The hydraulic characterization of fractures is crucial for geothermal energy production, hydrocarbon exploration, CO2-sequestration, and nuclear waste disposal. We propose to estimate the effective hydraulic aperture and the mechanical compliance of isolated fractures intersecting a borehole through a Bayesian inversion of full-waveform tube-wave data recorded in a vertical seismic profiling setting. Following the successful application of the proposed inversion procedure to synthetic data, we show in this study initial results of an application to real data.