The Correlation Lengths and Hypocentral Positions of Great Earthquakes

Here, we revisit the issue of slip distributions modeled as spatially random fields. For each earthquake in the U.S. Geological Survey’s database of finite‐fault models (M 7–9), we measure the parameters of a best‐fitting von Karman autocorrelation function. We explore the source scaling properties of the correlation lengths and the Hurst exponent. We find that the behavior previously observed for more moderate events generally still holds at higher magnitudes and larger source dimensions. However, we find slightly larger correlation lengths and a lower mean Hurst exponent. The most important effect of these differences is that using our preferred parameters to generate stochastic slip models will lead to slightly larger asperities and more small‐scale structure in between them. We also define a new scaling relationship for the standard deviation of slip necessary for a full description of a spatially random field. Here, we also explore the patterns of where hypocenters are located within a fault. We find that strongly unilateral ruptures are comparatively rare and propose several probability density functions that can be used to randomly assign hypocentral positions when creating stochastic sources. When compared to simply randomly assigning the hypocenter anywhere on the fault, this leads to overall shorter duration sources.