Ocean acoustic tomography is traditionally performed using the travel-time variations of an acoustic path between a source and a receiver. In the context of shallow-water tomography and multipath propagation, the different acoustic paths can be correctly identified if the source and the receiver are arrays of transducers. Here, a double-beamforming algorithm can be applied to extract a collection of eigenbeams from the raw acoustic dataset. In this study, four observables can be measured for each eigenbeam: the travel-time, the amplitude, and the emitting and receiving angles. In this study, the sensitivity kernel (SK) formulation is used to establish a quantitative relation between a perturbation of the surface of an ultrasonic waveguide and the emitting and receiving angles of each eigenbeam. This theoretical relation is experimentally demonstrated using a forward model experiment designed to measure the SK. The SK formulation is then used in a second experiment to quantitatively and dynamically image the propagation of a surface wave traveling across the surface of the waveguide. The inversion results show that the quality of the joint inversion of the emitting and receiving angles is higher than previous results based on amplitude or travel-time observables.