# GAN-Based Inversion of Crosshole GPR Data to Characterize Subsurface Structures
## 3 Dataset  
The inversion network requires a large number of labeled data to train the model parameters, yet it is difficult to collect sufficient qualified crosshole GPR data in real-world measurements. On one hand, due to lack of knowledge of the subsurface structure, the collected data cannot be guaranteed to be consistent with the corresponding permittivity distribution. On the other hand, measured data always have noise that may adversely affect network training. In consideration of the above factors, we used the finite-difference time-domain (FDTD) method to create simulated crosshole GPR data from known permittivity distributions and prepared crosshole GPR waveform and defect distribution data pairs to form the training and test datasets for the inversion network. As a demonstration, we took underground diaphragm wall defect detection with crosshole GPR as an example to prepare the datasets. Referring to the structural properties of diaphragm walls in real-world applications, we constructed 1100 3D numerical diaphragm wall models with dimensions of 2.00 m \(\times\) 4.00 m \(\times\) 0.40 m using gprMax software (v3.1.5, Dr [PERSON], Edinburgh, UK) [40], as shown in Figure 4. Each model is spatially discretized with cubic grids of 0.005 m in edge length. The perfectly matched layer (PML) was adopted as the boundary condition, with 10 grid cells in each dimension. The material of the diaphragm walls was defined as concrete with relative permittivity of 9 and electric conductivity of 0.001 S/m. Inside the diaphragm walls, we put defects of different sizes and shapes with relative permittivity of 20 and electric conductivity of 0.01 S/m as targets. As both the concrete walls and defects were non-magnetic materials, the relative permeability and magnetic loss were set to 1 and 0 \(\Omega\)/m, respectively. The 1100 forward models simulated five different defect situations, which were a single cylinder defect, a single cuboid defect, two cylinder defects, two cuboid defects, and one cylinder defect and one cuboid defect. Each situation contained 220 numerical models. The diameters or side lengths of the defects were randomly generated in the range from one-quarter to one time the crosshole GPR wavelength (a center frequency of 500 MHz was used in the simulations), and the center positions were distributed randomly in the diaphragm wall models. For each diaphragm wall model, 36 transmitting- and 36 receiving-antenna measurement points were placed on the left and right sides of the model to collect crosshole GPR data. The wave source of the antenna was the Ricker wavelet, with a center frequency of 500 MHz. The detection depth range was 0.2 m to 3.8 m, while the distance between the measuring lines of the transmitting and receiving antennas was 1.8 m. In one crosshole GPR measurement, the transmitting antenna emitted electromagnetic waves in one borehole, and the receiving antenna collected data in the adjacent borehole with a sampling interval of 0.1 m. We sampled the electromagnetic waves on each discretized grid, and the number of the A-scan sampling points was 5194, with a time window of 50 ns. In this way, a time-domain crosshole GPR image was formed, as illustrated in Figure 5a. After repeating the same sampling process for the transmitting-antenna measurement points at  
Figure 3: Evaluation of the inversion effects of the low- and high-resolution GANs. 36 depths, we obtained 36 crosshole GPR B-scan images. The detailed modeling parameters are summarized in Table 2.  
In the next step, the 36 crosshole GPR images needed to be assembled into a single image to form the training dataset. Possibly, these images could be combined in the width, height, or channel direction, as shown in Figure 5b-d. In the field of medical imaging, data are usually superimposed in the width direction [41], but this suppresses features in the traveltime dimension. To stack images in the height direction is customary in the field of geophysics, but this reduces the number of data in the depth direction.