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.

中文翻译：

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具有合成和测量数据的2.5D井间GPR全波形反演

跨孔地面穿透雷达（GPR）数据的全波形反演（FWI）是一种有潜力研究地下结构的技术。典型的FWI应用程序通过渐近3D到2D数据转换（通常称为Bleistein滤波器）将3D测量值转换为2D域。尽管广泛使用了这种转换，但仍需要一些使它易于出错的假设。尽管已知误差的存在，但先前的研究未能量化介电常数和电导率估算中引入的误差。根据3D和2D建模的比较，在具有高对比度区域的分层结构中，误差可能达到原始幅度的30％。这些误差会严重影响井孔GPR FWI在估算介电常数，尤其是电导率方面的性能。我们已经通过引入使用3D有限差分时域正向求解器（gprMax3D）的新型2.5D井孔GPR FWI解决了这些潜在的误差。这使我们可以在3D模式下对GPR数据进行建模，而在2D平面中执行FWI。综合结果表明，通过实现介电常数和电导率模型的更高分辨率和更低平均误差，2.5D井间GPR FWI优于2D FWI。对于介电常数和电导率，整个域中的平均模型误差减少了约2％，而高对比度层中特定于区域的误差减少了约20％。我们使用井眼2.5D FWI测量数据验证了我们的方法，结果表明，该结果与先前的2D FWI结果和地质研究具有很好的一致性。此外，我们分析了各种方法，并在计算复杂度和结果准确性之间找到了适当的折衷，即在保持我们2.5D FWI方案的卓越性能的同时，减少了计算量。