Nonlinear generation of elastic waves in granite and sandstone: Continuous wave and travel time observations

Beams generated by nonlinear interaction have proved useful as low-frequency, highly directional sources in water and may ultimately find application in geophysical exploration. For nonlinear elastic waves to be used as seismic sources they must be detected as discrete arrivals; measuring travel times of pulsed, nonlinear beams is a necessary first step toward that end. In this paper we discuss two new observations of the interaction of nonlinear elastic waves in both crystalline rock and sandstone. We show that observed travel times of pulsed waves agreed with predicted times for the case where two P wave pulses interacted to produce an S wave pulse. The travel time measurement was difficult to obtain because conversion efficiency is low. In extending our continuous wave experiments to sandstone we also satisfied three criteria previously verified in crystalline quartz norite and in granite to demonstrate nonlinear interaction: (1) the frequency of the nonlinear-generated signal equalled the difference frequency f1–f2 when two P waves interacted to produce an S wave, (2) the amplitude of the signal was proportional to the amplitude product of the primary waves, and (3) in the case of intersecting P waves the trajectory of the nonlinear beam matched that predicted by nonlinear elasticity theory.