Richter Earthquake
Magnitudes Effects
Less than 3.5 Generally not felt, but recorded.
3.5-5.4 Often felt, but rarely causes damage.
Under 6.0 At most slight damage to well-designed buildings.
Can cause major damage to poorly constructed buildings
over small regions.
6.1-6.9 Can be destructive in areas up to about 100 kilometers
across where people live.
7.0-7.9 Major earthquake. Can cause serious damage over larger areas.
8 or greater Great earthquake. Can cause serious damage in areas several
hundred kilometers across.
Each earthquake has a unique amount of energy, but magnitude values
given by different seismological observatories for an event may vary.
Depending
on the size, nature, and location of an earthquake, seismologists use
several
different methods to estimate magnitude. The uncertainty in an estimate
of the magnitude is about plus or minus 0.3 units, and seismologists
often
revise magnitude estimates as they obtain and analyze additional data.
Richter showed that, the larger the intrinsic energy of the earthquake, the larger the amplitude of ground motion at a given distance. He calibrated his scale of magnitudes using measured maximum amplitudes of shear waves on seismometers particularly sensitive to shear waves with periods of about one second. The records had to be obtained from a specific kind of instrument, called a Wood-Anderson seismograph. Although his work was originally calibrated only for these specific seismometers, and only for earthquakes in southern California, seismologists have developed scale factors to extend Richter's magnitude scale to many other types of measurements on all types of seismometers, all over the world. In fact, magnitude estimates have been made for thousands of Moon-quakes and for two quakes on Mars.
The diagram below demonstrates how to use Richter's original method
to measure a seismogram for a magnitude estimate in Southern
California:
The scales in the diagram above form a nomogram that allows
you to do the mathematical computation quickly by eye. The equation for
Richter Magnitude is:
ML = log10A(mm)
+ (Distance correction factor)
Here A is the amplitude, in millimeters, measured directly from
the photographic paper record of the Wood-Anderson seismometer,
a special type of instrument. The distance factor comes from a
table
that can be found in Richter's (1958) book
Elementary Seismology.
The equation behind this nomogram, used by Richter in Southern
California,
is:
Thus after you measure the wave amplitude you have to take its logarithm,
and scale it according to the distance of the seismometer from the
earthquake,
estimated by the S-P time difference. The S-P time, in seconds, makes
.
Seismologists will try to get a separate magnitude estimate from every seismograph station that records the earthquake, and then average them. This accounts for the usual spread of around 0.2 magnitude units that you see reported from different seismological labs right after an earthquake. Each lab is averaging in different stations that they have access to. It may be several days before different organizations will come to a consensus on what was the best magnitude estimate.
To get an idea of the seismic moment, we go back to the elementary
physics
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. After
some
rather complicated mathematics, it can be shown that the moment of an
earthquake
is simply expressed by:
The formula above, for the moment of an earthquake, is
fundamental
to seismologists' understanding of how dangerous faults of a certain
size
can be.
Now, let's imagine a chunk of rock on a lab bench, the rigidity, or
resistance to shearing, of the rock is a pressure in the
neighborhood
of a few hundred billion dynes per square centimeter. (Scientific
notation
makes this easier to write.) The pressure acts over an
area
to produce a force, and you can see that the cm-squared units cancel.
Now
if we guess that the distance the two parts grind together before they
fly apart is about a centimeter, then we can calculate the moment, in
dyne-cm:
Again it is helpful to use scientific notation, since a dyne-cm is
really a puny amount of moment.
Now let's consider a second case, the Sept. 12, 1994 Double Spring
Flat
earthquake, which occurred about 25 km southeast of Gardnerville. The
first
thing we have to do, since we're working in centimeters, is figure out
how to convert the 15 kilometer length and 10 km depth of that fault to
centimeters. We know that 100 thousand centimeters equal one kilometer,
so we can write that equation and divide both sides by "km" to get a
factor
equal to one.
Of course we can multiply anything by one without changing it, so we
use it to cancel the kilometer units and put in the right centimeter
units:
Of course this result needs scientific notation even more desperately.
We can see that this earthquake, the largest in Nevada in 28 years, had
two times ten raised to the twelfth power, or 2 trillion, times as much
moment as breaking the rock on the lab table.
There is a standard way to convert a seismic moment to a magnitude.
The equation is:
Now let's use this equation (meant for energies expressed in dyne-cm
units) to estimate the magnitude of the tiny earthquake we can
make
on a lab table:
Negative magnitudes are allowed on Richter's scale, although such
earthquakes
are certainly very small.
Next let's take the energy we found for the Double Spring Flat
earthquake
and estimate its magnitude:
The magnitude 6.1 value we get is about equal to the magnitude reported
by the UNR Seismological Lab, and by other observers.
logES =
11.8
+ 1.5M
giving the energy ES in ergs from the
magnitude
M.
Note that ES is not the total ``intrinsic'' energy
of
the earthquake, transferred from sources such as gravitational energy
or
to sinks such as heat energy. It is only the amount radiated from the
earthquake
as seismic waves, which ought to be a small fraction of the total
energy
transferred during the earthquake process.
More recently, Dr. Hiroo Kanamori came up with a relationship between seismic moment and seismic wave energy. It gives:
Energy = (Moment)/20,000
For this moment is in units of dyne-cm, and energy is in units of ergs.
dyne-cm and ergs are unit equivalents, but have different physical
meaning.
Let's take a look at the seismic wave energy yielded by our two examples, in comparison to that of a number of earthquakes and other phenomena. For this we'll use a larger unit of energy, the seismic energy yield of quantities of the explosive TNT (We assume one ounce of TNT exploded below ground yields 640 million ergs of seismic wave energy):
Richter TNT for Seismic Example
Magnitude Energy Yield (approximate)
-1.5 6 ounces Breaking a rock on a lab table
1.0 30 pounds Large Blast at a Construction Site
1.5 320 pounds
2.0 1 ton Large Quarry or Mine Blast
2.5 4.6 tons
3.0 29 tons
3.5 73 tons
4.0 1,000 tons Small Nuclear Weapon
4.5 5,100 tons Average Tornado (total energy)
5.0 32,000 tons
5.5 80,000 tons Little Skull Mtn., NV Quake, 1992
6.0 1 million tons Double Spring Flat, NV Quake, 1994
6.5 5 million tons Northridge, CA Quake, 1994
7.0 32 million tons Hyogo-Ken Nanbu, Japan Quake, 1995; Largest Thermonuclear Weapon
7.5 160 million tons Landers, CA Quake, 1992
8.0 1 billion tons San Francisco, CA Quake, 1906
8.5 5 billion tons Anchorage, AK Quake, 1964
9.0 32 billion tons Chilean Quake, 1960
10.0 1 trillion tons (San-Andreas type fault circling Earth)
12.0 160 trillion tons (Fault Earth in half through center,
OR Earth's daily receipt of solar energy)