# Towards Automatic Landslide-Quake Identification Using a Random Forest Classifier
## 2 Study Materials and Method
### Automatic Classifier Using the Random Forest Algorithm
#### 2.2.2 Time-Domain Attributes  
[PERSON] et al. [18] developed an algorithm to automatically detect and characterize seismic waveforms in association with episodic tremor and slip events in northern Cascadia. Two significant attributes in the time domain were utilized to determine the pattern of a waveform: moving average (MA) and scintillation index (SI). MA is a common smoothing process to spot trends in seismic signals. Before calculating the value of MA, a fourth-order band-pass Butterworth filter was applied with a frequency band of 1-5 Hz to best manifest landslide signals [19]. The filtered seismic records were normalized by the mean of the eight largest amplitudes to avoid the presence of anomalies. In this study, the mean of the absolute amplitudes of all samples within a specific time window was calculated. That calculated mean value is assigned at the center point of the time window. The moving average can be expressed as:  
\[i\mu_{|y|}=\left(\sum\
olimits_{j=i-(t-1)/2}^{j=i+(t-1)/2}\bigl{|}y(j)\bigr{|} \right)/N, \tag{1}\]  
where \(i\mu_{|y|}\) is the value of the MA for a time window centered at point \(i\), \(y\) is the absolute amplitude within the time window, \(|y(j)|\) is the absolute value of the normalized amplitude at point \(j\), \(N\) is the total number of samples within the time window, and \(t\) is the length of the time window. Conventionally, the length of a time window has to be long enough to catch the trend of the variation in waveform. In our case, the length of the time window was 60 s, and a total of 1200 of data points measured at a sample rate of 20 data points per s were in a time window. Figure 5 shows the moving average functions for three classes of seismic events. For the moving average function, the signals are obviously smooth, the case of background noise shows only small fluctuation, and the mean value of the signal is greater than the two other cases. In contrast, the earthquake and landslide signals are significantly higher during the event, and outside of the duration, they are depressed. For earthquakes, the noise level in the moving average function is below 0.1, and the MA value during the event is higher than 1.0. For landslides, the noise level in the moving average function ranges between 0.5 and 1.0, and the MA value during the event can be higher than 1.5. The fluctuation of the moving average function of the earthquake is significantly larger than that of the landslide. In the presentation of [PERSON] et al. [18], four significant attributes were found to be important in association with the characteristics of the MA function: the mean (\(\mu\)MA), the standard deviation (\(\sigma\)MA), the moving average ratio (MAR), and the ratio of the mean value to the standard deviation (\(\sigma\)MA/\(\mu\)MA), which can be expressed as:  
\[\mu\text{MA}=\left(\sum\
olimits_{i=1}^{K}i\mu_{|y|}\right)/K, \tag{2}\]  
\[\sigma\text{MA}=\sqrt{\frac{\sum\
olimits_{i=1}^{K}\left(i\mu_{|y|}-\mu\text{ MA}\right)^{2}}{K}}, \tag{3}\]  
\[\text{MAR}=\frac{\text{MA}_{max}}{\mu\text{MA}}, \tag{4}\]  
where \(K\) is the total number of the data points, and \(\text{MA}_{max}\) is the maximum of the MA function. The scintillation index (SI), a parameter proposed by [PERSON] and [PERSON] [20] to measure the intensity of energy bursts of radio waves in the ionosphere, was used to characterize the intensity of the seismic signals. SI can be defined as the square root of the standard deviation of a seismic signal, and it sensitively increases for variation of the signal intensity during earthquake or landslide events. The expression of SI in mathematics can be written as:  
\[\mathrm{SI}_{i}=\sqrt{\left[\frac{\left(i\mu_{[y]^{2}}-i\mu_{[y]}^{2}\right)} {i\mu_{[y]}^{2}}\right]}, \tag{5}\]  
where \(i\mu_{[y]^{2}}\) is the MA value of the square of the absolute amplitude.