“…Today, more borehole sonic measurements are conducted in highly deviated or horizontal wells penetrating strongly transverse isotropic (TI) formations (either with a vertical axis of symmetry called VTI or a tilted axis of symmetry called TTI) or lower symmetries such as orthorhombic or monoclinic due for instance to the presence of fractures. In this context it is important to more accurately relate the three or four available sonic slowness measurements from sonic tools, i.e., one compressional, one or two dipole shear, and one tube-wave slowness, to the five elastic constants of intrinsic TI formations (Norris and Sinha, 1993;Walsh et al, 2006;Sinha et al, 2006;Walsh et al, 2007). For a vertical well within a VTI medium, each sonic measurement can be uniquely related to one component of the stiffness tensor, i.e., the components c 33 , c 55 , and c 66 are respectively related to one compressional, one dipole shear, and one tube-wave shear slowness (see Figure 1; the stiffnesses are expressed using Voigt notation).…”