MCMC Method of Inverse Problems Using a Neural Network—Application in GPR Crosshole Full Waveform Inversion: A Numerical Simulation Study

Abstract

Ground-penetrating radar (GPR) crosshole tomography is widely applied to subsurface media images. However, the inadequacies of ray methods may limit the resolution of crosshole radar images, since the ray method is a type of high-frequency approximation. To solve this problem, the full waveform method is introduced for GPR inversion. However, full waveform inversion is computationally expensive. In this paper, we introduce a trained neural network that can be evaluated very quickly to replace a computationally intensive forward model. Additionally, the forward error of the trained neural network can be statistically analyzed. We demonstrate a methodology for a full waveform inversion of crosshole ground-penetrating radar data using the Markov chain Monte Carlo (MCMC) method. An accurate forward model based on Maxwell’s equations is replaced by a quickly trained neural network. This method achieves a high computation efficiency, which is four orders of magnitude faster than the accurate forward model. The inversion result of the synthetic waveform data shows a good performance of the trained neural network, which greatly improves the calculation efficiency.