#### Luginbuhl, M; Rundle, JB; Turcotte, DL

The objective of this paper is to analyze the temporal clustering of large global earthquakes with respect to natural time, or interevent count, as opposed to regular clock time. To do this, we use two techniques: (1) nowcasting, a new method of statistically classifying seismicity and seismic risk, and (2) time series analysis of interevent counts. We chose the sequences of and earthquakes from the global centroid moment tensor (CMT) catalog from 2004 to 2016 for analysis. A significant number of these earthquakes will be aftershocks of the largest events, but no satisfactory method of declustering the aftershocks in clock time is available. A major advantage of using natural time is that it eliminates the need for declustering aftershocks. The event count we utilize is the number of small earthquakes that occur between large earthquakes. The small earthquake magnitude is chosen to be as small as possible, such that the catalog is still complete based on the Gutenberg-Richter statistics. For the CMT catalog, starting in 2004, we found the completeness magnitude to be . For the nowcasting method, the cumulative probability distribution of these interevent counts is obtained. We quantify the distribution using the exponent, , of the best fitting Weibull distribution; for a random (exponential) distribution. We considered 197 earthquakes with and found . We considered 15 earthquakes with but this number was considered too small to generate a meaningful distribution. For comparison, we generated synthetic catalogs of earthquakes that occur randomly with the Gutenberg-Richter frequency-magnitude statistics. We considered a synthetic catalog of earthquakes and found . The random catalog converted to natural time was also random. We then generated synthetic catalogs with 197 in each catalog and found the statistical range of values. The observed value of for the CMT catalog corresponds to a p value of leading us to conclude that the interevent natural times in the CMT catalog are not random. For the time series analysis, we calculated the autocorrelation function for the sequence of natural time intervals between large global earthquakes and again compared with data from synthetic catalogs of random data. In this case, the spread of autocorrelation values was much larger, so we concluded that this approach is insensitive to deviations from random behavior.