Applications
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Chapter 14: Waves and Sound Applications |
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According to a dictionary definition seismology is "the study of vibratory motions of the earth and other planetary bodies." The root of the word is the Greek verb seiein, to shake. Investigating the propagation of mechanical waves through the earth is useful in a number of endeavors, such the study of the physical properties of the earth, study of earthquakes, geophysical prospecting, and the monitoring of nuclear tests. The sources of mechanical waves propagating through the earth include earthquakes and explosions set-off by people, as well as volcanic eruptions, storms at sea and traffic. The latter two contribute to the seismic "noise" which often masks the effects seismologists are trying to investigate.
Mechanical waves can propagate from one point to another on
the earth's surface via many paths. Surface waves, marked by the red path between points e and s1 in
the diagram on the left, travel directly between the source and the observation point along the
surface of the earth. Body waves travel through the body of the earth. Discontinuities along the path
of the wave can produce reflections as in the blue path in the diagram as well as refractions as in
the black path in the diagram.  |
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| P-WAVE (longitudinal compression wave) |
In an S-wave the motion of the material particles is perpendicular to the direction of propagation of the wave. The material in the path of the wave is subjected to a shearing stress. The velocity of propagation of the S-wave will be affected by the shear modulus of the material.
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| S-WAVE (transverse shear wave) |
Compression P-waves travel through the earth about ten times faster than the S-waves. Typical
P-wave speeds are between 1 and 5 miles per second. The actual speeds depend on the material the waves
pass through, although the ratio of P-wave speed to the S-wave speed is fairly constant. This fact
enables seismologists to use the delay between P-wave and S-wave arrival times to estimate (quite
accurately) the distance between the earthquake (or explosion) source and the observation point.
The analysis of reflection and refraction data of the two types of waves gives valuable
information about the characteristics of the material medium the waves encountered. For example,
liquids cannot resist shear and thus cannot carry s-waves.
Seismic waves are detected and measured with
seismographs. In principle, anything that can give an indication of ground movement is a candidate to
be a seismograph. If the device does no more than give evidence of a tremor it is called a
seismoscope. A seismograph not only records the occurrence of a quake, but can provide additional
data. Historians of science credit the Chinese astronomer Zhang Heng with the invention of the first seismograph. The device was a
six foot vase with eight dragons arranged around the neck of the vase. Each dragon had a ball in his
mouth. Frogs sat around the vase, ready to intercept a ball that would drop from a dragon's mouth. The
noise made by the fallen ball would alert the emperor's household that an earthquake has occurred. One
only had to check which frog caught the ball to deduce the direction of the earthquake. The story goes
that several days after what was thought to have been a false alarm, visitors to the empirial court
brought news of an earthquake 400 miles away.
Heng invented his device in AD 132. Sixteen hundred
years later the first European seismograph was invented in France. It is not known what was inside
Heng's vase. We suspect that it contained some kind of pendulum.
Modern seismographs are based on the idea that an object, suspended in some way inside a
container, would be kept in place by its inertia as the container moves under the influence of a
ground tremor. A schematic diagram of such a device is shown in the diagram on the right. A massive
ball is pivoted on a horizontal boom and suspended from a spring. Such a device can respond to
vertical motions as well as motions parallel to the ground.
This is basically an oscillator. To
make it useful to investigate typical seismic waves several additional features have to be added. A
simple mass on a spring or a pendulum oscillator would not do. The periods of seismic waves range from
a few per second to several minutes. Simple oscillators with such periods would need impractical
spring constants and lengths. Note that the device depicted in the diagram is not a simple oscillator.
(What information would you need determine the period of such a device?) After a useful period is
assured, the device is damped. We don't want it to oscillate indefinitely. In practice it is in fact
critically damped, i.e. when disturbed from equilibrium it will go through one cycle and damp out.
To obtain a record of the wave, the relative displacement between the oscillating object and the container is sensed and recorded. The record is called a seismogram. In early devices a stylus was attached to the tip of the oscillator. The stylus would draw a trace on soot covered paper.
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| a modern seismogram |
Friction between the stylus and the paper was a problem. To deal with that an optical method was invented. A tiny mirror, attached to the oscillator, writes onto a photographic material with a beam of light. This method eliminates the stylus friction problem and it automatically magnifies the motion by a factor of several thousands, thus increasing the sensitivity of the device.
Modern seismographs monitor the oscillations with electronic sensors and feed the output into onboard computers. The computer then processes the data to fit the need of the seismologist using the device.
Seismology provides reliable monitoring of nuclear explosions, which
makes test ban treaties useful. It is relatively simple to distinguish an explosion from an earthquake
event. The onset of the compression P-wave will have the same phase at all monitoring station if the
originating event was an explosion. The first event reaching the seismograph is a pressure crest. When
the originating event is an earthquake the onset of the P-wave may be a pressure trough.
Seismology is a useful tool in geophysical prospecting. Detection and analysis of seismic waves, deliberately
set-off with known properties, yields valuable information about the layers of the earth traversed by
the wave.
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