Inversion methods that build on multiple-point statistics tools offer the possibility to obtain model realizations that are not only in agreement with field data, but also with conceptual geological models that are represented by training images. A recent inversion approach based on patch-based geostatistical resimulation using graph cuts outperforms state-of-the-art multiple-point statistics methods when applied to synthetic inversion examples featuring continuous and discontinuous property fields. Applications of multiple-point statistics tools to field data are challenging due to inevitable discrepancies between actual subsurface structure and the assumptions made in deriving the training image. We introduce several amendments to the original graph cut inversion algorithm and present a first-ever field application by addressing porosity estimation at the Boise Hydrogeophysical Research Site, Boise, Idaho. We consider both a classical multi-Gaussian and an outcrop-based prior model (training image) that are in agreement with available porosity data. When conditioning to available crosshole ground-penetrating radar data using Markov chain Monte Carlo, we find that the posterior realizations honor overall both the characteristics of the prior models and the geophysical data. The porosity field is inverted jointly with the measurement error and the petrophysical parameters that link dielectric permittivity to porosity. Even though the multi-Gaussian prior model leads to posterior realizations with higher likelihoods, the outcrop-based prior model shows better convergence. In addition, it offers geologically more realistic posterior realizations and it better preserves the full porosity range of the prior.