Short-Period Nonlinear Viscoelastic Memory of Rocks Revealed by Copropagating Longitudinal Acoustic Waves

Abstract

We describe a new sensitive acoustic method to measure nonlinear viscoelastic properties of rocks directly in the time domain. Unlike static stress-strain measurements, or dynamic acousto-elastic methods that use steady state resonance to load a strain field into a rock, our method uses two copropagating longitudinal acoustic waves, one to perturb the strain in the sample and the other to probe the effect of that strain. Experiments on Crab Orchard Sandstone and Lucite samples are presented. We evaluate the time-dependent nonlinear effects and find strong evidence that rocks have a short-period nonlinear viscoelastic memory that is a function of the time history of the loaded strain. We develop a phenomenological model to describe both this nonlinear viscoelastic memory and the nonlinear elastic behavior of rock. Our model shows that the viscoelastic memory is controlled by both the traditional nonlinear elastic coefficients and a memory strength parameter. These new observations and methods have significance for quantifying changes in microstructure. This short-term memory effect, on the order of a small fraction of a cycle, is shown to be related through viscoelasticity to absorption in the sample.