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Earthquakes as Seismic Sources

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Earthquakes as Seismic Sources

Lupei Zhu

- 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

EASA-130 Seismology and Nuclear Explosions

- Any radiator of seismic waves
- Earthquakes
- Explosions
- Landslides

- Parameters to describe a seismic source
- Location
- Occurrence time
- Source dimension
- Time duration
- Strength

EASA-130 Seismology and Nuclear Explosions

- 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)

EASA-130 Seismology and Nuclear Explosions

- 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.

EASA-130 Seismology and Nuclear Explosions

- 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.

EASA-130 Seismology and Nuclear Explosions

- 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)

EASA-130 Seismology and Nuclear Explosions

- 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 ???

EASA-130 Seismology and Nuclear Explosions

- 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.

EASA-130 Seismology and Nuclear Explosions

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

EASA-130 Seismology and Nuclear Explosions

- 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 ML = 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.

EASA-130 Seismology and Nuclear Explosions

Other Magnitude Scales

- The two most common modern magnitude scales are:
- MS, Surface-wave magnitude (Rayleigh Wave)
- mb, Body-wave magnitude (P-wave)

EASA-130 Seismology and Nuclear Explosions

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

EASA-130 Seismology and Nuclear Explosions

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.

EASA-130 Seismology and Nuclear Explosions

- The best magnitude should be based on the actual ruptured area and the amount of slip. This is how theseismic momentM0 is defined:Mo = (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.M0 has units of force*distance (Nm)
- The moment magnitude Mw is defined asMW = 2/3 log M0 - 6.0to tie it to the surface magnitude. It will never saturate.

EASA-130 Seismology and Nuclear Explosions

- For an earthquakes like the 1991 Landers, California, Earthquake that ruptures a fault of 100 by 10 km2 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).

EASA-130 Seismology and Nuclear Explosions

- 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 1014 J (20 kt TNT, a Hiroshima type nuclear bomb), which is 101.5 = 32 times greater than from a magnitude 5 earthquake.

EASA-130 Seismology and Nuclear Explosions

- 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 = N0 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 N0 varies from region to region, depending on local geology and stress environment.

EASA-130 Seismology and Nuclear Explosions

EASA-130 Seismology and Nuclear Explosions