Stress dependency and anisotropy of dynamic elastic properties of shales is important for a number of geophysical applications, including seismic interpretation, fluid identification, and 4D seismic monitoring. Using SayersKachanov formalism, we developed a new model for transversely isotropic (TI) media that describes stress sensitivity behavior of all five elastic coefficients using four physically meaningful parameters. The model is used to parameterize elastic properties of about 20 shales obtained from laboratory measurements and the literature. The four fitting parameters, namely, specific tangential compliance of a single crack, ratio of normal to tangential compliances, characteristic pressure, and crack orientation anisotropy parameter, show moderate to good correlations with the depth from which the shale was extracted. With increasing depth, the tangential compliance exponentially decreases. The crack orientation anisotropy parameter broadly increases with depth for most of the shales, indicating that cracks are getting more aligned in the bedding plane. The ratio of normal to shear compliance and characteristic pressure decreases with depth to 2500 m and then increases below this to 3600 m. The suggested model allows us to evaluate the stress dependency of all five elastic compliances of a TI medium, even if only some of them are known. This may allow the reconstruction of the stress dependency of all five elastic compliances of a shale from log data, for example.

Up‐scaling the elastic properties of digitized rock volumes as obtained from X‐ray computer tomography (CT) imaging via computer simulations has the potential to assist and complement laboratory measurements. This computational up‐scaling approach remains a challenging task as the overall elastic properties are not only dependent on the elastic properties of individual grains but also on the hardly resolvable pore spaces between adjacent grains such as micro‐cracks. We develop a digitized rock image and elastic up‐scaling workflow based on general‐purpose and widely available software packages. Particular attention is paid to CT image processing including filtering, smoothing and segmentation. A strategy for optimal meshing for subsequent finite‐element modelling is also proposed. We apply this workflow to the micro‐tomographic image of a well‐consolidated, feldspatic sandstone sample and determine the up‐scaled bulk and shear moduli. These effective elastic moduli are compared to the moduli inferred from laboratory ultrasound measurements at variable effective stresses (0–70 MPa). We observe that the numerically up‐scaled elastic moduli correspond to the moduli at a certain effective stress level (50 MPa), beyond which the effective‐stress dependency follows a linear trend. This indicates that the computational up‐scaling approach yields moduli as if all compliant (soft) porosity was absent, i.e., microcracks are closed. To confirm this hypothesis, we estimate the amount of soft porosity on the basis of the double‐porosity theory (Shapiro, 2003) and find that at 50 MPa the soft porosity is indeed practically zero. We conclude that our computational elastic up‐scaling approach yields physically consistent effective moduli even if some geometrical features are below CT resolution. To account for these sub‐resolution features either theoretical or additional computational approaches can be used.