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

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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