Array quadrupole data obtained in a LWD environment are processed to determine the shear velocity of an earth formation taking into account dispersion effects caused by the logging tool. When this processing is done in an azimuthally anisotropic formation, the shear velocity that is obtained is the slow shear velocity. When 4C (cross-dipole) data are also obtained, then both the fast and slow shear velocities of an azimuthally anisotropic formation can be obtained.