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.

Connecting Earthquakes and Faults

Thrust fault scarp at El Asnam, Algeria.

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 (MO) 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.

Connecting Earthquakes and Faults

1999 Chi-Chi earthquake, Taiwan

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."

Earthquake Magnitude

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

ML local magnitude

mb body wave magnitude

Ms surface wave magnitude

Mw moment magnitude

Easy to measure

Empirical - except for Mw, no

direct tie to physics of faulting

Note; not dimensionally correct

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 (MW) 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 (MW) 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 slip, and the force that was required to overcome the friction sticking the rocks together that were offset by faulting.

Seismic moment can also be calculated from the amplitude spectra of seismic waves.

Connecting Earthquakes and Faults

A more consistent measure of big earthquakes nowadays is the magnitude calculated on the basis of seismic moment (MO), called Moment Magnitude (MW).

Because fault geometry and displacement are a part of the MO, 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.

Seismic moment = a better measure of EQ size

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

Earthquake size and the area of slip

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 = 3x1011 dyne/cm2 in continental crust

A = Length x Width = fault area

S = average displacement or slip during fault rupture.

Seismic Moment

What is a dyne?

1 gram of mass an acceleration of a cm/s2

1 dyne = 1 gram x cm/sec2

MO = µSA

Mw = (2/3)log(µSA)-10.7 or MW = (2/3)log(MO) - 10.7 µ is the shear strength of the faulted rock A is the area of the faultS is the average slip or displacement on the fault. These factors have led to the definition of a new magnitude scale MW.

It is based on seismic moment, where MW = 2/3 log10(MO) - 10.7. (MO is in dyne/centimeter)

MW close approximates MS 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 (): 3x1011 dyne/cm2

 

Mo = SA: where S = avg slip, A = fault area; = shear modulus

Mo = (3x1011dyne/cm2)(6 m [100 cm/m])(100 km [100,000 cm/km] x 12 km [100,000 cm/km]) = 2.16 x 1027

Mw = 2/3logMo-10.7 = 7.5

Mo = (3x1011dyne/cm2)(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 M0

Magnitudes, moments (dyn-cm), fault areas, and fault slips for several earthquakes

Alaska & San Francisco differ much more than Ms implies

M0 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 Ms valuesvary by about 0.2 units.

- Uncertainties for historic earthquakes are large. Fault length estimates for the San Francisco earthquake vary from 300-500 km, Ms 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 yielddifferent 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 Mw

Magnitudes saturate:

No matter how big the earthquake

mb never exceeds ~6.4

Ms never exceeds ~8.4

Mw defined from moment so never saturates

THREE EARTHQUAKES IN NORTH AMERICA - PACIFIC PLATE BOUNDARY ZONE

Tectonic setting affectsearthquake 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 affectsearthquake 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 affectsearthquake 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

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

Wells and Coppersmith, 1994

Most Destructive Known Earthquakes on Record in the World (> 50,000 deaths)

(Listed in order of greatest number of deaths)

Date Location Deaths M CommentsJanuary 23, 1556 China, Shansi 830,000 October 11, 1737 India, Calcutta** 300,000July 27, 1976 China, Tangshan 255,000* 8.0December 26, 2007 Indonesia 225,000 9.3 Large tsunami

August 9, 1138 Syria, Aleppo 230,000May 22, 1927 China, near Xining 200,000 8.3 Large fractures.December 22, 856+ Iran, Damghan 200,000December 16, 1920 China, Gansu 200,000 8.6 Major fractures, landslidesMarch 23, 893+ Iran, Ardabil 150,000September 1, 1923 Japan, Kwanto 143,000 8.3 Great Tokyo fireDecember 28, 1908 Italy, Messina 70,000 7.5 Earthquake & tsunami (100,000)September, 1290 China, Chihli 100,000 November, 1667 Caucasia, Shemakha 80,000November 18, 1727 Iran, Tabriz 77,000November 1, 1755 Portugal, Lisbon 70,000 8.7 Great tsunami December 25, 1932 China, Gansu 70,000 7.6May 31, 1970 Peru 66,000 7.8 Great rock slide and flood1268 Asia Minor, Silicia 60,000January 11, 1693 Italy, Sicily 60,000May 30, 1935 Pakistan, Quetta 30,000 7.5 Quetta almost completely

destroyed (~60,000)February 4, 1783 Italy, Calabria 50,000June 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 Location Length Duration (km)

(sec)

7.8 January 9, 1857 Fort Tejon 360 130

7.7 April 18, 1906 San Francisco 400 110

7.5 July 21, 1952 Kern County 75 27

7.3 June 28, 1992 Landers 70 24

7.0 October 17, 1989 Loma Prieta 40 7

6.9 May 18, 1940 Imperial Valley 50 15

6.7 February 9, 1971 San Fernando 16 8

6.7 January 17, 1994 Northridge 14 7

6.6 November 24, 1987 Superstition Hills 23 15

6.5 April 9, 1968 Borrego Mountain 25 6

6.4 October 15, 1979 Imperial Valley 30 13

6.4 March 10, 1933 Long Beach 15 5

6.1 April 22, 1992 Joshua Tree 15 5

5.9 July 8, 1986 North Palm Springs 20 4

5.9 October 1, 1987 Whittier Narrows 6 3

5.8 June 28, 1991 Sierra Madre 5 2

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.

2004 Indonesia