# An Interactive System Based on the IASP91 Earth Model for Earthquake Data Processing
## 3 Major Functions
### Cross-Correlation Traveltime Picking of Numerical Simulation Records  
Based on the IASP91 standard earth velocity model and setting the source depth to 0 km, the validity of the traveltime picking using cross-correlation was verified by adding \(a\) 5% random time error to the theoretically calculated traveltimes after calculating the theoretical traveltimes of seismic phase P using ray tracing (see Table 1) and by using Leks wavelets in order to simulate the actual observed seismic data. \[R(t)=af_{0}[1-2b(cf_{0}t-1)^{2}]e^{-b(c_{0}t-1)^{2}} \tag{13}\]  
Figure 2: Two time series and their cross-correlation functions. Based on the IASP91 standard earth velocity model, and with a source depth of 0 km, the validity of the traveltime picking using cross-correlation was verified by adding a 5% random time error to the theoretical traveltime calculated using ray tracing for the seismic phase P (see Table 1), and using a Rake wavelet as the source in order to simulate the actual observed seismic data. Where\(f_{0}\) is the center frequency, take \(a=-0.576\), \(b=8\), \(c=0.6\) and set the sampling rate \(\text{dTsamp}=10\) ms in the Settings; the result of the constituted synthetic seismic waveform recording is shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Eicentral** & \begin{tabular}{c} **Theoretical** \\ **Travel Time (s)** \\ \end{tabular} & \begin{tabular}{c} **Random Error** \\ **(s)** \\ \end{tabular} & \
\begin{tabular}{c} **Travel-Time** \\ **Residual (s)** \\ \end{tabular} &
\begin{tabular}{c} **Theoretical** \\ **Error (s)** \\ \end{tabular} \\ \hline
71 & 679.520 & \(-1.738\) & \(-1.740\) & \(-0.002\) \\
72 & 685.560 & \(-1.403\) & \(-1.400\) & \(0.003\) \\
73 & 691.530 & 0.669 & 0.670 & \(0.001\) \\
74 & 697.420 & 1.817 & 1.820 & \(0.003\) \\
75 & 703.230 & 2.133 & 2.130 & \(-0.003\) \\
76 & 708.975 & \(-0.981\) & \(-0.980\) & \(0.001\) \\
77 & 714.648 & 0.316 & 0.320 & \(0.004\) \\
78 & 720.241 & \(-0.148\) & \(-0.150\) & \(-0.002\) \\
79 & 725.760 & \(-0.678\) & \(-0.680\) & \(-0.002\) \\
80 & 731.200 & 0.256 & 0.260 & \(0.004\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Random time error of adding 5% to the traveltime. Figure 3: Synthetic seismic waveform recordings with random noise added and theoretical traveltime curves and wavelet selection. Select Picking and Pick Wavelet in the Settings to select a wavelet. As this is a numerical simulation recording, there is no interference, so the P-wave signal from any of the stations can be selected as a wavelet, e.g., station D075.00. At the same time, the length of the wavelet is adjusted by Tlength in the Settings, and then Display\(\rightarrow\)Display Seismograms is run for wavelet selection. In the Settings, the Pick Wavelet is unchecked and Auto Picking is selected. The starting position of the correlation is set in the Settings by setting Tstart according to the distance of most of the phases from the theoretical traveltime. Then run Functions\(\rightarrow\)Phase correlation to correlate the seismic waveforms of other stations with the selected sub-waves. After confirming that the correlation results meet the requirements, set the start time of the data segment by Tstart and Tlength in the Settings, and run Functions\(\rightarrow\)Plot correlation to output the correlation effect as shown in Figure 4.  
After correcting the P-wave seismic phase for arrival residuals at each station (middle panel of Figure 4), it can be seen that the signal maxima of the P-wave seismic phase at all stations lie on a straight line; at the same time, the correlation coefficient curve (right panel of Figure 4) also shows that the picking of traveltimes is effective. The results are shown in Table 1, and the correlation results and traveltimes are automatically stored in the Pick directory under this project. The file name is composed of the date, end time (hour, minute, second) and phase of this numerical calculation. The exported file is 20200318000000P.pic. Figure 4: Cross-correlation evaluation system.