Western Atlas Logging Services, 10201 Westheimer, Houston, TX 77042
Stanford Univ., Stanford, CA 94305
Murnaghan's second-order elasticity theory is applied to studying the directional- and stress-dependence of elastic wave velocities in intrinsically isotropic rocks. At any stress within the ``perfectly'' elastic range, the velocity change with stress (slope) and direction is determined by three third-order elastic (TOE) constants. However, the three TOE constants are not all independent for most rock samples measured in this study. This observation reduces the number of independent TOE constants from three to two, which allows the prediction of stress-induced velocity anisotropy from P- and S-wave velocity measurements under hydrostatic pressures. Compared with the approach that adopts linear stress-strain relation but allows stress-dependent elastic constants (second-order), this method avoids the modeling of rock pore compressibilities and has a clearer physical meaning. The origin of the elastic nonlinearity in rocks is shown to be the prevalence of compliant pore space in rocks, with geometries ranging from thin cracks in igneous rocks to cemented grain contacts in granular sedimentary rocks undergoing diagenesis. By using elastic solutions for cracks, contacts, and cemented contacts and assuming a mixture of these different types of pores, it is shown that the TOE constants of rocks can be related to their textural or petrographical properties.