A brief history of the nonlinear acoustics of rocks

Much of the early measurements done to study the nonlinearity of rocks in the late 1980s were analogs to many of the classic nonlinear acoustics experiments performed by students working under the watchful eye of David Blackstock. However, it soon became apparent that nonlinear waves in rocks did not behave as expected. Wave propagation measurements in a long waveguide (a sandstone core) did not generate the usual harmonic dependencies. The nonlinear resonance of a long thin bar of sandstone did not look at all like the nonlinear resonance of a tube of air. A host of other experiments produced equally puzzling behavior. In general, waves in the rock experience considerable nonlinear distortion, exhibit peculiar hysteresis, have memory, and have confounded researchers looking for a tidy theory to describe them. Moreover, it has recently been discovered that rocks are but one member of a larger class of materials—most all of which are granular—which all exhibit similar behavior. We describe all these experiments and how the results drove us away from classical nonlinear acoustics to new theoretical descriptions and applications. [Work supported by Office of Basic Energy Sciences, Geosciences.]