The Empirical Model

Karen FelzerUSGS 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 1850-1906 were 2.2 x above long term rates.

• Rates from 1951-1998 were lower than 1850-1906 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 1951.• Final recommendation: Set all rates to 0.58 x long term

rates for 2001-2031.

1850-1905 vs. 1951-1998 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)Ra

te

YearNote: 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

0.79

0.46

0.64

0.66

0.64 Statewide:0.82

*Average short term = average of 1906-2006, 1942-2006, and 1984-2006

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 1977-2008” (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

1932-2010 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)2

0

-2

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

2006-10 smoothed seismicity /forecast for last 5 years

Performance of 1932-2005 smoothed seismicity forecast for 2006-2010

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

2006-2010 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

1932-2010 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

Name Year Month Magnitude On SAF?

Lompoc 1927 11 7.1 No

1934 12 7.0 No

Kern County 1952 7 7.5 No

Landers 1992 6 7.3 No

Hector Mine 1999 10 7.1 No

El Mayor-Cucapah

2010 4 7.2 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 changeOld 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≥6.0 1857-1927 is ~65% of

1927-2006

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%: