For the purposes of this study, we are only interested in surface waves.
P-Waves (primary waves) are a compressional wave, and travel by compressing and rarefacting the medium. This is very similar to the movement of a spring. Compressional waves can propagate through solids, liquids and gases because all three can sustain changes in density. They are called primary waves because they travel faster, they are the first waves to be recorded after the occurance of an earthquake.
S-Waves (secondary waves) are transverse or shear waves. This means that particles in the medium are pushed perpendicular to the direction of motion of the wave. S-waves only transmit through solids where particles have enough cohesion to be pulled (perpendicular tp the direction of travel) by one another. Click here for animation demonstrating the propagation of body waves. (Takes a while.)
The velocity of P-Waves therefore depends on the density and compressability of a medium (resistance to compression) wheras the velocity of S-Waves depends on the density and rigidity of a medium (resistance to distortion or shearing).
An approximation for the velocity of P-Waves is 6 - 14 km/s. The velocity of S- Waves, in contrast, is less than 6km/s. The arrival of these waves at various points on the Earth's surface are detected by a seismogram.
This is a typical reading of a seismogram over the period of a disturbance. Note the time lag betwwen the respnse to P-Waves and the response to S-Waves.
If we imagine the earth as a sphere of uniform density and elasticity, then we should get a pattern of body wave travel away from the focus, in straight lines: there would be no variations in speed across the globe. Seismogram readings at various points on the earth's surface would reveal that the waves had all travelled at the same velocity, and none had diverted in course. This is what would happen if the earth had the composition of a rubber ball.
However, it is not this simple. Seismic waves are reflected and refracted. Velocities of waves, as mentioned, change with density. The relationship between velocities at a discontinuity in density is shown by Snell's Law.
The shaded side of the line is more dense, the unshaded side is less dense. A wave can be seen to be refracting away from the normal on pasing into a less dense medium. Its velocity has increased. If the wave in the more dense medium has a velocity ,v1, and the wave in the less dense medium has a velocity, v2, the relationship between the two velocities is:
(sin theta 1/sin theta 2) = (v1/v2)
We would therefore expect the velocities of body waves to decrease with depth. This should be as a result of density increasing with depth. However, resistance to deformation (related to elastic modulus in wave velocity equation) also increases. The latter is infact more influential and the net result is that V increases with depth. The waves have curved paths because their velocities increase with depth. If this were the full story, we would have arcs of P-Wave paths going smoothly right through the earth. This is very similar to the pattern we would get on the moon, in the event of an earthquake there.
If we introduce into the Earth a core at the centre, then there would exist an S-Wave Shadow on the opposite side of the globe to the earthquake. The core 'shields' side of the globe from the S-Waves. S-Waves stop completely at this Core-Mantle Discontinuity. They cannot penetrate the core. The core must therefore be liquid (which the S-waves cannot propagate through) in contrast to the mantle which is solid. S-Waves instead are reflected back at various angles, depending on the angle of incidence with the core-mantle boundary. S-Waves can reach the S- Wave shadow zone, however, via a diverted circuitous reflective route around the globe. The angles at which they would intersect the crust would obviously be different, and there would be a considerable time lag, than if they had been able to propagate through the core.
There will, of course, be no P-Wave shadow behind the core. Indeed, the P-Waves are infact refracted again towards the the normal in this more dense, liquid core. Again, the waves have a curved path as they travel deeper into the core. There does exist, however, a P-Wave shadow in the region that the P-Wave would have propagated through, had it not been refracted into the mantle. This can be seen on the diagram below:
In 1936, Inge Lehman, a Danish seismologist suspected that there may exist an even deeper discontinuity, enclosing an inner core, suspected to be solid. Seismic records of underground H-bomb explosions later confirmed this. P-Waves are refracted away from the normal at this core-inner core boundary. Their paths are again curved as velocity increases further with depth.
The Structure of the Earth.
Sufficient data has been provided for calculations of velocity depth curves. These show large discontinuities in velocity at the Moho, the core-mantle boundary, and the core-inner core boundary.
The Mohorivicic (Moho) discontinuity is that aproximately between the crust and mantle, and occurs at a depth of approximately 30km. The core-mantle discontinuity is at around 2900km, and the inner core discontinuity is at around 5200km depth. Thse discontinuities define three concentric layers with differing properties, chemical and physical. The core constitutes around 19% of the earth's volume, the mantle around 80%, and the crust a mere 1%:
If there is an earthquale station within a few kilometres of the earthquake epicentre, and the earthquake originated in the crust, then the recorded waves would have travelled through crust only. This can help us to gain information about the thickness of the crust from place to place.
Many stations around the globe take data from eartquakes, eg. P and S wave velocities and the angle of their arrival at the station. We can combine this information to show us the structure of the earth. The use of seismic data is crucial in this field.
Sources of illustrations:
Seismogram- http://www.imsa.edu/edu/geophysics/geosphere/tectonics/seismogram.html
Wave refracion diagram- http://www.mikroprecision.com/futurnew/optics/Snells_Law.html
Earth cross sections- http://www.seismo.unr.edu/ftp/pub/louie/class/100/interior.html
Bibliography:
Skinner and Porter-The Dynamic Earth
Holmes' Principles of Physical Geology
McAlester-The Earth
Jon Blundy's lecture notes.
John Howells 1997.
email-jh6550@bris.ac.uk