# GAN-Based Inversion of Crosshole GPR Data to Characterize Subsurface Structures
## 1 Introduction  
As a fast and accurate non-destructive testing method, crosshole ground-penetrating radar (GPR) has been increasingly used in deep-foundation defect detection [1], engineering geology investigation [2; 3], water-resource exploration, etc. [4; 5; 6]. Crosshole GPR excites high-frequency electromagnetic waves from a transmitting antenna and collects electromagnetic waves with a receiving antenna in the boreholes of subsurface media [7]. These electromagnetic waves form refracted and reflected waves when passing through different underground media. Then, the image of the underground media can be characterized by analyzing the measured crosshole GPR data [8]. However, crosshole GPR data are not the direct imaging of a subsurface structure, and interpretation involves geophysical data inversion, which is highly complicated and time-consuming. The commonly used ray-based tomography methods employ the first-arrival travel-times or first-cycle amplitudes of crosshole GPR data to infer the subsurface wave velocity or attenuation distribution. These methods use just a small proportion of the information from crosshole GPR data, so they merely lead to a low-resolution inversion output, resulting in the inability to accurately characterize features with sub-wavelength [9]. On the contrary, the full-waveform inversion (FWI) method, which takes into account the entire waveform information of crosshole GPR data, is capable of providing high-resolution inversion results [10; 11; 12]. Yet, FWI requires the correct selection of the source wavelet and startingmodel to prevent the inversion result from being the local minimum [9; 13; 14], which makes this method difficult to apply to real-world data inversion. Then, probabilistic inversion methods with Bayesian inference have been proposed [15; 16; 17; 18]. These approaches allow for the treatment of different sources of error and return an ensemble of statistically acceptable solutions. They are capable of preventing the inversion results from being trapped in the local minimum and able to quantify the uncertainties of the inversion results. Nevertheless, the probabilistic inversion methods involve thousands to millions of forward simulations to ensure the inversion results are converged to the posterior distribution, which leads to the consumption of considerable computing resources [19; 20]. Deep learning is a novel branch of machine learning [21]. With the emergence of convolutional neural networks [22; 23], it has received great attention. The network used in deep learning can spontaneously learn low-order features (edges, textures, etc.) and high-order features (high-dimension features related to specific training tasks) in an image, and there is no need to manually design features in advance as required in traditional machine learning methods [24; 25]. Additionally, after the appearance of the generative adversarial network (GAN) [26], the capability of deep learning is no longer limited to image classification and object detection. It can also generate virtual images that do not exist in reality from training data. By adding labels to the input of generators and discriminators or introducing a group of generators and discriminators, the improved GAN can learn the non-linear mapping relationship between different domains and realize end-to-end image conversion [27]. This capability makes it possible to translate crosshole GPR images to their corresponding dielectric properties, which are defined by permittivity or conductivity images, with deep learning models. In recent years, some studies have applied the GAN framework to assist GPR data analysis, such as eliminating clutters in GPR images [28; 29] and performing GPR-image simulation for data augmentation [30; 31]. All these works are for ground-coupled GPR data, but crosshole GPR uses different antenna arrangements; therefore, the interpretation of crosshole GPR data involves more non-linear and ill-posed problems.