Fault healing was first modeled by R. Madariaga (Dynamics of an expanding circular fault, Bull. Seis. Soc. Am., 66, 639-666, 1976) using a finite-difference approach. Healing of an expanding circular rupture was initiated simultaneously at the edges, and subsequently propagated inward toward the center of the fault at a large fraction of the shear-wave velocity. The fault did not stop slipping at interior points until information that the rupture had stopped propagated inward from the edges.

S.M. Day, Three-dimensional finite difference simulation of fault dynamics: Rectangular faults with fixed rupture velocity, Bull. Seis. Soc. Am., 72, 705-727, 1982.

T.H. Heaton, Evidence for and implications of self-healing pulses of slip in earthquake rupture, Phys. Earth Planet. Int., 64, 1-20, 1990.

Quasi-dynamic models are dynamic models constructed to reproduce the principal features of kinematic models, which were previously obtained by modeling seismic data. Examples of quasi-dynamic models with short rise times include the following: H. Quin, Dynamic stress drop and rupture dynamics of the October 15, 1979 Imperial Valley, California, earthquake, Tectonophysics, 175, 93-117, 1990; T. Miyatake, Dynamic rupture processes of inland earthquakes in Japan; Weak and strong asperities, Geophys. Res. Lett.,19, 1041-1044, 1992; E. Fukuyama and T. Mikumo, Dynamic rupture analysis; Inversion for the source process of the 1990 Izu-Oshima, Japan, earthquake (M = 6.5), J. Geophys. Res., 98, 6529-6542, 1993; G.C. Beroza and T. Mikumo, Short slip duration in dynamic rupture in the presence of heterogeneous fault properties, J. Geophys. Res., 101, 22,449-22,460, 1996.

T.H. Heaton, J.F. Hall, D.J. Wald, and M.W. Halling, Response of high-rise and base-isolated buildings to a hypothetical Mw 7.0 blind thrust earthquake, Science, 267, 206-211, 1995.

Early references suggesting such behavior include E. Vesanen (On the character interpretation of seismograms, Ann. Acad. Sci. Fenn., AIII, 5, 1942); T. Usami, Quart. J. Seis., 21, 1-13, 1956); S.S. Miyamura, R. Omote, R. Teisseyre, and E. Vesanen, Multiple shocks and earthquake series pattern, Bull. Int. Inst. Seis. Earthquake Eng., 2, 71-92, 1965); and M. Båth (Seis. Bull., Uppsala, February 4, 1965). M. Wyss and J.N. Brune (The Alaska earthquake of 28 March 1964: A complex multiple rupture, Bull. Seis. Soc. Am., 57, 1017-1023, 1967) found that the Good Friday earthquake of 1964 consisted of six subevents of higher than average slip and that, based on the timing of these subevents, rupture propagated primarily to the southwest from the epicenter. Studies of moderate to large earthquakes in the far field using P- and S- wave pulse shapes often depict earthquake rupture with multiple point sources (H. Kanamori and G.S. Stewart, Seismological aspects of the Guatemala earthquake of February 4, 1976, J. Geophys. Res., 83, 3427-3434, 1978), which have been termed asperities (T. Lay and H. Kanamori, An asperity model of great earthquake sequences, in Earthquake Prediction—An International Review, D.W. Simpson and P.G. Richards, eds., American Geophysical Union, Maurice Ewing Series, 4, Washington, D.C., pp. 579-592, 1980). For an isolated point source or even for multiple point sources, it is often sufficient to allow for the finite duration through the moment rate function, without considering the spatial extent of each source.

For a thorough review of source tomography in the far field, see the review by L. Ruff, Tomographic imaging of seismic sources, in Seismic Tomography, G. Nolet, ed., D. Reidel, Boston, pp. 339-366, 1987. The pulse shape of far-field body waves can be used to infer the spatial and temporal distribution of slip on the fault; however, only in the case of particularly large earthquakes is it possible to resolve spatial and temporal variation of slip on the fault plane at teleseismic distances. See, for example the study of the 1985 Michoacan, Mexico, earthquakes by C. Mendoza (Coseismic slip of two large Mexican earthquakes from teleseismic body waveforms: Implications for asperity interaction in the Michoacan plate boundary segment, J. Geophys. Res., 98, 8197-8210, 1993). Moreover, it is theoretically impossible to reconstruct the slip distribution from the far-field data alone. In the Fraun-