Towards 3D Full-waveform Inversion of Crosshole GPR Data

2D crosshole ground penetrating (GPR) full-waveform inversion (FWI) has shown superior resolution compared to ray-based inversion tomograms for synthetic and experimental data. To invert measured 3D data with a 2D model that has a reduced geometrical spreading and assumes infinite source and receiver dimensions perpendicular to the 2D inversion plane, the Bleistein transformation can be used to convert the measured 3D data to 2D. This far-field conversion consists of a phase shift and amplitude correction that is based on the first arrival travel time of each trace. In the case of late arrival and high amplitude events that can occur due to low-velocity waveguides andfast propagating refracted waves, this transformation can introduce errors especially in the amplitude such that the inverted conductivity is less accurate. To overcome these problems, we have replaced the 2D finite difference time domain FDTD forward model in the FWI scheme with the well-known gprMax3D FDTD modeling program. In this way, we do not need to use the Bleistein 3D-to-2D filter with its far-field approximation, and we can deal with the correct geometrical spreading and approximate better realistic point source and receivers. Currently, the 2D FWI algorithm has been extended to 2.5D by replacing the 2D FDTD with the gprMax 3D FDTD modeling program. The first test of the 2.5D FWI is based on inversion results of a data set acquired at the Widen site in Switzerland that contained a low-velocity waveguide. The new 2.5D FWI performed well in reconstructing the models. The new 2.5D FWI enables a more reliable re-construction of the subsurface image, especially the electrical conductivity tomograms and to the full use of all the modeling possibilities of the gprMax modeling tool.