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Estimating Background Activity Based on Interevent-Time Distribution

¹ Institute of Geosciences
University of Potsdam
Postfach 60 15 53
D-14415 Potsdam, Germany
hainzl{at}geo.uni-potsdam.de

View larger version (19K): [in this window] [in a new window]   Figure 1. Stacked probability distributions of normalized interevent times for earthquakes having occurred in (a) California (L = 100 km and Mmin = 3) and (b) ETAS simulations.

View larger version (14K): [in this window] [in a new window]   Figure 2. Two examples of interevent-time probability distributions for California for L = 100 km, Mmin = 3 and central points: crosses (36.7°, –121.3°); circles (33.9°, –118.3°) with different fraction of mainshocks (Reasenberg declustering: 74% and 30%). In (a) the distributions are compared with the fit of the gamma distribution that yields a mainshock fraction of 47% and 11%, respectively. In (b) the distributions are compared with the distribution of long ETAS simulations with a mainshock fraction of 47% and 11%.

View larger version (26K): [in this window] [in a new window]   Figure 3. Scatter plot of the mainshock fraction estimated by the Reasenberg algorithm and from the interevent-time distribution for (a) California and (b) 1000 ETAS and 1000 STAS model sequences. The line indicates the regression line for the data points in (a).

View larger version (47K): [in this window] [in a new window]   Figure 4. The estimated percentage of mainshocks based on the Reasenberg declustering algorithm (dark crosses) and the interevent-time distribution (light squares) as a function of the real value in the ETAS simulations.

View larger version (18K): [in this window] [in a new window]   Figure 5. The real percentage of mainshocks µ as a function of the estimation based on the interevent-time distribution µinter = 1/β for catalogs consisting of 100, 1000, and 10,000 earthquakes, respectively. The small deviation from the identity can be described by the correction curve µ = 1/β + (solid line), with = 0.044 – 0.176 (1/β – 0.5)2.

View larger version (31K): [in this window] [in a new window]   Figure 6. The left column shows (a) the number of M 3+ earthquakes per year, (b) the estimated background fraction, and (c) the resulting background rate in different regions of size 100 x 100 km in California. In each plot, the points indicate the values for the complete data set, whereas the bars show the span of values resulting from four different subsets. The time intervals of the subsets are 1980–2000, 1980–1990, 1990– 2000, and 1990–2004, respectively. For the complete data set, (d) shows a map of the estimated mainshock rate. In this case, we used circular regions with radius 50 km instead of square regions. White spots above 32.5° latitude are regions where less than 50 events with M 3 occurred since 1980 in a distance less than 50 km.

View larger version (42K): [in this window] [in a new window]   Figure 7. Parameters of the magnitude-frequency distribution of the background events estimated by the interevent-time distribution (crosses) and declustering procedure (black squares). For comparison, the results of the least-square fits are shown for the real background events (light dots) and the full catalog (light crosses).