Complete waveforms with periods longer than 30 sec recorded at teleseismic and regional distances are used to characterize the source of several earthquakes and underground nuclear explosions in the Lop Nor area, Xinjiang, China. Propagation effects of Earth's heterogeneities on data for several auxiliary events with well-constrained source mechanisms, in the vicinity of the primary event, are calibrated by frequency-domain division of each pair of observed and synthetic waveforms, with the synthetics being computed for a reference Earth model. The frequency-dependent deconvolution filters obtained for the auxiliary events are interpolated to construct a predicted deconvolution filter, which is convolved with observed waveforms for the primary event to remove the empirically determined propagation effects and to obtain simplified waveforms that are intrinsically well predicted by the reference Earth model. These waveforms are then inverted for the source mechanism and centroid time, location, and depth of the primary event. The inversion yields a centroid depth of 13 km for the 7 September 1994 earthquake (mb = 5.1), significantly shallower than the 33-km depth reported previously from routine determinations. The centroid depth of the 5 October 1993 nuclear explosion plus tectonic release is estimated at approximately 4 km, while the depth of the 21 May 1992 explosion plus tectonic release is less well resolved and may be deeper than 5 km, reflecting limited resolution of the passband used here. With extension to shorter-period energy, the method holds promise for reliable source inversion for small events in a calibrated region.