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For most of the readers of this article, the gap theory, which hypothesizes that an earthquake is more probable over the segment of a given plate boundary where the last rupture occurred earlier, may be a classic well rooted in plate tectonics, and its proposed rejection by Kagan and Jackson  on the basis of clustering found in the earthquake catalog was probably news. For me, the gap theory proposed in 1965 was a surprise, because almost all the statistical studies on earthquake catalogs indicated that earthquakes cluster in time and space at all levels of magnitudes [ Aki, 1956]. In other words, the probability of earthquake occurrence, as estimated from any catalog data, increases after another earthquake occurs, opposite to what the gap theory predicts.
The gap theory first formulated by Fedotov  and modified by Kelleher et al. , McCann et al. , Sykes and Nishenko , Nishenko and Jacob , Bakun and Lindh  and Nishenko  assumes that a ``characteristic earthquake'' can be identified for a given segment of plate boundary. This concept of characteristic earthquake was generalized by Schwartz and Coppersmith  to all faults including those in the mid-plate. A great merit of this concept has been to offer a linkage among multidisciplinary observations. For example, seismological observations on asperities and barriers that control the rupture process of the characteristic earthquake may be related to geological and geophysical observations on fault segmentation and fault zone structures [ Aki, 1984].
Once a characteristic earthquake is identified for a given fault segment, it becomes an individual, like a human being, to which life expectancy at a certain age can be evaluated and used for determining the premium for life insurance. The long-term prediction, based on the gap theory, gives the conditional probability of the occurrence of a characteristic earthquake, given the time from the last one. The probability is small immediately after the earthquake, opposite to the clustering tendency of earthquake occurrences revealed from statistical analysis of catalog data.
These two opposite trends are not logically conflicting because one is for the whole catalog of earthquakes, and the other is for its subset, namely, characteristic earthquakes. Both are also physically reasonable because the fault slip in an earthquake generates stress concentration wherever the slip is non-uniform, while stress is generally relieved in the scale of the whole fault plane.
The assumption of ``characteristic earthquake'' in the strict sense may be simplistic reflecting to some degree the wishful thinking of hazard analysts. For example, according to Segall and Du , the rupture of the Parkfield segment (considered to be the ideal case of characteristic earthquake) apparently stopped at the right step in the fault trace in the Cholame Valley in 1934, but went through it in 1966, although the starting point and total seismic moment were indistinguishable between the two events. There is a need for modifying the characteristic earthquake concept to allow for some variations like this, but it would be a mistake to abandon the concept entirely and give up identifying a geologically meaningful subset of earthquakes in the earthquake catalog. For example, detailed analysis of nearly identical seismograms of eighteen small earthquakes that occurred on the Calaveras fault over a period of 11 years by Vidale et al.  yielded a systematic dependence of duration on the time since the previous earthquake, offering in-situ data relevant to fault zone healing.