High amplitude, bifrequency experiments in porous rocks

Fluid-filled, porous, sedimentary rocks have the general characteristic that the sound speeds are strongly dependent on the state of stress and therefore, the third-order elastic coefficients (i.e., A, B, C) are generally much larger than for normal solids. However, the linear attenuation can also be very large such that in nonlinear wave propagation, the Gol’dberg number is small. Experiments studying harmonic generation in porous rocks have been made using an ultrasonic immersion system (i.e., water/solid/water) where a high amplitude (e.g., 500 kPa), bifrequency (0.95 and 1.05 MHz), tone burst is emitted and then sum and difference frequencies are detected after propagation through the water/solid/water system. A frequency domain numerical implementation of the KZK (Khokhlov–Zabolotskaya–Kuznetsov) nonlinear parabolic wave equation is used to describe the nonlinear propagation in the three layer system. Experiments on solids with well-known acoustic properties (linear and nonlinear) were used to validate the model. Measurements were then made on several sandstones and limestones and the model used to derive the nonlinear propagation parameter, β=f(A,B,C). Finally, these results are compared with independent measurements of A, B, C for these rocks.