Earthquakes as Seismic Sources
Lupei Zhu
FALL 2004
EASA-130 Seismology and Nuclear Explosions
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Topics
Earthquakes as seismic sources
 How do earthquakes happen?
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– Rupture on faults; stress buildup
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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
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Seismic Sources

Any radiator of seismic waves
– Earthquakes
– Explosions
– Landslides

Parameters to describe a seismic source
–
–
–
–
–
Location
Occurrence time
Source dimension
Time duration
Strength
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How Earthquakes happen
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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
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Locating Earthquakes
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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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EASA-130 Seismology and Nuclear Explosions
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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 ???
FALL 2004
EASA-130 Seismology and Nuclear Explosions
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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
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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.
FALL 2004
EASA-130 Seismology and Nuclear Explosions
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Other Magnitude Scales
 The
two most common modern magnitude
scales are:
 M S,
Surface-wave magnitude (Rayleigh Wave)
 mb, Body-wave magnitude (P-wave)
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EASA-130 Seismology and Nuclear Explosions
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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).
FALL 2004
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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
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The best magnitude should be based on the actual ruptured
area and the amount of slip. This is how the seismic
moment M0 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 as
MW = 2/3 log M0 - 6.0
to tie it to the surface magnitude. It will never
saturate.
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Some Magnitude Examples
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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).
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EASA-130 Seismology and Nuclear Explosions
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Seismic Energy and Magnitude
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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.
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Magnitude-Frequency Law
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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 GutenbergRichter 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.
FALL 2004
EASA-130 Seismology and Nuclear Explosions
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