18 earthquake prediction - ucl - london's global … earthquake...gnh7/gg09/geol4002 earthquake...

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Forecasting Earthquakes

Lecture 18

Earthquake Prediction


The meaning of uncertaintyEpistemic uncertainty

Lack of knowledge18th century classical determinism lack of knowledge was a deficiency which might be remedied by further learning and experimentIt is this lack of knowledge which the insurance industry tries to addressBut we know now there is an intrinsic uncertainty, over and above our lack of knowledge, e.g. quantum mechanics, dynamical chaos, etc.

Aleatory uncertaintyUncertainty associated with randomness

Named after Latin for diceAleatory uncertainty can be better estimated, but it cannot be reduced by through advances in theory or observation


Different types of probabilityOur old friend Harold Jeffreys: tossing a coin

The probability of a head pH depends on the properties of the coin and is unknown with a prior distributionEstimate pH from results of tosses: epistemic probabilitiesFor instance they may be an epistemic probability of 0.7 that the aleatory probability pH lies between 0.4 and 0.6With repeated tosses the epistemic probability will be reduced, but the aleatory probability is an inherent property of the coin can it won’t change

For earthquake faults aleatory uncertainty arising party from the erratic nature of the fault ruptureThere is an epistemic uncertainty because we don’t know where all the faults are (yet?)


Forecasting earthquakesParkfield projectIn 1983 the USGS predicted that there would a 5.5-6 magearthquake at Parkfield in 1988+/- 5 years

Forecasted probabilities of occurrence of California earthquakes as endorsed by the NEPEC IN 1988

Loma Prieta earthquake17.10.89, caused $6bn damage and killed 68 peopleUSGS promptly claimed to have predicted it

Forecast mapBut the uncertainties in the estimation of the mean recurrence time are so large to make the 1988 map “virtually meaningless”.


“Forecasted but not predicted”

Loma PrietaSome USGS scientists had published a “speculation”, not a formal prediction that an earthquake would occur at Calaveras Reservoir. A Loma Prieta foreshock was ironically found afterwards on the map containing the flawed prediction.So the claim that Loma Prieta was predicted is not true.The claim that it was forecast in the statistical sense of the hazard map is pretty shaky.But the claim remains that it was “Forecast but not predicted”.


Are earthquakes predictable?

Many geophysicists believe that earthquake prediction is hopeless or plain wrongThese ideas have been jumped on by engineers to ignore trying to close the knowledge gapBut predicting from local geology that the damage in San Francisco due to an earthquake in the Marina and at the Nimitz Freeway is a predictionSo prediction or forecasting must still have an important part to play in earthquake hazard mitigation: seismologists can and must predict how earthquakes can affect particular structures in specific locationsThe failure of the Tokai and Parkfield earthquake prediction programmes clearly has dented or destroyed the old ideas of predicting earthquakes – but this does not negate the need to look for what we can predict


Earthquake prediction

We have to answer 4 question:1. Where?2. How often?3. How big?4. When?

Earthquake prediction can be split into two types:1. Statistical prediction (background seismic hazard)

based on previous events and likely future recurrence –uses instrumental catalogue, archaeological record, geological (Quaternary) record

2. Deterministic predictionthe place, magnitude and time of a future event from

observation of earthquake precursors


Where?Earthquakes occur because of slip on active faults

These can be found from Quaternary mappingwhere faults break the surface of from seismicity (instrumental or historical)

Plate tectonicsis only useful on a large

scale

But note many active faults are only identified after the earthquake!

N-S normal fault on the Rhine rift


How often?Palaeoseismology

Geological investigation of active faults (palaeoseismology) can reveal 2 important constraints on average recurrence interval of past events:

Tectonic slip ratefrom lithological offsetor plate tectonics (upper bound)

Trenchingreveals a section of the recent fault activity

contained in recent sediments (requires rapid sedimentation from a stream crossing the fault (e.g., Pallet Creek) and shows 140 yrs between major earthquakes on San Andreas – varies between 50-300 years

A stream channel offset by the San Andreas fault, Carrizo Plain, (photo by Robert E. Wallace) right lateral displacement


How often?Trenching

Trenching has revealed that earthquake recurrence is irregular. However the average recurrence can be reconstructed to evaluate the backgroundhazard (statistical prediction)

Hayward Fault, California

Frequency-magnitude statisticsshows synthesis of instrumental, slip rate and

average recurrence from palaeoseismology for southern California

The slope on the log-linear plotlog N = a – b m

Note how well-correlated the 3 data sets are, justifying any statistical prediction based on a continuation of past behaviour

This information can be used to construct:


How often?Probabilistic prediction

The probability increases with time most rapidly in subduction zones, slowest in intraplate zones

probability

recurrence time14050 300

discrete

cumualative

Average recurrence intervals20-30 yr Circumpacific subduction100-200 yr San Andreas transform1000-10000 yr Intraplate

for SAF at Pallet Creek


How big?Size or previous event

Magnitude, intensity, extent of fault breachParticularly “characteristic earthquake”

Most predictions of the size of a future event are based on past observation

Seismic gapSubduction earthquakes gradually filled the

Japan-Kurile arc with aftershocks, leaving gap which was filled by 1973 earthquake

The earthquake magnitude was predicted by the size of the gapMw = 2/3 (log10 M0 – 9) [M0 in Nm]M0 = µ A s A= l x ws/w = 10-4 (strain drop equivalent to 30

bar stress drop)


How big?Fault segmentation

The Anatolian fault has ruptured this century in well-documented segments, like the San Andreas

Not only that the individual fault breaks migrate along the fault, so that the whole fault is eventually broken in sequence

NB seismic gap south of Istanbul


How big?Faults are segmented by bends,en-echelon offset, and variations in frictional strength.There lead to zones of local compression (asperities) and tension (fault jogs).

Parkfield GEOMETRY

asperity jog

SHEAR STRESS20 km

(Exercise: 20km x 10km x 10-4 [shear stress] ≈ 6.5 mag)

The asperity represents an increase in rock strength and must be broken before slip can occur on the segment


How big?The fault jog represents a ‘shatter zone’ of dispersed fracture which stops the earthquake by absorbing energy

further extension resisted by:

a) suction of fluids filling fractures (e.g., capillary force)

b) further distributed cracking

The fault jog may not be observable if the fracture at depth does not reach the surface, but may see:

EN-ECHELON OFFSET

zones of distributed deformation


How big?

Summary – earthquake magnitudeSubduction 8< Mw <10 (e.g, Chile 1960)Cont. transform Mw ∼ 8 (e.g. San Andreas )Active intraplate Mw ∼ 7 (e.g. New Madrid)Oceanic ridge Mw ∼ 6Moderate intraplate Mw ∼ 5-6 (UK, N. Sea)Continental cratons Mw ∼ 5 (Antarctic 4.5)

N.B. These are related to (a) the width of the seismogenic zone, and (b) the rate of tectonic activity

The smallest fault capable of breaking the surface is about M6


Statistical distribution

Gutenberg-Richter magnitude-frequency distribution:

log10 N = a - b MN - number of earthquakes in magnitude rangeM - earthquake magnitudeSeismic b-value defines log-linear distribution

1

10

100

1000

10000

100000

Num

ber o

f Eve

nts

3 4 5 6 7 8Magnitude

Seismic b-value


Poisson statistics•Some events are rather rare , they don't happen that often. For instance, car accidents are the exception rather than the rule. Still, over a period of time, we can say something about the nature of rare events.

The Poisson distribution was derived by the French mathematicianPoisson in 1837, and the first application was the description of the number of death by horse kicking in the Prussian army.

The Poisson distribution is a mathematical rule that assigns probabilities to the number occurrences. The only thing we have to know to specify the Poisson distribution is the mean number of occurrences.

The Poisson distribution resembles the binomial distribution if the probability of an accident is very small .


Earthquakes as Poisson process

Basis of linear treatment of earthquake risk as stochastic process - randomness

Earthquakes are independentSeismicity is stationaryEarthquakes can’t be simultaneous

Use instrumental / historic catalogues


(i) Independence

Pr[A|B] = Pr[A]where A and B are any two events in the process. That is to say the probability of A occurring given B occurring

is equal to the probability of just A occurring. In other words it makes no difference whether any other

event B occurs or not – much less when it occurs, how large it is and so on.


(ii) StationarityThe probability of exactly 1 event occurring in this short interval of

length ∆t is equal to λ.∆t, proportional to the length of the interval.

λ is the rate of the process.

(iii) Orderliness

In a sufficiently short length of time, ∆t, only 0 or 1 event can occur. (Simultaneous events are impossible.)


Poisson Process

Any process showing independence, stationarity & orderliness is a Poisson process.

But any Poisson-distribution has not necessarily been generated by a Poisson process.

A Poisson process can result from random operations performed on a set of non-Poisson processes. It is a limiting case to which other point processes converge in a statistical sense. Palm-KhinchinTheorem.


Poisson model - discrete caseIf have a Poisson process, N is the number of events in

time, t, λ is the rate, then the probability function for N is:

N is a Poisson random variable with parameter, µ = λt. E[N] = µ

Number of earthquakes in time t

( ) ,...2,1,0!

)(]Pr[ ==== − xextxpxN t

x

Nλλ

Poisson distribution λ=3


Poisson model - continuousIf T is elapsed time till the first event occurs then T has exponential

probability density function:

E[T] = 1/λ Mean interval between earthquakes

0,)( >= − tetf tT

λλ

Continuous Poisson distribution


Gutenberg-Richter magnitude-frequency distribution

log10 N = a - b MEmpirical distributionSet β = b ln 10 ≅ 2.3 b

can re-write as:fM(x) = β e-βx

Exercise for the studentThis is exponential pdf for Poisson process

β-1 estimates mean magnitude

1

10

100

1000

10000

100000

Num

ber o

f Eve

nts

3 4 5 6 7 8Magnitude


Scale invariance of nature

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