3.4 Elastic anisotropy

Real rocks are not isotropic due to layering, particle orientation during deposition, and fracturing. Sedimentary rocks are usually well explained with transverse isotropic symmetry. Vertical transverse isotropy assumes symmetry around a vertical axis such that mechanical properties are the same when measured along any direction in a horizontal plane but different in the vertical direction (the direction perpendicular to bedding). The presence of vertical fractures in a preferred orientation can break this symmetry and make the medium orthorhombic. Accurate determination of horizontal stresses with elastic models (e.g., Eq. 3.34) may need anisotropic models to properly account for rock stiffness anisotropy.

Figure 3.21: Stiffness matrix coefficients in anisotropic media.

Most sedimentary rocks are stiffer in the horizontal direction than in the vertical direction $E_h > E_v$.

Figure 3.22: Stiffness parallel and perpendicular to bedding. [add real data]