# The Cut-Off Frequency of High-Pass Filtering of Strong-Motion Records Based on Transfer Learning
## 1 Introduction  
Strong-motion records provide important primary data for scientific research and engineering practice in earthquake engineering. Strong-motion records usually need to be processed scientifically and reasonably to obtain correct analysis results. Data processing is indispensable in many research subjects such as site effect analysis [1, 2, 3], studies on the attenuation relation of ground motion [4, 5, 6, 7], structural design and seismic performance assessment [8, 9], and seismic resilience assessment [10, 11]. In structural dynamic time history analysis, appropriate natural ground motion input can effectively reduce the uncertainty in the analysis results [12, 13]. However, slight baseline drift and noise in strong-motion-acceleration records will lead to significant shifts in velocity and displacement time history, which do not correspond with the physical meaning of practical earthquake events and are not appropriate for engineering input and research analysis. Therefore, it is necessary to carry out proper strong-motion records processing in earthquake engineering research. Various methods have been proposed worldwide to process strong-motion records. The data processing method presented by the NGA strong-motion database [14, 15] is firstly to remove the instrument response and zero-line offset from the acceleration time series and then to reduce the noise interference by filtering. The processing flow of theReference database for seismic ground-motion in Europe (RESORCE) [16] is: (i) the zero-line adjustment of the acceleration time series; (ii) filtering via a fourth-order non-causal filter; (iii) polynomially fitting the baseline of the displacement time series; (iv) subtracting the second derivative of the baseline with the filtered acceleration. For the Chilean strong-motion database [17], the trigger type of all records is determined, and different methods are applied for the normal trigger and post-trigger records to taper strong-motion records before calculating the Fourier Amplitude Spectrum (FAS). The subsequent filtering process is similar to RESORCE. The data processing method proposed by the European Strong Motion Engineering Database (ESM) [18] and the Italian Strong Motion Database (ITACA) [19] is similar to the one described above. However, the zero-line correction, the taper length, the filter order, and other parameters are different, and post-processing after obtaining the filtered acceleration time series is added. In the above processing of strong-motion records, the effects of noise are all removed by filtering, in which the high-pass and low-pass cut-off frequencies are essential parameters. For the Internet Site for European Strong-Motion Data (ISESD) [20], two constant values (0.25 Hz and 25 Hz) are used as high-pass and low-pass cut-off frequencies in band-pass filtering. In the NGA strong-motion database [14], the high-pass cut-off frequency is determined by visually examining the FAS and the integrated displacements, while the high-pass and low-pass cut-off frequencies are both determined via the visual inspection of FAS in the ESM [18] and ITACA [19]. Furthermore, in RESORCE [16], the high-pass cut-off frequency is selected by referring to the theoretical corner frequencies of the double-corner source spectrum [21], and the low-pass cut-off frequency is determined based on the recommendations of [PERSON] et al. [22]. In addition, the signal-to-noise ratio (SNR) can also be used to calculate the high-pass and low-pass cut-off frequencies. In the Chilean strong-motion database [17], the high-pass cut-off frequency is determined by limiting the SNR to be greater than 3.0, while the Nyquist frequency is selected as the low-pass cut-off frequency. The high-pass and low-pass cut-off frequencies were determined by limiting the SNR to be greater than 3 by [PERSON] et al. [23]. [PERSON] et al. [24] determined the high-pass cut-off frequency by limiting the SNR to be greater than 2, and choosing the low-pass cut-off frequency requires an SNR to be greater than 1. [PERSON] et al.