Strong Rayleigh waves are expected to bring the shallow subsurface into frictional failure. They may nonlinearly interact with high‐frequency S waves. The widely applied Drucker and Prager (1952) rheology predicts that horizontal compression half‐cycle of strong Rayleigh waves will increase the strength of the subsurface for S waves and predicts that S waves with dynamic accelerations >1g will reach the surface. We did not observe this effect. Rather, we observed that strong high‐frequency S waves arrived at times of low Rayleigh‐wave particle velocity. Physically, high‐frequency S waves cause failure on horizontal fractures in which Rayleigh waves do not change the normal traction. Failure then may depend on the ratio of the shear invariant to the ambient vertical stress. The shear invariant is the square root of the sum of the squares of terms proportional to the resolved horizontal velocity from Rayleigh waves and to the resolved high‐frequency dynamic acceleration from S waves. That is, an ellipse should bound resolved dynamic acceleration versus resolved particle velocity. Records from seven stations from the 2011 Tohoku earthquake and El Pedregal station during the 2015 Coquimbo Chilean earthquake exhibit this expected effect of this nonlinear interaction.