# Towards Automatic Landslide-Quake Identification Using a Random Forest Classifier
## 2 Study Materials and Method
### Automatic Classifier Using the Random Forest Algorithm
#### 2.2.3 Frequency-Domain Attributes  
We collected the seismic signals of ten earthquakes (three in M3.0-3.9, four in M4.0-4.9, and three in M5.0-5.9) from the MASB station to calculate their frequency spectrum. Since these seismic signals reflect different earthquake magnitudes, we normalized each spectra to the range of 0-1.0 by its maximum value of amplitude. Subsequently, the normalized spectrum were used to calculate the average spectra for earthquakes. The above-mentioned calculation approach was used to obtain the spectrum for landslide-quakes and background noise. Through this normalization, the average frequency spectrum display the energy distribution in the frequency domain for different classes of seismic events, and eliminate the influence of magnitude/size and distance. Figure 6 shows the frequency spectra for the earthquake, landslide, and noise cases, and each one is the average of 10 samples normalized by its maximum. At higher frequency (\(>1\) Hz), the energy of an earthquake is greater than that of a landslide, but the situation is reversed at lower frequency (\(<1\) Hz). Spectral  
Figure 5: Moving average (MA) and scintillation index (SI) functions for the three commonly observed seismic events: (a) earthquakes; (b) landslides; (c) background noise. energies from different frequency ranges were calculated to characterize the distribution of energy related to a seismic event as the attributes in the frequency domain. For the seismic data of the BATS, the frequency passband is from 0.00833 Hz to 8 Hz. Any records beyond that frequency limit might be distorted, so the upper frequency limit is 8 Hz for the calculation of attributes in the frequency domain. [PERSON] [21] proposed a method for the estimation of power spectral density (PSD). The energy distribution along a frequency can be obtained by a continuous waveform through fast Fourier transform. In this study, the frequency difference was 0.01 Hz, the length of the time window was 5 s, and the overlap was 50%. To eliminate the effect of geometric spreading between the epicenter and the seismic station, the PSD was normalized by its maximum. For landslide analysis, [PERSON] et al. [22] and [PERSON] et al. [23] proposed frequency ranges of 0.02-0.05 Hz and 1-5 Hz as suitable; therefore, seven frequency ranges were chosen for the BATS data according to the limits of the passband as follows: (1) 0.02-0.05 Hz, (2) 0.05-0.1 Hz, (3) 0.02-0.1 Hz, (4) 0.1-1 Hz, (5) 1-5 Hz, (6) 5-8 Hz, and (7) 1-8 Hz. Due to the greater energy for earthquake cases at higher frequency, five ratios of PSD among different frequency ranges were chosen for attributes in the frequency domain as follows: (1) 0.02-0.1 Hz/1-8 Hz, (2) 0.02-0.05 Hz/1-5 Hz, (3) 0.05-0.1 Hz/1-5 Hz, (4) 0.02-0.05 Hz/5-8 Hz, and (5) 0.05-0.1 Hz/5-8 Hz. In Figure 5, the energy distribution patterns of seismic signals for the three classes are quite different. In addition to the PSD values for the different frequency ranges, the PSD ratios were also used to reflect the difference of energy distribution of seismic signals in the frequency domain. [PERSON] et al. [14] used frequencies in the range of a spectral peak as attributes of classification, including the peak frequency (F_max), the highest frequency (F_high), and the lower frequency (F_low). The determination of the above frequencies can be used as an example, as shown in Figure 6. First, the peak frequency of a frequency spectrum, calculated from a waveform through fast Fourier transformation, is the frequency of the spectral peak. A threshold value is determined by multiplying the peak value of the spectrum by 0.2; then the higher and lower frequencies of the intersection of the  
Figure 6: Average spectra of 30 seismic signals induced by 10 landslide-quakes, 10 earthquakes, and 10 noise signals. All seismograms are taken from the vertical components of the stations listed in Figure 1.  
frequency and the threshold value are the highest and lowest frequencies, respectively.