Smoothed Seismicity Rates

Karen FelzerUSGS

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?

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

National Hazard Map smoothing method

Final 2008 map after manual adjustments,

courtesy of Chuck Mueller

log scale

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

Approximated Helmstetter et al. (2007) method using M 4+ back to 1850

1850-2010 catalog data

Normalized log10 scale

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

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).

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

€

G = exp(L − LunifN

)

The different methods can be evaluated using the MLE Gain given in Helmstetter et al. (2007)

G = Gain L = log likelihood of forecasting map Lunif = log likelihood of a uniform probability mapN = Number of earthquakes

Evaluation is performed only within the UCERF polygon

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?

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 nth neighbor 50 km

Binning Smoothing kernel drawn around

each hypocenter

Smoothing kernel drawn around the center of each bin