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ICRM S
emina
r 201
4
3
The district of Ronchi,
located at an altitude
of 318 m,
has about 140
inhabitants and is
located in the south
of Termeno village,
Northern Italy. ICRM S
emina
r 201
4
Disaster: an unfavourable aspect of a star
What actually happened historically was NOT pre-determined;
it is just one specific realization of what might have happened
in a stochastic process.
Where event data are abundant, and events are frequent,
most of what can happen has already happened
a number of times.
However, for rare extreme events,
the actual historical dataset is sparse.
Consideration of counterfactual ‘near-miss’
scenarios augments a meagre dataset. Antikythera
ICRM S
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‘Lateral thinking is concerned with
the generation of new ideas,
and breaking out of the concept
prisons of old ideas.’
Lateral thinking avoidance
of systemic risk
ICRM S
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Stochastic modelling of the past
2014
Whereas stochastic analysis of future scenarios
is commonly undertaken, this is hardly ever done
for past events. ICRM S
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4
Earthquake recurrence on faults
STRESS STRESS
TIME TIME
Idealized Periodic Model Actual Behaviour
Variable
strength Variable stress drop
Identical
strength
Constant stress build-up
Constant stress drop
Non-uniform stress build-up
ICRM S
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Aperiodic recurrence intervals
EAST NANKAI TROUGH SAN ANDREAS FAULT (S. Cal.) 1944 1857 dt = 90 years dt = 45 years
1854 1812 147 years 332 years
1707 1480 209 years 130 years
1498 1350 138 years 250 years 1360 1100
264 years 100 years
1096 1000 ICRM S
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Stochastic modelling the past:
The Parkfield sequence 1857
1881
1901
1922
1934
1966
24
20
21
12
32
Average interval of about 22 years
1966 + 22 = 1988! ICRM S
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The Parkfield puzzle
Stress loading increase over time:
includes a Brownian motion term. A better sense of the
next occurrence is obtained by randomizing the accidental
historical dates.
( )t W t
Yes - in 2004
ICRM S
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Recognizing the bounds of knowledge
12
A great M8.6 strike-slip earthquake occurred off Sumatra on 11 April 2012.
This may be the largest strike-slip earthquake ever recorded in the world.
The large Sumatran earthquakes in 2004, 2005, and 2007 triggered one another and
may have triggered this event. Future earthquakes near Sumatra may be more likely
to happen sometime in the coming decades.
Why are
seismologists
surprised
so often?
ICRM S
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Counterfactual history Catastrophes are extreme events.
In all branches of catastrophe science, history is a vital data
resource because catastrophes are rare.
But much can be gleaned from a detailed study of near-misses
- catastrophes that might have been.
‘The terror of the unforeseen
is what the science of history hides.’
Philip Roth IC
RM Sem
inar 2
014
16 January 2013: terrorist attack
on gas plant at InAmenas, Algeria
A stray terrorist bullet
accidentally caused a
power outage
that automatically
shut down the plant.
This prevented the
terrorists from
setting off a large
explosion. ICRM S
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4
Interactions between the natural, man-made and virtual environments.
Multi-hazard events coupling geological and meteorological actions.
Unusual and bizarre combination of natural and technological (Na-Tech) disasters.
Risks unknown to science
Emergent phenomena can arise from complex nonlinear
systems, which may constitute novel modes of risk, e.g...
ICRM S
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Counterfactual disasters:
resampling history
The risk state of a system can be represented in terms of n
underlying risk variables, some of which may be hidden and
not directly observable:
{ (1), (2),... ( )}S X X X n
Perturbing these state variables leads to a resampled
virtual disaster history.
These variables include measures of both physical hazard
proximity parameters, and organizational parameters,
e.g. system defences and controls.
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{ X(1), X(2),….X(n)}
Danger
Physical
Space
(distance
to hazard
threshold)
Organizational space
(adequacy of system defences and controls)
Proximity to danger in both physical
and organizational space
ICRM S
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East Bay Hills wildfire
October 1991
19
The Oakland Hills fire, killed
25 people, injured 150, and
destroyed more than 3,800
homes.
Eleven died in traffic jams
while evacuating. Eight others
died on narrow streets in the
same area.
The economic loss has been
estimated at $1.5 billion. X(1): wind strength
X(2): ignition number
X(3): fire-fighting capacity
“It’s hard to get organized and run for
your life at the same time!”
ICRM S
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FEMA: US Fire administration commentary The most significant factor that should be recognized from this incident is that the
fire was beyond the capability of fire suppression forces to control.
The stage was set by a number of contributing factors that created the
opportunity for disaster. When the Santa Ana wind condition was added to
those risk factors, the combination was more than any fire department could
handle.
One fire official said that if the same fire risk factors had been present in a park or
forest, the area would have been closed to all activities.
As long as the wind was present, the fire was going to continue to spread,
no matter what strategy and tactics were used and no matter how much
equipment and how many firefighters were there to try to stop it.
‘The fire was contained only when the wind changed.’ IC
RM Sem
inar 2
014
Deterministic view of history
Historical hazard experience is regarded as binary –
an event either happened or it did not.
If it didn’t, …then it didn’t.
But what if the environmental
circumstances had been somewhat
different? What was the chance of a
disaster? ICRM S
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Long Wharf, Boston: the blizzard of February 2013
A four-foot storm surge hit Boston at low tide, not high tide.
With the high tide already a foot higher than average because of the
new moon, coincidence of the storm surge with this high tide would
have given rise to the 100-year flood. ICRM S
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As of August 25th, 2011,
a counterfactual analysis can be
undertaken to assess the likelihood
that the insured loss from Hurricane
Irene might have been in excess of
$50 billion.
This is estimated from an RMS study
of the possible track evolution of the
hurricane as it funnelled through the
track selection gates marked in green.
This likelihood is estimated to be in
excess of 1%. ICRM S
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Random aspects of event history
25
0 1 2 3 4 5 6 7 8 Years
Suppose that over a period of 8 years, there are four crisis events
when a dice is thrown, with an event arising if the outcome is a
six. The expected number of events is 4/6, yielding an annual
frequency of (4/6)/8 = 1/12.
But there is about an even chance (0.48) of no event occurring.
IC
RM Sem
inar 2
014
Probability distribution function
for key dynamic hazard parameter
Threshold T for
hazard event
to occur
( )f z
TICRM S
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Time series of danger periods
0 1 2 3 4 5 6 7 8 years
The expected number of events over the 8 year time interval
is the sum of the tail probabilities:
4
1
( )k
k T
f z dz
T T T T
ICRM S
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Counterfactual
volcano hazard analysis
In the 1994 edition of ‘Volcanoes of the
World’, published by the Smithsonian
Institution, the known volcanic eruptions
are catalogued.
However, unrest periods are not given
so much attention.
ICRM S
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Site hazard: American University of the
Caribbean School of Medicine
The government of Montserrat granted AUC a 25-
acre parcel of land near Plymouth, where a new
campus of 17 buildings was built. AUC began
conducting classes at its new campus in Montserrat
in January 1980.
On September 17, 1989, Hurricane Hugo hit the
island, severely damaging the campus.
The Montserrat campus was rebuilt and AUC reopened it
for classes in September 1990. ICRM S
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Montserrat volcano hazard in the 1980’s
Montserrat provides a practical
application for counterfactual
analysis.
Volcano-seismic activity
damaged buildings in the 1890s,
1930s and 1960s.
For previous episodes of unrest, a counterfactual analysis
allowing for the aleatory uncertainty in volcano dynamics would
inform assignments of the probability that the unrest is magmatic,
potentially leading to an eruption. IC
RM Sem
inar 2
014
Maximizing the use of historical unrest data
The crisis in the mid-1930s raised fears of a potential major eruption.
For the unrest in 1966-1967, instrumental monitoring data exist to support
the estimation of a high eruption likelihood. e.g. Shepherd J.B. et al. (1971)
Volcano-Seismic crisis in Montserrat, West Indies, Bulletin Volcanologique:
‘Sharp increases in seismic and solfataric activity occurred in 1966 and these events
indicated the abnormally high risk of an eruption in the near future. A network of four
short period seismographs was established in the island in May 1966 and between
this date and the end of 1967, 723 local earthquakes were recorded, of which 32
were reported felt in the island. Hypocentres were determined for 189 of these
earthquakes, and most of these lay in a WNW to ESE belt beneath the Soufriere
Hills, at depths of less than 15 km.’ ICRM S
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Time series of volcanic unrest periods
1890 1930 1960
For each unrest period, the time-dependent eruption probability
can be estimated from the available data.
The expected number of eruptions over the century time interval
is the sum of the tail unrest probabilities:
3
1
( )k
k T
f z dz
T T T
ICRM S
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‘Near-miss’ data in volcano risk analysis
Stochastic models for unrest periods, rather than just actual eruptions, need to be developed.
For Montserrat, the expected number of eruptive events in the century from 1890 – 1990 is about 1.
33
Plymouth was destroyed
in August 1997 A baseline frequency would thus have
been about 1%, which is higher than
using the time to the last eruption in
1630, and would have yielded a more
pessimistic and realistic assessment of
volcanic hazard at Plymouth. IC
RM Sem
inar 2
014
An unusual day
‘The really unusual day would be one
where nothing unusual happens.’
Persi Diaconis,
mathematician and magician
ICRM S
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The Improbability Principle
‘As someone who happened to meet his future
wife on a plane, on an airline he rarely flew,
I wholeheartedly endorse David J. Hand’s
fascinating guide to improbability,
a subject that affects the lives of all,
yet until now has lacked a coherent
exposition of its underlying principles.’
ICRM S
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4
‘Traces of the tsunami damage were found from
Miyagi Prefecture (4) to Fukushima Prefecture. (7)
However, in the most recent study, the researchers
found evidence of damage in Iwate Prefecture (3),
leading them to believe the earthquake that caused
the tsunami might have measured around a
magnitude of 9.’ Japan Society of Engineering Geology meeting,
Osaka, 12 October 2007
Sanriku
earthquake
869
‘When you have eliminated the
impossible, whatever remains,
however improbable,
must be the truth.’
Sherlock Holmes,
The Sign of the Four
ICRM S
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The law of inevitability
The law of truly large numbers
The law of selection
The law of the probability lever
The law of near enough
Hand’s five laws of improbability
ICRM S
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The Law of Inevitability
From a complete list of outcomes,
one of them must occur.
‘It’s a little difficult to ascertain
where the NASA satellite will
come down because there are
so many variables involved.
But it will definitely come down
in some part of the world.’ ICRM S
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4
On 15 February 2013, the Russian district of Chelyabinsk, with a population of more
than 1 million, suffered the impact and atmospheric explosion of a 20-meter-wide
asteroid, the largest impact on Earth by an asteroid since Tunguska, 1908.
Popova et al., Science, November 2013 IC
RM Sem
inar 2
014
Virginia State Lottery
In the 1990s, the Virginia State Lottery was based on choosing
6 numbers from 1 to 44, giving a probability of 1 in 7,059,052
That any one ticket would be a jackpot winner.
On 15 February 1992, the jackpot had rolled over to $27 million.
A consortium of 2500 small investors, mostly Australian, formed
an international Lotto Fund to buy every combination of numbers.
ICRM S
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If two targets are equally
attractive, terrorists will tend
to attack that which has worse
security.
Terrorist target substitution
Once a terrorist moves to a target, alternative targets of
opportunity will be chosen if the designated target is too secure.
ICRM S
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On October 17, 2012, Quazi Nafis, a 21-year-old Bangladeshi, attempted to set
off a 1,000 bomb outside the Federal Reserve Bank, after originally intending to
strike Wall Street.
Target substitution in New York
Liberty Street, NY Wall Street, NY ICRM S
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The Law of Truly Large Numbers
With a large enough number of opportunities,
any outrageous thing is likely to happen.
On 14 June 1999, in Arizona, a 14 year old girl, Shannon Smith,
was killed by a bullet that landed on top of her head.
[It has since become illegal to fire guns into the air.]
ICRM S
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Evelyn Marie Adams won the New Jersey Lottery twice in
just four months: first in 1985, then again the next year.
Her winnings were $5.4 million.
The chance of her winning twice in this time span was about
one in a trillion.
However, accounting for all the lotteries in the world; the
number of players; the number of tickets they buy; and the
number of weeks they play; all leads to a truly large number.
With enough events, the chance that one will happen can be
very large.
Double lottery wins
ICRM S
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Animal earthquake forecasting
A population of reproductively active
common toads was monitored over a
period of 29 days, before, during and
after the M6.3 earthquake at L'Aquila,
Italy, which occurred on 6 April 2009.
Toads at the study site, 74 km distant from L'Aquila, showed a dramatic
change in behaviour 5 days before the earthquake, abandoning spawning
and not resuming normal behaviour until some days after the event. ICRM S
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The zoologists remark that,
‘Whether toads would exhibit similar behaviour at other
locations and preceding other large seismic events
remains to be seen, but the results reported here suggest
that toads detect whatever phenomenon is giving rise to
the perturbations in the ionosphere and are thus able to
anticipate seismic events.
Testing this hypothesis would, however, be very difficult,
given the rarity and unpredictability of earthquakes.’ ICRM S
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The Law of Selection
You can make probabilities as high as you like,
if you choose after the event.
By looking back at what actually happened,
probabilities can be changed.
This is postdiction rather than prediction. ICRM S
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Postdiction of catastrophes
The postdiction of catastrophes with the advantage of
hindsight raises an important issue in catastrophe
modelling.
The original event probabilities may have been
underestimated.
How can probabilities be better updated?
ICRM S
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Time variation of the cumulative strain
for the eastern part of the southern Aegean
Papazachos
et al.
BSSA
2002
Benioff
Strain
1.0E+8
8.0E+7
6.0E+7
4.0E+7
2.0E+7
0.0E+7
1960 1970 1980 1990 2000
The generation of the strong Cythera
earthquake on 8 January 2006 with M 6.9,
epicenter coordinates φ = 36.2° N
and λ = 23.4° E satisfies this
intermediate-term prediction.
(BSSA, 2007)
ICRM S
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The Law of the Probability Lever
A slight change in circumstances
can have a huge impact on probabilities.
A slight change in the shape of a distribution can alter probabilities from
being incredibly small to being part of the familiar course of events. ICRM S
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Very few people have ever experienced an electric shock
due to lightning. In UK, for example, the average number
per year from 1988 to 2012 is only 29.
However, this risk is far higher for those whose work or
recreation keeps them outdoors.
Major Walter Summerford was struck twice by lightning,
before a third strike left him completely paralysed.
Even his gravestone was struck by lightning.
Non-uniform casualty risk : Lightning
ICRM S
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The % Death Per Case (DpC) is modelled by a Weibull distribution: Pr (DpC > X ) = exp ( - [X/A]B )
Infectious disease lethality modelling
Long-tailed distribution for the % Death Per Case (DpC)
Likelihood of Lethality of Pandemic Virus
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0 10.0 20.0 30.0
Death per Case (%)
Probability of Exceedance
ICRM S
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The Law of Near Enough
Events which are sufficiently similar
are regarded as identical.
By relaxing the criteria for a match, we can increase the
probability of an apparent coincidence. Events which
might seem extremely unlikely can turn out to be quite
probable on closer examination. ICRM S
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Near coincidences
The psychoanalyst Carl Jung, has recounted the following
coincidence:
‘A young woman I was treating had a dream in which she
was given a golden scarab. Suddenly I heard a noise
behind me, I turned round and saw a scarabeid beetle,
which is the nearest analogy to a golden scarab that one
finds In our latitudes.’ ICRM S
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Ensemble probability forecasting of weather
What about ‘coincident’
clusters of hazard events,
e.g. large earthquakes?
ICRM S
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4
‘Coincidence
is God’s way
of remaining
anonymous.’
Albert
Einstein
Unknown Unknown Centre
ICRM S
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