Connecting Earthquakes and Faults

An earthquake is also defined as the sudden slip of one part of the Earth's crust, relative to another, along a fault surface.

A gradual build-up of mechanical stress in the crust, primarily the result of tectonic forces, provides the source of energy for earthquakes; sudden motion along a fault releases it in the form of seismic waves. It's unclear when the connection between faults and earthquakes was first made, but by the late 19th Century most scientists accepted this association as fact, even if the mechanisms behind it were still a mystery.

Thrust fault scarp at El Asnam, Algeria.

Connecting Earthquakes and Faults

Fault research received a tremendous boost in the aftermath of the great San Francisco earthquake of 1906.

This was one of the first earthquakes for which both seismographic and fault-rupture studies were conducted. The fault rupture occurred in through a very well-surveyed, developed area.

Connecting Earthquakes and Faults

Because of this, researchers could not only map the offset across the fault trace, but also the amount of displacement between points far removed from the fault. This work led to the formulation of the elastic rebound theory of fault rupture by Princeton geologist Harry F. Reid.

Connecting Earthquakes and Faults

As technology improved, seismic networks grew, and research into the mechanism of fault rupture increased, new methods arose that helped quantify the link between earthquakes and faults. One important find helped link magnitude (energy) with the severity of fault rupture. The seismic moment ( M O ) of an earthquake, which can be estimated from analysis of seismic waves, was discovered to be directly proportional to the extent of the actual fault rupture. 1999 Chi-Chi earthquake, Taiwan

Earthquake Magnitude

How big is an earthquake?

Depends on how big a patch of the fault breaks. If the patch that breaks is a few square miles, you may have a magnitude five earthquake. If it's up to a couple hundred square miles, you have a magnitude seven. If it's a couple of thousand square miles, you get a M 7.8, 1906 San Francisco quake." 1999 Chi-Chi earthquake, Taiwan

EARTHQUAKE SOURCE PARAMETERS Magnitude, fault area, fault slip, stress drop, energy release

“the big one”

EARTHQUAKE MAGNITUDE

Earliest measure of earthquake size Dimensionless number measured various ways, including M L local magnitude m b body wave magnitude M s surface wave magnitude M w moment magnitude Easy to measure Empirical - except for M w , no direct tie to physics of faulting Note; not dimensionally correct

Connecting Earthquakes and Faults

The seismic moment is the product of the area of fault surface that ruptures, the average displacement along that surface, and a constant -- a measure of the elastic property of rock (i.e. how easily it can be stretched) called the modulus of rigidity. Moment magnitude ( M W ) is based upon the seismic moment, and represents a kind of bridge between the seismological and geological views of an earthquake.

Connecting Earthquakes and Faults

The seismic moment is the product of the area of fault surface that ruptures, the average displacement along that surface, and a constant - a measure of the elastic property of rock (i.e. how easily it can be stretched) called the modulus of rigidity. Moment magnitude ( M W ) is based upon the seismic moment, and represents a kind of bridge between the seismological and geological views of an earthquake.

Connecting Earthquakes and Faults

Seismic moment The seismic moment is a measure of the size of an earthquake based on the area of fault rupture, the average amount of offset by faulting. slip , and the force that was required to overcome the friction sticking the rocks together that were Seismic moment can also be calculated from the amplitude spectra of seismic waves.

Seismic moment = a better measure of EQ size

A more consistent measure of big earthquakes nowadays is the magnitude calculated on the basis of seismic moment (M O ), called Moment Magnitude (M W ). Because fault geometry and displacement are a part of the M O , moment is a more consistent measure of earthquake size than is magnitude, and more importantly, moment does not have an upper bound.

Moment does not tend to saturate as Richter magnitude does. The seismic moment is related to the faulting process.

Earthquake size and the area of slip

The size of the area that slips during an earthquake is increases with earthquake size.

The largest earthquakes generally rupture the entire depth of the fault, which is controlled by temperature. The temperature increases with depth to a point where the rocks become plastic and no longer store the elastic strain energy necessary to fail suddenly.

The shaded regions on the fault surface are the areas that rupture during different size events

Seismic Moment

Seismologists have more recently developed a standard magnitude scale that is completely independent of the type of instrument. It is called the

moment magnitude

, and it comes from the

seismic moment

. To get an idea of the seismic moment, go back to the concept of torque. A torque is a force that changes the angular momentum of a system. It is defined as the force times the distance from the center of rotation. Earthquakes are caused by internal torques, from the interactions of different blocks of the earth on opposite sides of faults. The moment of an earthquake is simply expressed by: The moment of an earthquake, is fundamental to our understanding of how dangerous faults of a certain size can be.

Seismic Moment

Seismic Moment = µ S A

µ = shear modulus = 3x10 11 dyne/cm 2 in continental crust A = Length x Width = fault area S = average displacement or slip during fault rupture.

What is a dyne?

1 gram of mass an acceleration of a cm/s 2 1 dyne = 1 gram x cm/sec 2

M O = µSA Mw = (2/3)log(µSA)-10.7 or M W = (2/3)log(M O ) - 10.7

µ is the shear strength of the faulted rock A is the area of the fault S is the average slip or displacement on the fault.

These factors have led to the definition of a new magnitude scale M

W

. It is based on seismic moment, where

M W = 2/3 log 10 (M O

) - 10.7. (M

O

is in dyne/centimeter)

M W

close approximates M

S

up to magnitude 7.0, but continues to rise without saturation to values as large as 9.5 for the 1960 Southern Chile earthquake.

fault length: 100 km Seismic moment and Moment Magnitude fault depth: minimum of 12 km average slip: 6

±

2 m average shear modulus (

m

): 3x10 11 dyne/cm 2 Mo =

m SA: where S = avg slip, A = fault area; m = shear modulus Mo = (3x10 11 dyne/cm 2 )(6 m [100 cm/m])(100 km [100,000 cm/km] x 12 km [100,000 cm/km]) = 2.16 x 10 27 Mw = 2/3logMo-10.7 = 7.5

Mo = (3x10 11 dyne/cm 2 )(8 m [100 cm/m])(100 km [100,000 cm/km] x 12 km [100,000 cm/km]) = 2.88 x 1027 Mw = 2/3logMo - 10.7 = 7.6

COMPARE EARTHQUAKES USING SEISMIC MOMENT M

0 Magnitudes, moments (dyn cm), fault areas, and fault slips for several earthquakes Alaska & San Francisco differ much more than M s implies M 0 more useful measure Units: dyne-cm or Nt-M Directly tied to fault physics Doesn’t saturate

Stein & Wysession, 2003

EARTHQUAKE SOURCE PARAMETER ESTIMATES HAVE CONSIDERABLE UNCERTAINTIES FOR SEVERAL REASONS:

- Uncertainties due to earth's variability and deviations from the mathematical simplifications used. Even with high-quality modern data, seismic moment estimates for the Loma Prieta earthquake vary by about 25%, and M vary by about 0.2 units. s values - Uncertainties for historic earthquakes are large. Fault length estimates for the San Francisco earthquake vary from 300-500 km, M s was estimated at 8.3 but now thought to be ~7.8, and fault width is essentially unknown and inferred from the depths of more recent earthquakes and geodetic data. - Different techniques (body waves, surface waves, geodesy, geology) can yield different estimates.

- Fault dimensions and dislocations shown are average values for quantities that can vary significantly along the fault Hence different studies yield varying and sometimes inconsistent values. Even so, data are sufficient to show effects of interest.

Moment magnitude M w Magnitudes saturate: No matter how big the earthquake m b never exceeds ~6.4

M s never exceeds ~8.4

M w defined from moment so never saturates

THREE EARTHQUAKES IN NORTH AMERICA PACIFIC PLATE BOUNDARY ZONE

Tectonic setting affects earthquake size

San Fernando earthquake on buried thrust fault in the Los Angeles area, similar to Northridge earthquake. Short faults are part of an oblique trend in the boundary zone, so fault areas are roughly rectangular. The down-dip width controlled by rocks deeper than ~20 km are weak and undergo stable sliding rather than accumulate strain for future earthquakes.

Stein & Wysession, 2003

THREE EARTHQUAKES IN NORTH AMERICA PACIFIC PLATE BOUNDARY ZONE

Tectonic setting affects earthquake size

San Francisco earthquake ruptured a long segment of the San Andreas with significantly larger slip, but because the fault is vertical, still had a narrow width. This earthquake illustrates approximately the maximum size of continental transform earthquakes.

Stein & Wysession, 2003

THREE EARTHQUAKES IN NORTH AMERICA PACIFIC PLATE BOUNDARY ZONE

Tectonic setting affects earthquake size

Alaska earthquake had much larger rupture area because it occurred on shallow-dipping subduction thrust interface. The larger fault dimensions give rise to greater slip, so the combined effects of larger fault area and more slip cause largest earthquakes to occur at subduction zones rather than transforms.

Stein & Wysession, 2003

LARGER EARTHQUAKES GENERALLY HAVE LONGER FAULTS AND LARGER SLIP

Wells and Coppersmith, 1994 M7, ~ 100 km long, 1 m slip; M6, ~ 10 km long, ~ 20 cm slip Important for earthquake source physics and hazard estimation

Most Destructive Known Earthquakes on Record in the World (> 50,000 deaths) (Listed in order of greatest number of deaths)

Date Location Deaths M Comments January 23, 1556 China, Shansi 830,000

October 11, 1737 India, Calcutta** 300,000

July 27, 1976 China, Tangshan 255,000* 8.0

December 26, 2007 Indonesia 225,000 9.3

Large tsunami

August 9, 1138 Syria, Aleppo 230,000 May 22, 1927 China, near Xining 200,000 8.3 Large fractures.

December 22, 856+ Iran, Damghan 200,000 December 16, 1920 China, Gansu 200,000 8.6 Major fractures, landslides March 23, 893+ Iran, Ardabil 150,000

September 1, 1923 Japan, Kwanto 143,000 8.3 Great Tokyo fire

December 28, 1908 Italy, Messina 70,000 7.5 Earthquake & tsunami (100,000) September, 1290 China, Chihli 100,000 November, 1667 Caucasia, Shemakha 80,000 November 18, 1727 Iran, Tabriz 77,000 November 1, 1755 Portugal, Lisbon 70,000 8.7 Great tsunami December 25, 1932 China, Gansu 70,000 7.6

May 31, 1970 Peru 66,000 7.8 Great rock slide and flood 1268 Asia Minor, Silicia 60,000 January 11, 1693 Italy, Sicily 60,000 May 30, 1935 Pakistan, Quetta 30,000 7.5 Quetta almost completely destroyed (~60,000) February 4, 1783 Italy, Calabria 50,000 June 20, 1990 Iran 50,000 7.7 Landslides * Official casualty figure--estimated death toll as high as 655,000. + Note that these dates are prior to 1000 AD. No digit is missing.

** Later research has shown that this was a typhoon, not an earthquake. (1737 Calcutta Earthquake Bilham, 1994)

TEN LARGEST EARTHQUAKES IN THE UNITED STATES Magnitude Date (UTC) Location Length Duration

(km) (sec)

9.2 03/ 28/1964 Prince William Sound, Alaska

8.8 03/09/1957 Andreanof Islands, Alaska 8.7 02/04 /1965 Rat Islands, Alaska 8.3 11/11/1938 East of Shumagin Islands, Alaska 8.3 07/10/1958 Lituya Bay, Alaska 8.2 10/10/1899 Yakutat Bay, Alaska 8.2 10/4/1899 Near Cape Yakataga, Alaska 8.0 05/7/1986 Andreanof Islands, Alaska 7.9 11/3/2002 South central Alaska 340 7.9 02/7/1812 New Madrid, Missouri

7.9 01/9/1857 Fort Tejon, California 360 130

7.9 04/3/1868 Ka'u District, Island of Hawaii 7.9 10/9, 1900 Kodiak Island, Alaska 7.9 11/30/1987 Gulf of Alaska 7.5 03/18/1906 San Francisco, California (downgraded from M 8)

For comparison, the largest earthquake ever recorded was a moment magnitude 9.5 in Chile on May 22, 1960. The largest earthquake ever recorded in the United States was in Alaska on March 27, 1964, with moment magnitude 9.2

A longer fault produces a bigger earthquake that lasts a longer time.

Magnitude Date 7.8 January 9, 1857 7.7 April 18, 1906

7.5 July 21, 1952 7.3 June 28, 1992 7.0 October 17, 1989 6.9 May 18, 1940 6.7 February 9, 1971

6.7 January 17, 1994

6.6 November 24, 1987 6.5 April 9, 1968 6.4 October 15, 1979 6.4 March 10, 1933 6.1 April 22, 1992 5.9 July 8, 1986 5.9 October 1, 1987 5.8 June 28, 1991

Location Length (km) Fort Tejon San Francisco

Kern County Landers Loma Prieta Imperial Valley San Fernando

Northridge

Superstition Hills Borrego Mountain Imperial Valley Long Beach Joshua Tree North Palm Springs Whittier Narrows Sierra Madre

360 400

75 70 40 50 16

14

23 25 30 15 15 20 6 5

Duration (sec)

5 5 4 3 2

130 110

27 24 7 15 8

7

15 6 13

2004 Indonesia Earthquakes of a given magnitude are ~10 times less frequent than those one magnitude smaller. An M7 earthquake occurs approximately monthly, and an earthquake of M> 6 about every three days. Magnitude is proportional to the logarithm of the energy released, so most energy released seismically is in the largest earthquakes. An M 8.5 event releases more energy than all other earthquakes in a year combined. Hence the hazard from earthquakes is due primarily to large (typically magnitude > 6.5) earthquakes.