1. Chapter 4: The SFBR Earthquake Source Model: Magnitude and Long-Term Rates Ahyi Kim 2/23/07 EQW

2. SFBR Earthquake Source Model SFBR earthquake model  Size  Size Locations Locations Magnitude Magnitude Long-term recurrence rate Long-term recurrence rate Earthquake: fixed, floating and back ground Constructed from variety of geologic, geodetic and seismic data

3. Outline Compute rate of characterized earthquake, γ char Compute rate of characterized earthquake, γ char Long-term occurrence rate and interval Long-term occurrence rate and interval Evaluating the SFBR model Evaluating the SFBR model

4. Introduction: Calculating Rupture Source Rates in Complex Model If each segment act as independent rupture source, the rate of earthquake, γwill be Long-term moment release rate of segment Mean moment of earthquakes However, SFBR model allows segments to fail in combination Char: characterized rupture source Fchar: fraction of seismogenic moment rate expended in characterized eq

5. Steps in the calculation sequence Eq. 4-2a

6. Estimating the magnitudes and moments of earthquakes Mean characteristic Magnitude: M-logA relations Wells and Coppersmith(1994) Regression of 83 continental eq WG99 4-5a and 4-5c: 95% bound of 4-5b Hanks and Bakun(2001) : based on constant stress drop source scaling. For 7<M, L-model scaling of average fault slip U=αL, α=2E-5 4-6a4-6b 4.4 4-5a4-5b4-5c

7. Comparison of candidate M-logA relationships

8. 1906 San Francisco event (1)The 1906 eq is one instance in a global dataset (2)1906 eq is the one of the event which is relevant to SFBR

9. Weight of M-logA models

10. Calculating mean moment approximation

11. Estimating rupture source moment rates

12. Fault segment moment rate μ=3E11dyne/cm^2 ν ： long-term slip rate (Table 3.8)

13. Regional slip rate constraint Prescott et al. (2001): GPS data between 1992 and 2000 in central California  39.8+-1.2mm/yr Argus and Gordon (2001): GPS and VBLI  39+-2m/yr Long-term estimates DeMets and Dixon (1999) and Prescott et al.(2001):global plate- motion models. 41+-1mm/yr

14. Defining relative likelihoods of rupture Moment rate for each rupture source: product of available moment rate and the moment-balanced factors, summed across all rupture scenarios

15. Partitioning moment rate across earthquake types Fchar characteristic earthquake Fchar characteristic earthquake Fchar Fractions of seismogenic moment rate aftershocks Fafter small earthquake Fsmall small earthquake Fsmall Fchar + Fafetr + Fsmall = 1

16. Seismic moment rate in aftershocks Summed moment of aftershock=10% of main shock moment But This is because of some of very large aftershocks If the large aftershocks are removed, 3+-2% Fafter = 0

17. Seismic moment rate in smaller earthquakes

18. Magnitude-frequency distributions for faults Pi(M>Mτ) is the probability that the magnitude of rupture i is greater than the threshold value fmi(m) is the magnitude pdf for the ith rupture source

19. Background earthquakes Based on Gutenberg-Richter distribution For the 1951-1998(M>3) a=3.67(3.6-3.74 at 95% confidence) b=0.89 For the 1836-2001(M>5.5) a=3.94(3.62-4.3 at 95% confidence) b=0.89 Wesson et al.

20. Results: Long-term earthquake rates in the SFBR

22. Evaluating the SFBR Model (Regional comparisons) M>6.7 0.031eq/yr b=1.02 M<6.7 b=0.9

23. Timing of Large EQ on SFBR faults

24. Evaluating the SFBR Model (Fault-specific comparisons)

25. Comparison of SFBR model to other models Frequency of events (6.7>M) Andrews and Schwere(2000) 0.0378/yr 1 B=(2/3)b 1 B=(2/3)b SFBR model 0.031/yr using eq1 in Andrews and Schwere(2000): 0.028/yr Using roll-off model: 0.043/yr