# Calculation of Theoretical Travel Time and Automatic Picking of Actual Travel Time in Seismic Data
## 5 Conclusions  
Teleseismic tomography is playing an increasingly important role in studying the velocity structure of the deep Earth. The accuracy of the relative travel time residuals used directly determines the credibility of the imaging results. Therefore, it has become an urgent problem for seismologists to obtain high-precision relative travel time residuals automatically from the huge amount of teleseismic waveform data, especially those with poor signal-to-noise ratio.  
In this study, based on the IASP91 Earth model, we used a shooting method with a non-meshing scheme to trace raypaths and calculate the travel times of global seismic phases. The orthogonal travel times predicted by simulation for each phase can closely match the [PERSON] calculated seismic wave travel times for the corresponding phases. A comparison with SAC has also been done and the error time is within the range of 0.001 s.  
This technique can show the kinematic properties of seismic phases moving within the Earth. The method does not require gridding of the Earth model and is simple to operate, fast to calculate, and highly accurate.  
Figure 10: Cross-correlation evaluation system of seismic records of Brazilian earthquakes. (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 SD21 is selected as the reference wavelet, and its correlation coefficient is 1).  
The advantage of correlation analysis is its simplicity and speed. There is a corresponding parameter window limit in calculating the number of interrelationships between two waveforms, and only the best wavelets are screened within the window range to improve the recognition of effective seismic phases. In the application of the teleseismic cross-correlation evaluation system, the theoretical arrival times and actual arrival times calculated using the IASP91 Earth velocity model can roughly align with the initial waveforms, and the relative residuals are determined directly from the actual arrival times picked up during correlation analysis without any inversion or reference time information. The effectiveness of the travel time method for picking the seismic phase by correlation analysis can be demonstrated.  
Conceptualization, W.G. and S.P.; methodology, W.G.; software, S.Y.; validation, Y.W., S.P. and S.Y.; formal analysis, W.G.; writing--original draft preparation, W.G. and S.P.; writing--review and editing, L.L. and Y.W.; supervision, L.Y. and Y.Y. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Natural Science Foundation of China (No. 42062015), Innovation Program for College Graduates of Guangxi (No. YCSW2022312), and the Natural Science Foundation of Guangxi (No. 2018 AD19204).  
Not applicable.  
Data Availability Statement: Data available in a publicly accessible repository ([[https://earthquake.usgs.gov/](https://earthquake.usgs.gov/)]([https://earthquake.usgs.gov/](https://earthquake.usgs.gov/))) (accessed on 1 December 2022).  
Thanks to the USGS website for the data.  
The authors declare no conflict of interest.