An important seismic attenuation mechanism in fractured environments is related to energy conversion into reflected and transmitted waves at fracture interfaces. Using full-waveform sonic (FWS) log data, we show that it is possible to quantify transmission losses across a set of fractures from time delays and amplitude differences of the critically refracted P-wave as compared to intact sections along the borehole. In the presence of fractures, the transmission coefficient associated with a given fracture is obtained by combining information on transmission losses from multiple receivers and source positions into a linear system of equations for all fractures intersecting the borehole. Fracture compliance is computed from the inferred transmission coefficient based on a linear slip model. For validation, we use synthetic FWS log data obtained from numerical simulations of wave propagation in a water-filled borehole surrounded by low-permeability rocks with discrete fractures. The methodology is then applied to field data acquired along boreholes penetrating multiple fractures in a granodioritic host rock. We show that our estimations of mechanical compliance are consistent with previously reported values, which were estimated for individual fractures intersecting one of the boreholes with a related method valid only for isolated single fractures. Comparison between our estimates of fracture compliance and transmissivity profiles from previous hydraulic characterizations of the fractures suggests that the proposed method may also allow to locate the most permeable fractures along a borehole, which, in turn, opens the perspective of enhancing the design and effectiveness of subsequent hydraulic testing and fracturing experiments.