Nonlinear elastic wave propagation is related to the dependency of wave velocity on stress. In our studies, we investigated how the velocity depends on small amplitude stress oscillations. The oscillations aim to simulate a low frequency acoustic pulse used in a new two-frequency technique for measuring nonlinear elasticity. These controlled axial stress variations manipulate the elastic properties of rock, which are detected by the high frequency acoustic pulses. Here, the nonlinear propagation is examined for both P- and S-waves, which show the dependency of the wave propagation direction and polarization on the direction of applied stress. The sensitivity of the velocity gradient is investigated through given changes xternal stress and pore pressure. The impact of pore fluid type is tested on samples fully saturated with brine and kerosene, as well as dry samples. All our tests, preformed on Castlegate sandstone, indicate that the nonlinearity is mainly related to the rock structure and far less to the pore fluid. Moreover, it confirmed an idea of the micro- and macro-cracks as the primary source of nonlinear behavior of rock.
The tests presented in this paper concern an investigation of the still growing issue of the anonlinear elasticity of geomaterials. The interest in this phenomenon began several decades ago and has been investigated in numerous studies. Nowadays, literature provides a large number of experimental data that confirm a significant - compared to other materials - nonlinear elastic response of rocks . That places them in the mesoscopic class of the nonlinear materials, which are characterized by nonlinearity several orders of magnitude higher than that of materials belonging to the atomic elastic class like fluids and monocrystalline solids . This large difference in nonlinear elastic behavior is connected with its origin, and in case of rocks it is associated with the complexity and high heterogeneity of their structures. More precisely, the source of a nonlinearity in rock includes all compliant features present in a hard rock matrix. These soft features are the weakest parts of the rock'' structure, i.e. discontinuities such as pores, macro- and micro-fractures, joints, and grain-to-grain contacts. They determine rocks deformability and thus are the main, but not only, sources of nonlinearity. Another factor commonly quoted is saturation, where both the amount and type of pore fluid influence nonlinerity.
Nonlinear elastic response of rock is manifested in many different ways [3, 4] and revealed both in mechanical and acoustic experiments. The most common are : the nonlinear character of stress-strain curves, hysteresis (difference between stress-strain relation for loading and unloading paths), pulse distortion (generation of higher harmonics), side bands (appearance of new frequency), etc. That large number of nonlinear phenomena, as well as the high magnitude of nonlinearity, suggest that the nonlinear elasticity of rocks should not be neglected. Moreover, it should be treated as an attribute, since it brings additional information about the rock. Thus, many studies, including that discussed here, attempt to create a commercial method of rock testing based on the nonlinear elasticity alone, or on its combination with other methods. The most promising applications, particularly for the petroleum industry, are the detection of fractures  and determination of pore fluid content (saturation) .