Time-domain characterization of the nonlinear viscoelastic memory of rocks with ultrasound waves

The nonlinear elastic response of rocks is known to be caused by internal microstructure, particularly cracks and fluids. In order to quantify this nonlinearity, we describe a new sensitive acoustic method to measure nonlinear viscoelastic properties of rocks directly in the time domain. Our method utilizes co-propagating longitudinal acoustic waves to perturb rocks with dynamically applied strain. Data indicates that rocks have a short period nonlinear viscoelastic memory that is a function of the time history of the loaded strain. We developed a phenomenological model with second and third order nonlinear elastic constants and a memory strength parameter to describe the short period nonlinear viscoelastic memory and the nonlinear elastic behavior of rock. Results of experiments on Crab Orchard sandstone and Lucite samples are presented. We have found both Lucite and Crab Orchard sandstone to be viscoelastic but the sandstone is much more nonlinear. These new observations and methods have significance fo...