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

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

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

MOMENTS HAVE SIMILAR CURVE TO MAGNITUDES

Total global seismic moment release dominated by few largest events

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

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

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%).

Useful to distinguish between hazards and risks for earthquakes or other natural disasters.

Hazard is natural occurrence of earthquakes and the resulting ground motion and other effects.

Risk is the danger the hazard poses to life and property.

Hazard is unavoidable geological fact, risk is affected by human actions. Areas of high hazard can have low risk because few people live there, and areas of modest hazard can have high risk due to large populations and poor construction.

Earthquake risks can be reduced by human actions, whereas hazards cannot.

MITIGATING EARTHQUAKE RISK

In US, earthquake risk is primarily to property, though there are deaths

Property loss can be high: $20 billion damage from the Northridge earthquake

Some other countries have much greater risk

The most destructive earthquakes occur where large populations live near plate boundaries.

Highest property losses occur in developed nations where more property is at risk

Fatalities are highest in developing nations.

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"

STRONG GROUND MOTION DECAYS RAPIDLY WITH DISTANCE

0.2 g Damage onset for modern buildings

EARTHQUAKE-RESISTANT CONSTRUCTION REDUCES EARTHQUAKE RISKS

“Earthquakes don't kill people; buildings kill people."

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

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”