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There are many examples of earthquakes whose surface expressions are much more complicated than the seismologically derived faulting models. Seismologists also have found seismic source complexity and improved seismicity data have shown that rupture may occur on irregular or multiple shear surfaces. To simultaneously map both geometrical and temporal variation of the seismic sources for a complex rupture history from observed seismograms, it is possible to use a time dependent moment tensor (TDMT) inversion. The TDMT inversion algorithm has been tested with three synthetic data examples with varying degrees of complexity. The first example demonstrates that a multiple source with no focal depth change can be recovered, and the source parameters of each of the subevents can be accurately determined. In the second case we allowed the depth to vary for subevents (9-km and 13-km source depth, respectively). The two subevents can be identified on the basis of simultaneous shape-change of the moment tensor elements along with non-causality and the size of the CLVD component. The third example introduced source complexity by having two subevents which overlapped in time. The overlapped period could be seen in the moment tensor elements as unusually abrupt changes in the time function shape. The TDMT inversion was also performed on long-period body waves for three earthquakes: the 1982 Yemen earthquake, the 1971 San Fernando earthquake, and the 1952 Kern County earthquake. The Yemen earthquake was mapped as two simple, normal-slip subevents (with onset timing of the second subevent 5 seconds after the first) without a significant component of left- or right-lateral displacement or source depth change. The San Fernando earthquake is interpreted as two shear dislocation sources with changing source depths, possibly indicating upward rupture propagation (from 13-km to 7-km). The interpretation of the TDMT inversion for the Kern County earthquake was also a double point source which propagates upward from 20-km to 5-km. The resultant moment tensor functions from inversion of the synthetic waveforms, a combination of isotropic and tectonic release, demonstrated that the tectonic release associated with underground nuclear explosion can be separated and identified if the source depth between the explosions and tectonic release are different.

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