lab 2: earthquakes april 7 2009 - university of...

ESS 210 Lab 2: Earthquakes

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Name: ____________________________

Lab 2: Earthquakes April 7, 2009

Sudden movements within the lithosphere give rise to vibrations that travel both through the planet and along its surface. These vibrations, known as seismic waves, may be detected and recorded by instruments called seismometers even at great distances from the original point of movement (the focus). These movements are brought about by the release of energy through processes such as slip along a fault, volcanic eruption, or magmatic intrusion and the resulting seismic events are called earthquakes. Each earthquake produces several types of seismic waves that propagate at different velocities and are affected differently by the material through which they pass. The characteristic arrival times and wave forms of these various waves can be interpreted to provide information on the location, size, and type of the earthquake’s source and to determine the characteristics of the paths the waves travel between the focus and the seismometer. The three most common types of seismic waves are:

1) P waves, short for “primary waves”. P waves are compressional waves, travel the fastest, and are the first to arrive at the seismometer.

2) S waves, short for “secondary waves”. These are shear waves, travel slower than the P waves, and therefore reach the seismometer after the P waves. S waves cannot travel through liquids.

3) Surface waves. Surface waves are slower than both P and S waves, arriving after the other waves. They can propagate only along the surface of the planet and must travel a longer path to reach the seismometer, further delaying their arrival times. There are many types of surface waves, collectively referred to as L waves.

Locating and Timing Earthquakes Travel time curves have been compiled for various types of seismic waves. These curves show the time it takes for each wave to reach points on the earth’s surface at a given distance from the epicenter (point on Earth’s surface directly above the focus) of the earthquake. By measuring the difference in the P and S wave arrival times, it is possible to determine the distance between the seismometer and the epicenter. This does not provide any information about the direction to the epicenter from the seismometer but places the epicenter on a circle of that calculated radius from the seismometer. If the travel distance can be calculated for at least three seismometers, then the location of the epicenter is constrained to lie at the unique intersection of their three respective circles. Note that there can be some variation to travel time curves depending on the material properties of the rocks involved; the attached Figure 1 represents average travel time curves measured worldwide.


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Figure 1. Average travel time curves for P waves, S waves, and L waves.


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Figure 2. Seismogram recorded at Dallas, TX. A sample seismogram (the output of a seismometer) is shown in Figure 2. The arrivals of the P and S waves are indicated. The difference in P and S arrival times shown above is 3.1 minutes, corresponding to a distance of 1000 miles between the source and the seismometer. The travel-time curve also indicates that the P wave arrived approximately 3.5 minutes after the earthquake occurred, so the earthquake must have taken place at 8:04.7. Earthquake Magnitude Seismometers don’t directly record the amount of energy released by an event. Instead, the signal on a seismogram results from the interaction of this energy with the lithologic materials around the focus, the variable geologic structures along the paths of the waves, local structure at the site of the instrument, and the biases in the physical response of the instrument itself. It isn’t possible to filter out all of these effects so several scales have been proposed for calculating the magnitude of an earthquake from seismograms. These magnitude scales are simply empirical relations that, by common agreement, are taken to be valid only under certain circumstances. The use of different scales will produce different “magnitudes” for the same event, so it is necessary to determine which methods were used to determine the magnitude before comparing different events. One scale in widespread use for shallow-focus earthquakes (<50 km depth) is the surface-wave magnitude, denoted Ms, sometimes improperly called the Richter magnitude. The following information is taken from the seismogram:

Δ, the angular distance from the receiving station to the epicenter. X, the maximum amplitude of the surface waves. T, the period of the surface waves at maximum amplitude.

From these, the magnitude is calculated as Ms = log10(X/T) + 1.66 log10(Δ) + C where C is a constant that must be determined independently for each location and type of seismometer.


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Part 1. Earthquake Location Use the seismograms in Figure 3 to answer the following questions.

1. Estimate, to the nearest tenth of a minute, the arrival times of the P and S waves at each location.

Location P arrival S arrival Difference (S minus P)

Sitka, AK

Charlotte, NC

Honolulu, HI

2. Using the differences between P and S arrival times (S minus P), and the travel time curves, estimate the distances from the epicenter to each location.

Location Distance (mi)

Sitka, AK

Charlotte, NC

Honolulu, HI

3. Find the epicenter by the following procedure: a. Mark and label the three seismometer locations on the map (Figure 4).

Sitka, AK: 57°N 135°W Charlotte, NC: 35°N 81°W Honolulu, HI: 21°N 158°W

b. Using a compass, draw a circle centered at each location with a radius

corresponding to the appropriate distance determined above. Do the three circles intersect at a point (epicenter)? Where is the epicenter?


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c. If the circles do not intersect perfectly, what errors might be involved?

4. When did the earthquake occur?

5. When did the L waves (surface waves) reach Sitka? 6. On what major fault did this earthquake likely occur? Was this earthquake probably

shallow or deep? (Hint: Consider the tectonic setting.)


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Figure 3. Seismograms recorded at three different locations for a single earthquake. Times

shown have been standardized to Eastern Standard Time for purposes of comparison.


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Figure 4. Map of part of Earth's surface.

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Part 2. Earthquake Magnitude The last three pages of the lab show three representations of a single seismogram for an earthquake that occurred near Sakhalin Island (Russia, just north of Japan) on 4 August 2000. The seismometer that recorded this is located in West Lafayette, Indiana (40.484N, 86.881W). The first representation is of a 24-hour period and is read left to right, top to bottom. The event begins in the middle of the line labeled "21" and continues for over an hour. The second representation shows the same record from just before the P arrival to roughly the middle of the extensive surface wave signal, and the third representation is of the surface wave activity near its peak amplitude. Note that the P arrival is sharply indicated but that the S arrival is not easy to pinpoint. This highlights the value in having several seismometers record an event so that comparisons may be made.

7. Use the globe and a length of string to estimate the angular distance between the

epicenter (which has NOT been given to you precisely) and the seismometer. To do this, compare the distance between Sakhalin Island and Indiana with the same distance in degrees along the Equator. Alternatively, determine the distance in kilometers and use the conversion that one degree of angular distance is approximately equal to 111.2 km on Earth's surface. The distance in degrees is Δ.

8. Find the amplitude (actually the half-amplitude, from the zero line to a maximum or minimum) of the surface waves. Measure this amplitude to determine X. This value must be in units of 10-6 m, but the seismogram scale is given in millivolts of signal. To convert this, measure the amplitude with a ruler in cm and multiply by 3 × 10-6. For example, an amplitude of 5.0 cm on this record corresponds to an absolute ground motion of 15 × 10-6 m beneath the seismometer, so X would equal 15.

9. Determine the period of the surface waves at their maximum amplitude. Measure the elapsed time for ten full cycles, then divide by ten. T must be converted to seconds.


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10. Finally, calculate the surface-wave magnitude using the formula given above. For this instrument, use C = 3.3, which is a typical value for such a determination.

11. The USGS reported a magnitude of 7.1 for this event. How does your calculation compare? Discuss sources of error and uncertainty.


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Figure 5. The first representation is of a 24-hour period and is read left to right, top to bottom. The event begins in the middle of the

line labeled "21" and continues for over an hour.


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Figure 6. The second representation shows the same record from just before the P arrival to roughly the middle of the extensive surface

wave signal.


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Figure 7. The third representation is of the surface wave activity near its peak amplitude.

lab 2: earthquakes april 7 2009 - university of...

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