Seismology

From Geophysics 300

The seismology wiki

1 History
- 1.1 Ancient History
- 1.2 Modern History
2 Theory
- 2.1 Seismic Waves
  - 2.1.1 Body waves
    - 2.1.1.1 P-waves
    - 2.1.1.2 S-waves
  - 2.1.2 Surface waves
    - 2.1.2.1 Rayleigh waves
    - 2.1.2.2 Love waves
3 Application
4 References
5 Authors

History

Seismology - the word comes from the Greek, seismos, for earthquake. The Dictionary of Geological Terms defines Seismology as "The study of earthquakes, and of the structure of the earth, by both natural and artificially generated seismic waves." (18)

Ancient History

Earliest humans depended on stories which modern scholars term myths, to explain the natural phenomena of earthquakes. The Judeo-Christian Bible contains stories (Joshua and the fall of Jericho, Sodom & Gomorrah) which modern theologians feel reflect actual earthquake events. (1) (2)

Ancient Greek philosophers such as Aristotle came up with explanations that earthquakes resulted from the escape of air trapped within the Earth. (3) Early Greek philosphers had abandoned the mythological explanation in favor of natural causes of earthquakes inside the earth. (4)

The earliest instrument known to us that was made to respond to earthquake ground motion is the seismoscope, invented in 132 A.D. by the Chinese scholar Chang Heng. (4) The instrument (Fig 1)

Figure 1: Chinese seismoscope Source:Seismoscope

used a finely balanced ball to show the direction of ground motion when the ball fell into one of 4 cups.

Modern History

Japanese monks have been recording earthquakes in their country for the last 1000 years. (5) In early 1700, they detected a Tsunami which they recorded but did not have any other evidence to locate the related earthquake. Researchers in Washington State had found evidence in the 1970's of a large Tsunami which hit the Northwest coast around 1600 - 1700. When this information was put together, it was determined that a large Tsunami hit Washington State on January 26, 1700. The earthquake which caused the Tsunami was on the Juan de Fuca plate, just west of the State of Washington. (6)

In 1750 a series of five strong earthquakes occurred in England. When another cataclysmic shock and tsunami occurred in Lisbon, Portugal on Sunday, November 1 of 1755, "numerous studies into the effects, locations, and timing of earthquakes" began, marking "the beginning of the modern era of :seismology".(19)

The Lisbon, Portugal earthquake of 1755 is considered the "trigger" which shifted the field of :Seismology from mythological explanations in favor of natural causes of earthquakes inside the earth begun by the ancient Greeks. The Ben-Menahem article in the Bulletin of the Seismological Society of America (4) covers "a succinct description of the landmarks (alias signposts; alias milestones) in the evolution of earthquake lore."

Figure 2: Lisbon, Portugal earthquake, 1755 Source: History of seimology

Some high points covered by Ben-Menahem (4) are below:

- "The Rev John Michell (1761) professor of geology at Cambridge,...firmly established that earthquakes were waves set up by the shifting masses of rock miles below the surface...the motion of the earth in earthquakes is partly tremulous and partly propagated by waves which succeed each other".

- The foundation of instrumental seismology was laid by Robert Mallet (1810 to 1881, Ireland). He suggested "setting up a network of observatories over the Earth's surface. He published the first world seismicity map and made the first systematic attempt to apply physical principles to earthquake effects (1862). Mallet made estimates of the epicentral depth and also carried out a number of experiments to determine the velocity of earth waves by setting off charges of explosives in different soils and by measuring the results on bowls of mercury set at varying distances up to 800 m away."

- "The first useful seismograph system, recording ground displacements, was constructed in Japan in 1880 by John Milne...(but) could record only local earthquakes."

- "...by 1894 Milne was able to design, construct, and test...(a model) capable of detecting earthquake waves that had traveled many thousands of kilometers from their origin....From this time onward, precise instrumental data on earthquakes began to accumulate, and seismology has developed from the qualitative toward the quantitative side."

- "The existence of the Earth's core was established by Richard Dixon Oldham (1857 to 1936, India and England) in 1906, from observations of earthquake waves."

- "In 1909, Andrija Mohorovicic (1857 to 1936, Zagreb) discovered a sharp material discontinuity at some level below the Earth's surface (known today as the moho), which could explain the travel times of seismic rays from a local earthquake." A number of people continued to work on "fine tuning" the differences between layers of the earth as well as identifying the specific types of waves (Rayleigh, Love).

_ "Following the catastrophic San Francisco earthquake of 18 April 1906, Harry Fielding Reid (1859 to 1944, U.S.A.) advanced his elastic rebound theory (1911): that earthquakes are associated with large fractures, or faults, in the Earth's crust and upper mantle. As the rock is strained, elastic energy is stored in the same way that it is stored in a wound-up watch spring."

- "Apart from the obvious goal of imaging the Earth's interior, which is now proceeding with great vigor, the prediction of earthquakes is the most important target of contemporary seismology."

After World War II, Hugo Benioff described the distribution of deep earthquakes on steeply dipping surfaces of seismicity. In 1954 he proposed as an explanation of the phenomenon that the ocean floor was being "subducted" underneath the adjacent land. (20) This, as well as other evidence set the stage for the plate tectonic theory proposed in the 1970's.

In 1959, a very modern looking diagram was published which showed the distribution of earthquakes at varying depths up to 400 miles below the Andes mountains. The distribution slopes inland along a path we today, would interpret as a descending plate. The specific information used in any publication regarding Plate Tectonics was all there but few people were voicing such a radical idea. In 1964, the author of an Introduction to Geology textbook stated: "This curious linear distribution of deep earthquake foci along the surface of what appears to be a dipping plane has suggested to some geologists that these may represent points of failure where strains have built up along fractures akin to thrust faults inclined inland away from the Pacific basin." (7) This is about as close as this author gets to suggesting a Continental Drift theory - which is otherwise never mentioned in this book. Plate Tectonics was yet to became a mainstream concept.

Theory

The linear portion of the graph is where Hooke's law applies.

Waveforms for the Sumatra Earthquake gathered from seismographs around the world. Seismic waves travel at different velocity so the seismograms from different stations show the Dispersion of the arrival times of each wave.

Seismology is the study of earthquakes and seismic waves. Seismic waves are waves of energy that travel through the earth due to the breaking of rock or an explosion among other things. These seismic waves are propagated in a harmonic motion because of the elastic behavior of the materials in the Earth.

Hooke's Law

law of elasticity discovered by the English scientist Robert Hooke in 1660, which states that, for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load. Under these conditions the object returns to its original shape and size upon removal of the load. Elastic behaviour of solids according to Hooke’s law can be explained by the fact that small displacements of their constituent molecules, atoms, or ions from normal positions is also proportional to the force that causes the displacement.Mathematically, Hooke’s law states that the applied force F equals a constant k times the displacement or change in length x, or F = kx. The value of k depends not only on the kind of elastic material under consideration but also on its dimensions and shape.(15)

Hooke’s law may also be expressed in terms of stress(σ) and strain(ε). Stress is the force on unit areas within a material that develops as a result of the externally applied force. Strain is the relative deformation produced by stress. For relatively small stresses, stress is proportional to strain.(15)

$\sigma\propto\epsilon\,\!$

Stress(σ) $\propto$ Strain(ε)

As the stress on a rock increases the Strain increases linearly according to Hooke's law, this is in the elastic range. As the force increases, evientually the rock reaches the failure point. This is the point when the rock breaks, causing an Earthquake. The energy of the earthquke is transmitted through seismic waves.

Seismic Waves

$Snell's Law for refraction$

Snell's Law for refraction $\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}$

Seismic waves travel in a harmonic motion that can be described using the wave equation:

$\frac{\partial^2 u}{\partial t^2}=c^2\frac{\partial^2 u}{\partial x^2}$

u = displacement

x = distance

t = time

c = velocity

There are two main types of seismic waves: Body waves and Surface waves. Body waves propagate through the Earth's interior while surface waves travel along the Earth's surface. Seismic waves are measured using a seismograph. The data from an ever increasing network of seismographs around the world has dramatically increased our understanding of earthquakes and the Earth.

Using the data collected from seismograms, many different types of interations between the seismic waves and the matereials in the earth are observed, incliuding:Refraction,Reflection, Disperion,Diffraction, and Attenuation.(12)

When a wave encounters a change in material properties (seismic velocities and or density) its energy is split into reflected and refracted waves.(12) With this data, it was determined that the outer-core is liquid.

Body waves

There are two types of body waves:P-waves or pressure waves and S-waves or shear waves.

P-waves

P-waves are compressional waves in which the particle motion is in the same direction as the wave proagation. P waves can move through solid rock and fluids, like water or the liquid layers of the earth. It pushes and pulls the rock it moves through just like sound waves push and pull the air.

(8)

Click here for animation (10)

In the Earth, P waves travel at speeds from about 6 km (3.7 miles) per second in surface rock to about 10.4 km (6.5 miles) per second near the Earth's core, some 2,900 km (1,800 miles) below the surface.(9)

S-waves

An S wave is slower than a P wave and can only move through solid rock, not through any liquid medium. It is this property of S waves that led seismologists to conclude that the Earth's outer core is a liquid. S waves move rock particles up and down, or side-to-side--perpindicular to the direction that the wave is traveling in (the direction of wave propagation).(11)

(8)

Click here for animation (10)

Typical S-wave propagation speeds are on the order of 1 to 8 km/sec. The lower value corresponds to the wave speed in loose, unconsolidated sediment, the higher value is near the base of Earth's mantle.(12)

Surface waves

There are two types of Surface waves: Rayleigh waves and Love waves

Rayleigh waves

Raleigh surface waves have both longitudinal and transverse motion. The particles in a solid, through which a Rayleigh surface wave passes, move in elliptical paths, with the major axis of the ellipse perpendicular to the surface of the solid. As the depth into the solid increases the "width" of the elliptical path decreases. Rayleigh waves are different from water waves in one important way. In a water wave all particles travel in clockwise circles. However, in a Rayleigh surface wave, particles at the surface trace out a counter-clockwise ellipse, while particles at a depth of more than 1/5th of a wavelength trace out clockwise ellispes. The movie below shows a Rayleigh wave travelling from left to right along the surface of a solid. Two particles have been identified in blue to illustrate the counterclockwise-clockwise motion as a function of depth.(13)

(13)

Rayleigh waves travel about 2.0 - 4.2 km/s in the Earth depending on frequency of the propagating wave, and therefore the depth of penetration of the waves.(10)

Love waves

Love waves exist because of the Earth’s surface. They are largest at the surface and decrease in amplitude with depth. Love waves are dispersive, that is, the wave velocity is dependent on frequency, generally with low frequencies propagating at higher velocity. Depth of penetration of the Love waves is also dependent on frequency, with lower frequencies penetrating to greater depth.(10) Love waves are named for A.E. H. Love, a British mathematician who worked out the mathematical model for this type of wave in 1911. Love waves move like a snake, shaking the ground from side to side. Although they travel slowly from the seismic source, they are very destructive. It is these waves that are most often responsible for causing buildings to collapse during an earthquake.(14)

(14)

Click here for animation (10)

The Love wave travels about 2.0 - 4.4 km/s in the Earth depending on frequency of the propagating wave, and therefore the depth of penetration of the waves. In general, the Love waves travel slightly faster than the Rayleigh waves.(10)

Application

References

1. "The Interpreter's Bible", Vol. 2, Abingdon press, c. 1981, p. 582.
2. Achlemeier, Paul J., Gen. Editor, "Harper's Bible Dictionary" Harper & Row, c. 1985, p. 232.
3. Putnam, William C., "Geology", Oxford Press, c. 1964, p. 217.
4. Ben-Menahem, Ari, "A Conscise History of Mainstream Seismology: Origins, Legacy, and Perspectives, Bulletin of the Seismological Society of America", Vol 85, No. 4, pp. 1202-1225. (p. 1204)

<cobweb.ecn.purdue.edu/~ce597m/Handouts/ConciseHistory_BenMenahem.pdf

5. Satake, K., "Times and size of a giant earthquake in Cascadia inferred from Japanese tsunami records of January, 1700", Nature, v. 379, p. 246-249.
6. Trehu, Anne M., "Probable low-angle thrust earthquakes on the Juan de Fuca-North America plate boundary", Geology, February 2008, v. 36, no. 2, p. 127.
7. Putnam, p. 223.
Fig 1 - About.com. "Strange Seismometers." http://geology.about.com/library/weekly/aa070598.htm. Accessed in May, 2008.
Fig 2 - Myweb.facstaff.wwu.edu/caplanj/pdg/GEO417/history/pdf. Accessed in May, 2008.
8. Louie, John N.. "Seismic Deformation." About Earthqukes. 07 Oct 1996. Nevada Seismological Laboritory. 7 May 2008

<http://www.seismo.unr.edu/ftp/pub/louie/class/100/seismic-waves.html>.

9. "P wave: The P wave." Online Animation. Encyclopædia Britannica Online. 7 May 2008 <http://www.britannica.com/eb/art-76034>.
10. Braile, L.. "Seismic Wave Demonstrations and Animations." Earth and Atmospheric Sciences. Dec 2005. Purdue University. 7 May 2008

<http://web.ics.purdue.edu/~braile/edumod/waves/WaveDemo.htm>.

11. "What Is Seismology?." UPSeis. 2007. MichiganTech. 7 May 2008 <http://www.geo.mtu.edu/UPSeis/waves.html>.
12. http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/waves_and_interior.html
13. Russell, Dr. Dan. "Longitudinal and Transverse Wave Motion." Acoustics Animations. 2001. Kettering University Applied Physics . 7 May 2008

<http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html>.

14. http://www.seed.slb.com/en/scictr/watch/seismology/waves.htm
15. "Hooke’s law." Encyclopædia Britannica. 2008. Encyclopædia Britannica Online. 07 May. 2008

<http://www.britannica.com/EBchecked/topic/271336/Hookes-law>.