entered the accelerated deformation stage, and this intersection point is defined as the OOA. If there is a negative intersection between SMA and LMA, it indicates that the slope at that location begins to undergo decelerated deformation, accompanied by a Termination of Acceleration  
Figure 3: Logarithmic curve graph.  
(TOA) point. This method enables rapid and automated identification of hazardous areas in slopes.  
\[\overline{v}=\frac{v_{t}+v_{t-1}+\ldots\ \ \ldots+v_{t-n+1}}{n} \tag{5}\]  
[PERSON] [24] and others believe that directly using the OOA point as the time of occurrence \(T\) in the reciprocal velocity method can lead to low accuracy in landslide time prediction. They suggest that a new starting point should be selected after the OOA point, but they do not provide a specific calculation method.  
During the second stage of uniform deformation in slope landslides, the measurement errors of the monitoring data follow a normal distribution. However, the measurement errors of the monitoring data during the acceleration stage do not follow a normal distribution [30; 31]. Therefore, the normal distribution confidence interval can be considered for dynamically identifying the Time of Start Point (\(T_{SP}\)) for the slope deformation acceleration. When the deformation velocity falls outside the confidence interval of the normal distribution, it indicates that the deformation velocity begins to increase significantly. The monitoring data point determined at this time is taken as the \(T_{SP}\).  
The specific methods are as follows:  
1. Data Preparation and Processing: Collect continuous deformation velocity data from slope radar monitoring and perform statistical analysis at a certain time step (for example, recording the deformation velocity at regular intervals).
2. Calculation of Normal Distribution Parameters: Calculate the expected value (\(\mu\)) and standard deviation (\(\sigma\)) of the monitoring data samples. These two parameters constitute the characteristics of the normal distribution. According to the normal distribution, approximately 68.27% of the data fall within the interval (\(\mu-\sigma,\ \mu+\sigma\)), and 95.45% of the data fall within the interval (\(\mu-2\sigma,\ \mu+2\sigma\)), and so on.
3. Confidence Interval Testing: Set a confidence level (such as the commonly used 95%) and determine the width of the corresponding confidence interval (such as 1\(\sigma\), 2\(\sigma\), or 3\(\sigma\)). During the monitoring process, check whether the deformation velocity at each monitoring time point falls within this confidence interval.
4. Identification of \(T_{SP}\): When the deformation velocity points monitored consecutively for several times do not fall within a certain confidence interval of the normal distribution and the deformation velocity shows a clear upward trend, it is thought that the deformation velocity has increased significantly. At this time, the last monitoring data point that falls outside the confidence interval is identified as the \(T_{SP}\) for the slope deformation acceleration.
5. Dynamic Updating and Confirmation: As time passes, continuously update the monitoring data and repeat the above steps until a series of deformation velocity values are found that continuously exceed the start point of the normal distribution confidence interval, confirming the existence of \(T_{SP}\).