Most shale reservoirs are described assuming transverse isotropy. A full characterization of such reservoirs requires the knowledge of six elastic parameters comprising, for instance, the density; P- and S-wave vertical velocities; and the three anisotropic Thomsen parameters , , and . For hydraulic fracturing monitoring purposes, the parameters and are typically estimated from perforation microseismic data by analyzing the variation with phase angles of the traveltimes of direct P-waves and direct SH-waves. The estimation of the Thomsen parameter is more challenging because most perforation microseismic data do not exhibit direct SV-waves to which the parameter is the most sensitive. A Bayesian inference method is proposed to estimate from traveltimes of secondary SV-waves observed on microseismic data. Because the interpretation of the physics underlying the observation of these secondary SV-waves is often not readily available for wellsite operations, a marginalization scheme is used to account for uncertainties associated with not knowing, or only partially knowing, the locations where they originated from. I determined the benefits of the proposed method by applying it to data sets collected in the Jonah field using a single monitoring well. The results revealed a significant variance reduction of more than 15-fold on the posterior probability distribution associated with when using the secondary-source SV-waves. Moreover, a more accurate estimate of the microseismically derived fractured volume is achieved with variance reduced by more than a factor of 75.