1. 9: EARTHQUAKE RECURRENCE Crucial for hazards, earthquake physics & tectonics (seismic versus aseismic deformation) Recordings of the east-west component of motion made by Galitzin instruments at DeBilt, the Netherlands. Recordings from the 1922 earthquake (shown in black) and the 1934 and 1966 events at Parkfield (shown in red) are strikingly similar, suggesting virtually identical ruptures.

2. EARTHQUAKE FREQUENCY - MAGNITUDE LOG-LINEAR Gutenberg-Richter RELATION

3. LEVEL OF ACTIVITY (a value) VARIES REGIONALLY BUT b ~ 1

4. MOMENTS HAVE SIMILAR CURVE TO MAGNITUDES but slope  = 2/3

5. WHY TOO FEW VERY LARGE EARTHQUAKES? EXPECT  = 2/3 LARGE EVENTS SHOW  = 1

6. Most earthquakes between solid lines with slope 1/3, showing M 0 proportional to L 3. However, strike-slip earthquakes (solid diamonds) have moments higher than expected for their fault lengths, because above a certain moment fault width reaches maximum, so fault grows only in length. Romanowicz, 1992

7. Total global seismic moment release dominated by few largest events Total moment for 1976-1998 ~1/3 that of giant 1960 Chilean earthquake

8. AFTERSHOCKS FOLLOWING MAINSHOCK HAVE A CHARACTERISTIC DECAY IN SIZE AND TIME Largest aftershock is usually more than a magnitude unit smaller than the main shock, and the aftershocks have a size distribution with b ~ 1, so the total energy released by aftershocks is usually <10% of that of the main shock.

9. Global EarthquakesContinental Intraplate Stein & Wysession, 2003 Triep & Sykes, 1997 CHALLENGE: INFER UNKNOWN RATE OF LARGEST EARTHQUAKES FROM RECORDED RATE OF SMALLER ONES Use standard log-linear Gutenberg-Richter relationship With seismological data only, log-linear relation breaks down Largest earthquakes (M > 7-7.5) less frequent than expected, presumably due to fault finiteness (large event lengths >> width) Magnitude (Ms) Number per year

10. GUTENBERG-RICHTER RELATIONSHIP: INDIVIDUAL FAULTS Wasatch Basel, Switzerland paleoseismic data instrumental data Youngs & Coppersmith, 1985 Meghraoui et al., 2001 paleoseismic data historical data Largest events deviate in either direction, often when different data mismatch When more frequent than expected termed characteristic earthquakes. Alternative are uncharacteristic earthquakes Could these differences - at least in some cases - be artifacts? Characteristic Uncharacteristic

11. EARTHQUAKE RECURRENCE IS HIGHLY VARIABLE M>7 mean 132 yr  105 yr Estimated probability in 30 yrs 7-51% Sieh et al., 1989 Extend earthquake history with paleoseismology

12. Magnitude POSSIBLE ARTIFACTS CAUSING SPURIOUS CHARACTERISTIC OR UNCHARACTERISTIC EARTHQUAKES Magnitude Earthquake Rate Undersampling: record comparable to or shorter than mean recurrence - most events characteristic, because can’t have a fraction of an earthquake. Can also miss largest events. Effect similar for longer records. Direct paleoseismic study: Magnitude overestimated, events appear characteristic. Events missed, recurrence overestimated, events appear uncharacteristic Indirect paleoseismic using assumed geologic slip & earthquake size: Long term slip rate overestimated or aseismic slip unaccounted for, events appear characteristic CHARACTERISTIC UNCHARACTERISTIC

13. LONG RECORDS SHOW RECURRENCE VARIABILITY  ~ 0.4 T av or higher seems reasonable description of variability Log-normal with  ~ 0.2 T av (Nishenko & Buland, 1987) can underestimate

14. SIMULATIONS For histories = 0.5 T av any M7 earthquakes appear characteristic. No uncharacteristic ones since cannot record fractions of events. Often miss largest earthquakes (no M7 observed) 10,000 synthetic earthquake histories for G-R relation with slope b=1 Gaussian recurrence times for M> 5, 6, 7 Various history lengths given in terms of T av, mean recurrence for M>7

15. SHORT SIMULATIONS For histories = 1,2 T av many earthquakes appear characteristic For 2 T av as many uncharacteristic & characteristic events

16. LONGER SIMULATIONS Distributions about T av tighten up No bias: as many uncharacteristic as characteristic events Still likely to overestimate or underestimate large event rate

17. CHARACTERISTIC EARTHQUAKE RESULTS VARY WITH SPATIAL SAMPLING Characteristic earthquakes on Wasatch fault (Chang and Smith, 2002), but not in entire Wasatch front (data from Pechmann and Arabasz, 1995)

18. ESTIMATING EARTHQUAKE PROBABILITIES A game of chance, with unknown rules, and very little data from which to infer them

19. CHALLENGE: DON’T KNOW WHAT PROBABILITY DISTRIBUTION DESCRIBES EARTHQUAKE RECURRENCE TIMES

20. POISSON DISTRIBUTION TIME INDEPENDENT MODEL OF EARTHQUAKE PROBABILITY Used to describe rare events: include volcanic eruptions, radioactive decay, and number of Prussian soldiers killed by their horses

21. TIME INDEPENDENT VERSUS TIME DEPENDENT MODEL

22. GAUSSIAN DISTRIBUTION TIME DEPENDENT MODEL OF EARTHQUAKE PROBABILITY Probability of large earthquake a time t after the past one is p(t, ,  ) Depends on average and variability of recurrence times, described by the mean  and standard deviation  p is probability that recurrence time for this earthquake will be t, given an assumed distribution of recurrence times.

23. CONDITIONAL PROBABILITY Use the fact that we know the next earthquake hasn’t already happened

24. Gaussian SAN ANDREAS FAULT PALLETT CREEK SEGMENT Gaussian (time dependent) model In 1983, estimate 9% probability by 2003, increases with time

25. Gaussian SAN ANDREAS FAULT PALLETT CREEK SEGMENT Poisson (time independent) model In 1983, estimate 10% probability by 2003, constant with time

26. SYNTHETIC EARTHQUAKE HISTORIES Gaussian model yields more periodic series; Poisson model yields clustering Which looks more like earthquake history?

27. SEISMIC GAP MODEL Long plate boundary like the San Andreas or an oceanic trench ruptures in segments Expect steady plate motion to cause earthquakes that fill in gaps that have not ruptured for a long time Gap exists when it has been long enough since the last major earthquake that time-dependent models predict earthquake probability much higher than expected from time-independent models Sounds sensible but seems not to work well, for unknown reasons GAP? NOTHING YET

28. EARTHQUAKE FORECASTS: EASY TO MAKE, HARD TO TEST Hard to prove right or wrong Because the estimates must be tested using data that were not used to derive them, hundreds or thousands of years (multiple recurrences) will be needed to assess how well various models predict large earthquakes on specific faults or fault segments. The first challenge is to show that a model predicts future earthquakes significantly better than the simple time-independent Poissonian model Given human impatience, attempts have been made to conduct alternative tests using smaller earthquakes or many faults over a short time interval. To date, results are not encouraging.

29. RECENT SEISMICITY MAY NOT REFLECT LONG-TERM PATTERN WELL Random seismicity simulation for fault along which probability of earthquake is uniform Apparent seismic gaps develop May take long time to fill compared to length of earthquake record Stein & Wysession, 2003

30. PARKFIELD, CALIFORNIA SEGMENT OF SAN ANDREAS Characterized by smaller earthquakes that occur more frequently and appear much more periodic than other segments. Earthquakes of M 5-6 occurred in 1857, 1881, 1901, 1922, 1934, and 1966. Average recurrence is 22 yr; linear fit made 1988 likely date of the next event. In 1985, predicted at 95% confidence level that the next earthquake would occur by 1993 Actually didn’t occur till 2004 (16 years late) Problems: Limitations of statistical approach in prediction (including omission of 1934 earthquake on the grounds that was premature and should have occurred in 1944) Unclear whether Parkfield shows such unusual quasi-periodicity because it differs from other parts of San Andreas (in which case predicting earthquakes there might not be that helpful for others), or results simply from the fact that given enough time & fault segments, random seismicity can yield apparent periodicity somewhere

31. Within 10 years of prediction, 10 large events occurred in these areas. None were in high- or intermediate- risk areas; 5 were in low- risk areas. GLOBAL TEST OF SEISMIC GAP HYPOTHESIS Gap map forecasting locations of major earthquakes did no better than random guessing. Many more large earthquakes occurred in areas identified as low risk than in presumed higher-risk gaps (reverse colors?) Result appears inconsistent with ideas of earthquake cycles and seismic gaps Kagan & Jackson, 1991

32. EARTHQUAKE PROBABILITY MAPS Hard to assess utility of such maps for many years Major uncertainties involved Perhaps only meaningful to quote probabilities in broad ranges, such as low ( 90%).

33. EARTHQUAKE PREDICTION? Because little is known about the fundamental physics of faulting, many attempts to predict earthquakes searched for precursors, observable behavior that precedes earthquakes. To date, search has proved generally unsuccessful In one hypothesis, all earthquakes start off as tiny earthquakes, which happen frequently, but only a few cascade via random failure process into large earthquakes This hypothesis draws on ideas from nonlinear dynamics or chaos theory, in which small perturbations can grow to have unpredictable large consequences. These ideas were posed in terms of the possibility that the flap of a butterfly's wings in Brazil might set off a tornado in Texas, or in general that minuscule disturbances do not affect the overall frequency of storms but can modify when they occur If so, there is nothing special about those tiny earthquakes that happen to grow into large ones, the interval between large earthquakes is highly variable and no observable precursors should occur before them. Thus earthquake prediction is either impossible or nearly so. “It’s hard to predict earthquakes, especially before they happen”

34. PROBABILISTIC SEISMIC HAZARD ASSESSMENT (PSHA) Seek to quantify risk in terms of maximum expected acceleration in some time period (2% or 10% in 50 yr, or once in 2500 or 500 yr) Maps made by assuming: Where and how often earthquakes will occur How large they will be How much ground motion they will produce Because these factors are not well understood, especially on slow moving boundaries or intraplate regions where large earthquakes are rare, hazard estimates have considerable uncertainties and it will be a long time before we know how well they’ve done “A game of chance of which we still don't know all the rules"

35. 10% EXCEEDENCE PROBABILITY (90% NON EXCEEDENCE) WITHIN 50 YEARS Jimenez, Giardini, Grünthal (2003)

36. SHORT RECORD OF SEISMICITY & HAZARD ESTIMATE Predicted hazard from historic seismicity is highly variable Likely overestimated near recent earthquakes, underestimated elsewhere More uniform hazard seems more plausible - or opposite if time dependence considered Map changes after major earthquakes Africa-Eurasia convergence rate varies smoothly GSHAP NUVEL-1 Argus et al., 1989

37. SHORT RECORD OF SEISMICITY & HAZARD ESTIMATE Predicted hazard from historic seismicity is highly variable Likely overestimated near recent earthquakes, underestimated elsewhere More uniform hazard seems more plausible - or opposite if time dependence considered Map changes after major earthquakes Africa-Eurasia convergence rate varies smoothly GSHAP 1998 NUVEL-1 Argus et al., 1989 2004 2003

38. M>7

39. Canadian east coast: seismicity clusters Seismic zone along eastern coast of Canada & US passive continental margin May reflect reactivation of rifting faults from continental breakup, perhaps by deglaciation and/or other stress Largest events (M 7) in Baffin Bay, Grand Banks Are these concentrations a real phenomenon or artifacts of seismic record length? Issue important for both passive margin tectonics and earthquake hazard Stein et al., 1979

40. Years 100 500 1000 3000 5000 8000 # of events 3 12 24 72 117 187 recurrence 33 42 42 42 43 43 time Stein et al., 1979 Synthetic M>7 earthquake history 0 3500 7000 distance (km) CLUSTERS COULD EASILY BE ARTIFACT OF SHORT RECORD LONG- TERM SEISMICITY & HENCE HAZARD COULD BE UNIFORM

41. Peak Ground Acceleration 10% probability of exceedance in 50 years GSHAP (1999) Present Study HUNGARY: ALTERNATIVE HAZARD MAPS Historic seismicity Seismicity + geoology: Diffuse hazard Toth et al., 2004

42. EASTERN US versus CANADA: ALTERNATIVE HAZARD MAPS Historic seismicity Diffuse Hazard Halchuk and Adams, 1999

43. IS NEW MADRID AS HAZARDOUS AS CALIFORNIA? Frankel et al., 1996 Proposed new building code would require California standards

44. EFFECTS OF ASSUMED GROUND MOTION MODEL Effect as large as one magnitude unit Frankel model, developed for maps, predicts significantly greater shaking for M >7 Frankel M 7 similar to other models’ M 8 Frankel & Toro models averaged in 1996 maps; Atkinson & Boore not used Newman et al., 2001

45. UNCERTAINTIES IN NMSZ HAZARD MAPS Areas of predicted significant hazard differ significantly, depending on poorly known parameters. Assumed M max on main fault has largest effect near fault. Assumed ground motion model has regional effect, because it also influences predicted hazard from earthquakes off main fault. Newman et al., 2001

46. UNCERTAINTIES IN NMSZ HAZARD MAPS Areas of predicted significant hazard differ significantly, depending on poorly known parameters. Differences have major policy implications (e.g. Memphis & St. Louis). Uncertainties won’t be resolved for 100s-1000s years Uncertainties dominated by systematic errors (epistemic) and hence likely underestimated Newman et al., 2001

47. ASSUMED HAZARD DEPENDS ON TIME WINDOW Over 100 years, California site much more likely to be shaken strongly than NMSZ one Over 1000 years, some NMSZ sites shaken strongly a few times; many in California shaken many times Short time relevant for buildings with 50-100 yr life Shaken areas MMI > VII Random seismicity simulation including seismicity & ground motion differences

48. $100M seismic retrofit of Memphis VA hospital, removing nine floors, bringing it to California standard Does this make sense? How can we help society decide? THERE ARE NO UNIQUE OR CORRECT STRATEGIES, SO SOCIETY HAS TO MAKE TOUGH CHOICES. Mitigating risks from earthquakes or other natural disasters involves economic & policy issues as well as the scientific one of estimating the hazard and the engineering one of designing safe structures.

49. SHOULD BUILDINGS IN MEMPHIS MEET CALIFORNIA STANDARD? New building code IBC 2000, urged by FEMA, would raise to California level (~ UBC 4) Essentially no analysis of costs & benefits of new code Year J. Tomasello Code

50. Proposed new code results largely from redefining the hazard from maximum shaking at a geographic point over 500 yr (10% in 50 yr) to the maximum every 2,500 yr ( 2% in 50 yr. Much shorter life of ordinary structures. Definition allows New Madrid hazard to be similar to that in California, although annual California hazard is much lower. By similar argument, in very long (three million hand) poker game. probability of at least one pair and royal flush are comparable - although in one hand, the probability of a pair is ~ 43%, whereas that of a royal flush is far less, ~ 1 / 100,000 Using this argument would lose money in ordinary duration game.

51. THOUGHT EXPERIMENT: TRADEOFF Your department is about to build a new building. The more seismic safety you want, the more it will cost. You have to decide how much of the construction budget to put into safety. Spending more makes you better off in a future large earthquake. However, you’re worse off in the intervening years, because that money isn't available for office and lab space, equipment, etc. Deciding what to do involves cost-benefit analysis. You try to estimate the maximum shaking expected during the building's life, and the level of damage you will accept. You consider a range of scenarios involving different costs for safety and different benefits in damage reduction. You weigh these, accepting that your estimates for the future have considerable uncertainties, and somehow decide on a balance between cost and benefit.

52. THIS PROCESS, WHICH SOCIETY FACES IN PREPARING FOR EARTHQUAKES, ILLUSTRATES TWO PRINCIPLES: “There's no free lunch” Resources used for one goal aren’t available for another, also desirable, one. In the public sector there are direct tradeoffs. Funds spent strengthening schools aren’t available to hire teachers, upgrading hospitals may mean covering fewer uninsured (~$1 K/yr), stronger bridges may result in hiring fewer police and fire fighters (~$50 K/yr), etc... “There's no such thing as other people's money” Costs are ultimately borne by society as a whole. Imposing costs on the private sector affects everyone via reduced economic activity (a few % cost increase may decide whether a building isn’t built or build elsewhere), job loss (or reduced growth), and the resulting reduction in tax revenue and thus social services.

53. INITIAL COST/BENEFIT ESTIMATES: MEMPHIS AREA I: Present value: FEMA estimate of annual earthquake loss $17 million/yr, part of which would be eliminated by new code, ~ 1% of annual construction costs ($2 B). II: Life-of-building: Use FEMA estimate to infer annual fractional loss in building value from earthquakes. If loss halved by new code, than over 50 yr code saves 1% of building value. If seismic mitigation cost increase for new buildings with IBC 2000 >> 1%, probably wouldn't make sense. Similar results likely from sophisticated study including variations in structures, increase in earthquake resistance with time as more structures meet code, interest rates, retrofits, disruption costs, etc.

54. LIFE SAFETY U.S. earthquake risk primarily to property; annualized losses estimated at ~$4 billion. Also ~10 deaths/yr, averaged over larger numbers in major earthquakes. Annual fatalities roughly constant since 1800, presumably in part because population growth in hazardous areas offset by safer construction. Situation could likely be maintained or improved by strengthening building codes, so the issue is how to balance this benefit with alternative uses of resources (flu shots, defibrillators, highway upgrades, etc.) that might save more lives for less. Estimated cost to save life (in U.S.) varies in other applications: ~$50 K highway improvements ~$100 K medical screening ~$5 M auto tire pressure sensors Different strategies likely make sense in different areas within the U.S. and elsewhere, depending on earthquake risk, current building codes, and alternative demands for resources.

55. Hence seismic mitigation costs in Memphis area - $20-200 M/yr (1-10% new construction cost) + any retrofits - could insure 20,000 - 200,000 people and save some lives that way Tricky tradeoff here

56. TAKE TIME TO GET THINGS RIGHT Because major earthquakes in a given area are infrequent on human timescale, we generally have time to formulate strategy carefully (no need to rush to wrong answer) Time can also help on both the cost and benefit sides. As older buildings replaced by ones meeting newer standards, overall earthquake resistance increases. Similarly, even where retrofitting isn't cost-effective, higher standards for new ones may be. Technological advances can make additional mitigation cheaper and more cost-effective. If understanding of earthquake probabilities becomes sufficient to confidentially identify how probabilities vary with time, construction standards could be adjusted accordingly where appropriate.

57. WE ARE NOT ALONE There's increasing interest in making mitigation policy more rationally for other hazards with considerable uncertainties. “The direct costs of federal environmental, health, and safety regulations are probably ~$200 billion annually, about the size of all federal domestic, nondefense discretionary spending. The benefits of those regulations are even less certain. Evidence suggests that some recent regulations would pass a benefit-cost test while others would not.” (Brookings Institution & American Enterprise Institute) Viewing seismology and engineering as part of a holistic approach to hazards mitigation will make our contributions more useful to society. This utility will grow as we learn more about earthquakes and their effects in different areas.