Smoothed Seismicity Rates Karen Felzer USGS Smoothed seismicity

Smoothed Seismicity Rates Karen Felzer USGS

Smoothed seismicity • Smoothed seismicity is used in many forecasts, including the National Hazard Maps and UCERF 2, 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 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 created from 1850 -2010 catalog data

Helmstetter et al. (2007) smoothing method log 10 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

Modified Helmstetter et al. (2007) smoothing method log 10 scale 1850 -2010 catalog data • 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 simpler

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 map N = Number of earthquakes Evaluation is performed only within the UCERF polygon

Retrospective tests performed • NHM vs. modified Helmstetter 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 helpful Christchurch, 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 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 decrease. 3) Do not alter the magnitude-frequency distribution 4) 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 the each hypocenter of each bin