Observations of nonlinear elastic wave behavior in sandstone

Abstract

An experimental investigation of nonlinear elastic wave behavior was conducted using a 2-m-long cylindrical rod of Berea sandstone in order to study the strong elastic nonlinearity that is characteristic of microcracked materials. Measurements of the displacement field at distance x from the source show rich harmonic content with harmonic amplitudes depending on x, source frequency, and source amplitude. The amplitude of the 2ω harmonic is found to grow linearly with x and as the square of both the source frequency ω and the source amplitude U. This behavior is in agreement with the predictions of nonlinear elasticity theory for a system with cubic anharmonicity. From the measured amplitude of the 2ω harmonic the parameter ‖β‖, a measure of the strength of the cubic anharmonicity, is found to be of order 104 (7.0×103±25%). This value is orders of magnitude greater than that found in ordinary uncracked materials. These results suggest that wave distortion effects due to nonlinear elasticity can be large in seismic wave propagation and significantly influence the relationship of seismic signal to seismic source.