20 Earthquake Warning - University College London Earthquake War… · After the earthquake three-quarters of Lisbon is destroyed. The wise men at the University of Coimbra to prevent

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Forecasting Earthquakes

Lecture 20Earthquake Warning


Journal of Astrology: Some time in 1965-66, the late Pune astrologer, SK Kelkar, came out with his startling prediction that there would be an earthquake in Koyna in

the first fortnight of December 1967. An earthquake of the magnitude of 6.5 on Richter scale shook Koyna on 10 December. Kelkar had worked on the lunar eclipse

of 18 October 1967 and come to the conclusion that the movement of Mars in Capricorn, an earth sign, would cause it. Subsequently, Kelkar correctly predicted the

earthquakes

After the earthquake three-quarters of Lisbon is destroyed. The wise men at the University of Coimbra to prevent another earthquake arrest a Biscayan for marrying his godchild’s grandmother and two men for not eating bacon. They also arrest Candide and Pangloss. Candide is badly flogged. Pangloss is hanged. Others are burned. There is another earthquake on that same day.

In Japan a committee of six 'wise men' can be called in by the meteorological agency at any time to examine seismic data that might indicate that an earthquake is imminent

Deciding to warn


Earthquake Precursors

What is a precursor?

“Standard” signature of earthquake precursors, according to Russian theorists. The precursor γ begins to drop before the earthquake and recovers when the earthquake is imminent

The precursor γhere is the ratio between velocities of compressional and shear waves


Observation of precursors: groundwater

Tangshan earthquake (Hebei Province, July 28, 1976, M = 7.8)

244,000 to 655,000 people died

Pattern of groundwater anomalies according to Chinese researchers. Note the precursory reversal (“imminent rebound”).

Geographical distribution of water-level precursors. Open circles, down.


Observation of precursors: tilt

Tilt of Rapel Reservoir. Chile, before and after 1985 earthquake, computed from the difference in water levels between two gauges 20km apart. Note that the anomaly begins in mid-1984.

Niigata earthquake


Observation of precursors: electrical potential

VAN earthquake prediction method

Some geopotential anomalies observed at Vitosha, Bulgaria.(Ralchovsky & Komarov, 1991).


Test of a precursor

Probability gainProbability rate P(M) of an

earthquake M=6.5 in Izu-Oshima estimated asP0 = 10-4/day

Probability of an earthquake occurring after a precursor is P(X)

Then the probability gain due to a recognisable precursor= P(X) / P0

1978 Izu-Oshima-kinkai earthquakeprecursory observations in wells; -

- - - geodetic uplift; X major seismic events


2) Intermediate-term prediction - anelastic

Changes in physical parameters predicted by the dilatancy-diffusion model. Roman numerals indicate various stage in a seismic cycle (Scholz, Sykes & Aggarwal, 1973).

Anelastic models help explain the duration of earthquake precursors, since the

dilatant volume α size of earthquake

Dilatancy-diffusion model

Phases of:

I – elastic build-up

II – strain hardening

III – strain softening


Precursor duration

Precursor time, T, (measured in days) versus magnitude, M, relations by: a) Tsubokawa (1969, 1973); b) Scholz, Sykes & Aggarwal (1973); c) Whitworth, Garmany & Anderson (1973) and d) and e) Rikitake (1975)


3) Short-term & intermediate term prediction: fault asperity model• Short-term precursors can be explained by the existence of a fault

x Asperities (strong patches)

free to slip

(NUCLEATION ZONE)

LOCKED

stress

displacement1 2 3

a b c

1. Elasticity

2. Dilatancy

3a. Microcrack coalescence

3b. Fluid diffusion

3c. Accelerating slip through asperity

Phases 3a) and 3b) are quiescent


Fracture mechanics model with time-varying stress

Intermediate and short-term precursors follow from correlation with stress intensity:

K = Y σ √x

Note double b-value anomaly.

(Main et al., 1989)

stress intensity peaks due to acceleration of crack through asperity

b ∝ 1/K


Experimental verification

Triaxial deformation experiment on rock under “undrained” conditions. Note time varying stress and double b-value anomaly.

(Sammonds et al., 1992)


Western Nagano earthquake

Event rate and b-value for Western Nagano earthquake, Japan.

Note double b-value anomaly.

(Main et al., 1989)


Brune’s dilemmaBrune (1979):

Suppose large earthquakes are always triggered by small earthquakesThen we must either be able to tell the small shocks that trigger a large earthquake from the enormously more numerous small shocks that don’t, or else predict every small earthquake that occurs on every plate boundaryThe same argument could be applied to other precursorsIf true this would preclude earthquake prediction

Solution of a sort:Small shocks and large earthquakes are not the same kinds of eventsThe confusion lies in the idea of triggeringLarge earthquakes are not triggered by precursors, or by anything, they are embedded in a larger transient that starts ahead of theearthquake and lasts beyond its occurrence


Earthquake warningSeismic Alert System (SAS) of Mexico City

Series of digital strong motion seismometer stations along 100’s km of Mexican coast, spaced at 25km intervalsEach station monitors activity within 100km and is capable of detecting and estimating the magnitude of an earthquake within 10s of its onsetIf estimated M ≥ 6, a warning message is sent to a central control unit in Mexico City over 230km awayOwing to the lag of seismic over electromagnetic waves, a one-minute warning is available for the publicThe decision to broadcast an early warning is taken after receiving data from all stationsSome quite sophisticated pattern recognition techniques in signal processing are available, but the decision making component of SAS is simple and deterministic, with a alarm broadcast if two stations estimate M > 6Gave a 72s warning of the 1995 M=7.3 earthquake 300km south of Mexico City: sufficient for notification of emergency military and civilian response centres, and for orderly evacuation of schoolswhich had alarm systems fitted


The Concept of ProbabilityKolmogorov 1933: total probability theorem

Two sets: A and B, with probabilities P(A) and P(B)The intersection of the two sets is: A ∩ BThe conditional probability of B given A (that is the probability B occurs given that we already know A has occurred) is:

P(B|A) = P(A ∩ B) / P(A)or P(A ∩ B) = P(A) P(B|A)

A

P(A ∩ B) – Probability that both events occur

P(A)

A ∩ B

BP(B)


The Concept of Probability

Two sets which are mutually exclusive: A ∪ BHave a set: Ω = A ∪ B ∪…∪ C which are exclusiveLet X be an arbitrary set, then probability of X is:P(X) = P(X ∩ A) + P(X ∩ B) +….+ P(X ∩ C)

= P(A) P(X|A) + P(B) P(X|B) + ….+ P(C) P(X|C)

Note Ai = A,B,C… :P(Ai|X) P(X) = P(Ai ∩ X) = P(X | Ai) P(Ai)

Ω = A ∪ B ∪…∪ C

A B ……..C

X


Bayes’ TheoremThomas Bayes, an English churchman, in 1761, a few months before his death proved one of the most pivotal theorems in statistics, which has since given his name to a scientific school, the BayesiansBayes’ Theorem allows you to compute the probability that a hypothesis is true provided that one knows the probable truth of all supporting argumentsBayesian statistics tend to be controversial as the arguments are often evaluated subjectively and not in terms of hard data

)|()(...)|()()|()()|()()|(

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Bayesian practice is to update the probabilities on the receipt of new information: everything is a conditional probability


The Murder TrialJames is being tried for a murder. The onlyevidence against him is the forensic evidence - blood and tissue samples taken from the scene of the crime match James's. The chance of such a match happening if James were in fact innocent and the match were just a coincidence is calculated (by the prosecution's expert witness) as 1 in 10,000 (0.0001). What do you think is the probability of guilt?

If you think the answer is 0.9999 you are wrong: this is known as the prosecutor's fallacy.The defence's expert witness, however, points out that James was found through a systematic examination of everyone in the local community. There are 40,000 such people, and no evidence


The Murder TrialThis situation can be described by Bayes Theorem.

H1 (the first hypothesis) = James is guilty H2 (the second hypothesis) = James is innocent (not guilty)These are the two hypotheses between which we have to decide.

E (the evidence) = The forensic evidence of a match

We can assume that Prob(E given H1) = 1If he is guilty, the forensic evidence is bound to show a match Prob(E given H2) = 1/10,000 = 0.0001If he is innocent the probability of a match is 0.0001. These two probabilities are known as likelihoods. Notice that they are both "Evidence given hypothesis". Bayes theorem reverses these conditional probabilities and tells us the probability of the hypothesis given the evidence.


The Murder Trial

To use Bayes’ theorem we also need to know P(H1) and P(H2). These are the prior probabilities of guilt and innocence. They are "prior" in the sense that these are the initial estimates before the evidence is considered.

If we assume that the murder must have been committed by someone in the local community, then P(guilty) = 1/40,000 = 0.000025 P(innocent) = 1 - 0.000025 = 0.999975

The first equation above now gives: Prob(guilty given evidence) = (1x0.000025) / (1x0.000025+0.0001x0.999975) = 0.2 = 20%

which means that the probability of James's guilt is only 20%. This is probably a lot less than your initial estimate!


The Murder Trial: tree diagram

Murder

James not guilty

James guilty

No tissue match

Tissue match

No tissue match

Tissue match

p = 1

p = 1/10,000

p = 1/40,000

p = 39,999/40,000

Prior probabilities Likelihoods

p = 1 * 1/40,000

= 0.000025

p = 39,999/40,000 * 1/10,000

= 0.0001

Bayes theorem gives the posterior probabilities:

Prof(James guilty given tissue match) = 0.000025/(0.0001+0.000025) = 0.2


The Murder Trial: tree diagram

Murder

Not guilty

Guilty

No tissue match

Tissue match

No tissue match

Tissue match

p = 1

p = 1/10,000

1 person

39,999 people

Prior probabilities Likelihoods

1 person

4 people

5 people in the community will have matching tissue. James in 1

Therefore the probability of James being guilty is 1 in 5 or 0.2


Bayes’ Theorem: exampleThe probability that an earthquake of magnitude M occurs given the

previous occurrence of some precursory set of phenomena A, B, C,.. :

)~|,..,,Pr()Pr()|,..,,Pr()Pr()|,..,,Pr(,..),,|Pr(

MCBAMMCBAMMCBACBAM

+=

the probability of occurrence of the phenomena given that the earthquake actually does occurs times the probability of of occurrence of an earthquake magnitude M

the sum of the probability of all possible outcomes: but for an earthquake it either occurs or it doesn’t occur


Lomnitz: are equinoxes earthquake precursors?Richter’s Law: “All major earthquakes occur within 3 months of an equinox”.How relevant is it to know exactly when the next earthquake willoccur?To what accuracy do we really need to predict?It is not obvious that equinoxes fail to qualify as precursors?

Two criteria for earthquake precursor have been proposed:

1. Precursors always precede the target earthquake2. Individual precursors almost always give false alarms

So for equinoxes:1. Equinoxes occur regularly twice a year2. They nearly always yield a false alarm3. Their occurrence is rare enough to generate a large

probability gain: but this is what you are looking forBut how to we assess the usefulness of a precursor?


Equinox as a precursorFor precursors that always precede the target earthquake, the probability Pr(A,B,C,..|M) = 1

)..]Pr()Pr()[Pr()Pr()Pr(,..),,|Pr(

CBAMMCBAM

+=

If we assume the precursors occur independently of each other, so if the earthquake does not occur:

)..Pr()Pr()Pr()~|,..,,Pr( CBAMCBA =Then:

Pr(A), Pr(B) etc. are very small. So add any new precursor and the probability of future earthquake may be made to increase!

For the Izu earthquake probability gain due to equinox = Pr(X)/P0

= 0.0055/10-4 = 55

This compares with a combined probability gain of 33 from radon anomalies, change in water level and volumetric strain changes


Conclusions

Bayes’ Theorem tests hypotheses – and can be updated on the basis of new informationIt been a long-standing idea that there are precursors to earthquake – Bayes theorem shows there is a big probability gain in using precursors for predictionBut here is where it all comes apart – because there is a physical occurrence doesn’t mean to say it is a precursor! We can use Bayes theorem to cheat


Hazard warning communication links

Deciding to warnTechnical Expert 1

Technical Expert 2

Technical Expert 3

Technical Expert 4

Technical Expert 5

DECISION SUPPORT SYSTEM

Hazard Operational Scientist / Manager

Civil Defence Officer

Individual expert

judgement

Collective scientific opinion

Decision on hazard warning


Deciding to warn: “Certainty Theory”

To a mathematician, decision analysis is a branch of probabilitytheory applied to decision-makingPolicy makers have been slow to follow a probabilistic approach:reticence which reflects the predominant training of administrators and civil engineersIn traditional engineering practice, a safety factor in design ensures that a building is safe, involving engineering judgement


Bayes’ Theorem

Bayes’ Theorem allows you to compute the probability that a hypothesis is true provided that one knows the probable truth of all supporting arguments

)|()(...)|()()|()()|()()|(

2211 nn

iii AXPAPAXPAPAXPAP

AXPAPXAP+++

=

Bayesian practice is to update the probabilities on the receipt of new information: everything is a conditional probability


Specific siting decisionsSeismic hazard evaluation: Bayesian approach

Ground motion attenuation relation

Magnitude / fault rupture relation

Fault activity

rate

Logic-tree segment for a fault, showing three of its branches. The first corresponds to a choice of attenuation relations, the second to choice between event magnitude and fault rupture geometry and the third to a choice of four activity rates for the fault

Comparison of logic-tree seismic hazard curves. Disparities between the three curves result from epistemic uncertainty in hazard model parametrization. In contrast aleatory uncertainty is incorporated within each hazard curve


Specific siting decisionsGuidelines from the International Atomic Energy Agency

A fault is considered capable if:1. It shows evidence of past movement of a recurring nature, within such a period that it is

reasonable to infer that further movement at or near the surface can occur2. A structural relationship has been demonstrated to a known capable fault such that

movement may cause movement of the other at or near the surface3. The maximum potential earthquake associated with a seismogenic structure, as

determined by its dimensions and geological and seismological history is sufficiently large and at such a depth that it is reasonable to infer that movement at or near the surface can occur

Trench location

Reactor siteLandslide failure

surface

Fault planeAmbiguity that can arise in the geological interpretation of thedisplacement observed in a trench

Nuclear test reactor at Vallecitos, n. California, 35 miles from downtown SF, refused operating license

Successful application of Bayesian probabilistic approach to weighing evidence – but took 6 years


Certainty Theory

The prior probability of hypothesis H, P(H) represents an expert’s judgemental belief in the hypothesis. The expert’s disbelief is P(~H):

P(H) + P(~H) = 1If an expert receives evidence E, such that the probability of the hypothesis given the evidence is greater than the prior probability, i.

P(H|E) > P(H)then the expert’s belief in the hypothesis is:

)(1)()|(),(

HPHPEHPEHBelief

−−

=

The expert’s disbelief in the hypothesis is:

)()|()(),(

HPEHPHPEHDisbelief −

=

Certainty factor = CF(H,E) = Belief (H,E) – Disbelief (H,E)


Certainty Theory

Dynamical reasoning tree for a Certainty Theory expert system showing login, reasoning paths from evidence to hypothesis to the conclusion

Hypothesis

H[1]

Hypothesis

H[m]

EvidenceE[1] E[2] E[3] E[4] E[j] E[j+1] E[k]

CF(H[1],E[1]) CF(H[1],E[4]) CF(H[m],E[k])

CONCLUSION

Documents

20 Earthquake Warning - University College London Earthquake War… · After the earthquake three-quarters of Lisbon is destroyed. The wise men at the University of Coimbra to prevent