The Empirical Model Karen Felzer USGS Pasadena

A low modern/historical seismicity rate has long been recognized in the San Francisco Bay Area Stein 1999

The Bay Area rate changes was carefully studied by WGCEP 2002 (Reasenberg et al., 2003). They found: Average seismicity rates from were 2.2 x above long term rates. Rates from were lower than rates. The rate change amplitude varied by fault. No current physical model adequately explains the rate changes. The rate changes have been fairly stable since Final recommendation: Set all rates to 0.58 x long term rates for

vs rates, by fault, as compared to the long term average Figure 8, Reasenberg et al. (2003) Note: Variability of rate change on different faults

Seismicity rate plots as a function of time with various smoothing kernels Figure 5, Reasenberg et al. (2003) Rate Year Note: Rate >1951 fairly stable and deemed unlikely to change without a large earthquake

Important take-away points Over ≥50 year periods seismicity rates can be relatively but significantly different from the long term average. The change in rates throughout the San Francisco Bay Area is spatially variable

Statewide:0.8 2 *Average short term = average of , , and Results from WGCEP 2007, Appendix M WGCEP 2008 found that the rate change actually extends over most of the state of California

Is this real? A low current seismicity rate statewide also agrees with geodetic/deformation studies “The western U.S. has been 37% below its long- term-average seismicity during ” (Bird, 2009) “73-86% of the geodetic moment rate in California appears in the existing earthquake catalogue” (Ward, 1998)

However: The statewide seismicity rate decrease is spatially variable, with some areas above their long- term average M≥4 seismicity divided by long term seismicity rate forecast of Bird (2009) Will a spatially variable empirical model forecast better? Log(Smoothed Seismicity/Strain)

A spatially variable, completely empirical model = smoothed seismicity This is the Helmstetter et al. approach, which is the winning the 5 year RELM forecasting test Normalized log of rate

Smoothed seismicity performs better than long term rates over the last 1, 5, 10, and 50 years Correlation coefficient between forecast and realized seismicity rates

We look at the performance of the 5 year smoothed seismicity forecast in detail Correlation coefficient between forecast and realized seismicity rates

smoothed seismicity /forecast for last 5 years Performance of smoothed seismicity forecast for

Decay of Landers/Hector Mine aftershocks could be corrected for Baja aftershocks could be added Aftershocks could be placed preferentially on high slip faults We might be able to improve performance with aftershock and fault modeling smoothed seismicity /forecast for last 5 years

Can the spatially variable empirical model be applied to the largest earthquakes?

Most of the statewide rate decrease comes from the San Andreas fault M≥4 seismicity vs. long term seismicity rate forecast of Bird (2009)

Overall the San Andreas should host at least ~40% of California’s M≥7 earthquakes NameYearMonthMagnitudeOn SAF? Lompoc No No Kern County No Landers No Hector Mine No El Mayor- Cucapah No M≥7 earthquake record south of the triple junction >1906 The absence of M≥7 earthquakes from the San Andreas is significant at 95% confidence

Proposal for change Old Method Start with long term slip rate, known-faults based model + smoothed seismicity. Move all rates up or down to empirically fit modern catalog. New Method Start with smoothed seismicity rates. Simulate where aftershocks might occur over the forecast period, and add aftershocks in real time. Adjust azimuth of smoothing kernel for spontaneous events and aftershocks to produce more events where long term rates are high (on faults!) Goal: Forecast where seismicity will occur in the short term, match the long term model over the long term

Conclusions We observe that regional seismicity rates vary significantly from their long term rates over periods at least as long as 50 years. Propagating empirically observed rate changes has historically produced a better forecast. The rate changes appear to apply to M≥7 earthquakes. Simple smoothed seismicity maps may provide the best forecasts for ≤50 year periods provided that the map is updated as aftershocks occur with input from the long term slip model.

Statewide, rate of M≥ is ~65% of The statewide rate decrease can also be seen if we just look at larger earthquakes

Smoothed seismicity performs better than long term rates over the last 1, 5, 10, and 50 years Fraction of bins in which forecast and realized rates agree by >50%: