# GAN-Based Inversion of Crosshole GPR Data to Characterize Subsurface Structures
## 5 Inversion Results
### Experiment Data Inversion Results  
A field experiment was carried out to collect real-world crosshole GPR data. The experiment site is shown in Figure 8a: a 5 m long, 3 m wide, and 5 m deep foundation pit enclosed with four 0.35 m thick concrete retaining walls. Inside one panel of the retaining walls, a cube-shaped defect with side length of 0.15 m was arranged, as depicted in Figure 8b. We performed crosshole GPR measurements through two boreholes placed in the retaining wall with spacing of 1 m. The transmitting antenna emitted electromagnetic waves in one borehole within the depth range of 1.0 to 3.9 m with step size of 0.1 m, while the receiving antenna received signals in the adjacent borehole within the depth range of 1.0 to 3.8 m with the same step size. As a result, we obtained a total of 870 A-scan traces, which formed 30 B-scan images, as depicted in Figure 8c.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Indicator**} & \multicolumn{8}{c}{**Case Number**} \\ \cline{3-10}  & & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline \multirow{2}{*}{Proposed method} & MSE & 1024.29 & 1273.77 & 1167.94 & 1465.12 & 2543.65 & 1918.53 & 1640.71 \\  & SSIM & 0.93 & 0.93 & 0.93 & 0.92 & 0.85 & 0.91 & 0.91 \\  & Time (s) & 2.4 & 2.3 & 2.5 & 2.5 & 2.7 & 2.5 & 2.5 \\ \multirow{2}{*}{Ray-based tomography} & MSE & 2625.57 & 3063.00 & 4130.67 & 2178.10 & 4967.70 & 1440.1 & 5136.34 \\  & SSIM & 0.34 & 0.33 & 0.30 & 0.30 & 0.25 & 0.43 & 0.23 \\ \multirow{2}{*}{FWI} & Time (ns) & 4.5 & 4.6 & 4.6 & 4.7 & 4.6 & 4.8 & 4.7 \\  & MSE & 231.76 & 81.4 & 53.67 & 871.19 & 634.41 & 506.46 & 713.47 \\  & SSIM & 0.99 & 0.99 & 0.99 & 0.97 & 0.98 & 0.98 & 0.97 \\ \multirow{2}{*}{FWI} & Time (s) & 29.3 & 29.5 & 29.5 & 29.6 & 30.0 & 29.9 & 29.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance indicators of different inversion and image segmentation methods.  
Figure 7: Inversion results of synthetic crosshole GPR data.  
Then, we input the measured crosshole GPR data into the trained GAN-based network, ray-based tomography, and FWI, respectively. The output defect reconstruction images of different methods are shown in Figure 9. The inversion network successfully revealed the location of the defect with the position error of 4.97 cm. Compared with ray-based tomography and FWI, the proposed method could generate clearer results when inverting real crosshole GPR data. Quantitatively, our method had the lowest MSE (981.19) and the highest SSIM (0.92), which were superior to those of ray-based tomography (MSE: 5547.35; SSIM: 0.80) and FWI (MSE: 5727.27; SSIM: 0.84). Since FWI requires the correct selection of initial model and source wavelet, which is easy to implement in a numerical simulation dataset but difficult to achieve in a measured dataset, although FWI had the best performance in the inversion of simulated data, it performed worse than the proposed method when inverting real-world crosshole GPR data. Note that this network is trained on a synthetic dataset, demonstrating that our inversion framework has a good generalization ability to invert real-world data.  
Figure 8: Crosshole GPR measurement: (**a**) collection scene of diagram wall, (**b**) detection model and measuring points, (**c**) measured crosshole GPR data.  
Figure 9: Results of inversion of real crosshole GPR data.