Mapping high permeability sand occurrences in clayey till is fundamental for protecting the underlying drinking water resources. Crosshole ground penetrating radar (GPR) amplitude data have the potential to differentiate between sand and clay, and can provide 2D subsurface models with a decimeter-scale resolution. We develop a probabilistic straight-ray-based inversion scheme, where we account for the forward modeling error arising from choosing a straight-ray forward solver. The forward modeling error is described by a Gaussian probability distribution and included in the total noise model by addition of covariance models. Due to the linear formulation, we are able to decouple the inversion of traveltime and amplitude data and obtain results fast. We evaluate the approach through a synthetic study, where synthetic traveltime and amplitude data are inverted to obtain slowness and attenuation tomograms using several noise model scenarios. We find that accounting for the forward modeling error is fundamental to successfully obtain tomograms without artifacts. This is especially the case for inversion of amplitude data since the structure of the noise model for the forward modeling error is significantly different from the other data error models. Overall, inversion of field data confirms the results from the synthetic study; however, amplitude inversion performs slightly better than traveltime inversion. We are able to characterize a 0.4 - 0.6 m thick sand layer as well as internal variations in the clayey till matching observed geological information from borehole logs and excavation.