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We have developed a technique for inverting microseismic waveform data, recorded at the surface and/or downhole, to obtain simultaneously the centroid location and moment tensor of a microseismic event. Our inversion approach is conceptually similar to the “Centroid—Moment Tensor algorithm”, which has been very widely applied in the field of global seismology, except that we forward model the seismic wavefield using a method that is amenable to the efficient, accurate and stable computation of synthetic microseismic waveforms and their partial derivatives with respect to source parameters. We obtain an initial source model by performing a least-squares inversion of waveform data for the moment tensor, with the centroid position fixed at the hypocentral coordinates determined by conventional body wave travel-time methods. Assuming that non-linearity in the relationship between the source location and data is weak, we may use this source as the starting point for an iterative least-squares inversion for the centroid and moment tensor of a microseismic event. Here, we present centroid locations, moment tensors, and estimates of their uncertainty calculated using this method for microseismic events induced during hydraulic fracturing operations at Preese Hall, UK and Cotton Valley, USA.