Earthquakes and Earthquake Prediction

Andrei GabrielovPurdue University

West Lafayette, IN, USAwww.math.purdue.edu/~agabriel

San Francisco, April 18, 1906

Plate Tectonics

• Major tectonic plates and world seismicity

Plate Tectonics

• Plate boundaries and tectonic faults

North American Plate

Pacific Plate

Elastic Rebound Theory Discovered after the great 1906 San Francisco

earthquake (before plate tectonics theory).

Elastic Rebound Theory Discovered after the great 1906 San Francisco

earthquake (before plate tectonics theory).

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

Earthquake Focus and Epicenter

Earthquakes generate elastic waves:Body waves: P (pulse), S (transverse) Surface waves: R (Rayleigh), L (Love)

P-wave

First arrival

S-wave

Surface waves

Time

Seismogram for a distant earthquake

A wave pulse (P-wave)

Animation courtesy of Dr. Dan Russell, Kettering University

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

Transverse wave (S-wave)

Animation courtesy of Dr. Dan Russell, Kettering University

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

Rayleigh wave

Animation courtesy of Dr. Dan Russell, Kettering University

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

Seismic waves through the Earth’s interior that indicate structure (crust, mantle, outer core, inner core, etc.)

Seismic Waves in the Earth

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

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

Moment Magnitude Mw

Epicenter (location on Earth’s surface above the hypocenter)

Focus or hypocenter(point of initiation of the rupture)

*

Dep

th

Gutenberg-Richter Law

Descriptor Magnitude Average AnnuallyGreat 8 and higher 1 ¹Major 7 - 7.9 17 ²Strong 6 - 6.9 134 ²

Moderate 5 - 5.9 1319 ²Light 4 - 4.9 13,000 (est.)

Minor 3 - 3.9 130,000 (est.)Very Minor 2 - 2.9 1,300,000 (est.)

¹ Based on observations since 1900. ² Based on observations since 1990.

Worldwide earthquakes per year (from USGS):

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

World’s largest earthquakes since 1900

  Location Date UTC Mag.

Lat. Long.

1 Chile 1960 05 22

9.5 -38.29 -73.05

2 Prince William Sound, Alaska 1964 03

289.2 61.02 -

147.653 Northern Sumatra, Indonesi

a 2004 12 26

9.1 3.30 95.78

4 Honshu, Japan 2011 03 11

9.0 38.32 142.37

5 Kamchatka 1952 11 04

9.0 52.76 160.06

6 Maule, Chile 2010 02 27

8.8 -35.85 -72.72

7 Off the Coast of Ecuador 1906 01 31

8.8 1.0 -81.5

8 Rat Islands, Alaska 1965 02 04

8.7 51.21 178.50

9 Northern Sumatra, Indonesia 2005 03

288.6 2.08 97.01

10

Assam - Tibet 1950 08 15

8.6 28.5 96.5

11

Northern Sumatra, Indonesia 2012 04

118.6 2.31 93.06

12

Andreanof Islands, Alaska

1957 03 09

8.6 51.56 -175.39

13

Southern Sumatra, Indonesia

2007 09 12

8.5 -4.44 101.37

14

Banda Sea, Indonesia 1938 02 01

8.5 -5.05 131.62

15

Kamchatka 1923 02 03

8.5 54.0 161.0

16

Chile-Argentina Border 1922 11 11

8.5 -28.55 -70.50

17

Kuril Islands 1963 10 13

8.5 44.9 149.6

Continental USA largest earthquakes

Largest Earthquakes in the Continental USA

  Location Date Magnitude

1. Cascadia subduction zone 1700 01 26 ˜92. Fort Tejon, California 1857 01 09 7.93. San Francisco, California 1906 04 18 7.84. Imperial Valley, California 1892 02 24 7.85. New Madrid, Missouri 1811 12 16 7.76. New Madrid, Missouri 1812 02 07 7.77. New Madrid, Missouri 1812 01 23 7.58. Owens Valley, California 1872 03 26 7.49. Landers, California 1992 06 28 7.310. Hebgen Lake, Montana 1959 08 18 7.311. Kern County, California 1952 07 21 7.312. West of Eureka, California 1922 01 31 7.313. Charleston, South Carolina 1886 09 01 7.314. California - Oregon Coast 1873 11 23 7.315. N Cascades, Washington 1872 12 15 7.3

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

Ferndale

M ammoth

Loma PrietaCoalinga

NorthridgeLanders

Superstitions Hills

Imperial Valley

Big Bear

A reas w here the epicen te rs ofearthquakes can be s itua ted .

E p icen te rs o f earthquakes :

m agnitude 6 .5 o r m ore

m agnitude 6.5 o r m ore

B efore 1976.

A fte r 1976 .

Chalfant Valley

Hector Mine

San Sim eon

Non-precursory state

Precursory state

Clustering

Range ofcorrelation

in space

Intensity

Magnitude-frequency

relation

lgN

m

lgN

m

Earthquake predictionA strong earthquake is preceded by the following changes in seismicity:

Spac

e

Time

Failure to predict

False alarm

Correct alarm Correct alarm

POSSIBLE OUTCOMES OF PREDICTION

Intermediate-term (5 yrs) PredictionAlgorithm M8-MSc, Keilis-Borok and Kossobokov

Predicting the 3/11/2011 M9 earthquake in Japan

Predicting the 4/11/2012M8.6 and M8.2 Earthquakes off the Western coast of Northern Sumatra,Indonesia

FRONTIERS OF SIMILARITY

Precursors have been defined for earthquakes.Only the final scale was adjusted for starquakes.

SOCIO-ECONOMIC PREDICTIONS

Prediction of US Recessions

1960 19 6 5 19 70 197 5 19 80 1985 19 90 1 995 2000 2005 2 010

1960 1965 1 970 197 5 19 80 1985 19 90 1 995 2000 2005 2 010

Prediction o f recessions

P rediction of recovery from recessions

A d v a n c e p re d ic tio n

- R e c e s sio n - A la rm

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.

Retrospective Analysis: 1860 - 1980

0 1 2 3 4 5 6 7 8 9N u m b e r o f fa ctor s in fa v o r o f ch a llen g er

* years when popular vote was reversed by electoral vote.Red - incumbent won, blue – challenger won.

Predictions published months in advance: all 8 - correct

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 during the election

campaign.Key 6: (Long-term economy): Real per-capita economic growth during 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.

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. (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)

Answers for the 2012 presidential election(published 28 months before the election)