Nonlinearity in rock: Evidence from Earth tides

Abstract

The earth is sinusoidally stressed by tidal forces; if the stress‐strain relation for rock is nonlinear, energy should appear in an earth tide record at frequencies which are multiples of those of the larger tidal lines. An examination of the signals to be expected for different nonlinear deformation laws shows that for a nonlinear response without dissipation, the largest anomalous signal should occur at twice the forcing frequency, whereas for nonlinear laws involving dissipation (cusped hysteresis loops) the anomalous signal will be greatest at 3 times this frequency. The size of the signal in the dissipative case depends on the amount by which dissipation affects the particular response being measured. For measurements of strain tides this depends on whether dissipation is assumed to be present throughout the earth or localized around the point of measurement. An analysis of 5.7 years of strain tide records from Piñon Flat, California, shows a small signal at twice the frequency of the largest (M2) tide. Most of the observed signal can be explained by loading from nonlinear water tides in the Gulf of California and the Pacific Ocean; the residual nonlinear tide is 65 dB less than the M2 tide. The signal at 3 times the M2 frequency is compatible with a linear model or with nonlinear hysteresis loops provided that nonlinear dissipation occurs throughout the earth. Nonlinear dissipation in the rocks near the strainmeter would produce a larger signal than is seen.