Fiber-optic distributed acoustic sensing (DAS) cables are now used to monitor microseismicity during hydraulic-fracture stimulations of unconventional gas reservoirs. Unlike geophone arrays, DAS systems are sensitive to uniaxial strain or strain rate along the fiber direction and thus provide a 1C recording, which makes identifying the directionality and polarization of incoming waves difficult. Using synthetic examples, we have shown some fundamental characteristics of microseismic recordings on DAS systems for purposes of hydraulic fracture monitoring in a horizontal well in anisotropic (vertical transverse isotropy [VTI]) shales. We determine that SH arrivals dominate the recorded signals because their polarization is aligned along the horizontal cable at the near offset, although SV will typically dominate for events directly above or below the array. The amplitude of coherent shear-wave (S-wave) arrivals along the cable exhibits a characteristic pattern with bimodal peaks, the width of which relates to the distance of the event from the cable. Furthermore, we find that S-wave splitting recorded on DAS systems can be used to infer the inclination of the incoming waves, overcoming a current limitation of event locations that have constrained events to lie in a horizontal plane. Low-amplitude SV arrivals suggest an event depth similar to that of the DAS cable. Conversely, steep arrivals produce higher amplitude SV-waves, with S-wave splitting increasing with offset along the cable. Finally, we determine how polarity reversals observed in the P and SH phases can be used to provide strong constraints on the source mechanisms.