Some rock properties show surprisingly stable relationships, to the extent that any deviation therefrom should be regarded as a signal of anomalous behavior. One of these stable relationships is the linear trend between compressional (Vp) and shear velocities (Vs), which is observed for both sandstones and mudstones. We infer that anomalous stresses, notably deviations from the basin-wide relationship between horizontal and vertical effective stresses, may cause deviations from the basin-wide Vp-Vs trends. An anomalously high or low shear velocity can therefore be indicative for an anomalous stress regime.