A global index earthquake approach to probabilistic assessment of extremes

This paper applies recent innovations in flood frequency analysis to regional series of earthquake magnitudes in the global Centroid Moment Tensor (CMT) catalog from 1976 to 2005. Probability plot correlation coefficient hypothesis tests and L ‐moment goodness‐of‐fit evaluations reveal that the Gumbel (GUM) distribution provides a good approximation to the probability distribution function (pdf) of series of annual maximum (AM) earthquake magnitudes. Homogeneity tests based on the theory of L ‐moments further reveal that broad regions of the globe are homogeneous in the sense that the AM observations of earthquake magnitudes are well approximated by a GUM pdf with fixed upper moments. The homogeneity of global earthquake data across broad tectonic environments enables us to pool data into a regional pdf of earthquake magnitudes, termed an index earthquake distribution. Research in hydrology has shown that frequency analysis based on pooling of data using an analogous index‐flood method are much more accurate than frequency analysis based on site or region specific data. The index earthquake distribution is a dimensionless GUM distribution with fixed scale parameter so only the mean earthquake magnitude must be estimated for a region to define the frequency distribution of large earthquakes. We show how the degree of spatial homogeneity of earthquake magnitudes across broad tectonic environments can be exploited to yield improved estimates of the risk posed by extreme earthquake magnitudes.