Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA ,SHORT-TERM PROPERTIES OF EARTHQUAKE CATALOGS AND MODELS OF EARTHQUAKE SOURCE We review the short-term properties of earthquake catalogs, in particular the time and size distributions and the completeness of the early part of aftershock sequences for strong, shallow earthquakes. We determine the parameters of the Omori and Gutenberg-Richter laws for aftershocks close-in-time to a mainshock. Aftershock sequences of large earthquakes in southern California (1952 Kern County, 1992 Joshua Tree--Landers--Big Bear sequence, 1994 Northridge, and 1999 Hector Mine), recorded in the CalTech catalog are analyzed to demonstrate that at the beginning of these series, many small earthquakes are absent from the catalog. The number of missing earthquakes increases with the magnitude range of a catalog and for some datasets exceeds the number of aftershocks close to a mainshock listed in a catalog. Comparing global earthquake catalogs (Harvard CMT and PDE) with local datasets indicates that the catalogs based on longer period waves miss many early aftershocks even when their magnitudes are well above the stated magnitude threshold. Such short-term incompleteness may introduce significant biases to the statistical analysis of the seismicity pattern, in particular for branching models of earthquake occurrence incorporating the Omori law, widely employed for short-term seismicity forecasts. Analyzing the source rupture process of several recent large earthquakes suggests that rupture propagation is highly inhomogeneous in space, time, and focal mechanism. These random variations in the rupture process can be viewed as an extension of the aftershock stochastic generating mechanism towards the origin time of a mainshock.Accepted by BSSA, scheduled for August issue Temporal distribution of earthquakes Omori (1894) found that aftershock rate for the 1891 Nobi earthquake decayed about as 1/time. This decay still continues now in the focal zone of the earthquake. Statistical analysis of earthquake catalogs indicates that the power-law dependence characterizes occurrence of both foreshocks and aftershocks. Mainshock can be considered as an aftershock which happen to be stronger than the previous event. n(t) = 1/(t+c): c-value does not have physical meaning Positive c-value means that aftershock rate goes to infinity before the mainshock. It is usually interpreted as delay between mainshock rupture end and the start of aftershock activity. Negative c-value means that aftershock rate singularity occurs after the mainshock. This is a more natural assumption. No reliable empirical regularities in c-value behavior have been found. From Fig. 2 Reasenberg (JGR, 1999): b -- Pairs with foreshock magnitude >= 5.0 and mainshock magnitude >= 5.0, N=1966; d -- Mf >=5.0, Mm >=6.0, N=562. C > 0 means that aftershock rate goes to infinity at negative time (t