The detection of cavities with geophysical methods is a challenging task for which a general approach has not yet been found. We have found that viscoelastic SH full-waveform inversion (FWI), focusing primarily on reflection events, is able to accurately locate the position of cavities, areas of decompacted sediments, and, more generally, seismic low-velocity anomalies down to 30 m depth. The key for a successful FWI application is the enhancement of the reflected wavefield relative to the surface wavefield. For this purpose, we apply automatic gain control normalization in the objective function. By focusing the inversion on the reflected wavefield, we determine that one can differentiate between air-filled cavities with zero shear-wave (S-wave) velocity and low-velocity zones. Additionally, we test the FWI approach on a field data set, with a known collapsed tunnel system inside a 32 m high monumental antique grave mound. The results show that the location and extent, as well as the density and S-wave velocity of the collapsed tunnel system, can be determined with sufficient accuracy by applying a 2D FWI approach to intersecting profiles, despite the 3D nature of the problem.