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Earthquakes and Earthquake Prediction. Andrei Gabrielov Purdue University West Lafayette, IN, USA www.math.purdue.edu/~agabriel. San Francisco, April 18, 1906. Plate Tectonics. Major tectonic plates and world seismicity. Plate Tectonics. Plate boundaries and tectonic faults.

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earthquakes and earthquake prediction

Earthquakes and Earthquake Prediction

Andrei Gabrielov

Purdue University

West Lafayette, IN, USA

www.math.purdue.edu/~agabriel

plate tectonics
Plate Tectonics
  • Major tectonic plates and world seismicity
plate tectonics1
Plate Tectonics
  • Plate boundaries and tectonic faults
slide5

North American

Plate

Pacific

Plate

slide6

Elastic Rebound Theory

Discovered after the great 1906 San Francisco earthquake (before plate tectonics theory).

slide7

Elastic Rebound Theory

Discovered after the great 1906 San Francisco earthquake (before plate tectonics theory).

slide8

Elastic Rebound

Slow build-up of deformation (strain) in the rocks by plate motion. Strain (energy) is released suddenly as fault slips.

slide10
Earthquakes generate elastic waves:

Body waves: P (pulse), S (transverse)

Surface waves: R (Rayleigh), L (Love)

Surface waves

S-wave

P-wave

Time 

First

arrival

Seismogram for a distant earthquake

a wave pulse p wave
A wave pulse (P-wave)

Animation courtesy of Dr. Dan Russell, Kettering University

http://www.kettering.edu/~drussell/demos.html

transverse wave s wave
Transverse wave (S-wave)

Animation courtesy of Dr. Dan Russell, Kettering University

http://www.kettering.edu/~drussell/demos.html

rayleigh wave
Rayleigh wave

Animation courtesy of Dr. Dan Russell, Kettering University

http://www.kettering.edu/~drussell/demos.html

slide15

Seismic Waves in the Earth

Seismic waves through

the Earth’s interior

that indicate

structure

(crust, mantle,

outer core,

inner core, etc.)

magnitude
Magnitude
  • Measure of the ENERGY released in the earthquake, based on vibration caused by seismic waves
  • Logarithmic scale ― M = 6 is ten times greater vibration, and a hundred times more energy, than M = 5 (at the same distance)
  • Should not be mistaken for INTENSITY― the measure of the damage caused by the earthquake
slide17

Moment MagnitudeMw

Focus or hypocenter

(point of initiation

of the rupture)

Epicenter (location on Earth’s surface

above the hypocenter)

*

Depth

Moment = M0 = µ A D(dyne-cm) (dyne is a unit of force)

µ = shear modulus ~ 32 GPa in crust (~3.2 x 1011 dynes/cm2),

~75 GPa in mantle (a measure of strength of rocks)A = LW = area (cm2), D = average displacement (cm)

Mw = 2/3 log10(M0) - 10.7

aftershocks
Aftershocks
  • Earthquakes that happen following a mainshock, in the same region but of smaller magnitude
  • Aftershock frequency distribution in time t after the mainshock satisfies Omori Law:
  • Bath’s Law: Aftershock’s magintude is approximately 1.2 less than mainshock’s
  • Aftershocks frequency-magnitude distribution satisfies Gutenberg-Richter law
strong earthquakes nucleate in some dangerous structures d nodes
Strong Earthquakes Nucleate in Some “Dangerous” Structures (D-nodes)

Gelfand, et al., 1976.

Qualitatively, D-nodes are recognized

  • by local depression on the background of NG‑Q depression (“local tension on the background of general compression”)
  • by proximity of hydrothermal reservoirs
earthquake prediction

Intensity

Clustering

Range of

correlation

in space

Magnitude-

lgN

lgN

frequency

Precursory state

Non-precursory

state

relation

m

m

Earthquake prediction

A strong earthquake is preceded by the following changes in seismicity:

slide31

Predicting the

4/11/2012

M8.6 and M8.2

Earthquakes off the

Western coast of

Northern Sumatra,

Indonesia

frontiers of similarity
FRONTIERS OF SIMILARITY

Precursors have been defined for earthquakes.

Only the final scale was adjusted for starquakes.

slide35

US PRESIDENTIAL ELECTIONS (Keilis-Borok and Lichtman)

Prediction is based on thirteen socio-economic and political factors.

Victory of challenging party is predicted when 6 or more factors are in its favor.

Otherwise victory of incumbent party is predicted.

Predictions published months in advance: all 8 - correct

Retrospective Analysis: 1860 - 1980

* years when popular vote was reversed by electoral vote.

Red- incumbent won, blue – challenger won.

slide36

13 Keys to Presidency (Keilis-Borok and Lichtman)

Answer YES favors re-election of the incumbent party

Key 1: (Party Mandate): After the midterm elections, the incumbent party holds more seats in the U.S. House of Representatives than it did after the previous midterm elections.

Key 2: (Contest): There is no serious contest for the incumbent-party nomination.

Key 3: (Incumbency): The incumbent-party candidate is the sitting president.

Key 4: (Third party): There is no significant third-party or independent campaign.

Key 5:(Short-term economy): The economy is not in recession duringthe election campaign.

Key 6: (Long-term economy): Real per-capita economic growthduring the term equals or exceeds mean growth during the previous two terms.

Key 7: (Policy change): The incumbent administration effects major changes in national policy.

Key 8: (Social unrest): There is no sustained social unrest during the term.

Key 9: (Scandal): The incumbent administration is untainted by major scandal.

Key 10: (Foreign/military failure): The incumbent administration suffers no major failure in foreign or military affairs.

Key 11: (Foreign/military success): The incumbent administration achieves a major success in foreign or military affairs.

Key 12: (Incumbent charisma): The incumbent-party candidate is charismatic or a national hero.

Key 13: (Challenger charisma): The challenging-party candidate is not charismatic or a national hero.

slide37

Answers for the 2012 presidential election

(published 28 months before the election)

• KEY 1: Party mandate. After the midterm elections, the incumbent party holds more seats in the U.S. House of Representatives than it did after the previous midterm elections. (FALSE)

• KEY 2: Contest. There is no serious contest for the incumbent-party nomination. (TRUE)

• KEY 3: Incumbency. The incumbent-party candidate is the sitting president. (TRUE)

• KEY 4: Third party. There is no significant third-party or independent campaign. (TRUE)

• KEY 5: Short-term economy. The economy is not in recession during the election campaign. (TRUE)

• KEY 6: Long-term economy. Real per capita economic growth during the term equals or exceeds mean growth during the previous two terms. (FALSE)

• KEY 7: Policy change. The incumbent administration effects major changes in national policy. (TRUE)

• KEY 8: Social unrest. There is no sustained social unrest during the term. (TRUE)

• KEY 9: Scandal. The administration is untainted by major scandal. (TRUE)

• KEY 10: Foreign/military failure. The administration suffers no major failure in foreign or military affairs. (TRUE)

• KEY 11: Foreign/military success. The administration achieves a major success in foreign or military affairs. (FALSE)

• KEY 12: Incumbent charisma. The incumbent-party candidate is charismatic or a national hero. (FALSE)

• KEY 13: Challenger charisma: The challenging-party candidate is not charismatic or a national hero. (TRUE)