Background Seismicity Model (smoothing & Mmax)

Report
Smoothed Seismicity Rates
Karen Felzer
USGS
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
linear scale
• 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
National Hazard Map smoothing
method
log scale
Final 2008 map
after manual
adjustments,
courtesy of Chuck
Mueller
Helmstetter et al. (2007) smoothing
method
log10 scale
• 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
Approximated Helmstetter et al.
(2007) method using M 4+ back to
1850
Normalized log10 scale
1850-2010 catalog data
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
2006-2010 smoothed seismicity /1932-2005
smoothed seismicity
Decrease the
Landers/Hector
signal, but not
too much!
Decrease the Kern
County signal, but
not too much!
The different methods can be evaluated using
the MLE Gain given in Helmstetter et al. (2007)
L  Lunif
G  exp(
)
N

G = Gain
L = log likelihood of forecasting map
Lunif = log likelihood of a uniform probability
map
N = 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 Smoothing kernel
drawn around
drawn around the
each hypocenter center of each bin

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