## 3 Experimental Validation  
First traveltime data are among the most commonly used data in inversion problems, involving the propagation of elastic seismic and electromagnetic waves [25; 26]. The inverse problem involves inferring information about the velocity field, which leads to the decay of the travel time of a specific phase in the wave field. Here, we consider a traveltime-based inversion problem called \"crosshole first arrival time inversion\", which is related to the inversion of the first arrival time delay of the wave field propagating from a set of source positions in one borehole to a set of receiver positions in another borehole. The inverse problem includes inferring the velocity distribution between boreholes. Originally proposed in the context of seismic traveltime data [27], the approach of traveltime inversion has expanded to extensive research into the application of near-surface GPR techniques. The process of inverting crosshole GPR data is recognized as a commonly addressed inverse problem. In this article, using a multivariate Gaussian probability distribution to generate a reference model m with a mean velocity of 0.14 m ns\({}^{-1}\), a variance of 0.000215 m\({}^{2}\) ns\({}^{-2}\), and a spherical covariance model with an isotropic range of 6 m, the dimensions of the model are 7 \(\times\) 13 m (36 \(\times\) 66 pixels with dimensions of 0.2 m \(\times\) 0.2 m). The settings of this recording geometry and parameters are the same as those employed by [PERSON] et al. (2013) [28], who used two-dimensional finite difference modeling of electromagnetic wave propagation to compute a set of 702 noise-free travel time data via  
Figure 3: Process of Monte Carlo sampling of inverse problems based on SE-CNN network. automatic first picking; this method is described by [PERSON] et al. (2014) ([PERSON] et al., 2014) ([PERSON] et al., 2014) and is based on the work of [PERSON] et al. (2007a,2007b) ([PERSON] et al., 2007; [PERSON] et al., 2007) and [PERSON] et al. (2012) ([PERSON] et al., 2012). Uncorrelated zero-mean Gaussian noise with a standard deviation of 0.1 m ns \({}^{-1}\) was added to the noise-free traveltime data, and a reference data set was obtained. Figure 4 shows the recording geometry and corresponding reference velocity model m\({}_{\text{ref}}\), with red dots representing the emission source and black dots representing the receiver; the positions of the ND = 702 group source and receiver can be identified by connecting the ray paths. Figure 5 shows the corresponding first-arrival travel time data that were automatically retrieved. Before inversion, the SE-CNN neural network needed to be trained first. The input of the network is a \(36\times 66\) two-dimensional image of the velocity model, and the output is \(1\times 702\) one-dimensional travel time data. The input model was obtained by sampling prior information, and the corresponding travel time data were obtained through an accurate but time-consuming 2D FDTD model. In this study, we designed four training datasets with a size of [1000 5000 10,000 20,000], and the corresponding forward models based on the neural network are g\({}_{1000}\), g\({}_{5000}\), g\({}_{10000}\), and g\({}_{20000}\). Figure 6 shows four velocity model samples obtained by sampling prior information, and the velocity distribution in the model is random. After training, we obtained neural network forward models based on different training sizes. Compared with the accurate 2D FDTD model g\({}_{\text{fd}}\), the forward model based on neural networks has more errors. A sample model was randomly selected to test the  
Figure 4: Reference model and recording geometry. forward performance of the neural network model. The forward performance of \(\textsl{g}_{1000}\), \(\textsl{g}_{5000}\), and \(\textsl{g}_{10000}\) is shown in Figure 7. From Figure 7, it can be seen that as the training size increases, the forward modeling of the neural network model becomes more accurate, and \(\textsl{g}_{10000}\) is already very similar to the observed data.