Physical Properties of the Earth

The Earth is an oblate spheroid, being slightly flattened at the
poles:

Equatorial radius = 6378 km Polar radius = 6357 km

These measurements are calculated on the assumption that the Earth's surface is smooth, but this is only an approximation since it disregards mountains and ocean depths. However, the difference between the height of Mount Everest and the depth of the Marianas trench is only about 20 km. Most land is concentrated in seven continents each fringed by shallow seas (flooded continent). Separating these are a number of major oceans including the Pacific, Atlantic and the Indian oceans.

It was Cavendish in 1798 who first calculated the mass of the Earth as 5.977 x 1024kg, and since its volume is known (from 4/3 ∏ r^3 where r is the radius of the Earth), then it can be calculated that the average density is 5.516 g/cm3. However, most rocks exposed at the surface have densities of less than 3g/cc, for example:

sandstone: 1.9 - 2.4 g/cm3
limestone: 1.9 - 2.7 g/cm3
granite: 2.6 - 2.7 g/cm3
basalt: 2.8 - 3.0 g/cm3 

Therefore, a material of greater density must exist at deeper levels within the Earth. The Earth has a series of layers or "shells", but only the outer few km of the Earth can be directly observed; the upper crust, and the deepest boreholes which reach to only about 12.5 kms. Earthquakes provide the key to the structure at depth.

Earthquakes

Stresses which develop in the Earth may become great enough to break the rocks, and cause slip along the resulting in fractures (faults). Although the slip distance in a given earthquake may be small (cm to metres), the rock masses involved are large and so the energy released is great. The resulting shock waves, or earthquakes, may cause great damage; greatest near the centre or focus, and less further away. The epicentre is the point on the surface of the Earth vertically above the focus.

Detection of seismic waves.
Earthquake energy is transmitted by several types of waves. Two types will be described:

P waves (primary or compressional) are transmitted by vibrations oscillating in the direction of propagation (push/pull).

S waves (secondary or shear), which vibrate at right angles to the direction of propagation. S waves cannot be transmitted through liquids because liquids have no elastic strength.

Recording Earthquakes

The arrival of earthquake waves is recorded by a seismograph. A mass is loosely coupled to the Earth by a spring. A chart is firmly coupled to the Earth. A pen linking them traces the difference in motion between the mass and the Earth's surface. The arrival of waves from a distant earthquake is recorded as a seismogram on the rotating drum.

Consider what happens to P and S waves as they travel through the Earth.

The most important property of seismic waves is their speed of propagation. The velocity is governed by the physical properties (density, compressibility, rigidity) of the medium through which the wave is travelling.

Earlier in this lecture, it was deduced that the density of the Earth increases with depth. The wave propagation velocity must therefore change with depth, and this causes the wave to refract.

Refraction

If a wave travelling through a medium with a fixed density encounters a new medium with a different density, the wave will change its direction. This "bending" of the wave is called refraction.

Data from seismometers located around the world can record waves from any given earthquake. The differences between recordings at different seismometers reveal properties of the sub-surface and hence the internal structure of the Earth.

For example, it has been discovered that the mantle is solid rock, but the outer core is a liquid. This was discovered, because for any given earthquake:-

1. Both P and S waves are recorded by seismometers at distances of up to 103o from the epicentre.

2. At distances greater than 103o, no S waves are recorded. This means that S waves that would have reappeared at > 103o have not propagated. The material at depths travelled by such waves must be liquid and be unable to transmit S waves.

Also, it has been discovered that the outer core must have a lower P wave velocity than the mantle. This is because at distances of 103o to 142o, no strong P waves are recorded. The liquid outer core has a lower P wave velocity, causing the P waves to be refracted to a steeper angle, so they cannot re-emerge between 103o to 142o. They actually re-emerge at angles > 186o. There is one small caveat to this observation. The inner core appears to be solid because some weak P wave arrivals occur between 103o to 142o. This is thought to be due to a slight increase in P wave velocity as waves enter the inner core, causing them to be refracted to a shallower angle, to re-emerge between 103o to 142o. If the inner core is solid, S waves could propa- gate there. The graph shows some calculations of what expected S wave velocities would be, but the inner core structure is still a source of controversy.

The MOHO

In the early 20th century a Yugoslavian seismologist by the name of Mohorovicic was studying seismograms from shallow focus earthquakes (< 40 km) that were nearby <800km. He noticed that there were 2 distinct sets of P waves and S waves involved. He interpreted these waves as a direct set and a refracted set. In the refracted set, waves travel down and are refracted at a boundary by a medium of higher velocity.

This boundary separates the crust with VP of 6-7km/sec from the upper mantle where VP starts at 8km/sec. It is called the Mohorovicic discontinuity but is commonly known as the MOHO.

Today, seismologists use artificial explosions to determine the structure beneath the surface and it is from these data that the depth of the MOHO can be calculated and thus the thickness of the crust. The MOHO is at 5-15 km under ocean crust and 35 km beneath normal thickness continental crust. The MOHO can be as much as 70 km deep beneath mountain belts where converging plates have caused an orogeny or mountain building event.

The Structure of the Earth

Recent advances in seismology now allow tomographic images of the interior of the Earth to be produced from P and S wave velocity data. Just as tomographic images of the interior of human bodies are produced by density contrasts in human tissue and bone subject to wave propagation, density contrasts in the Earth can be mapped by combining wave velocity data from large numbers of earthquakes.

The basic idea is that where solid mantle is relatively hot, the P and S wave velocities should be anomalously low because the heat will result in a density decrease. One should be able to image hot, ascending plumes of mantle asthenosphere by looking for areas of anomalously low seismic velocity. Conversely, where solid mantle is relatively cool, the P and S wave velocities should be anomalously fast because the lack of heat will result in a relatively high density.

One should be able to image cool, descending slabs of mantle lithosphere by looking for areas of anomalously high seismic velocity. Such images allow us to study subduction zones and constrain how deep the slabs penetrate. It appears that some slabs do not penetrate beneath 670 km whereas others continue down to the core-mantle boundary. This is an area of controversy in geology.