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.

Although each earthquake has a unique

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.

With permission from
http://www.comics.com/comics/franknernest/index.html

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:

*M*_{L} = log_{10}*A(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
.

Click here to learn more about the mathematical logarithm.

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.

log*E*_{S} = 11.8 + 1.5*M*

giving the energy *E*_{S} in **erg**s from the magnitude
*M*. Note that *E*_{S} 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 transfered 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)

160 trillion tons of dynamite is a frightening yield of energy. Consider, however, that the Earth receives that amount in

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