# Calculation of Theoretical Travel Time and Automatic Picking of Actual Travel Time in Seismic Data
## 1 Introduction  
For a determined model of the Earth's interior, it is possible to calculate from seismological methods what phases will occur at different epicentral distances and source depths according to the law of seismic wave propagation, and to determine the time they take to propagate from the source to the station (i.e., travel time), and, for an earthquake at a certain depth, the epicentral distance can be found from the arrival time difference between the subsequent phase and the first arrival phase [1]. Seismic phase identification is a very important task in seismology. Seismic phase analysis is a powerful tool for studying seismic activity, source physics, earthquake engineering, and the internal physics of the Earth, and it is a fundamental tool for determining the three elements of an earthquake (time, epicenter and magnitude). In 1935, [PERSON] and [PERSON] published the paper \"Propagation times of seismic waves\". In 1940, they collaborated on completing the Jeffreys-Bullen time table, referred to as the \"J-B time table\", which included most of the possible seismic waves on Earth [2]. In the early 1980s, [PERSON] et al. obtained the Preliminary Reference Earth Model, a new generation of global one-dimensional seismic time model, which is the most accurate model compared to the J-B model. PREM is widely used in seismic research, especially in earthquake localization [3]. Later, in order to meet the needs of global earthquake studies, the International Association of Seismology and Geophysics of the Earth's Interior (IASPEI), based on the preliminary Earth reference model, established an Earth model reflecting the global average properties in 1991, called the IASP91 model, and based on this model [4; 5]. Numerous ray tracing methods have been updated and improved as a result of the ongoing research and study of ray tracing techniques by various experts [6; 7; 8; 9; 10; 11; 12]. With the increasing number of seismic stations around the world, the seismic monitoring capability is increasing, but the consequent data generation is increasing exponentially, and how to process the massive seismic observation data quickly and effectively is a key problem faced. Seismic tomography has been widely applied to study the velocity structure of the Earth's interior and has achieved fruitful geological results [13; 14; 15; 16]. At present, the data used for laminar imaging of remote seismic body waves are usually the relative traveltime residuals of the first arrival phase [15]. The methods for obtaining first arrival times from waveform data mainly include manual identification and automatic computer detection methods. Although the manual identification method is simple to implement, it cannot meet the accuracy requirements for seismic waveform data with low signal-to-noise ratio, and it has a limited application because of its low efficiency and labor intensity; whereas the automatic computer detection method has become more and more popular among researchers due to its high accuracy and efficiency, such as the Akaike Information Criterion (AIC) arrival detection technique [17; 18], the relative and absolute travel time difference simulated annealing method [19] and multiscale wavelet transform method [20]. The short term average/long term average (STA/LTA) technique proposed by [PERSON] (1978) [21] was used to perform automated picking. [PERSON] and [PERSON] proposed a robust method based on instantaneous-spectral Shannon entropy for capturing microseismic events in noisy environments without data preprocessing [22]. [PERSON] et al. proposed an improved multi-channel cross-correlation method [23]. Work on automatic picking through machine learning based technology is reported in [24; 25]. [PERSON] proposed a research using machine learning and geophysical inversion. The author proposed that machine learning can be used for large amounts of data as an alternative to geophysical inversion [26].