We propose a dynamic method to detect the nonlinear elastic hysteretic characteristics of rock. The method is easily implemented and requires injecting two co-propagating longitudinal waves into the rock and receiving them. One of the waves is a high energy low-frequency longitudinal wave that loads strain in the rock, and a other is the low energy high-frequency longitudinal wave that is used to detect the elastic modulus variation induced by the loaded strain. Analyzing the relationship between elastic modulus variation and the loaded strain, we quantify the nonlinear elastic characteristics of the rock, including the nonlinear coefficients and slow dynamics, and evaluate hysteretic loops. A typical sandstone experiment is displayed and results show the nonlinear coefficients are independent of input amplitude of the longitudinal waves, but slow dynamics are a function of the input amplitude of the low fequency longitudinal waves.
