1. The 2002 Working Group Approach to Modeling Earthquake Probabilities Michael L. Blanpied U.S. Geological Survey Earthquake Hazards Program, Reston, VA For WGCEP workshop, Lake Arrowhead, March 6-8, 2007

2. 2 Plus contributions from dozens of other earth scientists in government, academia, and the private sector. Working Group 2002 Oversight Committee Michael Blanpied, USGS (co-chair) David Schwartz, USGS (co-chair) Norm Abrahamsen, PG&E William Bakun, USGS William Ellsworth, USGS William Foxall, L. Livermore Labs Thomas Hanks, USGS Kathryn Hansen, Geomatrix William Lettis, Lettis & Assoc. James Lienkaemper, USGS Mark Petersen, USGS Paul Reasenberg, USGS Michael Reichle, CGS also Mary Lou Zoback, USGS

3. 3 Faults and Plate Motions in the San Francisco Bay Region A network of faults slip in response to ~40mm per year of plate tectonic motion Large, damaging earthquakes in 1868, 1906, 1989 WG02 calculated probability of all quakes and especially M≥6.7 2002-2031 (and also at other time intervals)

4. Long-term Model Outputs Model represents a complete description of the long-term rate of earthquake occurrence: – For each rupture source, a magnitude distribution (truncated Gaussian) and long-term mean rate of occurrence – Magnitude-frequency distribution of an “exponential tail” of smaller events on those faults – Magnitude-frequency distribution of background earthquakes – Logic tree used to capture epistemic uncertainties; each path through the logic tree is a viable realization of model Goal: Probability of earthquakes in the 1, 5, 10, 20, 30 and 100 years beginning in 2002

5. 5 Logic Tree for the Seismic Area of a Fault

6. 6 Fault moment rate (dyne-cm/yr) Realizations Fault length, km Fault width (km) Value of R Fault slip rate (mm/yr) Seismic fault area (km 2 ) 30 180 330 480 630 0.5 10 24 1 10 24 1.5 10 24 2 10 24 2500 2000 1500 1000 500 0 Seismic fault area Fault energy rate 2000 1500 1000 500 0 Logic-tree calculations

7. 7 Time-dependent Probabilities: WG02’s Approach Employ a suite of probability models spanning the range of complexity and range of probability Employ models that had been sufficiently vetted Employ enough models to reflect the range of reasonable scientific judgment Include models in the logic-tree calculation; weight branches through aggregated expert opinion

8. 8 Probability Models: Considerations Amount of information varies between the seven major faults Possible influence of earthquakes (e.g., 1868, 1906, 1989) and timing of rupture on nearby segments Observation that M≥5 rate higher before than after 1906 (“stress shadow”?) Range(!) of expert opinion on how each of these points should be handled

9. Five models for short-term earthquake probability Earthquake occurrence rate

10. 10 Regional Probability of M≥6.7 in 30 yr Poisson probability given calculated mean rates

11. Probability of the Next Quake T0T0 T1T1 T2T2 Time of the last quake Probability density function for time of the next quake Today Time interval of interest

12. 12 Time Probability Density Recurrence model pdf’s Mean=1, Aperiodicty=0.5

13. 13 Effect of state steps BPT model mean=1 aperiodicity=0.5

14. 14 Calculate conditional probability of earthquake nucleation within time interval Inputs: fault segment mean recurrence rate, aperiodicity (weighted branches 0.3, 0.5, 0.7), and time of most recent event For interaction (“-step”) calculations, also require a representative state step for each fault segment influenced by 1906 or 1989 At the end, merge results to calculate conditional probability for rupture sources BPT and BPT-step calculations

15. 15 BPT and BPT-step calculations

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18. 18 30-year Probability of Rupture, M>6.7 Fault Segment Red Red: Any 30 year interval (on average) Green Green: The next 30 years (2002-2031)

19. 19 Stressing from 1906 quake Stress steps equivalent to 1-55 years of earthquake cycle time on each fault segment

20. 20 Stressing of SAF by Loma Prieta

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22. 22 Time-predictable model Slip rate San Andreas fault only Shimazaki and Nakata, 1980 Thatcher, 1997 slip model Slip last Slip Required to know: stress drop in previous quake, segment stressing rate, aperiodicity, influence of 1989 earthquake Calculate expected time of next hypocenter and fault segment Given segment rupture, determine which rupture source fails

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24. 24 Significant Earthquakes in the SFBR Between 1836 and 1999

25. 25 Magnitude Number per year SFBR Earthquake Rates: A Change in 1906 100 10 1 0.1 0.01

26. 26 Rates of Bay Area earthquakes Bakun M ≥ 5.5 Catalog BPT Poisson Year Magnitude Extrapolated Annual Rate (M≥6.7)

27. 27 Empirical model Model is a proxy for physics-based models, to represent the view that the regional seismicity rate is suppressed relative to the long-term mean. Modulation of long-term rupture rates Assumptions: –Regional earthquake rates vary in sync around their long-term means –Rates are correlated across faults in the region –Rates are correlated across range of magnitudes Thus, the rate of smaller earthquakes is an observable measure of the rate of the largest events –Observed seismicity rates may be extrapolated into the future to forecast probability of largest events

28. Empirical Model

29. 29 Models vs. Historical Data 30-year Probability Year Annual Number of M≥6.7 Events Catalog M≥5.5

30. 30 Empirical model calculation ≥

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33. Five probability models Model weights determined by WG vote Disagreement on regional consistency

34. 34 Considerations For the quasi-periodic models, expert weights hinged on the amount and quality of geologic data on faults, accuracy of knowledge of the MRE date, and confidence in stressing and stress-change calculations. For the Empirical model, weights hinged on confidence that the “stress shadow” persists, that small-M rates represent the probability of large-M events, and in the extrapolation of earthquake rates forward in time. For the Poisson model, weights hinged on opinion on whether the model is appropriate

35. 35 Probability model weights determined by WG votes

36. 36 Combining the five models with voted weights and sorting

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38. 38

39. 39 SourceProbability95% Confidence Bounds SFBR region0.62[0.37 to 0.87] San Andreas fault0.21[0.02 to 0.45] Hayward/ Rodgers Creek fault0.27[0.10 to 0.58] Calaveras fault0.11[0.03 to 0.27] Concord/Green Valley fault0.04[0.00 to 0.12] SanGregorio fault0.10[0.02 to 0.29] Greenville fault0.03[0.00 to 0.08] Mt.Diablo thrust fault0.03[0.00 to 0.08] Background0.14[0.07 to 0.37] Probabilities of One or More M6.7 Earthquakes in the SFBR (2002-2031)

40. 40 Probability vs. Exposure Time Exposure time, years Probability M>6.7

41. 41 WG02 on fault interactions Elastic interaction calculations insufficient to explain 1906 stress shadow Stress interactions: No available model was completely satisfactory. “What appears to be needed are fully time- dependent stress interactions involving the poorly constrained rheology of the lower crust and upper mantle.”

42. 42 WG02 on physics-based approaches Tantalizing observations worldwide on post- seismic quiescence, but data sparse. –“A suite of viscoelastic and rate-and-state models needs to be developed, evaluated and made available for use by the next working group.” –“It will be necessary to gain confidence in model parameters, or at least to narrow the allowable range of values, to limit uncertainties in probability calculations.” –“Advances in the rheologic character of the lithosphere, the deep configuration of faults, and rate/state parameters are needed.” Earthquake simulators also examined, and deemed to be a promising approach for the future.

43. 43 WG02 on expert opinion On aggregated expert opinion: –“We doubt that any future, comprehensive study of earthquake probabilities will be credible in the absence of sampling and quantifying the body and range of scientific judgments.” –“Even in the best of circumstances, the process of actually exercising [expert opinion] is time-consuming and cumbersome.” –“A well-structured process should include feedback loops to the experts, with sufficient time for the experts to digest the consequences of their decisions.”

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45. Extra Slides

46. 46 Working Group 2002 study We constructed a long-term model for large-earthquake production in the SFBR –balances slip rates and plate tectonic rates –accounts for overlapping ruptures, fault creep, earthquake interactions, and other complexities –provides magnitudes and rates of earthquakes We then interrogated the long-term model for short-term earthquake probability forecasts Results are applicable to hazard and loss calculations, and scenario planning

47. 47 Conclusions from Working Group 2000 Damaging earthquakes are likely in the coming years and decades 62% chance of a Northridge-sized event in 30 years Moderate damaging quakes very likely (80 to 90+%) M>7.5 earthquakes less likely but possible (10%) Shaking hazard is high throughout the region Potential loss is highest along the Bay margins

48. 48 USGS Earthquake Information:http://earthquake.usgs.gov SF Bay Region probability study:http://quake.usgs.gov/research/seismology/wg02/

49. 49 Empirical model: Pros & Cons

50. 50 San Francisco Bay Region Earthquake Probability Probability for one or more M6.7 or greater earthquakes from 2002 to 2031 21% 27% 10% 11% 14% 4% 3% 62%

51. 51 San Francisco Bay Region Earthquake Probability

52. 52 Conclusions on Working Group Method The Working Group approach is an effective means of dealing with complex assessments –limited knowledge of the process –competing models –limited observations Logic-tree computations track uncertainties This approach provides bounds on the answer –most viable views are embraced –low likelihood that the answer is wrong –(but answer not precisely determined)

53. 53 Logic Tree for the Seismic Area of a Fault

54. 54 Fault moment rate (dyne-cm/yr) Realizations Fault length, km Fault width (km) Value of R Fault slip rate (mm/yr) Seismic fault area (km 2 ) 30 180 330 480 630 0.5 10 24 1 10 24 1.5 10 24 2 10 24 2500 2000 1500 1000 500 0 Seismic fault area Fault energy rate 2000 1500 1000 500 0

55. 55 Fault moment rate (dyne-cm/yr) Realizations Fault length, km Fault width (km) Value of R Fault slip rate (mm/yr) Seismic fault area (km 2 ) 30 180 330 480 630 0.5 10 24 1 10 24 1.5 10 24 2 10 24 2500 2000 1500 1000 500 0 Seismic fault area Fault energy rate 2000 1500 1000 500 0

56. 56 Fault moment rate (dyne-cm/yr) Realizations Fault length, km Fault width (km) Value of R Fault slip rate (mm/yr) Seismic fault area (km 2 ) 30 180 330 480 630 0.5 10 24 1 10 24 1.5 10 24 2 10 24 2500 2000 1500 1000 500 0 Seismic fault area Fault energy rate 2000 1500 1000 500 0

57. Model long-term rates Matches regional b ~ 0.9 Matches regional rate of M ≥ 6.7 1836-2001 Number / yr Magnitude

58. 58 Working Group Approach: Expert Opinion in Action Science for public policy requires: –using the most appropriate methods –systematically tracking uncertainty Epistemic uncertainty (limited knowledge of models and parameters) Aleatory uncertainty (natural variability) Expert opinion approach –methods developed for shaking hazard analysis for nuclear plants –expert group represents opinions of the broader scientific community –discussion and evaluation of viable models –weighting of models and parameter values –a feedback process for examination of trial results Logic tree method

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60. 60 Probability Density vs. Magnitude Magnitude Probability Density

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62. 62 Sensitivity of 30-year probability to aperiodicity BPT-step model M ≥ 6.7 WG02’s Figure 6.13