Post on 24-Feb-2016
description
Smoothed Seismicity Rates
Karen FelzerUSGS
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 UCERF 3
• 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 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 created from 1850-2010
catalog data
linear 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
Modified Helmstetter et al. (2007) smoothing method
• No declustering.*• Uses M≥4 seismicity back to 1850,
all magnitudes treated equally.*• 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 implementation.
*Improves result *Makes life simpler1850-2010 catalog data
log10 scale
€
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
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 magnitude-frequency statistics by a-posteriori removing the smaller earthquakes in a cluster. This is not helpful for a-priori forecasting.
Failing to predict aftershocks is not helpful
Darfi
eld,
M 7
.1
Chris
tchu
rch,
M
6.3
Sorry, but according to our b value you
didn’t have an earthquake!
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 declustering.
A proposed modified approach1) 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 decrease.
3) Do not alter the magnitude-frequency distribution4) 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 approach?
• 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
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