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In theory, a single horizontally polarized seismometer can be used to find the six independent elements of the seismic moment tensor of a buried point source, provided that the instrument is neither longitudinally nor transversely polarized. Also, two vertically polarized seismometers can be used, provided that the epicentre does not lie on the great circle through the two instruments. These results form the theoretical basis for a procedure for retrieving the source mechanism from a sparse seismographic network.
Freeman et al. (Fri,) studied this question.