Adaptive Kernel Estimation and Continuous Probability Representation of Historical Earthquake Catalogs

To develop spatially continuous seismicity models (earthquake probability distributions) from a given earthquake catalog, the method of kernel estimation has been suggested. Kernel estimations with a global (spatially invariant) bandwidth deal poorly with earthquake hypocenter distributions that have different spatially local features. For example, a typical earthquake catalog has several areas of high activity (clusters) and areas of low-background seismicity. An alternative approach is adaptive kernel estimation, which uses a bandwidth parameter that is spatially variable. Its performance compared to kernel estimations with spatially invariant bandwidths suggests that (discrete) earthquake distributions require different degrees of local smoothing to provide useful spatial seismicity models. Using adaptive kernel estimation, the (local) indices of temporal dispersion of any earthquake probability distribution can be estimated and used to model the spatial probability distribution of mainshocks. The application of these methods to New Zealand and Australian earthquake catalogs shows that the spatial features (earthquake clusters) in which the mainshocks occurred have been reasonably stable throughout the observation period. The observed regions of higher activity persisted throughout the observation period, and none of these regions decreased to background activity during that time. This suggests that these regions will continue to represent higher risk for the occurrence of moderate to large earthquakes within the next few years or decades. Furthermore, it has been observed that shallow earthquakes are mostly part of temporal sequences (e.g., aftershocks or swarms), whereas the earthquakes within the subduction zones in New Zealand showed only small temporal variation during the observation period.