## 1 Introduction  
In the near-surface seismic exploration, the refraction exploration has been widely used due to its simplicity and high efficiency. The refracted wave exploration is mainly based on the basic theory that the velocity of the underlying stratum is higher than that of the overlying stratum. By recording the wave's arrival time, the physical parameters such as the thickness and velocity of the subterranean stratum structure can be estimated. The refracted wave exploration method first appeared in the 1930s and was developed for computer automated interpretation in the 1970s [1]. At present, the engineering refracted wave method is commonly used to detect the thickness of the cover layer [2], study the undulation of the bedrock surface [3], identify the hidden fault, measure the depth of the diving surface, and detect underground cavities and tunnels [4]. [PERSON] pointed out that the seismic refracted wave method can provide the near-surface geological information for engineering geological applications [5]. In an actual survey, [PERSON] applied a set of engineering seismic refracted wave exploration methods to explore dam diseases, which achieved good results [6]. Tomography was first used in the medical field. It was subsequently introduced into the field of seismic exploration. In the 1970s, [PERSON] et al. first used the seismic first arrival tomography method to invert the deep crust structure of the Earth [7]. This method was then widely used in the study of deep structure imaging of the Earth [8; 9; 10; 11; 12; 13; 14; 15; 16]. Seismic tomography is also used in the field of engineering and exploration geophysics. Due to its dependence on ray density, cross-well tomography research has also achieved good results [17; 18; 19; 20]. Surface tomography is mainly used to invert the near-surface velocity structure and provide an initial model for the more accurate waveform inversion method [21; 22; 23]. [PERSON] compared the effectiveness of phase waveform inversion and travel time tomography [24]. [PERSON] et al. introduced the first arrival wave travel tomography method based on the double square root function Equation [25]. [PERSON] et al. introduced wide-angle tomography methods at different scales [26]. [PERSON] et al. solved the model non-uniqueness problem by using the traditional minimum structure regularization technique and proved the superiority of frequency-dependent tomography (FDTT) [27]. In the forward modeling of refracting tomography, the traditional ray method is used to solve the travel time along the ray direction and then interpolate that information to obtain the travel time of each node of the underground section, but this method cannot adapt to complex underground structures [28; 29; 30]. [PERSON] proposed a method of approximating the eikonal equation by using the finite difference method [31; 32]. The core idea of this method is to calculate the travel time of each node by tracing the front of the wave. After subsequent research and development, there are several kinds of travel time calculations and ray tracing methods based on high frequency approximation, such as the fast scan method (FSM) [33] and the fast marching method (FMM) [34; 35]. In the process of refraction tomography inversion, regularization is usually used to overcome the instability of the inversion solution [36; 37]. [PERSON] used the regularization method to smooth the model and obtain good results [38]. [PERSON] et al. introduced prior information into the inversion process as well as internal constraints on the model [39]. Refraction travel time tomography utilizes the travel time information of the seismic wavefield without being affected by the characteristics of its source and detector. At the same time, the computational efficiency of refraction travel time tomography is much higher than that of the full waveform inversion method. Based on its mature theory and high efficiency, this method is widely used to establish the near-surface and deep velocity models.