Variability of Displacement at a Point: Implications for Earthquake‐Size Distribution and Rupture Hazard on Faults

To investigate the nature of earthquake-magnitude distributions on faults, we compare the interevent variability of surface displacement at a point on a fault from a composite global data set of paleoseismic observations with the variability expected from two prevailing magnitude-frequency distributions: the truncated-exponential model and the characteristic-earthquake model. We use forward modeling to predict the coefficient of variation (CV) for the alternative earthquake distributions, incorporating factors that would effect observations of displacement at a site. The characteristic-earthquake model (with a characteristic-magnitude range of +/- 0.25) produces CV values consistent with the data (CV similar to 0.5) only if the variability for a given earthquake magnitude is small. This condition implies that rupture patterns on a fault are stable, in keeping with the concept behind the model. This constraint also bears upon faultrupture hazard analysis, which, for lack of point-specific information, has used global scaling relations to infer variability in average displacement for a given-size earthquake. Exponential distributions of earthquakes (from M 5 to the maximum magnitude) give rise to CV values that are significantly larger than the empirical constraint. A version of the model truncated at M 7, however, yields values consistent with a larger CV (similar to 0.6) determined for small-displacement sites. Although this result allows for a difference in the magnitude distribution of smaller surface-rupturing earthquakes, it may reflect, in part, less stability in the displacement profile of smaller ruptures and/or the tails of larger ruptures.