Fracture- and stress-induced sonic anisotropy is distinguished using a combination of image and sonic logs. Borehole image and sonic logs are acquired via known techniques. Analysis of sonic data from monopole P- and S-waves, monopole Stoneley and cross-dipole shear sonic data in an anisotropic formation are used to estimate at least one compressional and two shear moduli, and the dipole fast shear direction. Fracture analysis of image logs enables determination of fracture types and geometrical properties. Geological and geomechanical analysis from image logs provide a priori discrimination of natural fractures and stress-induced fractures. A forward quantitative model of natural fracture- and stress-induced sonic anisotropy based on the knowledge of fracture properties interpreted from image logs allows the computation of the fast-shear azimuth and the difference in slowness between the fast- and slow-shear. The misfit between predicted and observed sonic measurements (i.e. fast-shear azimuth and slownesses) is then optimized in order to discriminate depth zones with an elastic medium as being influenced by the presence of open natural fractures, closed natural fractures and fractures induced by non-equal principal stress effects.