2.5D crosshole GPR full-waveform inversion with synthetic and measured data

Full-waveform inversion (FWI) of cross-borehole ground-penetrating radar (GPR) data is a technique with the potential to investigate subsurface structures. Typical FWI applications transform 3D measurements into a 2D domain via an asymptotic 3D to 2D data transformation, widely known as a Bleistein filter. Despite the broad use of such a transformation, it requires some assumptions that make it prone to errors. Although the existence of the errors is known, previous studies have failed to quantify the inaccuracies introduced on permittivity and electrical conductivity estimation. Based on a comparison of 3D and 2D modeling, errors could reach up to 30% of the original amplitudes in layered structures with high-contrast zones. These inaccuracies can significantly affect the performance of crosshole GPR FWI in estimating permittivity and especially electrical conductivity. We have addressed these potential inaccuracies by introducing a novel 2.5D crosshole GPR FWI that uses a 3D finite-difference time-domain forward solver (gprMax3D). This allows us to model GPR data in 3D, whereas carrying out FWI in the 2D plane. Synthetic results showed that 2.5D crosshole GPR FWI outperformed 2D FWI by achieving higher resolution and lower average errors for permittivity and conductivity models. The average model errors in the whole domain were reduced by approximately 2% for permittivity and conductivity, whereas zone-specific errors in high-contrast layers were reduced by approximately 20%. We verified our approach using crosshole 2.5D FWI measured data, and the results showed good agreement with previous 2D FWI results and geologic studies. Moreover, we analyzed various approaches and found an adequate trade-off between computational complexity and accuracy of the results, i.e., reducing the computational effort while maintaining the superior performance of our 2.5D FWI scheme.