Inference of multi-Gaussian relative permittivity fields by probabilistic inversion of crosshole ground-penetrating radar data

In contrast to deterministic inversion, probabilistic Bayesian inversion provides an ensemble of solutions that can be used to quantify model uncertainty. We have developed a probabilistic inversion approach that uses crosshole firstarrival traveltimes to estimate an underlying geostatistical model, the subsurface structure, and the standard deviation of the data error simultaneously. The subsurface is assumed to be represented by a multi-Gaussian field, which allows us to reduce the dimensionality of the problem significantly. Compared with previous applications in hydrogeology, novelties of this study include an improvement of the dimensionality reduction algorithm to avoid streaking artifacts, it is the first application to geophysics and the first application to field data. The results of a synthetic example show that the model domain enclosed by one borehole pair is generally too small to provide reliable estimates of geostatistical variables. A real-data example based on two borehole pairs confirms these findings and demonstrates that the inversion procedure also works under realistic conditions with, for example, unknown measurement errors.