Section 3: Measuring Earthquakes

Activity #4: THE RICHTER SCALE

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.

Warning! This interactive tool was designed with layers, and is unlikely to function in any current browser (it will work in Netscape 4.x). Please see the new version at:

http://siovizcenter.ucsd.edu/library/TLTC/TLTCmag.htm

Materials:

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 frames and layers. If your browser does not support these features, but you do have access to a printer, you can try the alternate exercise, which covers the same material.

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, an written with a capital M (an abbreviation for magnitude) preceeding 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 (seen at right) 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 top will bring up that seismogram in another frame. You will see three arrows superimposed on this seismogram.

Your job is to drag these arrows into positions that mark three specific points: the arrival of the P wave (the red arrow), the arrival of the S wave (the blue arrow), and the maximum amplitude shown on that seismogram (the green arrow). Once you have dragged these arrows into position, you will need to lock them there, using an obviously-labelled ("Lock Arrows") button. This will bring up a display showing the numerical values that correspond to your selections. It also readies the computer to calculate the Richter magnitude for this earthquake. By clicking on another button, this one labelled "Compute Magnitude," you tell the computer to find the Richter magnitude of the earthquake, and display it on the screen. It will do this graphically, using the nomograph at the bottom of the screen. Record these answers on your own sheet of paper to compare them to an answer key later.

Full descriptions of each of the frames and features of this activity are given on an explanation page. Though it may not be absolutely vital for completing the activity (the controls are mainly self-explanatory), you should read through this explanation page if you want to understand all of what is going on "behind the scenes".

Go now to the explanation page, or start the online Richter Scale activity!

Alternate Exercise

If your browser does not support frames and layers, there is an alternate exercise available for you, provided you can print from your browser window. If so, please print out a copy of the Richter Scale print-out page, and have it in front of you as you read through the following directions. If you worked through the online activity successfully, please skip ahead to the numbered questions below.

Your print-out should have three main sections. The uppermost is the title -- "Activity #4: The Richter Scale." Below this is a rectangular area containing a portion of a seismogram of a real earthquake recorded in southern California. The time scale of this seismogram is given directly beneath the rectangle; marks on the rectangle's borders correspond to these numbers, which give hours, minutes, and seconds. Below the seismogram is the third section of the print-out: the Richter Scale nomograph. This graph is name up of three scale bars, labelled below each. The nomograph allows you to find the Richter magnitude of an earthquake by connecting the points that represent two other values (arrival-time difference and maximum amplitude) with a straight line. The point where that line intersects the third and middle scale corresponds to the Richter magnitude of the earthquake.

Just as with the online activity, to find the Richter magnitude you will need to choose three positions on the seismogram: the two wave arrivals (P and S), and the maximum trace deflection, or amplitude.

Use what you've learned from Section 3 to select the locations of the P-wave and S-wave arrivals on the waveform recorded within the seismogram rectangle. Remember that the P-wave arrival is the first point (going from left to right) at which the trace deflects from a "resting" position (generally a flat line), and that the S-wave arrival is typically marked by an obvious increase in amplitude and/or an increase in the wavelength of the "wiggles" in the waveform trace. Once you have decided where these arrivals occur, mark them with vertical lines on your paper, making sure they intersect with the borders of the rectangle.

Now translate the points of intersection of the arrival lines into times, using the numerical time scale given just below the seismogram. Estimate these times to the nearest tenth of a second. Subtract the P-wave arrival time from the S-wave arrival time to find the difference in the travel times of these waves, in seconds. Plot this value on the left-hand scale of the nomograph at the bottom of the printed page. Note that this scale is not linear. It is based upon the empirically-derived graph (shown at right) that Richter created from a sample data set of earthquakes in southern California during January 1932.

Next, find the maximum amplitude for this waveform. This is the point on the waveform where the trace is at its greatest distance from the position of rest -- a horizontal line running across the center of the seismogram. It is clearly marked by the flat trace at the left side of the seismogram, before the P wave arrives. Draw a horizontal line through this point of maximum trace deflection, parallel to the top and bottom edges of the seismogram rectangle. Then, using a metric ruler, measure the separation between the line you drew and the line marking the "resting" position of the trace. This distance is the amplitude. Mark this value on the right-hand scale of the nomograph on your print-out. Note that this amplitude scale is logarithmic, not linear, and plot accordingly.

With a point plotted on each side of the nomograph, you are ready to draw a line connecting them. Do this now.

Find the point at which your line intersects the center scale of the nomograph, labelled "RICHTER MAGNITUDE." Given that this scale is strictly linear, read off the value of this point of intersection. This value is the Richter magnitude of the earthquake recorded on the seismogram; you've completed the exercise! Now work through the questions below, ignoring those that focus exclusively upon the online version of this activity -- the rest are still applicable.


  1. If you kept track of the magnitudes you determined for each of these earthquakes, you can now compare them to this list of magnitudes determined using the same data and methods.

    1. Do your results compare favorably to this list?

  2. Which of the arrows -- P, S, or amplitude -- did you feel was the most difficult to position accurately? (i.e. The position of which arrow was likely the greatest source of error in the calculations made to find magnitude?)

  3. Where in these waveforms did the maximum amplitudes -- the greatest deflection of the trace from its "resting" position -- tend to occur?

    1. Does that bode well for a person's chances to take shelter after they feel the first shaking of an earthquake, but before the most severe (and damaging) shaking strikes?

  4. The stylus on a standard recording drum used to create paper seismograms has a maximum lateral range of motion of about 110 mm (55 mm to either side of its "resting" position), meaning it will "pin" (be unable to move any farther laterally) for an earthquake that generates a maximum trace deflection of 55 mm or greater at that particular seismometer. Event #2 in this activity was of magnitude 5.3 and had a maximum amplitude three times that size (possible because it was recorded digitally, not on paper, as was done when the Richter magnitude scale was created)!

    1. Imagine what would happen if a large earthquake struck near your small network of seismometers and "pinned" the stylus on every one of the seismographs creating records of the event; would you be able to find a Richter magnitude for such an earthquake?

    2. What are some possible solutions to such a problem?

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