First-arrival traveltimes inversion based on a minimal number of parameters in shallow cross-well GPR tomography

Ground-penetrating radar (GPR) is a powerful tool to characterize the subsurface electromagnetic properties, and therefore related quantities such as the water-content. In this paper, we present a new algorithm for cross-well tomographic inversion of GPR first-arrival traveltimes. It is based on a blocky description of the propagating medium, and only a limited number of parameters are inverted. This methodology has been developed for media with significant contrast of electrical permittivity, for instance near-surface sedimentary media, where the occurrence of head waves is frequent. In a first step, the distribution of the electromagnetic wave velocity is determined between two wells. In a second step, we address the question of the layers continuity for several successive tomographic panels. This methodology allows us to obtain a 2D velocity profile of the medium between successive pairs of wells. The inversion scheme takes into account both the direct and refracted waves generated at interfaces with strong velocity contrast. It was tested on synthetic data for a single pair of wells, and on real data, first for one tomographic panel, then for a set of three successive tomographic panels. For comparison, inversion was also conducted with a classical LSQR algorithm, which delivers a smooth velocity model, and does not take into account head waves. As expected, the velocities obtained with our method are more contrasted, and free from the head waves generated artefacts.