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
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 Rebound
Slow 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)
Surface waves
S-wave

P-wave
First
arrival
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 in the Earth
Seismic waves through
the Earth’s interior
that indicate
structure
(crust, mantle,
outer core,
inner core, etc.)
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 Magnitude Mw
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
Gutenberg-Richter Law
Worldwide earthquakes per year (from USGS):
Descriptor
Magnitude
Average Annually
Great
8 and higher
1¹
Major
7 - 7.9
17 ²
Strong
6 - 6.9
134 ²
Moderate
5 - 5.9
1319 ²
Light
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.
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 28
9.2
61.02
-147.65
3 Northern Sumatra, Indonesia
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 28
8.6
2.08
97.01
10 Assam - Tibet
1950 08 15
8.6
28.5
96.5
11 Northern Sumatra, Indonesia
2012 04 11
8.6
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
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Location
Date
Cascadia subduction zone
Fort Tejon, California
San Francisco, California
Imperial Valley, California
New Madrid, Missouri
New Madrid, Missouri
New Madrid, Missouri
Owens Valley, California
Landers, California
Hebgen Lake, Montana
Kern County, California
West of Eureka, California
Charleston, South Carolina
California - Oregon Coast
N Cascades, Washington
1700 01 26
1857 01 09
1906 04 18
1892 02 24
1811 12 16
1812 02 07
1812 01 23
1872 03 26
1992 06 28
1959 08 18
1952 07 21
1922 01 31
1886 09 01
1873 11 23
1872 12 15
Magnitude
˜9
7.9
7.8
7.8
7.7
7.7
7.5
7.4
7.3
7.3
7.3
7.3
7.3
7.3
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
Areas where the epicenters
of magnitude 6.5 or more
earthquakes can be situated.
Epicenters of magnitude
6.5 or more earthquakes:
Ferndale
Before 1976.
After 1976.
Mammoth
Chalfant Valley
Loma Prieta
Coalinga
San Simeon
Hector Mine
Big Bear
Landers
Northridge
Superstitions Hills
Imperial Valley
Earthquake prediction
A strong earthquake is preceded by the following changes in seismicity:
Intensity
Clustering
Range of
correlation
in space
Magnitudefrequency
relation
lgN
m
Non-precursory
state
lgN
m
Precursory state
POSSIBLE OUTCOMES OF PREDICTION
Space
Failure to predict
False alarm
Correct alarm
Correct alarm
Time
Intermediate-term (5 yrs) Prediction
Algorithm M8-MSc, Keilis-Borok and Kossobokov
Predicting the 3/11/2011
M9 earthquake in Japan
Predicting the
4/11/2012
M8.6 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
Advance prediction
Prediction of recessions
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
1995
2000
2005
2010
Prediction of recovery from recessions
1960
1965
1970
- Recession
1975
1980
- Alarm
1985
1990
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
0
1
2
3
4
5
6
7
8
Number of factors in favor of challenger
* years when popular vote was reversed by electoral vote.
Red - incumbent won, blue – challenger won.
9
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 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.
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)