Abstract
Static and dynamic behavior of isotropic or anisotropic media, including rocks, are conveniently described with a second-order stiffness matrix using the Voigt notation, which linearly relates stress changes to strains. However, experimental and field observations indicate that the dynamic stiffness of rocks is stress dependent. We investigate a model proposed by Fuck and Tsvankin employing a constitutive third-order elastic tensor to describe the non-linear strain sensitivity of the stiffness. By using laboratory measurements of strains and ultrasonic P- and S-wave velocities in multiple directions, we were able to invert for all the third-order parameters. We used the third-order elastic tensor to model changes in ultrasonic velocities and investigated the impact of different third-order tensor component optimization schemes on the accuracy of the velocity estimates. To our knowledge this is the first fit of dynamic stiffness of a shale to a third order constitutive model that is not restricted to isotropic strain sensitivity.