Microseismic data recorded by surface monitoring arrays can be used to estimate the effective anisotropy of the overburden and reservoir. In this study we used the inversion of picked P-wave arrival times to estimate the Thomsen parameter and the anellipticity coefficient . This inversion employs an analytic equation of P-wave traveltimes as a function of offset in homogeneous, transversely isotropic media with a vertical axis of symmetry. We considered a star-like distribution of receivers and, for this geometry, we analyzed the sensitivity of the inversion method to picking noise and to uncertainties in the P-wave vertical velocity and source depth. Long offsets, as well as a high number of receivers per line, improve the estimation of and from noisy arrival times. However, if we do not use the correct value of the P-wave vertical velocity or source depth, the long-offset may increase the inaccuracy in the estimation of the anisotropic parameters. Such inaccuracy cannot be detected from time residuals. We also applied this inversion to field data acquired during the hydraulic fracturing of a gas shale reservoir and compared the results with the anisotropic parameters estimated from synthetic arrival times computed for an isotropic layered medium. The effective anisotropy from the inversion of the field data cannot be explained by layering only and is partially due to the intrinsic anisotropy of the reservoir and/or overburden. This study emphasizes the importance of using accurate values of the vertical velocity and source depth in the P-wave arrival time inversion for estimating anisotropic parameters from passive seismic data.