# Calculation of Theoretical Travel Time and Automatic Picking of Actual Travel Time in Seismic Data
## 4 Application Examples  
The distribution of seismic stations is mostly located in Guangxi region, and Tables 2 and 3 shows the seismic records of two earthquakes observed by 16 stations of the broadband mobile seismic network in Guangxi region (Figure 4) as an example (rotated), #1. The Alo Islands experienced a magnitude 6.5 earthquake on 4 November 2015, at 03:44:15 (UTC = 0), at a source depth of 20 km, far from Guangxi. The P phase should be the initial arrival wave phase of this earthquake at a distance greater than 3000 km. With a source depth of 599.35 km and a distance of more than 17,000 km from Guangxi, the magnitude 6.7 earthquake in Brazil #2 occurred at 05:45:18 (UTC = 0) on 26 November 2015. The PKIKP phase should be the first arrival wave phase of this earthquake. The theoretical arrival time of the seismic phase was calculated according to the IASP91 Earth velocity model parameter table (Figures 5 and 6).  
Figure 4: Map of stations.  
Figure 5: Theoretical arrival times of seismic records and \(P\) and \(S\) phases in the Alo Islands.  
The selected reference wavelet (SB11 station is used as the reference wavelet in Figure 7; SD21 is used as the reference wavelet in Figure 8). Use a shorter wavelet wherever possible to ensure the accuracy of the seismic phase picking. In general, the wavelet should not be longer than 15 s to prevent the wavelet from incorporating another seismic phase and influencing the accuracy of the travel time picking. The window length of the selected wavelets of other stations is set according to the length of the reference wavelet, so that the wavelets of other stations can be filtered to the best wavelets in the window set by the parameters (which will only be correlated within the window of the control parameters) even in the environment of low signal-to-noise ratio.  
Figure 6: Brazilian earthquake records and theoretical arrival times of PKIKP, PKPab, SKIKP, PKIKS, PP, SKIKS, and PPP seismic phases.  
Figure 7: Correlation results of earthquake records in the Alo Islands.  
Figures 9 and 10 show the cross-correlation effects, and the correlation coefficients are used to further assess the accuracy of the seismic phase travel time picking.  
Figure 8: Cross-correlation results of Brazilian earthquake records.  
Figure 9: Cross-correlation evaluation system of seismic records in the Alo Islands. (The **(left)** figure shows the waveform with the theoretical arrival time of 0 line; the **(middle)** figure shows the waveform with the measured arrival time of 0 line; the red solid line in the **(right)** figure shows the correlation coefficient. The coordinate axis is the upper red coordinate, the black dashed line is the relative travel time residual, and the coordinate axis is the lower black coordinate in seconds; the station SB11 is selected as the reference wavelet, and its correlation coefficient is 1).  
The middle plots of Figures 9 and 10 are actually the results after correcting the P-wave seismic phase and PKIKP seismic phase when actual at each station with relative travel time residuals. It can be shown that the usage of cross-correlation travel time picking works effectively when combined with the correlation coefficient curves.  
The imperfect alignment of the P-phase and PKIKP-phase in Figures 9 and 10 reflects the presence of lateral structures below the stations. In the middle panel, most of the stations are perfectly aligned, in the physical sense by subtracting the relative residuals, and in the mathematical sense by pulling the wavelets of all 16 stations to the line where they were actual. In the right panel, it can be seen that the wavelets of each station are well correlated.