# Inter-Story Drift Ratio Detection of High-Rise Buildings Based on Ambient Noise Recordings
## 3 Data and Processing Methods
### Polarization Analysis  
#### 3.2.1 Calculating the Polarization Parameters  
Wind noise is a wide-band signal, and the frequency range of wind-induced noise differs between studies [23]. According to [PERSON]'s conclusion, monsoons and large-scale meteorological perturbations cause ambient noise in the frequency band of 0.16-0.5 Hz, while cyclones over the oceans excite ambient noise in the frequency band of 0.5-3 Hz [24; 25]. Since the Zhonghe Building is in Shanghai, a coastal city with relatively strong winds, and is in the city center with many surrounding high-rise buildings resistant to cyclones, it is mainly affected by large-scale meteorological perturbations and only slightly affected by cyclones. Therefore, ambient noise in the frequency band of 0.3-0.6 Hz was used to conduct the research, which is slightly higher than the frequency range of monsoons and large-scale meteorological perturbations, as suggested by [PERSON]. The ambient noise in this frequency band can be considered to be generated from the main influencing factor of the Zhonghe Building. Ideally, the particle motion of a Rayleigh wave is on a vertical plane, and its trajectory is similar to an ellipse limited to a range between the instrument site and the source of ambient noise. However, due to out-of-plane contamination, the actual particle motion will not be two-dimensional and will not be on a plane. The actual particle motion can be described by an ellipsoid defined by three orthogonal semi-principal axes (\(\overset{\rightarrow}{a}_{1}\), \(\overset{\rightarrow}{a}_{2}\), and \(\overset{\rightarrow}{a}_{3}\), where \(\overset{\rightarrow}{a}_{1}\) and \(\overset{\rightarrow}{a}_{3}\) are the semi-major and semi-minor axes) (Figure 2a). In polar coordinates, these axes are defined by \(\lambda_{X}\), \(\varphi_{X}\), and \(\theta_{X}(X=1,2,3)\), where \(\lambda\), \(\varphi\) and \(\theta\) are the lengths, back azimuths (clockwise from the north), and dip angles (from the horizontal plane) of the axes, respectively (Figure 2b). Here, \(X\). is the serial number sorted by the length of the axes from largest to smallest, and it is used to specify the axes. In this way, the particle motion of the ambient noise can be fully determined by understanding the nine semi-principal axes parameters. The polarization orientation of the ellipsoids can be described by the parameters \(\varphi_{1}\) and \(\theta_{1}\)[26], but the parameter \(\varphi_{1}\) is mainly dependent on the source locations of the Rayleigh waves that dominate the microseisms [27], and it is less affected by the structure. However, it is difficult and unnecessary to determine the source of microseisms in buildings under wind loads. Therefore, \(\varphi_{1}\) is unsuitable to calculate IDRs. While the particle motion of Rayleigh waves is always modified by the structure of the building, Rayleigh waves' \(\theta_{1}\) obeys a stationary stochastic process. Additionally, \(\theta_{1}\) can reflect the angle of the polarization orientation of the ellipsoids based on the horizontal plane, which can represent the rotation angle of vertical components based on the floor plane in a sense and is helpful in calculating IDRs. Therefore, only the parameter \(\theta_{1}\) was used to calculate IDRs for this study. Further, \(\theta_{1}\) represents the angle between the longest axis of the polarized vibration ellipse and the horizontal plane. Since \(\theta_{1}\) describes the polarization orientation of the ellipsoids, it can reflect the characteristics of the components in the seismic wave propagation path. Although the relationship between the initial value of \(\theta_{1}\) and the initial conditions of structures is weak, the variation in \(\theta_{1}\) is closely related to the changes in structures. In general, when subjected to a horizontal load, the horizontal deformation is certainly large. However, when subjected to horizontal loads, the polarization orientation of the ellipsoids is close to the horizontal direction, causing \(\theta_{1}\) to become small.