Slow nonlinear dynamics in rock

Recent experiments on the elastic response of Berea sandstone show that nonlinear excitation of a resonant bar is accompanied by a slow dynamics, a dynamics involving time scales many orders of magnitude longer than the excitation period, 2π/ω. A lumped-element description of a resonant bar is developed. A complementary phenomenological theory of slow nonlinear dynamics is postulated. This phenomenological theory is used in the lumped-element description to explain the experiments. The results illustrate the possibility of experimental exploration of slow nonlinear dynamics using the acoustic analogue of a NMR experiment. [Work partially supported by OBES, Engineering and Geosciences Grant No. W7405-ENG-36, the National Science Foundation Grant No. EAR-9528965, and the Institute of Geophysics and Planetary Physics at Los Alamos National Laboratory.]