## 4 Program Implementation Process  
Through the introduction in the first three sections, we can understand the formation principle, process, and required seismic record data of the time-domain response spectrum. However, a large number of calculations must be completed by the program. The following describes the specific process of program implementation for obtaining the response spectrum surface (response spectrum matrix) according to the above principle. In this study, the elastic seismic response analysis was performed on a concrete structure with a damping ratio \(\xi\) of 0.05. The seismic wave data used for the analysis were recorded by a high-precision digital seismograph in the Japanese seismic network (the seismic records in the east-west direction at the AOM021 seismic station during the Great East Japan Earthquake on 11 March 2011). The time interval for the seismic acceleration data was 0.01 s, the total recording duration was 300 s, and the period response spectrum calculation ranged from 0 to 6 s. In the row-column conversion processing method for seismic acceleration data, the number of rows is the segmentation time interval divided by 0.01, as shown in Figure 3, and the number of columns is the total length of the seismic records divided by \(\Delta t\); The number of rows of the produced response spectrum matrix is divided by the cycle interval of the calculated response spectrum (such as 0.02 s in Figure 4, \"T = 0.02:0.02:6\"), and the number of columns is the same as the number of columns converted from the seismic acceleration records. The block diagram of the calculation program for the time-domain seismic response spectral matrix (response spectral surface) is shown in Figure 4.  
The acceleration response spectra were calculated using a self-developed program based on the seismic records in the east-west direction at the AOM021 seismic station during the Great East Japan Earthquake on 11 March 2011 (with a recording duration of 300 s, the peak acceleration amplitude-modulated to 35 cm/s\({}^{2}\), and a damping ratio \(\xi\) of 0.05. Note that an estimation of the epicentral location of the Great East Japan Earthquake could be achieved a few months in advance by means of natural time analysis of the Japanese seismicity). Figure 5 shows the time interval of 10 s selected for the time-domain seismic response spectra. The seismic wave data had to be converted to 1000 rows and 30 columns, and the generated response spectral matrix consisted of 300 rows and 30 columns. Figure 3: Schematic diagram of seismic wave splitting. Using the projection of the time-domain response spectrum's curved surface on the \(\alpha_{\text{OT}}\) plane, the constructed curve is shown in Figure 5.  
The physical meaning of the seismic influence coefficient curve in Figure 5 is consistent with that in the seismic code. Since the seismic influence coefficient is generated by projection onto the axis representing the period, the seismic response's temporal effect is lost, compared to the seismic influence coefficient's curved surface. It represents only the maximum seismic response at each periodic point. The response spectrum matrix can be used to analyze the time-domain response of the building structure because the response spectrum surface increases in the time dimension compared with the response spectrum curve. The time interval for calculating the seismic influence coefficient in the time domain was 0.01 s. Figures 6 and 7 depict the curved surfaces of the seismic influence coefficient  
Figure 4: Flow chart for generating the time-domain seismic response spectral matrix. Figure 5: Time-domain curved surface of the seismic influence coefficient of absolute acceleration (with a time interval of 10 s). generated via the recorded seismic data acceleration and absolute acceleration responses, respectively.