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Smoothed Seismicity Rates Karen Felzer USGS

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Decision points #1: Which smoothing algorithm to use? National Hazard Map smoothing method (Frankel, 1996)? Helmstetter et al. (2007) smoothing method down to M 2, back to 1981? Helmstetter et al. (2007) smoothing method down to M 4, back to 1932? Helmstetter et al. (2007) smoothing method down to M 2, back to 1932 or 1850, with extended planes for large historical sources? Gaussian or power law smoothing kernel?

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National Hazard Map smoothing method The catalog is declustered using Gardner and Knopoff (1975) The Weichert method is used to calculate rates in each bin from M≥4, M≥5, and M≥6 earthquakes from different periods. Rates are smoothed around each bin using a Gaussian kernel and a fixed 50 km smoothing constant. Map through 2010 created from automated part of algorithm linear scale

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National Hazard Map smoothing method Final 2008 map after manual adjustments, courtesy of Chuck Mueller log scale

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Helmstetter et al. (2007) smoothing method The catalog is declustered using Reasenberg (1985). Remaining catalog still has some clustering. M≥2 earthquakes are used from >1981 only. A Gaussian or power law kernel with an adaptive smoothing constant is expanded around each hypocenter. Map uses 1981-2005 catalog data log10 scale

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Approximated Helmstetter et al. (2007) method using M 4+ back to 1850 1850-2010 catalog data Normalized log10 scale

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Using the full Helmstetter method would require using small earthquakes not in the UCERF catalog – okay?

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Decision points #2: What declustering algorithm to use? Gardner and Knopoff (1975): Traditional, good for removing aftershocks, but maybe not optimal for a smoothed forecast. Reasenberg (1985): Arbitrarily chosen by Helmstetter et al. One of the other methods from Andy’s Oxnard talk ? Try different routines to find what works best for smoothed seismicity forecasting (My recommendation).

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How we want the perfect declustering routine to work Decrease the Landers/Hector signal, but not too much! Decrease the Kern County signal, but not too much! 2006-2010 smoothed seismicity /1932-2005 smoothed seismicity

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The different methods can be evaluated using the MLE Gain given in Helmstetter et al. (2007) G = Gain L = log likelihood of forecasting map L unif = log likelihood of a uniform probability map N = Number of earthquakes Evaluation is performed only within the UCERF polygon

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Summary Do we have enough support to switch to Helmstetter et al. smoothing? Do we have enough support to go down to M 2+ earthquakes? (And represent large historic earthquakes with planes?) Do we have support to switch to a new declustering method?

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Some differences between Helmstetter et al. and NHM Helmstetter et al. National Hazard Map Minimum magnitude 2.0 (1981-2005) 4.0, 5.0, 6.0 (1850-2010) Smoothing constant Distance to n th neighbor 50 km Binning Smoothing kernel drawn around each hypocenter Smoothing kernel drawn around the center of each bin

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