California State University, Long Beach
Geography 458/558: Hazards and Risk Assessment

Earthquake Magnitude

Introduction

This laboratory exercise will familiarize you with one measure of the strength of an earthquake: Local or Richter magnitude. It will demonstrate the basic process underlying the Richter method for estimating local magnitude. To do the lab, you need only a ruler and a pencil or pen.

A rather handy graph lets you estimate the local (Richter) magnitude of an earthquake or the M_L. To use it, you need to know the maximum amplitude of the ground motion, measured in millimeters as traced on a particular kind of seismograph (Woods-Anderson torsion seismograph). You also need to figure out the difference in time between the first record of the primary wave and the first record of the secondary wave on the seismograph.

The Woods-Anderson seismograph features a roll of paper, which rotates under a delicately suspended pen, which writes a line along the roll of paper continuously. The paper roll is offset a little bit with each rotation, so that the line can spiral around the drum several times, to reduce wasting paper. When an earthquake happens, the pen will be jerked around on its suspension system, and that makes the line squiggle in proportion to the energy of the earthquake. You can look at a real-time seismogram for a Los Angeles County recording station (Oat Mountain, in the Santa Susana Mountains to the north of the San Fernando Valley) by clicking here. Each row is a continuous trace for a 15 minute time period. If an earthquake happens, its trace will write directly over the traces for the preceding and following 15 minute time frames.

You can measure the amplitude of the largest squiggle in an earthquake trace. By careful examination of the trace, you can pick out the first arrival of the primary wave (where the squiggling begins) and that of the secondary wave (where there is a dramatic change in amplitude). Since the paper drum moves at a constant rate, you can figure out how much time elapsed between the primary and the secondary wave arrivals by measuring the distance between them and converting that distance into time.

In the nomogram figure below, you see the use of the nomogram for an earthquake producing a 23 mm maximum amplitude trace and a 24 second lag between the primary and secondary waves' arrival. By drawing a straight line from the 23 mm amplitude to the 24 second S-P time, you'll cross the magnitude axis at 5.0. The seismograph amplitude and the difference in arrival times, then, corresponds to a distance of just over 200 km and a magnitude of 5.0.

To use the nomogram properly, be sure to note the logarithmic scale of amplitude and of distance/S-P time. On amplitude, notice that 10 is half the way from 1 to 100, rather than one tenth the distance from 1 through 100. Keep that in mind as you eyeball places to enter the nomogram in the problems below. Please type in your answers in this answer form, so that you can easily upload your work to the BeachBoard Dropbox for the nomogram lab: https://home.csulb.edu/~rodrigue/geog458558/labs/nomogram.ods. Note that this is an OpenOffice Calc spreadsheet. It's optimal if you download OpenOffice, for free, from https://www.openoffice.org. If you're more comfortable in Excel, that should work, too, as long as your Microsoft Office is newer than the 2007 version. You don't need to include a copy of your lines on the nomogram.

Nomogram Questions

So, what would be the magnitude of an earthquake with the following characteristics?

1. a time difference of 6 seconds and a 100 mm amplitude? ______________

2. a time difference of 20 seconds and 1 mm? ______________

3. a time difference of 2 seconds and 100 mm? ______________

4. a distance of 500 km and 100 mm? ______________

5. a distance of 20 km and 0.2 mm? ______________

6. Looked at another way, what would be the seismic wave trace amplitude in mm of a M_L=4.0 earthquake, if it were 100 km away? ______________

7. How many seconds would separate the arrival times of P waves and S waves if a M_L=2.0 earthquake produced a maximum trace amplitude of 0.5 mm? ______________

Nomogram Figure

CSULB Department of Geography

First placed on web: 11/26/98
Last revision: 10/18/21
© Dr. Christine M. Rodrigue