**Concept:** Magnitude is a measure of the energy of an
earthquake. The magnitude scale developed by Charles Richter assigns a
numerical value for the magnitude of an earthquake based upon a comparison of
the maximum amplitude of deflection on a seismogram, as recorded by a standard
Wood-Anderson torsion seismometer, and the distance from that seismometer to
the earthquake's source. That distance can be found by comparing the arrival
times of the first P and S waves to reach the seismometer.

**Materials:**

· A browser with Macromedia Flash Player

· Explanation Section for the interactive portion of the activity (below)

**Procedure:**

In this activity, you will have the chance to find the Richter magnitude of several earthquakes through the use of an online activity that utilizes Macromedia Flash.

Charles
Richter is credited with publishing the first method for assigning a numerical
value to an earthquake to represent its energy. On the suggestion of Harry O.
Wood, he called this numerical value "**magnitude**"; it is
generally given to a single decimal place, and written with a capital **M**
(an abbreviation for magnitude) preceding it. Determining the magnitude of an
earthquake by Richter's method requires one to inspect a seismogram and find
the difference in time between the P-wave and S-wave arrivals, as well as the
maximum amplitude of the trace deflection on that same seismogram. Using these
two values, and a conversion table based upon a graph that Richter created from
empirical data, it was possible to calculate the **Richter magnitude** of an
earthquake.

To find the Richter magnitude of an earthquake using this online activity, you will also need a seismogram to work with. There are several different earthquakes to work on, each represented by a single seismogram. Clicking on one of these events in the list at the right will bring up that seismogram in the Earthquake Window. You will see three sliders superimposed on this seismogram.

Your job is to drag these sliders into positions that mark three specific points: the arrival of the P wave (the red “P” slider), the arrival of the S wave (the blue “S” slider), and the maximum amplitude shown on that seismogram (the green “A” slider). The computer will automatically calculate the magnitude and display it in pink. It will also dynamically move the sliders on the nomograph to demonstrate how a nomograph can be used to calculate the magnitude of an event.

All the earthquakes for which seismograms are
available are listed in the Earthquake List.
You must click on one of these to start the activity. When you click on
an earthquake, it will pan into the Earthquake Window. The date of the event will appear above the
Earthquake Window. All of the
seismograms have the same horizontal time scale but different vertical scales.

The Earthquake Window is where the
seismograms get loaded into when you click on one of the earthquakes. The window starts out blank until you load in
an earthquake. Once an earthquake is
loaded in, the proper scale for each earthquake is automatically loaded into
the computer.

There are three arrows that are crucial to
the operation of this activity. They are draggable,
and with them you will select the P-wave arrival, the S-wave arrival, and the
maximum amplitude on the seismogram. These selections give the computer the
data it needs to calculate the Richter magnitude for you. The placement of the
arrows is discussed below.

Three sliders -- a red one labeled "P", a blue one labeled "S", and a green one labeled "A" -- are superimposed atop the seismogram in the earthquake window. The red and blue sliders run vertically, and are to be used to pick the arrivals of the P wave and the S wave on the seismogram. The green arrow runs horizontally, and should be used to select the point of maximum trace deflection -- the amplitude -- on the seismogram.

The arrival of the P wave is marked by the
first deflection, reading from left to right (the direction of elapsing time),
away from the "resting" position of the seismogram's trace. The
arrival of the S wave is generally marked by an obvious increase in the amplitude
and/or the wavelength of the oscillations within the waveform. For this
activity you will need to mark these arrivals with the appropriate arrows by
dragging those arrows to the correct spots on the seismogram.

Choosing the maximum amplitude should be
comparatively easy. First, locate the "level" of the trace when it is
at rest (on the far left side of the seismogram, before the P-wave arrival).
Then find the part of the waveform with the greatest trace deflection -- the
most distance between the peak or crest of an oscillation and that initial
"quiet" level of the trace.

This job is made easier by the green amplitude
marker on the right-hand scale of the nomograph below. This marker will move as
you move the amplitude arrow over the seismogram. This marker goes to zero when
you align the arrow with the initial level of the trace at rest. The amplitude
reading is always positive; it doesn't matter if the arrow lies above or below
the initial trace level. Note, however, that while the pixel-per-millimeter
scale on every seismogram is linear, the right-hand scale on the nomograph is
not; it is logarithmic. Thus, the amount of motion the amplitude marker
experiences will **not** mirror the amount of motion through which you drag
the amplitude arrow.

A similar marker will move along the
left-hand scale of the nomograph as you adjust the positions of the P and S
arrows.

Below the seismogram is the interactive nomograph. A nomograph is a sort of graphical calculator used to find a third value based upon two known quantities. Nomographs generally consist of three scale bars; the two outer scales represent the known quantities and the center scale is used to read off the desired third value. In our case, the outer scales are represented by the S-P time (proportional to the distance from the seismometer to the source) on the left, and the amplitude on the right. The center scale is a linear scale off of which we will read the Richter magnitude.

Sliding along each of the outer scales is a
marker. Each of these markers, covered below, moves in response to your
manipulation of the P, S & amplitude arrows on the seismogram above.

The computer automatically draws a line
connecting the two side markers. The point where this line crosses the center
scale is the magnitude as calculated by the nomograph. The real magnitude that was computer
calculated by formula is shown as a marker on the middle section of the
nomograph. It is possible that the
intersection of the line and the actual magnitude marker may not perfectly
align. On the bottom of the middle
nomograph section is a dynamically changing number that says how far off the
nomograph line is from the real magnitude.
This goes to show that the nomograph is not the most accurate method of
calculating an earthquake’s magnitude. It is however, relatively close.

The left-hand scale of the nomograph represents the
difference in time between the P-wave and S-wave arrivals, abbreviated as
"S-P", in seconds. A scale showing the equivalent distance in
kilometers is given on the same bar. Note that the values on this scale bar do
not represent a simple linear function. Instead, the scale represents the
original graph determined empirically by Charles Richter from data acquired on
earthquakes in southern

The sliding marker on this scale is red in color.
The difference between the two arrows is calculated as an absolute value, so
the arrows can be switched, and this scale will still yield the correct value
for their difference in time. Note how this sliding marker moves as you move
either the P or S arrow.

This marker will be one of the two endpoints
of the line drawn to find the Richter magnitude of the earthquake you chose
from the Earthquake List.

The green amplitude marker will slide up and down the right-hand scale of the nomograph as you move the amplitude arrow over the seismogram. The amplitude scale is logarithmic, and the amount of motion along it will vary from seismogram to seismogram, as the different seismograms are displayed with differing (linear) vertical scales.

This marker will always move to
"zero" (actually, its lowest possible position, since there is no
zero on the logarithmic scale as shown) when the amplitude arrow matches the
level of the trace at rest. Keep in mind that amplitude cannot be negative,
regardless of whether the amplitude arrow falls above or below the center line.

The amplitude marker will anchor the right
end of the line drawn by the computer across the nomograph in its calculation
of the Richter magnitude.