Modern downhole microseismic surveys often employ geometries in which ray trajectories generated by a collection of locatable events provide full polar and azimuthal coverage, making it possible to estimate the in situ seismic anisotropy. We show that traveltimes and particle motions of the direct P- and shear-waves acquired in suchgeometries 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 data recorded in a single vertical well is relatively straightforward, the same methodology does not necessarily succeed in layered formations because the 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. As our numerical tests indicate, the multi-well eventlocation methods are expected to perform better than their single-well counterparts because they rely solely on triangulation and eliminate the usually pronounced azimuthal uncertainties in the event locations that stem from noises adversely affecting hodogram analysis
