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.

EARTHQUAKE FREQUENCY - MAGNITUDE

LOG-LINEAR Gutenberg-Richter

RELATION

LEVEL OF ACTIVITY (a value) VARIES

REGIONALLY

BUT b ~ 1

MOMENTS HAVE SIMILAR CURVE TO MAGNITUDES

but slope = 2/3

WHY TOO FEW VERY LARGE EARTHQUAKES?

EXPECT = 2/3

LARGE EVENTS SHOW = 1

Most earthquakes between solid lines with slope 1/3, showing M0 proportional to L3. However, strike-slip earthquakes (solid diamonds) have moments higher than expected for their fault lengths, because above a certainmoment fault width reaches maximum, so fault grows only in length.

Romanowicz, 1992

Total global seismic moment release dominated by few largest events

Total moment for 1976-1998 ~1/3 that of giant 1960 Chilean earthquake

Global Earthquakes Continental Intraplate

Stein & Wysession, 2003Triep & 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) Magnitude (Ms)

Nu

mb

er

per

yea

r

GUTENBERG-RICHTER RELATIONSHIP: INDIVIDUAL FAULTSWasatch

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?

CharacteristicUncharacteristic

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

Magnitude

Magnitude

POSSIBLE ARTIFACTS CAUSING SPURIOUS CHARACTERISTIC

OR UNCHARACTERISTIC EARTHQUAKES

Magnitude

Ear

thqu

ake

Rat

e

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

LONG RECORDS SHOW RECURRENCE VARIABILITY

~ 0.4 Tav or higher seems reasonable description of variability

Log-normal with ~ 0.2 Tav (Nishenko & Buland, 1987) can underestimate

SIMULATIONS

For histories = 0.5 Tav 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 Tav, mean recurrence for M>7

SHORT SIMULATIONS

For histories = 1,2 Tav many earthquakes appear characteristic

For 2 Tav as many uncharacteristic & characteristic events

LONGER SIMULATIONS

Distributions about Tav tighten up

No bias: as many uncharacteristic as characteristic events

Still likely to overestimate or underestimate large event rate

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)

ESTIMATING EARTHQUAKE

PROBABILITIES

A game of chance, with unknown rules, and very little data from which to infer

them

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

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

TIME INDEPENDENT VERSUS TIME DEPENDENT

MODEL

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.

CONDITIONAL PROBABILITY

Use the fact that we know the next

earthquake hasn’t already happened

Gaussian

SAN ANDREAS FAULT PALLETT CREEK SEGMENT

Gaussian (time dependent) model

In 1983, estimate 9% probability by 2003, increases with time

Gaussian

SAN ANDREAS FAULT PALLETT CREEK SEGMENT

Poisson (time independent) model

In 1983, estimate 10% probability by 2003,

constant with time

SYNTHETIC EARTHQUAKE HISTORIES Gaussian model yields more periodic series; Poisson model yields clustering

Which looks more like earthquake history?

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 modelspredict earthquake probability much higher than expectedfrom time-independent models

Sounds sensible but seems not to work well, for unknown reasons GAP?

NOTHING YET

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.

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

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

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 betterthan random guessing.

Many more large earthquakes occurred in areas identifiedas low risk than in presumed higher-risk gaps (reverse colors?)

Result appears inconsistent with ideas of earthquake cycles and seismic gaps

Kagan & Jackson, 1991

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 (<10%), intermediate (10-90%), or high (>90%).

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 togrow 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”

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"

10% EXCEEDENCE PROBABILITY

(90% NON EXCEEDENCE)

WITHIN 50 YEARS

Jimenez, Giardini, Grünthal (2003)

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-1Argus et al., 1989

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-1Argus et al., 1989

2004

2003

M>7

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

Years 100 500 1000 3000 5000 8000# of events 3 12 24 72 117 187recurrence 33 42 42 42 43 43time

Stein et al., 1979

Synthetic M>7 earthquake history

0

35

00

70

00

di

stan

ce (

km)

CLUSTERS COULD EASILY BE ARTIFACT OF SHORT RECORD

LONG-TERM SEISMICITY & HENCE HAZARD COULD BE UNIFORM

Peak Ground Acceleration10% probability of exceedance

in 50 years

GSHAP (1999)GSHAP (1999)

Present StudyPresent StudyHUNGARY:

ALTERNATIVE HAZARD MAPS

Historic seismicity

Seismicity + geoology:

Diffuse hazard

Toth et al., 2004

EASTERN US versus CANADA:

ALTERNATIVE HAZARD MAPS

Historic seismicity

Diffuse Hazard

Halchuk and Adams, 1999

IS NEW MADRID AS HAZARDOUS AS CALIFORNIA?

Frankel et al., 1996

Proposed new building code would require California standards

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

UNCERTAINTIES IN NMSZ HAZARD MAPS

Areas of predicted significant hazard differ significantly, depending on poorly known parameters.

Assumed Mmax 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

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

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

$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.

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

Proposed new code results largely from redefining the hazard frommaximum 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.

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.

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.

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.

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.

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

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.

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.