Characterizing the nonlinear interaction of S- and P-waves in a rock   sample
  The nonlinear elastic response of rocks is known to be caused by the rocks' microstructure, particularly cracks and fluids. This paper presents a method for characterizing the nonlinearity of rocks in a laboratory scale experiment with a unique configuration. This configuration has been designed to open up the possibility the nonlinear characterization of rocks as an imaging tool in a field scenario. The nonlinear interaction of two traveling waves: a low-amplitude 500 kHz P-wave probe and a high-amplitude 50 kHz S-wave pump has been studied on a room-dry 15 x 15x 3 cm slab of Berea sandstone. Changes in the arrival time of the P-wave probe as it passes through the perturbation created by the traveling S-wave pump were recorded. Waveforms were time gated to simulate a semi-infinite medium. The shear wave phase relative to the P-wave probe signal was varied with resultant changes in the P-wave probe arrival time of up to 100 ns, corresponding to a change in elastic properties of 0.2%. In order to estimate the strain in our sample, ae also measured the particle velocity at the sample surface to scale a finite difference linear elastic simulation to estimate the complex strain field in the sample, on the order of $10^{-6}$, induced by the S-wave pump. We derived a fourth order elastic model to relate the changes in elasticity to the pump strain components. We recover quadratic and cubic nonlinear parameters: $\tilde{\beta}=-872$, $\tilde{\delta}=-1.1\times10^{10}$, respectively, at room-temperature and when particle motions of the pump and probe waves are aligned. Temperature fluctuations are correlated to changes in the recovered values of $\tilde{\beta}$ and $\tilde{\delta}$ and we find that the nonlinear parameter changes when the particle motions are orthogonal. No evidence of slow dynamics was seen in our measurements. 
Thomas Gallot, Alison Malcolm, Thomas L. Szabo, and Stephen Brown,   Daniel Burns, Michael Fehler
physics.geo-ph