Modern downhole microseismic surveys employ geometries in which ray trajectories generated by locatable events provide full azimuthal and polar coverage, making it possible to estimate in-situ seismic anisotropy. Traveltimes and particle motions of the direct P- and shear-waves acquired in such geometries can constrain stiffness tensors of triclinic media. While obtaining all 21 stiffness coefficients of a homogeneous triclinic space simultaneously with locating pertinent microseismic events from records collected in a single vertical well appears relatively straightforward, the same methodology does not necessarily apply to layered formations because combination of their vertical heterogeneity and azimuthal anisotropy might invalidate the commonly adopted approximation of the event azimuths by those of the P-wave polarization vectors. When the event azimuths cannot be derived from the particle motions, traveltimes observed in two or more wells are required to locate the events and build layered triclinic or higher-symmetry azimuthally anisotropic velocity models. The multiwell event-location methods are expected to perform better than their single-well counterparts because they rely solely on triangulation and eliminate the usually pronounced azimuthal event-location uncertainties that stem from noises adversely affecting the results of hodogram analysis.