An acoustic logging system with a borehole tool comprising a transmitter assembly and an axially spaced receiver assembly. The transmitter and receiver assemblies are optionally rotatable with respect to each other, depending upon the embodiment of the logging system. The logging system is designed to measure, among other parameters, the velocity (or slowness) and amplitude of shear wave energy induced by the transmitter assembly within formation penetrated by the borehole. These parameters are extracted from full wave acoustic data responses of receiver elements comprising the receiver assembly, and are measured as a function of azimuth around the borehole. These parameters are subsequently used to determine anisotropic properties of the formation, such as the azimuthal direction of formation fracturing with respect to the well borehole. Optional rotation of the transmitter and receiver assemblies minimizes adverse effects of maintaining calibration and balance of multiple transmitters and receivers.