Earthquakes as Seismic Sources

Lupei Zhu EASA-130 Seismology and Nuclear Explosions FALL 2004 1

Topics

 Earthquakes as seismic sources  How do earthquakes happen?

– Rupture on faults; stress buildup  Locating earthquakes – Hypocenter, epicenter; how to locate?

 Earthquake magnitudes – Richter’s local magnitude – Body wave magnitude and surface wave magnitude – Moment magnitude  How often do earthquake happen?

– Gutenburg-Richter Law FALL 2004 EASA-130 Seismology and Nuclear Explosions 2

Seismic Sources

 Any radiator of seismic waves – Earthquakes – Explosions – Landslides  Parameters to describe a seismic source – Location – Occurrence time – Source dimension – Time duration – Strength FALL 2004 EASA-130 Seismology and Nuclear Explosions 3

How Earthquakes happen

 Earthquakes happen when rocks somewhere underground break along a surface called fault and the two sides pass each other in a sudden and violent motion. See Faults.

 The cause of this sudden faulting is due to a gradual buildup of stress by the long-term plate-tectonics process inside the Earth. This explains why earthquakes are concentrated at plate boundaries.

 Faults that were ruptured previously are weak zones and therefore are likely to be broken again in the future (Earthquake cycle). The time interval between earthquakes, however, is very irregular.

 New faults can also be produced (so no one is 100% safe) FALL 2004 EASA-130 Seismology and Nuclear Explosions 4

Locating Earthquakes

 The starting point of an earthquake rupture is called the earthquake hypocenter , which is given by the latitude and longitude of its projection on the surface (called epicenter ) and depth.

 Seismologists use arrival times of P and S waves at different seismic stations to locate an earthquake and determine its occurrence time.

 At least three stations are needed to determine the epicenter and occurrence time (three unknowns). One more station is needed if the depth is included.

 Earthquake depth trades off with its occurrence time and is more difficult to get accurately.

 Modern Seismic Networks usually use hundreds of stations.

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Travel Time

  Travel time, T, is defined as T = distance / velocity Since P-waves travel faster than S-wave, the time separation between the two is larger at greater distances.

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A “Rule of Thumb”

 Because of the structure of Earth, for distance ranges between about 50 and 500 km, we can use a formula to estimate the distance from the observed S-arrival time minus the P-arrival time:

distance = 8



(S-P arrival time)

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Example

 If the arrival time of an S wave is 09:30:15.0 (GMT) and the arrival time of a P wave is 09:29:45.0 (GMT), then the time difference is 30 s. Thus, the earthquake is located about 240 km away from the seismometer. 

But in which direction ???

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Distances and Circles

 In this case, if you know the distance the earthquake is from the seismometer, you know the earthquake must be located on a circle centered on the seismometer, with a radius equal to the distance.

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Triangulation

 With three or more stations, you can locate the earthquake using triangulation.

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Richter’s Local Magnitude

 Another important parameter is the magnitude of an earthquake. It is a measure of the energy it released in the form of seismic wave.

  Charles Richter in 1935 first developed a magnitude scale based on the peak amplitude

A

of the seismogram recorded by a particular type of seismometer  km away from the epicenter M L = Log A + 2.76 Log  - 2.48

Richter’s scale is a logarithmic scale. Earthquakes of 1 magnitude difference produce 10 times amplitude difference.

 Since the Richter Scale is defined for a old type of seismometer, it is rarely used today. But it is still widely and mistakenly quoted in news press.

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Other Magnitude Scales

 The two most common modern magnitude scales are:  M S , Surface-wave magnitude (Rayleigh Wave)  m b , Body-wave magnitude (P-wave) FALL 2004 EASA-130 Seismology and Nuclear Explosions 12

Problem with Ms and mb

 It was found that these two magnitudes saturate when earthquakes are large than certain levels (6 for mb and 7-8 for Ms).

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What Causes Saturation?

 The rupture process. Large earthquakes rupture large areas and are relatively depleted in high frequency (short wavelength) seismic signals which the Ms and mb are measured with.

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The Best Magnitude

  The best magnitude should be based on the actual ruptured area and the amount of slip. This is how the

seismic moment

M o M 0 is defined: = (rigidity)  (rupture area)  (slip) The rigidity is a measure of how strong the rock is. Rock rigidity is ~30 GPa. Water’s rigidity is zero.

M 0 has units of force*distance (Nm) The moment magnitude Mw is defined as M W saturate.

= 2/3 log M 0 - 6.0

to tie it to the surface magnitude. It will never FALL 2004 EASA-130 Seismology and Nuclear Explosions 15

Some Magnitude Examples

    For an earthquakes like the 1991 Landers, California, Earthquake that ruptures a fault of 100 by 10 km 2 with an offset of 3 m, the Mw is 7.3.

The hypothetical largest earthquake on Earth would to rupture the upper 100 km of the Earth around the globe, which corresponds to a magnitude of ~11-12.

An example of magnitude zero earthquake would be a 3 cm slip on a one square meter area.

So there are earthquakes of negative magnitudes (such as tearing a piece of paper, ~ -6).

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Seismic Energy and Magnitude

 Seismic energy E is the energy released from the source in the form seismic waves.

 It is only a small portion of the total energy released during the earthquake. A large portion (more than 90%) is spent on breaking rocks and producing permanent deformation in the source region.

  It is directly related to magnitude log E (in joule) = 1.5 M + 4.8

The seismic energy for a magnitude 6 earthquake is 10 14 (20 kt TNT, a Hiroshima type nuclear bomb), which is 10 1.5

= 32 times greater than from a magnitude 5 earthquake.

J FALL 2004 EASA-130 Seismology and Nuclear Explosions 17

Magnitude-Frequency Law

  Gutenberg and Richter did statistics on number of earthquakes of different magnitudes in a given time. They found a universal law ( the Gutenberg-Richter Law) log N = a - M or N = N 0 10 -M Globally, every year there are about two magnitude 8 earthquakes, 20 magnitude 7’s, 200 magnitude 6’s, …  The largest earthquake ever recorded is the 1960 Chile Earthquake of magnitude 9.8. According to the Gutenberg Richter law, earthquake of this size happens every 50 years (we are almost there).

 The parameter N 0 varies from region to region, depending on local geology and stress environment.

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