Objective:
Use the PEPP Learning Library to become familiar with the different
ways scientists calculate earthquake magnitudes.
We all want to know the size of an earthquake, but what does the size of an earthquake mean and how do we measure it? We have a sense that earthquakes can be bigger or smaller, but what do we mean by big or small ?
If a large earthquake occurs in a populated region, the people in the area will feel it. A seismic station located at the epicentre might be used to determine what the size of the earthquake is. But the intensity of ground shaking and damage diminishes the farther you move away from the epicentre. We cannot simply measure the displacement or amplitude of the P wave, as a measure of earthquake size, because this amplitude decreases as we move further from the epicentre. Thus we must also know the distance between the earthquake and the seismometer.
Seismologists refer to the size of an earthquake as its Magnitude.
There are a variety of different schemes called magnitude scales
used by seismologists to measure earthquake magnitudes. But they all have
two factors in common:
(i) They must use a measurement of some particular waveform recorded on
a seismogram, and,
(ii) they must take into account the distance from the earthquake to the
station that recorded the seismic trace. This distance is expressed
either in kilometres for local earthquakes, or in
the angular form, for distant earthquakes
as degrees of separation between two points
on the globe (usually referred to as 
(Delta)).
Use the PEPP Learning Library to learn more about the different magnitude scales developed by seismologists over the years. In the Learning Library, you will find information about:
In addition, there is information about a different kind of earthquake measurement call the Mercalli Index, which is an eye witness qualitative assessment of the level of damage caused by a particular earthquake. The Mercalli Index is primarily used by those studying historical earthquakes that occurred before seismic stations were in place around the world.
Body wave magnitude (mb) and surface wave magnitudes (Ms) are two ways scientists have developed to calculate earthquake magnitudes. Both calculations are based on seismic waves that can be identifed in a seismogram. Body wave magnitude uses the P wave; surface wave magnitude uses the surface waves. Typically the amplitude of these waves is used in the calculations. However, because the seismometers record ground displacement, presented by the ground velocity, seismologists at Princeton have modified the formulas to use velocity.
For mb, the formula is,
For Ms, the formula is,
where V is the velocity of the wave in micrometers/sec, and
(Delta) is the angular epicentral distance in degrees.
If your class seismometer has recorded an earthquake, calculate its
magnitude. You can compare this magnitude to the published one from
GNS.
Why have scientists developed so many different ways to calculate earthquake magnitudes?
We hear of the Richter scale whenever a large earthquake occurs
on Earth. What exactly is the Richter scale? Should the Richter scale be
used to calculate the magnitude of an earthquake that occurs in New Zealand,
Quebec, Japan or other locations on Earth?
What are the strengths and weaknesses of each of the different magnitude
scales?
What
do scientists need to take into account when they design a magnitude scale?
Objective:
To learn why earthquake magnitude scales are logarithmic.
When an earthquake is recorded on a seismogram as displacement, i.e. ground movement, the amount of that movement varies over an enormous range for earthquakes of differing sizes. For example, the ground movement for a quake of Richter Magnitude, ML = 1 at a distance of 100 km from the epicentre is 10 µm. For a magnitude, ML = 7 at a distance of 100 km from the epicentre, the recorded ground movement on the seismogram is 1 meter. This is equivalent to 10,000,000 µm, or 10^7 µm. Thus, there is a million times greater movement in a ML = 7 than a ML = 1 earthquake. It would be quite inconvenient to plot these two seismic traces together on a single plot. This wide range of magnitudes makes it necessary to use a logarithmic scale in order to make comparisons of quakes of differing size.
The Learning Library contains a demonstration in the discussion of Magnitudes which helps convey the enormity of this range in scale, by enabling you to plot seismograms of quakes of different magnitudes on the same, linear scale and then switching to a logarithmic axis. Go there now to experiment and visualize this problem if you need to.
Objective:
To begin to understand the relationship between earthquake magnitude
and energy.
When an earthquake occurs, energy is released. But how much energy do earthquakes of different sizes release? Or, how does the energy released by an earthquake compare with that released by a nuclear explosion? Scientists have determined the relationship between seismic energy and magnitude. To calculate the amount of energy released from an earthquake use the formula:
(where E is the energy released by the earthquake in Joules), or,
You will need:
1. For the seismogram, calculate the energy released by the earthquake.
2. Compare your energy calculations to other energy-releasing events. For example, how much energy did the atomic bomb at Hiroshima release? What size earthquake would produce the same amount of energy? Power plants release energy over time. How much energy does a typical power plant release in one day, one year? What magnitude earthquake produces this much energy?
1. What is the relationship between magnitude and angular distance,
called
or Delta, from the epicentre?
We have mentioned above that as you record a seismic wave farther and farther away from its source, the height of the recorded wave (i.e. its amplitude) should diminish. Test this assumption and develop a more quantitative assessment of this concept using a graphic scheme. Can you determine the relation between maximum P wave or surface wave velocity and angular distance to the epicentre?
Assemble a set of seismograms from different stations from around the
globe that have recorded a single event. Plot the amplitude of the P wave
vs.
(Delta) for your set of seismograms. Try this again using the amplitude
of the surface waves for each seismogram.
2. Create a Mercalli Index pattern for a real earthquake.
After a major quake has occurred in an occupied country, use the Internet to query school classes in the surrounding area to gather their assement of physical damage. Use their eyewitness accounts to build a Mercalli Index map for that particular quake. Plot your Mercalli Index as contours on a map.
3. Look for various magnitude correlations using the Hypocentre Catalogue
Data.
For example, is there a correlation between earthquake depth and size? To test for this, submit a query to the Earthquake Hypocentre Catalogue by filling out an Earthquake Catalogue Search Form. Export your file to a spreadsheet program. Now make a plot of magnitude vs. depth and test for any correlation.
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This document was revised on June 29, 1998
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