Implicit multiparameter full waveform inversion of multioffset ground penetrating radar data

SUMMARY Full waveform inversion (FWI) of ground-penetrating radar (GPR) data is one of the key methods for reconstructing high-resolution near-surface images and understanding changes in the near-surface environment. However, FWI faces great challenges due to the ill-posed nature of the optimization problem and its high sensitivity to the quality of the initial model. In this paper, we propose the implicit full waveform inversion (IFWI) algorithm for GPR that addresses these limitations by using an implicit and continuous function built by deep neural networks to represent multiple subsurface parameters. In this way, IFWI can be thought of as training a physically constrained neural network representation, allowing it to exploit the frequency principle in deep learning optimization, that is first recovering the low-frequency components of the subsurface parameters and large-scale structures, and then their high-frequency and fine-grained information, which makes IFWI an automated multiscale inversion approach without manual frequency band selection. Numerical experiments are conducted to verify the effectiveness and performance of IFWI relative to FWI. The results demonstrate that IFWI can accurately reconstruct subsurface images and anomalies even with a suboptimal initial model, while FWI and multiscale FWI struggle to provide useful information due to being trapped in local minima. Consequently, IFWI exhibits less dependence on the initial model compared to FWI and multiscale FWI. To better understand the behaviour of IFWI and its sensitivity to neural network architecture, we comprehensively discuss the influences of these hyperparameters on IFWI, providing initial selection guidelines and practical guidance for adjustments.