SHORT-TERM EARTHQUAKE PROBABILITIES BASED ON LONG-TERM PROBABILITY MODELS Andrew J. Michael

1. SHORT-TERM EARTHQUAKE PROBABILITIES BASED ON LONG-TERM PROBABILITY MODELS Andrew J. Michael Edward H. Field

2. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days?

3. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5%

4. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5% Karen Felzer: ETAS Model Probability of M4.8 being a foreshock to an M 7 event: PF = 0.05%

5. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5% Karen Felzer: ETAS Model PF = 0.05% Lucy Jones: Agnew & Jones Model PF = 5%

6. What is the Agnew and Jones (JGR, 1991) Model? • After discarding aftershocks, • earthquakes are divided into three categories for statistical purposes: • Mainshocks: which we want to forecast • Foreshocks: which are always followed by mainshocks • Background Events: which are never followed by mainshocks • When a candidate event occurs we can’t tell if it is • a foreshock or a background event. • We can calculate the probability that the candidate event • is a foreshock (PF) if we know: • The rate of background events (estimated from the seismicity) • The rate of mainshocks (estimated by models such as UCERF2) • The rate at which mainshocks are preceded by foreshocks. • Need these rates over the area of interest.

7. Implementation of Agnew and Jones Model 1991 Implementation: Characteristic Mainshocks on Segments Mainshock Fault Area of Integration Candidate Event Updated Implementation: Utilize current probability models such as UCERF2. Add Gutenberg-Richter mainshocks. Area of integration is foreshock-centric. Allows for multiple faults & area sources. Mainshock Fault Area of Integration Candidate Event

8. Details on Estimating the Three Input Rates • The rate at which mainshocks are preceded by foreshocks: • 50% of San Andreas physiographic province mainshocks • have a foreshock within 3 days, 3 units of magnitude, & • 10 km (Jones, 1984; Michael & Jones, 1998). • The rate of mainshocks (estimated by models such as UCERF2). • For linear sources we use a rate of nucleation which is • uniformly distributed along the fault (McGuire et al., 2002). • 3. The rate of background events (estimated from the seismicity). • Declustered to remove events with a larger event in the • previous 3 days. A candidate event could be a foreshock to mainshocks that nucleate within a 10 km radius. Mainshock source: 50 km long with rate of 0.1/year. Mainshock nucleation rate within 10 km of candidate: 0.1*(20km/50km) = 0.04/yr

9. Agnew and Jones in a Gutenberg-Richter World Candidate Event M = 5 ± 0.1 Mainshock 5.1 ≤ M ≤ 8 b=1, a=2 PF = 5%

10. Agnew and Jones in a Gutenberg-Richter World Candidate Event M = 5 ± 0.1 Mainshock 5.1 ≤ M ≤ 8 b=1, a=3 PF = 5% b=1, a=2 PF = 5%

11. Agnew and Jones in a Gutenberg-Richter World Candidate Event M = 5 ± 0.1 Mainshock 5.1 ≤ M ≤ 8 b=1, a=? PF = 5% Agnew and Jones Model Gives Spatial Variations If Gutenberg-Richter Behavior Is Not Universal With Constant b-value. b=0.7, a=? PF = 7%

12. Violating Gutenberg-Richter with Variable Maximum Magnitude Candidate Event M = 5 ± 0.1 b=1, a=2 Mainshock 5.1 ≤ M ≤ 8 PF = 5%

13. Violating Gutenberg-Richter with Variable Maximum Magnitude Candidate Event M = 5 ± 0.1 b=1, a=2 Mainshock 5.1 ≤ M ≤ 6 PF = 4% b=1, a=2 Mainshock 5.1 ≤ M ≤ 8 PF = 5% Maximum magnitude has a small effect on probabilities but may have a larger effect on hazard and risk.

14. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5% 1-yr Poisson Rate = 0.011 Nucleation uniformly distributed along segment

15. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5% 1-yr Poisson Rate = 0.011 Nucleation uniformly distributed along segment Background Seismicity: M≥ 3 1981 – 2008 Declustered by removing events with a larger event in the previous 3 days.

16. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5% 1-yr Poisson Rate = 0.011 Nucleation uniformly distributed along segment Background Seismicity: M≥ 3 1981 – 2008 Declustered by removing events with a larger event in the previous 3 days.

17. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5% 1-yr Poisson Rate = 0.011 Nucleation uniformly distributed along segment Background Seismicity: M≥ 3 1981 – 2008 Declustered by removing events with a larger event in the previous 3 days. Within 10 km: 25 Background Events 14 After Declustering 8 km of Fault Segment 11% of Fault Segment PF = 0.4%

18. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Within 10 km: 17 Background Events 13 After Declustering 20 km of Fault Seg. 29% of Fault Segment PF = 1% Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5% 1-yr Poisson Rate = 0.011 Nucleation uniformly distributed along segment Background Seismicity: M≥ 3 1981 – 2008 Declustered by removing events with a larger event in the previous 3 days. Within 10 km: 25 Background Events 14 After Declustering 8 km of Fault Segment 11% of Fault Segment PF = 0.4%

19. M4.8 Event At Bombay Beach On March 24, 2009 Could It Be A Foreshock To A Larger Earthquake In The Next 3 Days? Within 10 km: 17 Background Events 13 After Declustering 20 km of Fault Seg. 29% of Fault Segment PF = 1% Mainshock: SAF, Coachella Seg. UCERF2: Length = 69 km M 7 5-yr Prob. = 5% 1-yr Poisson Rate = 0.011 Nucleation uniformly distributed along segment Within 10 km: 0 Background Events 0 After Declustering 0.9 Assumed Max 20 km of Fault Seg. 29% of Fault Segment PF ≥ 14% Background Seismicity: M≥ 3 1981 – 2008 Declustered by removing events with a larger event in the previous 3 days. Within 10 km: 25 Background Events 14 After Declustering 8 km of Fault Segment 11% of Fault Segment PF = 0.4%

20. Summary Agnew and Jones reduces to standard clustering models (e.g. ETAS, Reasenberg & Jones) if the world is Gutenberg-Richter with constant b-value. Gutenberg-Richter holds for an entire region and for the entire southern San Andreas fault (Page et al., this meeting) but may not hold for individual rupture sources with background seismicity integrated over 10 km radius circles. Variations in maximum magnitude make only small changes in probabilities but larger changes in hazard and risk. Maximum magnitude variations could also be accomplished in simpler clustering models. Applicability of the Agnew and Jones model depends on our conclusions about Gutenberg-Richter behavior over small scales.

22. Conclusions Agnew and Jones Model has been updated to compute probabilities in a way that can be consistent with current probability models including: Gutenberg-Richter Behavior of Mainshocks Foreshock-Centric Calculations That Allow For Multiple Faults Key Factors Are: If Gutenberg-Richter behavior is universal with constant b-value then Agnew and Jones reduces to standard clustering models (e.g. ETAS). Utility of Agnew and Jones depends on deciding that Gutenberg-Richter behavior is violated due to: characteristic behavior or differences in the behavior of small and large earthquakes such as creeping versus locked sections. However changes in maximum magnitude from one region to another make only small differences in the resulting probabilities.

23. What is the Agnew and Jones (JGR, 1991) Model? After discarding aftershocks, earthquakes are divided into three categories for statistical purposes: Mainshocks: which we want to forecast Foreshocks: which are always followed by mainshocks Background Events: which are never followed by mainshocks When a moderate event occurs we can’t tell if it is a foreshock or a background event. We calculate the probability that it is a foreshock by PF = Rate of Foreshocks Rate of Foreshocks + Rate of Background Events Rate of Foreshocks = Rate of Mainshocks * Rate of Foreshocks Before Mainshocks 50% of mainshocks have a foreshock within 3 days, 3 M, & 10 km.

24. Seemingly Good Behavior of this Model PF = Rate of Mainshocks * Rate of Foreshocks (Rate of Mainshocks * Rate of Foreshocks + Rate of Background Events) • Then resulting probability goes • up with higher mainshock rate and • down with higher background rate.

25. Initial Implementation of Agnew & Jones A candidate event is analyzed with respect to a fault segment. Mainshock Rate and Background Rate are calculated for a Characteristic Event on that segment.

26. But, what if we don’t know which mainshock we are working on? • Different faults have • Different background rates • Different mainshock probabilities • Different resulting probabilities. Problem: Mainshock Centric Calculation!

27. Solution: Foreshock Centric Calculation! Integrate background event rate and mainshock nucleation rate around the foreshock. Also add Gutenberg-Richter distribution of mainshocks to match current probability models such as UCERF2.