A much-discussed topic in seismology deals with how and under which loading conditions soil shows nonlinear behavior and how this can be verified from seismograms. Seismologists have been seriously searching for signatures of nonlinear soil response to earthquakes for about two decades. A mechanism explaining the dispersion in the P-wave spectra due to the interaction between compressional (P) and shear (S) waves is presented. Shear waves in granular materials induce longitudinal dilatancy waves (so-called Δ waves) with approximately double frequency. This can be explained with dilatancy and contractancy, which is characteristic of granulates under shear deformations. The predicted dispersion is observed in laboratory experiments and verified by comparing accelerograms from hard-rock and soil stations from the Vrancea region, Romania. The arrival-time difference between Δ waves and S waves may theoretically be indicative of the thickness of nonsaturated granular layers. These results, modeled with nonlinear constitutive relations of the rate type, show a specific type of nonlinearity in granular sediments also for earthquakes of moderate magnitudes.