Earthquake and Shaking Probabilities:Helping society to make the right choice. Ettore Majorana Found

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• Earthquake and Shaking ProbabilitiesHelping
  society to make the right choice. Ettore
  Majorana Foundation for Scientific culture.
  International school of Geophysics, 26th
  Workshop.Erice 18-23 Oct. 2006
• Scaling relationships for great thrust
  earthquakes in the Himalaya
• Nicole Feldl and Roger Bilham
• Attempts to forecast future Himalayan earthquakes
  are hindered by the absence of repeatedly
  occurring great earthquakes in the past 1000
  years.
• Estimates of hazard based on potential slip since
  1800, or potential slip since 1505 (including
  inferred characteristic rupture areas), are
  frought with uncertainty.
• A theoretical approach to reconcile GPS geodesy
  in southern Tibet with the subsurface geometry of
  the plateau yields a relationship between rupture
  length and slip ( hence Mw) for Himalayan
  earthquakes.
• Mw vs rupture length for recent earthquakes
  compared to these synthetic curves, suggest that
  a recurrence interval of 500(200-100) years may
  prevail. The relationship between slip rupture
  length, however, suggests that very long ruptures
  repeat at intervals gt1000 years.
• Thus although 2/3 of the arc could rupture today
  in Mwgt8 earthquakes repeats of Medieval events
  with similar slip may not occur for a further 500
  years.
• The study suggests that earthquakes in the past
  200 years have unnefficiently released strain
  stored in southern Tibet i.e.areas that have
  recently slipped in Mw7.8 earthquakes could
  rupture in larger earthquakes sooner than
  anticipated.

Explanatory notes and URL links included in this
Powerpoint file
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Scaling relationships recurrence intervals for
the Himalaya Roger Bilham CIRES Geological
Sciences University of Colorado Boulder CO
80309-0399
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Thesis Great Himalayan earthquakes tap a
reservoir of elastic energy stored in the
southern half of the Tibetan Plateau.
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Text
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slip potential (m) based on past 200 years
Bilham et al 2001
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magnitude-potential (Mw) based on past 500 years
Bilham Wallace 2004
7.6
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forecast potential but useless for prediction
input time since last event and convergence rate
(19 mm/yr)
input time since last event with assumption that
inferred historic ruptures will repeat
problem! neither tell us time to next event
(because no great quakes historically repeat)
default solution use slip in last event to
predict time to next.
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3 new problems arise

• uncertain slip in trench excavations of
  paleoquakes (3-26 m)
• no surface slip in recent earthquakes (blind
  faults or blind geologists?) exception Kashmir
• slip in instrumental period derived from
  magnitude (assumes scaling law)

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Mwµ x slip x area (linear i.e. the longer
you wait the bigger the quake)
but slip also proportional to rupture
area (non-linear need to wait much longer for
much bigger quake) needs scaling law
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So what, exactly, is a scaling law?
8.5
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7.5
earthquake magnitude
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6.5
Data from Bonilla et al 1984
rupture length
6
10
100
1000 km
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New events change the relationship
8.5
8
7.5
earthquake magnitude
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6.5
Data from Bonilla et al 1984
rupture length
6
10
100
1000 km
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Conclusion universal empirical scaling laws are
flawed descriptions of the relationship between
slip and rupture area(surface rupture or
aftershock area can be misleading indications of
area, no account of mechanism, fault friction,
surface rheologies, fluids, etc)So try a new
approach- calculate the scaling relationship for
specific system using elastic theory and
calibrate it with real earthquakes
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constraints for Himalayan arc
Afghanistan
Kashmir
unconfirmed 1555 rupture
colored symbols indicate Intensity VIII for
earthquakes in the past 500 years. Continuous
lines indicate ruptures identified
paleoseismically.
1905
1400100 rupture
Assam
unconfirmed 1505 rupture
1934
Baluchistan
1897 Ms8 Shillong
1950 Mw8.5 (unmapped)
112550 rupture
1897
1. geological convergence 14-21 mm/yr 2. geodetic
convergence 17-21 mm/yr 3. five recent
earthquakes with known slip Mw 4. paleoquakes
slip 26 m
Burma
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Three-step process to calculate earthquake slip
freely slipping boundary elements shown in red
a.Calculate current strain rate using plateau
geometry and GPS velocity field. Interseismic
slip.
c. Now allow entire plateau to slip in response
to coseismic slip in b.Unrestrained (fully
relaxed afterslip
b. Increment strain by x years and drive frontal
thrusts -calculate length vs. coseismic
slip Restrained slip.
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1. boundary element calculations (mm/year) - vary
depth and position of locked zone to match GPS
convergence. Why push system from 500 km north?
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-need to reconcile geological convergence rate
with geodesy
Why push system from 500 km?
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21 mm/yr
14 mm/yr
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144 mm/yr
14
21
144 mm/yr
211 mm/yr
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N
S
Preseismic
100 km
300 km
1000 km
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coseismic displacement
coseismic displacement
Mwlt8
Mw9
coseismic strain change in plateau
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2-3 m
4-8 m
10-12 m
3-5 m
Max. coseismic slip
Map views of slip on interface between India and
Tibet for ruptures of different length - short
ruptures (small earthquakes with Mlt8) do not
drain Tibets reservoir of elastic energy long
ones do.
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Synthetic scaling laws
Calculations of slip for different rupture
lengths result in a characteristic curve (4
shown). The top of each curve indicates
unsrestrained slip, the bottom is restrained
slip. However, an infinite number of curves are
possible depending on the inter-event time.
Which is correct?
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observed data favor 500 year renewal time
?
For very few earthquakes are independent slip and
magnitude data available. When Himalayan data
are plotted on the synthetic curves they suggest
a 500200 year interevent time
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Maximum slip vs rupture length
1000 years
unrestrained
500 years
restrained
Similarly a suite of maximum slip vs rupture
length generates a series of curves with upper
and lower bounds determined by recurrence interval
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Maximum slip vs rupture length
recent quakes suggest 500 years,
but paleo-ruptures favor 1000 years
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Thus recent earthquakes with short ruptures (1934
Mw8.2) have left the reservoir of strain intact.
100 km 2005
40 km 1885
Afghanistan
120 km 1905
Kashmir
unconfirmed 1555 rupture
1905
gt350 km
200 km 1950
80 km 1803
200 km 1934
100 km 1897
1400100 rupture
gt400 km
Assam
unconfirmed 1505 rupture
1934
Baluchistan
1897 Ms8 Shillong
1950 Mw8.5 (unmapped)
112550 rupture
gt550 km
1897
gt350 km
Burma
but pre-16th century earthquakes (Mwgt8.4 with
long ruptures) may have drained Tibet's strain
reservoir. These rupture zones are now 50
recharged.
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Implications for strain reservoir

• massive events (Mw.8.5) essential to deplete
  strain reservoir - true for strike-slip and
  thrust.
• Small events (M8) tap only local strain and can
  be re-ruptured in larger events sooner than
  expected from seismic gap theory
• c.1100, c.1400 and 1505 ruptures could repeat
  today with Mwgt8.3 (slip 10m), or in 500 years
  with Mwgt8.5 (slip 20m)
• magnitude determined by length of rupture.
  possibly controlled by strength of along-arc
  asperities (whether a M6 or a M8.6 occurs depends
  only on segment connectivity- think of asperities
  as the base that controls emitter collector
  currents in a transistor)

VTibet strain potential
base asperity
Irupture length magnitude
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small events (Mlt7) tap only local strain massive
events tap entire reservoir Gutenberg Richter
a b-values may differ for large and small
events
numbers of earthquakes
transition controlled by asperities
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7
8
6
9
4
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Himalayan moment summation Bilham Ambraseys,
2004
three Mw8.5 overdue?
65 of Himalaya have not slipped in the past 200
years (consistent with a 500 year recurrence
interval)
7.8
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Does this study improve the forecast of future
Himalayan earthquakes?

• YES prior to this study there was no information
  on recurrence interval.
• YES we now realize that locations like Kangra
  1905 and Nepal 1833 are not immune to a future
  larger earthquake.
• YES Several segments of the Himalaya must now be
  considered overdue for a great earthquake.
• NO- forecast accuracy remains poor. The current
  estimate for 500 years is determined from
  Himalayan earthquakes whose parameters are
  uncertain by 50 which means that the recurrence
  interval is also constrained to no better than
  50.
• NO-the largest earthquakes seem to require much
  longer interevent intervals, possibly exceeding
  1000years. We know less about them and they may
  could exceed Mw8.6.

What is needed to improve forecast potential

• Rheologically realistic model for Tibetan
  plateau
• improved historical and paleoseismic rupture
  data
• more accurate slip vs magnitude data

Feldl, N., and R. Bilham, Great Himalayan
Earthquakes and the Tibetan Plateau, Nature, 9
Nov. 2006