An
aftershock is an
earthquake that occurs after a previous
earthquake (the
main shock). An aftershock is in
the same region of the main shock but is always of smaller
magnitude strength. If an aftershock is larger than the main shock,
the aftershock is redesignated as the main shock and the original
main shock is redesignated as a
foreshock.
Aftershocks are smaller earthquakes formed as the crust around the
displaced
fault plane adjusts to the
effects of the main shock.
Distribution of aftershocks
Most aftershocks are located over the full area of fault rupture
and either occur along the fault plane itself or along other faults
within the volume affected by the strain associated with the main
shock. Typically, aftershocks are found up to a distance equal to
the rupture length away from the fault plane.
The pattern of aftershocks helps confirm the size of area that
slipped during the main shock.
In the case of the 2004 Indian
Ocean earthquake and the 2008 Sichuan earthquake the aftershock distribution shows in both cases
that the epicenter (where the rupture
initiated) lies to one end of the final area of slip, implying
strongly asymmetric rupture propagation.
Aftershock size and frequency with time
Aftershocks tend to obey a number of empirical laws concerning
magnitude and frequency.
Omori's Law
Aftershocks occur with a pattern that follows Omori's law. Omori's
law, or more correctly the modified Omori's law, is an empirical
relation for the temporal decay of aftershock rates. In 1894, Omori
published his work on the aftershocks of earthquakes, in which he
stated that aftershock frequency decreases by roughly the
reciprocal of time after the main shock.
n(t) = \frac {K} {c+t}
where:
- n(t) is the rate of earthquakes measured in a certain
time t after the main shock,
- K is the amplitude, and
- c is the "time offset" parameter.
The modified version of Omori's law, now commonly used, was
proposed by Utsu in 1961.
n(t) = \frac {k} {(c+t)^p}
where
- p modifies the decay rate and typically falls in the
range 0.7–1.5.
According to these equations, the rate of aftershocks decreases
quickly with time. The rate of aftershocks is proportional to the
inverse of time since the mainshock. Thus whatever the odds of an
aftershock are on the first day, the second day will have 1/2 the
odds of the first day and the tenth day will have approximately
1/10th the odds of the first day (when
p is equal to 1).
These patterns describe only the mass behavior of aftershocks; the
actual times, numbers and locations of the aftershocks are
'random', while tending to follow these patterns. As this is an
empirical law values of the parameters are obtained by fitting to
data after the mainshock occurred and they have no physical
basis/meaning.
Bath's Law
The other main law describing aftershocks is known as Bath's Law
and this states that the difference in magnitude between a main
shock and its largest aftershock is approximately constant,
independent of the main shock magnitude, typically 1.1-1.2 on the
Moment magnitude scale.
Gutenberg-Richter law
Aftershock sequences also typically follow the Gutenberg-Richter
law of scaling, which refers to the relationship between the
magnitude and total number of earthquakes in a region in a given
time period.
\!\,N = 10^{A - b M}
Where:
- \!\, N is the number of events in a given magnitude range
- \!\, M is a magnitude minimum
- \!\, A and \!\, b are constants
In summary, there are more small aftershocks and fewer large
aftershocks.
Impact of aftershocks
Aftershocks are dangerous because they are usually unpredictable,
can be of a large magnitude, and can collapse buildings that are
damaged from the mainshock.
Bigger earthquakes have more and larger
aftershocks and the sequences can last for years or even longer
especially when a large event occurs in a seismically quiet area;
see, for example, the New Madrid Seismic Zone, where events still follow Omori's law from the
mainshocks of 1811–1812. An aftershock sequence is deemed to
have ended when the rate of seismicity drops back to a background
level; i.e., no further decay in the number of events with time can
be detected.
Land
movement around the New Madrid is reported to be no more than a
year. in contrast to the San Andreas Fault which averages up to a year across
California. Aftershocks on the San Andreas are now believed
to top out at 10 years while earthquakes in New Madrid are
considered aftershocks nearly 200 years after the
1812 New Madrid earthquake.
Foreshocks
Many scientists hope to use foreshocks to predict upcoming
earthquakes. In particular, the
East
Pacific Rise transform faults
show foreshock activity before the main seismic event. Reviews of
data of past events and their foreshocks showed that they have a
low number of aftershocks and high foreshock rates compared to
continental
strike-slip fault.
(McGuire
et al., 2005)
See also
Notes
- F. Omori (1894) "On the aftershocks of earthquakes,"
Journal of the College of Science, Imperial University of
Tokyo, vol. 7, pages 111–200.
- Utsu, T. (1961) "A statistical study of the occurrence of
aftershocks," Geophysical Magazine, vol. 30, pages
521–605.
- Utsu, T., Ogata, Y. ,and Matsu'ura, R.S. (1995) "The centenary
of the Omori formula for a decay law of aftershock activity,"
Journal of Physics of the Earth, vol. 43, pages 1–33.
- Richter, Charles F., Elementary seismology (San
Francisco, California, USA: W. H. Freeman & Co., 1958), page
69.
- Bath, Markus (1965) "Lateral inhomogeneities in the upper
mantle," Tectonophysics, vol. 2, pages 483–514.
- New Madrid fault system may be shutting down - physorg.com
– March 13, 2009
References
External links