Dr. J. G. Anderson, Spring 1995

This lab has three objectives:

1. Locate an earthquake.

2. Determine the magnitude of an earthquake.

3. Find the energy of the earthquake and put it into perspective of the energy of a more familiar object.

The principles of locating an earthquake are not difficult. The earthquake sends out different kinds of waves that travel at different speeds. At a station, they thus arrive at different times. The difference in travel times is proportional to the distance. Below we show examples of seismograms. In this, you should learn to identify two kinds of waves, the P-wave and the S-wave.

The travel time difference is described algebraically as follows:

• Let R be the distance from an earthquake to a station.

• Let Vp be the speed of the P-wave.

• Let Vs be the speed of the S-wave.

• The P wave will arrive at the station at time tp = R/Vp

• The S wave will arrive at the station at time ts = R/Vs

• Subtracting, one gets:

Lab Steps:

1. Solve Equation (1) for R. Substitute V p and V s to find a relationship between R and the difference in wave arrival times.

2. On September 12, 1994 a moderate earthquake occurred someplace in Nevada. Figure 1 shows a map of the region, and shows the location of some seismic stations. Digital seismograms from four of those stations are given on Figures 2a,b,c,d. Using the seismograms in Figure 2 and your solution in step 1, determine the distance of the earthquake from each station.

3. On the map in Figure 1, draw circles with the appropriate radius, around each station. These circles should all intersect at the same place. That place is the epicenter of the earthquake.

4. Your circles may not all intersect in the same place. Estimate the uncertainty you have in the location of this earthquake using these records. List as many possible reasons as you can for this uncertainty.

When Charles Richter invented the magnitude of an earthquake, he wanted a scale that would reduce the huge range of earthquake sizes into a numbering scheme that would be easier for the average person to understand. For that reason, he used the common logarithm of the amplitude of the seismogram. Richter also wanted a system where in principle, stations at any distance from the earthquake would come up with the same answer. The strength of seismic waves decreases as distance increases, so an adjustment is necessary.

Algebraically, this is expressed as follows:

• Let A be the largest amplitude on a seismogram of an earthquake.

• Let C(R) be the distance correction that depends on R .

• Let M L be the local magnitude, as defined by Richter.

• Then:
  ML = Iog A + C(R) (equation 2)

A table with values of C(R) is given below. There are a lot of reasons why different stations give slightly differing estimates for the magnitude. Therefore, when an earthquake happens, the best magnitude is always announced much later, after lots of stations have been read and averaged.

The seismograms in Figure 2 are recorded on the digital seismic stations in the Western Great Basin seismic network. The original seismograms are given in ``counts'' coming ftom the digitizer, so they differ from the kind of instrument that Richter used. Richter used a ``Wood-Anderson seismometer.'' The seismograms have already been converted to show what Richter's instruments would have recorded. The vertical scale is the amplitude this seismogram would have had on the Wood Anderson seismograph.

Richter invented the magnitude thinking it would be a measure for the amount of energy radiated in an earthquake. He and Gutenberg developed a formula for the relationship between energy Es and magnitude M which is still used today. It is:

logEs = 11.8 + 1.5M

where the energy, Es, is given in units of ergs.

Lab Steps

1. Using the magnitude you just found, estimate the seismic energy.

2. To put this energy into perspective, find out how fast a car would have to be traveling (in miles per hour) to have this much kinetic energy. If a car traveling at this speed were to crash into a mountain side, it would cause an earthquake of about the same magnitude.
   From high school science, the kinetic energy E of a car is:

E = 1/2 m v ²
where m is the mass of the car, and v is its speed. Suppose the car weighs 2200 pounds.

You will also need to know these conversion factors:

• At the surface of the Earth, a mass of 1 kilogram weighs 2.2 pounds.

• 1 erg = 1 (gram cm² ) / (second² )

• 1 mile/hour = 44.7 cm/sec

If you need any more conversion factors, you will find them in Appendix A of the Press and Siever text book.

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