Fracture-scale heterogeneity plays an important role in driving dispersion, mixing and heat transfer in fractured rocks. Current approaches to characterize fracture scale flow and transport processes largely rely on indirect information based on the interpretation of tracer tests. Geophysical techniques used in parallel with tracer tests can offer time-lapse images indicative of the migration of electrically-conductive tracers away from the injection location. In this study, we present a methodology to invert time-lapse ground penetrating radar reflection monitoring data acquired during a push-pull tracer test to infer fracture-scale transport patterns and aperture distribution. We do this by using a probabilistic inversion based on a Markov chain Monte Carlo algorithm. After demonstration on a synthetic dataset, we apply the new inversion method to field data. Our main findings are that the marginal distribution of local fracture apertures is well resolved and that the field site is characterized by strong flow channeling, which is consistent with interpretations of heat tracer tests in the same injection fracture.