# The Cut-Off Frequency of High-Pass Filtering of Strong-Motion Records Based on Transfer Learning
## 2 Database
### Data Pre-Processing  
[PERSON] et al. [39] showed that the causal filtering method does not produce interference signals in the noise segment before the seismic signal arrives, while acausal filtering causes interference vibration before the signal arrives. Moreover, the order of the filter is an important factor for filtering, and a higher-order filter will lead to more oscillation at both ends of the filtered record [40]. Therefore, the fourth-order Butterworth causal filter, a widely used filter [14; 16; 17; 24; 29], was used in this paper. The traditional method was used to find the high-pass cut-off frequencies of 4461 records, and 3065 records could only obtain qualified displacement time series curves only through band-pass filtering. Observing the processed records from CESMD showed that the cut-off frequencies were selected in a \"one-size-fits-all\" manner, i.e., the same cut-off frequency was adopted for all three components of the same record (Figure 2a). However, the velocity and displacement time series curves obtained in this way appeared to be qualified but may have had too much valid information filtered out, because the noise affecting the three components of the same record was not necessarily the same. Therefore, it was essential to find the high-pass cut-off frequency for every record. The high-pass cut-off frequencies corresponding to the 3065 records obtained using the traditional method were taken as the accurate values. The scatter plot of these values is shown in Figure 2b.  
The partial acceleration, velocity, and displacement time series curves of record AKBAW-n.0212o88 mof.BNE after filtering with different high-pass cut-off frequencies are shown in Figure 3. It was observed that the displacement time series curves obtained via filtering with the value before the accurate value as the cut-off frequency were all unqualified, and the ones after that were all qualified.  
Figure 2: The high-pass cut-off frequency for each record. (**a**) CESMD; (**b**) traditional method.  
Figure 3: _Cont._  
For each strong-motion record, up to six filtered displacement time series curves were selected for the purpose of building the database. These included three unqualified curves and three qualified curves. The three qualified displacement curves were obtained by filtering using the accurate value and two frequency values after it as the high-pass cut-off frequency. There was little difference between the displacement curves after filtering with two adjacent frequencies. The unqualified displacement curves were obtained by filtering with 0.01 Hz, 0.03 Hz, and 0.05 Hz as high-pass cut-off frequencies. The exact value of some records did not reach 0.05 Hz, so the frequency value of the unqualified time series curve was only 0.01 Hz and 0.03 Hz. A total of 8866 unqualified displacement curves and 9195 qualified displacement curves were obtained through the above method. Ultimately, 18,061 displacement curves were used as the dataset. Additionally, 80% of the data were input into the CNN as the training set, and the test and validation set was 10%; the dataset was divided randomly.  
The zero line was used as a reference in the artificial identification of the drift of the displacement curve, and to facilitate machine differentiation, the zero line was represented by a solid red line. To avoid the influence of axes and legends on model training, all graphs were cropped so that the CNN could only see the displacement curve. To meet the input requirement of the networks in this paper, the image was resized to 224 \(\times\) 224 \(\times\) 3. The result of the image resizing is shown in Figure 4.  
Figure 3: The post-filtering time series curve of record AKBAW–n.021 zo88 mof.BNE (**d**) and subsequent images are considered qualified, where figure f is the filtered time series curve using the frequency given by CESMD). (**a**) 0.01 Hz; (**b**) 0.05 Hz; (**c**) 0.10 Hz; (**d**) 0.12 Hz; (**e**) 0.17 Hz; (**f**) 0.30 Hz.