the fault is variable, and (4) slip deficits at the ends of fault are not “filled in” by slip from smaller earthquakes.

From the perspective of hazard assessments, this hypothesis offers tremendous simplification because only one earthquake scenario is considered (the characteristic earthquake) for each fault segment. Moreover, the size of this earthquake can be estimated from the length of the fault segment and moment-length scaling relations. In this way, the hypothesis reduces the dimension of the earthquake forecasting problem to one in which time is the only independent variable. Because of these simplifications, characteristic earthquakes have been incorporated into a large number of seismic hazards analyses (209).

Seismic Gap Hypothesis Building on the characteristic earthquake hypothesis, the seismic gap hypothesis addresses the distribution of these large events through time. To estimate earthquake likelihood for use in seismic hazard studies, the seismic gap model is implemented as follows. Mapped faults are divided into segments, and a characteristic magnitude is estimated for each segment. The slip rate on the fault is estimated from the displacement and age of features offset by the fault, and the characteristic slip is estimated from historical slip data or from regression relationships on magnitude and slip. The mean recurrence time is estimated from either the times of known earthquakes on the segment or the ratio of characteristic slip to fault slip rate. The probability distribution of recurrence times is estimated, and the conditional probability of an earthquake during some time interval is computed. The critical question to address is whether forecasted earthquakes in seismic gaps occur with greater probability than a simple random occurrence.

Moment-Rate Budgeting One approach to forecasting future earthquakes is to balance the long-term rates of fault slip and moment release as inferred from seismic monitoring. In practice, the application of moment-rate budgeting is difficult because the results are sensitive to the completeness of the historical catalog and the past distribution of earthquakes in space and time. Key, but controversial, assumptions of this method are that the long-term slip rates are representative of present rates and that the slip rates are completely seismogenic. The latter assumption may hold for crustal earthquakes, but it does not appear to be valid for many subduction zones, where significant aseismic deformation is occurring.

Clustering The term clustering is commonly used to describe concentrations of earthquakes in space, time, or both. Earthquakes are much more frequent in some places than in others, even along major faults or

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