Passive seismic tomography, in which the event locations and the velocity model are inferred simultaneously, is seldom used to process microseismic surveys acquired in the oil and gas industry. We discuss advantages of applying tomographic ideas to typical microseismic data recorded in a single, nearly vertical well to monitor hydraulic stimulation of a shale-gas reservoir. Microseismic events are conventionally located in the energy-industry applications using a velocity model derived from sonic logs and perforation shots. Instead of fixing the model, as is normally done, we alter it while locating the events. This added flexibility not only makes it possible to accurately predict traveltimes of the recorded P- and S-waves, but also provides a convincing evidence for anisotropy of the examined shale formation. While we find that velocity heterogeneity does not need to be introduced to explain the data acquired at each stage of hydraulic fracturing, the obtained models are suggestive of possible time-lapse changes in the anisotropy parameters that characterize the stimulated reservoir volume.