Smoothed Seismicity Rates - Working Group on California

Smoothed Seismicity Rates
Karen Felzer
Smoothed seismicity
• Smoothed seismicity is used in many forecasts,
including the National Hazard Maps and UCERF2,
to help constrain the off-fault hazard.
• It has been statistically demonstrated that
smoothed seismicity is predictive of future
earthquakes (Kagan and Jackson, 2000; Kafka
2007). It works for small earthquakes and for
M>6 (Kafka, 2007). An upper magnitude limit for
applicability has not been demonstrated.
Potential smoothing methods for
• National Hazard Map smoothing method
(Frankel, 1996)
• Helmstetter et al. (2007) smoothing method
(Currently winning RELM Southern California 5
year earthquake forecasting test)
• Modified Helmstetter et al. (this talk)
National Hazard Map smoothing
linear scale
• The catalog is declustered
using Gardner and Knopoff
• 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 created from 1850-2010
catalog data
Helmstetter et al. (2007) smoothing
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
Map uses 1981-2005 catalog data
Modified Helmstetter et al. (2007)
smoothing method
log10 scale
1850-2010 catalog data
• No declustering.*
• Uses M≥4 seismicity back to
1850, all magnitudes treated
• Uses power law kernels
centered at each hypocenter,
with the Helmstetter adaptive
smoothing constant.
• Calculates smoothed values at
bin centers rather than
integrating across bins.*
• Only relative rates have been
calculated for the current
*Improves result *Makes life simpler
The different methods can be evaluated using
the MLE Gain given in Helmstetter et al. (2007)
G  exp(
L  L unif
G = Gain
L = log likelihood of forecasting map
Lunif = log likelihood of a uniform probability
N = Number of earthquakes
Evaluation is performed only within the UCERF polygon
Retrospective tests performed
• NHM vs. modified Helmstetter for forecast of
M≥6 earthquakes over 1957-2006 (50 yrs):
30% higher gain for Helmstetter.
• Modified Helmstetter with no declustering vs.
modified Helmstetter with Gardner and
Knopoff (1975) declustering : Non-declustered
tend to have a higher gain, but statistical
difference not established. Reasenberg
(1985) declustering may improve results.
Retrospective tests needed
• NHM vs. Helmstetter over multiple 1 and 5
year periods.
• Modified Helmstetter vs. full Helmstetter over
1 year, 5 year, and 50 year periods.
• More tests with declustering (discussion
coming up next!).
Arguments against declustering
• All declustering methods are to some degree
arbitrary and incomplete.
• Earthquakes continue in aftershock zones for
years. We would not want to miss the next
Hector Mine or Christchurch.
• Current declustering methods bias magnitudefrequency statistics by a-posteriori removing
the smaller earthquakes in a cluster. This is
not helpful for a-priori forecasting.
Darfield, M 7.1
Failing to predict aftershocks is not
M 6.3
Sorry, but according
to our b value you
didn’t have an
Arguments for declustering
• Some declustered forecasts appear to perform better.
Why? Some thoughts:
• Declustering emphasizes larger earthquakes.
More aftershocks occur around larger
earthquakes => higher future risk in these areas.
• Declustering effectively decreases the hazard
from aftershock zones that may have been much
more active in the past than at present.
However, the risk from still-active aftershock
zones might be decreased too much by rigorous
A proposed modified approach
1) Use ETAS, rather than straight smoothing, to
model very large/recent earthquakes that are
still producing aftershocks at a rapid rate. This
will give the larger earthquakes the extra risk, at
a presumably more correct rate.
2) Decrease the risk associated with earthquakes in
long-dormant aftershock zones, using empirical
measures or ETAS to estimate amount of
3) Do not alter the magnitude-frequency
4) Test, Test, Test!!!
Decisions that need to be made
• Smoothing method: NHM, Helmstetter,
modified Helmstetter ?
• Declustering: Gardner and Knopoff,
Reasenberg , no declustering, or the modified
• Magnitude-frequency distribution:
Declustered distribution, or full catalog
magnitude-frequency distribution?
Decisions that need to be made
• What tests will be definitive for choosing one
method over another? What confidence level
do we want of improvement before selecting
a new method?
• Is there a measure of performance that we
want besides the Helmstetter MLE Gain?
Some differences between Helmstetter
et al. and NHM
et al.
Hazard Map
4.0, 5.0, 6.0
Distance to nth
50 km
Smoothing kernel Smoothing kernel
drawn around
drawn around the
each hypocenter center of each bin

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