Characterizing the nonlinear interaction of S (shear) and P (longitudinal) waves in reservoir rocks

Abstract

The nonlinear elastic response of rocks is known to be caused by internal microstructure, particularly cracks and fluids. In order to quantify this nonlinearity, this paper presents a method for characterizing the interaction of two nonresonant traveling waves: a low-amplitude P-wave probe and a high-amplitude lower frequency S-wave pump with their particle motions aligned. We measure changes in the arrival time of the P-wave probe as it passes through the perturbation created by a traveling S-wave pump in a sample of room-dry Berea sandstone (15 × 15 × 3 cm). The velocity measurements are made at times too short for the shear wave to reflect back from the bottom of the sample and interfere with the measurement. The S-wave pump induces strains of 0.3—2.2 × 10−6, and we observe changes in the P-wave probe arrival time of up to 100 ns, corresponding to a change in elastic properties of 0.2%. By changing the relative time delay between the probe and pump signals, we record the measured changes in travel time of the P-wave probe to recover the nonlinear parameters β~ −102 and δ ~−109 at room-temperature. This work significantly broadens the applicability of dynamic acousto-elastic testing by utilizing both S and P traveling waves.