## 4 Results
### Comparison of Direction Results  
We acquire the difference, \(\theta\), between the direction measurements, \(\theta_{1}\), from the two analysis methods and the actual azimuth, \(\theta_{2}\), of the cyclone center in relation to the location of YL in order to more easily compare the direction results from F-K and polarization analysis:  
\[\theta=\theta_{1}-\theta_{2}, \tag{1}\]  
A correlation coefficient \(C\) is defined as:  
\[C=\left\{\begin{array}{rl}(90-\theta)/90,&\theta\text{ is between }(0^{\circ},\;90^{\circ})\\ (\theta-90)/-90,&\theta\text{ is between }(90^{\circ},\;180^{\circ})\\ 0,&\theta\text{ is }90^{\circ}\end{array}\right., \tag{2}\]  
Figure 4: Back azimuth, black bar, and power spectral density from polarization analysis for YL and AU at four different times. (**a**) 10 March 2010 12:00; (**b**) 14 March 2010 18:00; (**c**) 15 March 2010 11:00; (**d**) 17 March 2010 12:00. Inset upper left is the PSDs for YL, black line, and AU stations, the dashed line. Inset circle is the zoom-in to show the back azimuths for YL array.  
The range of \(C\) is between \(-1\) and \(1\). After that, the correlation coefficients \(C\) obtained from the F-K and polarization analyses within 0.1-0.5 Hz are averaged.  
The F-K analysis had a high correlation with the azimuth of the cyclone center relative to the array (Figure 5), especially between 13 March and 17, when the cyclone wind speed reached typhoon level. Before 13 March, when the cyclone had low wind speeds and was far away from the array, the azimuth from the F-K analysis pointed to the South Ocean, which has high secondary microseism energy throughout the year due to less land and strong atmospheric movement. This resulted in a negative correlation coefficient. The azimuth results from the polarization analysis did not show a clear correlation with the location of the cyclone throughout the cyclone's lifetime.  
[PERSON] [13] analyzed seismic signals using a seismic array and a single station with three components and provided the azimuth estimate error:  
\[Var\{\theta\}\geq\Bigg{[}sin^{2}(\varphi)SNR\Bigg{(}1+\bigg{(}\frac{2\pi}{ \lambda}\bigg{)}^{2}3\Delta^{2}cos^{2}(\varphi)\Bigg{)}\Bigg{]}^{-1}, \tag{3}\]  
for an array with vertical elements and  
\[Var\{\theta\}\geq\Big{[}sin^{2}(\varphi)SNR\Big{]}^{-1}, \tag{4}\]  
for a single station with a three-component station, where \(SNR\) stands for the signal-to-noise ratio, \(\Delta\) is the radius of the array, \(\lambda\) is the wavelength of the incident wave, \(\theta\) is the azimuth angle from the north, and \(\varphi\) is the angle of incidence from the vertical. At this point, it is apparent that the azimuth error is smaller than that of a single station with three components.  
Overall, the F-K analysis gave better results for azimuth estimation than polarization analysis. The fact that polarization analysis used a single-station approach while F-K employed multi-stations could be the cause of this significant difference. The constraint of the array was stronger than that of a single three-component station, which led to a more accurate estimation of the direction. Additionally, at a particular signal-to-noise ratio,  
Figure 5: Correlation analysis for energy in between 0.1 and 0.5 Hz. Red: the F-K analysis results. Black: the polarization results. The error bar is the standard deviation.  
the F-K was unaffected by noise, whereas the polarization analysis was also impacted by additional polarization features [13].