A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks

Dynamic acoustoelastic testing is performed on a set of six rock samples (four sandstones, one soapstone, and one granite). From these studies at 20 strain levels 10^-7<μ<10^-5, four measures characterizing the nonlinear elastic response of each sample are found. Additionally, each sample is tested with nonlinear resonant ultrasonic spectroscopy and a fifth measure of nonlinear elastic response is found. These five measures of the nonlinear elastic response of the samples (approximately 3 × 6×20 × 5 numbers as each measurement is repeated 3 times) are subjected to careful analysis using model-independent statistical methods, principal component analysis, and fuzzy clustering. This analysis reveals differences among the samples and differences among the nonlinear measures. Four of the nonlinear measures are sensing much the same physical mechanism in the samples. The fifth is seeing something different. This is the case for all samples. Although the same physical mechanisms (two) are operating in all samples, there are distinctive features in the way the physical mechanisms present themselves from sample to sample. This suggests classification of the samples into two groups. The numbers in this study and the classification of the measures/samples constitute an empirical characterization of rock nonlinear elastic properties that can serve as a valuable testing ground for physically based theories that relate rock nonlinear elastic properties to microscopic elastic features.