Eigenpatterns in southern California seismicity

Earthquakes in seismically active regions of the world are known to be associated with a variety of spatial and temporal patterns. Examples include precursory quiescence or activation, seismic clustering, and Mogi donuts. Although the characteristics of these patterns can be qualitatively described, a systematic quantitative analysis has proved elusive. In this paper we employ a new method, developed using numerical simulations, that allows a systematic quantification of the spatial and temporal characteristics of the patterns in historic seismicity in southern California. This method decomposes a set of boolean activity functions, representing historic seismicity, into their orthonormal eigenvalues and eigenfunctions. Here we show the results of this analysis which strongly support the hypothesis that seismic activity is highly correlated across many space scales and timescales within large volumes of the Earth's crust.