Methods are provided for determining properties of an anisotropic formation (including both fast and slow formations) surrounding a borehole. A logging-while-drilling tool is provided that is moveable through the borehole. The logging-while drilling tool has at least one dipole acoustic source spaced from an array of receivers. During movement of the logging-while-drilling tool, the at least one dipole acoustic source is operated to excite a time-varying pressure field in the anisotropic formation surrounding the borehole. The array of receivers is used to measure waveforms arising from the time-varying pressure field in the anisotropic formation surrounding the borehole. The waveforms are processed to determine a parameter value that represents shear directionality of the anisotropic formation surrounding the borehole.
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