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When we hear that an earthquake has occurred, scientists ask the same basic questions that other people do:
- How bad was it? Were people killed, and was there severe damage?
- How big was it? Did its size alone make it unusual?
- Where was it? Did it affect places where we have friends or where lots of people live? Did it occur in a place where earthquakes occur often or somewhere that earthquakes have not occurred previously?
To answer questions like "how bad" or "how big," it helps to have quantitative measures—numbers that allow us to compare earthquakes in different places. Thus in this chapter we describe three important ways of measuring earthquake damage and size. We also explain how scientists determine where earthquakes have occurred.
How Bad Was It? Modified Mercalli Intensity
When an earthquake occurs near a heavily populated place, newspapers typically report the number of people injured or killed and the dollar value of damage done. These are apt measures of a quake's human impact, but they aren't very useful if we want to know how the earthquake itself compares to previous earthquakes. These measures are especially inadequate if we want to assess the potential hazard from future earthquakes. In many areas the population density changes regularly over time, as do the number and type of buildings and the quality of construction. Moreover, damage depends on the quake's intrinsic size and on its distance from areas of high population density.
When we ask, "How bad was the Valentine, Texas, earthquake of 1931?" the question is not precise. This question might mean we wish to know how intense the shaking was during that earthquake. Or we might wish to know how damaging an identical earthquake would be if it were to happen in the same place today. Finally, we might wish to know how a similar-sized earthquake would affect some other place like Dallas, were it to happen there next year. We could answer all three of these questions if we had some objective way of describing the intensity of ground motion at different places during the 1931 earthquake.
In 1902 an Italian, Guiseppe Mercalli, suggested measuring intensity by evaluating reports of damage or by asking people what they experienced during an earthquake. Then he assessed this information and assigned a number (see table 1.1); for example, if the quake was just strong enough to wake up most people who were asleep, he assigned an intensity of V (figure 1.1). Mercalli intensities are always given as Roman numerals—perhaps because Mercalli was Italian, but also so they aren't confused with Richter magnitudes, which we will explain later. Mercalli's scale is still used widely today, although it has been modified several times to account for geographic differences in building construction. The scale used now is called the Modified Mercalli Intensity scale, and to be explicit about this the numbers are preceded by the letters MMI.
Intensities on the Mercalli scale range from MMI I to MMI XII or 1 to 12. MMI I and MMI II correspond to motions so subtle that most people don't feel them. Those few who do sense something may just feel slightly queasy or notice hanging objects gently swaying. The highest intensity, MMI XII, is reserved for situations in which the shaking produces accelerations stronger than the pull of gravity, and heavy objects like statues get thrown into the air (figure 1.2).
After damaging earthquakes occur, seismologists interview people or use newspaper reports to construct maps indicating where people felt shaking of different intensities. Nowadays people who experience earthquakes can send Internet messages describing what they felt to the United States Geological Survey,1 and seismologists studying the events will incorporate this information into an intensity map (Wald and others 1999). For contemporary earthquakes, these maps are useful for engineers or planners who wish to assess "how bad it was" in different places and for different kinds of construction. However, sometimes it is possible to use historical reports to construct intensity maps for earthquakes which occurred a century or more ago (figure 1.3). Often, comparing intensity maps for contemporary and historical earthquakes is the only way to determine whether a historical quake was bigger or smaller than a modern one.
How Big Was It? Magnitude
On 25 March 1998, the world's largest earthquake for 1998 occurred near the Balleny Islands, just offshore of Antarctica (Antolik, Kavarina, and Dreger 2000). Since the nearest city was about 2,000 kilometers (km) distant in New Zealand, the quake caused no damage and apparently was not felt by humans. It was an insignificant event if we only measure earthquakes in terms of how they affect people. To borrow from the old philosophy question: "If an earthquake occurs and nobody felt it, did it occur at all?" Clearly, to maintain records of the world's earthquakes we need some measure of earthquake size other than maximum intensity—big is not always bad, and bad is not always big. The most common such measure is magnitude.
Charles Richter invented the first magnitude scale in 1935 (see sidebar 1.1), which is why people often say that the "magnitude is 4.8 on the Richter scale." He determined magnitude by measuring the amplitude of ground motion as recorded on a particular seismograph. This measurement was really easy—Richter simply used a ruler to measure the peak-to-peak size of the biggest waves on paper seismograms (figure 1.4). He then used tables to correct the measurement for instrument gain and the effects of distance. Magnitude is a "power of ten" scale, so that a 5.8 indicates ten times more ground motion than a 4.8; a 6.8 is 100 times more; a 7.8 is 1,000 times more, etc.
The Richter scale defines magnitude only in terms of the amplitude of ground motion recorded on a seismograph. Thus there is no limit to how small or how large magnitude can be. A very tiny earthquake might have a magnitude of minus 2. And a very large event might have a magnitude of 8; for example, both the 1906 earthquake in San Francisco and the 1998 Balleny Islands earthquake had magnitudes of about 8. In principle an extraordinarily large earthquake might have a magnitude of 12. However, since magnitude is a power-of-ten scale there are practical limits. People seldom feel earthquakes with magnitudes smaller than about 2.0, and even very sensitive seismographs seldom record earthquakes with magnitudes smaller than minus 1 or so. The Chile earthquake of 1960—the largest recorded since seismographs were invented about a century ago—had a magnitude Mw of 9.5. This is about as large as possible for natural earthquakes (see sidebar 1.2). To get a magnitude of 12 would require something entirely different than an ordinary earthquake—like a good-sized asteroid crashing into the earth.
How Big Was It? Scalar Moment
To be most useful, any statistic such as magnitude should have three properties. It should be (1) easy to measure, (2) strongly correlated with the phenomenon of interest, and (3) not strongly correlated with other phenomena.
Most familiar statistics satisfy at least one of these properties; few satisfy all three. For example, weight and height are the most common statistics reported for football and basketball players. Weight and height are easy to measure and often correlated with success in these sports, but we are all aware of very heavy or very tall people who are poor athletes. To measure mental ability, IQ is the most familiar statistic. However, while IQ is strongly correlated with success in school (at least), it is very difficult to measure, especially if you try to evaluate people from different backgrounds.
With respect to these three properties, magnitude is not a very good statistic. Measuring it is easy enough; essentially, this just involves measuring the biggest arriving signal on a seismogram. The problem is that when some very big earthquakes occur, their faults slip relatively slowly, and thus their biggest arriving signals are not as large as signals from earthquakes on much smaller faults that slip more suddenly. Moreover, since particular seismographs often are tuned to record signals at particular frequencies, they underestimate magnitudes for quakes having their strongest signals at another frequency. Thus magnitude is not correlated very well with the length of the fault that ruptured or the amount of slip.
For these reasons, in 1966 a seismologist named Keiiti Aki proposed a different measure of earthquake size that he called scalar moment (Mo), sometimes just called moment. Like magnitude, scalar moment can be determined directly from seismograms. As with magnitude, determining scalar moment involves correcting for the gain of the recording instrument and the effect of distance. However, in addition, the signal is manipulated to remove any other effects introduced by the seismograph; and the higher-frequency details of the signal are removed by filtering to determine the average strength of the signal radiated along the whole length of the fault. This process is routine but not nearly as easy as determining magnitude. Also, moment is not a dimensionless power-of-ten scale with simple, small numbers like magnitude. Instead, it has units of force times distance, so that a typical magnitude 4 earthquake will have a scalar moment of a thousand trillion newton-meters, and a magnitude 8 might have a moment a million times larger (see table 1.2).
Scalar moment does, however, have two important advantages over magnitude. First, scalar moment can be used to estimate the area of the fault that slipped to cause the earthquake. Indeed, the scalar moment is equal to the product of three factors, the surface area A of the part of the fault that slipped during the quake, the average slip S over this region, and the rigidity or stiffness (denoted by the symbol m) of the rock along the fault.2 This is quite useful, since one can determine moment from a seismogram and then figure out what combinations of rupture area and slip might have caused the earthquake. This allows us to estimate typical fault dimensions for quakes of various magnitudes (table 1.2). Thus a magnitude of minus 6 with a fault diameter of 7 mm corresponds to a crack in your car windshield, which explains why you seldom hear about earthquakes with negative magnitudes. A magnitude zero corresponds to a fault about the size of a two-car garage. Very damaging earthquakes with magnitudes between 7 and 8 have slips of several meters occurring along faults with dimensions of tens of km.
Second, unlike magnitude, scalar moment has the same value regardless of the instrument used to record seismic waves. There are not different moments for different kinds of seismographs (as in sidebar 1.1). For these two reasons, seismologists nowadays nearly always prefer to use moments rather than magnitude for measuring earthquake size. However, moments will never completely replace magnitudes, partly because magnitudes are just so familiar to the public and because moment numbers are so unwieldy.
Where Was It? How a Seismograph Works
For some earthquakes scientists have no problem figuring out where they occurred. If a quake happens in a populated area and is large enough, felt-report maps such as in figure 1.3 present approximately circular zones around the region where the fault slipped. Indeed, for historical earthquakes occurring before about 1900, such maps are usually the only means of location available. But to locate earthquakes that occur in unpopulated regions or which are too small to cause damage, it is useful to employ a seismograph, a detector of seismic waves that is more sensitive than humans. The power of the seismograph is that it provides a way to sense and locate earthquakes that are far too small to be felt or do damage.
When a fault slips suddenly, the disturbance travels away in all directions, much as waves on a pond travel away from the point where a pebble is dropped. Although a sizable portion of the fault may slip, the point where the slippage begins is called the earthquake focus; subsequently the area that slips grows larger as the rupture proceeds. A seismograph amplifies and records the elastic waves produced by the sudden slippage. Since waves arrive earliest at the closest seismograph stations, and since different kinds of seismic waves (figure 1.5) travel at different speeds, you can locate the focus if you know the arrival times at several seismograph stations.
For example, suppose that a station records a primary or "P" wave and a secondary or "S" wave (figure 1.4). Seismologists know that up to distances of 1,000 km, P waves travel at about 8 km per second (km/sec), and S waves travel at about 4.5 km/sec. Using high school math one can show that with these velocities, the epicentral distance in km is about ten times the difference in seconds between S and P arrivals. If the S arrives one minute after the P at a station, the quake-to-station distance is about 600 km. If P and S readings are available from three or more stations, you can locate the focus. Before about 1960 seismologists often located earthquakes on a globe by drawing arcs around the sites of seismograph stations. Seismologists now use computer programs that take all available readings and find the best-fitting epicenter.
How does a seismograph work? The essential element of a seismograph is just a loosely suspended object that, when the ground moves, can't quite keep up. For vertical motion, this object is just a mass suspended from a spring. For horizontal motion, this can just be a "swinging gate" (figure 1.6). To make a working seismograph, the motion of the suspended object must somehow produce an electric current. A simple way to do this is to use the fact that when an ordinary magnet moves through a coil of wire, it induces an electric current in the wire. Thus if the seismograph mass is a magnet and the coil of wire is fixed to the ground, the motion of the ground produces a current. After amplification, even imperceptible ground motions produce signals that can be displayed with a suitable chart recorder or on a computer screen.
A seismograph is just like an ordinary stereo speaker, but in reverse (figure 1.7). Your stereo speaker has a magnet and a coil of wire in it, with the magnet attached to the base of a cardboard cone. In the speaker, an electric current from your amplifier through the coil makes the magnet move, vibrating the paper in the cone and making sounds—vibrations of the air.
Several seismograph stations operate continuously in Texas (figure 1.8). In Hockley, Texas, a small town 50 km northwest of Houston, the University of Texas at Austin has placed modern seismic sensors about 500 meters beneath the surface in a salt mine operated by United Salt, Inc.3 The Hockley site is attractive for a seismograph station because its subsurface location reduces effects caused by manmade and weather-generated noise. In Lajitas, Texas, near Big Bend, Southern Methodist University operates a seismic array. A seismic array is several nearby seismograph stations operating together; arrays are especially useful because they allow the detection of weaker signals and because scientists can use them to determine the direction of arrival of seismic phases from distant earthquakes.
Elsewhere, in far West Texas the University of Texas at El Paso operates several stations, mainly to record small regional earthquakes. Texas Tech University operates stations in Lubbock and Amarillo, and Texas Tech and the University of Texas at Austin jointly operate a station in Junction, Texas.
Finally, sometimes amateurs build and operate seismographs. This is a bit tricky—not the kind of thing most people could do for a high school science project. However, articles in Scientific American in September 1975, July 1979, and April 1996 explain how to do it (Strong 1975; Walker 1979; Carlson 1996). There is even a website that lists amateurs worldwide and archives the seismograms they record.4 According to this site, five amateurs were operating seismic stations in Texas as of this writing.
- For the central United States, the USGS began the website to produce what are known as Community Internet Intensity Maps only in the year 2000. You can access this site at: http://pasadena.wr.usgs.gov/shake/cus/. At this website you can contribute felt reports for recent earthquakes and view intensity maps for current and past events.
- When a twisting or shearing force acts on any elastic solid, it will change shape until the force is removed, whereupon it springs back to its original shape. Some materials like steel or rock are very rigid; that is, they do not change shape much even when a large force is applied. Others, like foam rubber, are not very rigid. When scientists measure rigidity in the lab or use it in equations such as "scalar moment equals fault area times slip times rigidity," they usually use the symbol m,which is the Greek letter m.
- For the University of Texas' Hockley station, you can see today's data and pictures from down in the salt mine at: http://www.ig.utexas.edu/research/projects/eq/seismo/hkt/about/about/hkt.htm. Current data recorded at several stations in and near Texas are available at: http://www.ig.utexas.edu/TexSeis/. A website that includes a very complete set of links to various earthquake-related sites around the world is: http://www.geophys.washington.edu/seismosurfing.html. The U.S. Geological Survey Earthquake Hazards program website includes maps of earthquake hazard, recently occurring earthquakes, and much other useful and interesting information: http://earthquake.usgs.gov/.
- The so-called Public Seismic Network archives information from and about amateur seismologists; the web-address is: http://psn.quake.net. In January 2002 this site shows amateurs operating stations in Buda, Corpus Christi, Friendswood, Pearland, and Plano.