Physics and Chemistry of the Earth. Elastic waves

The geologist is trained to observe and describe the rocks, minerals and fossils of a particular area, quarry, mine or borehole. The geochemist and geophysicist can take a more experimental approach to the study of the Earth in keeping with the scientific nature of their parent disciplines of physics and chemistry. They can propose hypotheses or models, and test them against available data, or devise new techniques for collecting data.

Physicists and chemists had earlier made occasional interjections into geological debate, sometimes with later contradictory results, such as the 'proof (by Kelvin) of the 100 Ma age of the Earth, and (by Jeffreys) of the impossibility of continental drift. Without the assistance of geophysics and geochemistry, it would be impossible to answer the questions such as 'what is the Earth made of, and 'how does it work?' Conversely, physicists and chemists willing to turn their attention from the workbench to the larger laboratory of the Earth itself have found data to interpret and problems to solve on the grand scale.

Geophysics and geochemistry are by no means separate disciplines of the Earth sciences: indeed they are closely interdependent. The seismologist cannot interpret the passage of earthquake waves through the Earth without some knowledge of its possible range of chemical compositions, and the geochemist studying the derivation of the rocks of the crust from those of the mantle needs an appreciation of the physical phenomena of heat flow and convection. The vast bulk of the Earth is completely inaccessible to the geologist with his hammer and microscope, and only the measurement of physical variables and the study of extraterrestrial chemistry can answer some of the most fundamental questions about our planet.

Seismology and the deep structure of the Earth. Seismology is the study of earthquakes. Earthquakes can cause severe damage to buildings and loss of life, although many of the largest earthquakes occur under the oceans or in uninhabited parts of the Earth with little ill effect on human beings. On the other hand some quite small earthquakes cause heavy casualties and widespread destruction because they occur near the surface beneath cities whose buildings have not been designed to withstand the shaking of the Earth.

Considerable effort has gone into earthquake prediction and even earthquake control—so far without too much success. More positively, observations of the records of elastic waves generated by earthquakes or man-made explosions have provided the main source of our information about the Earth's deep interior. Moreover the pattern of earthquakes observed on the Earth's surface has played a major part in the development of the concept of plate tectonics—earth- quake belts marking plate boundaries.

Elastic waves. The Earth is continually undergoing deformation due to stresses that are set up within it. If the stresses continue to build up over a long time fracture may take place, resulting in an earthquake. This involves a sudden release of energy, part of which takes the form of elastic waves which travel through the Earth. These waves emanate from a confined region below the surface, called the focus. The point on the surface of the Earth vertically above the focus is called the epicentre.

There are three basic types of elastic wave: two body waves, ie waves that propagate within a body of rock, and surface waves, ie waves whose motion is restricted to near the surface, their amplitude decreasing with depth (Figure 3.1). The faster of the body waves is called the primary, or P. wave. It is a longitudinal wave, ie as it spreads out it alternately pushes (compresses) and pulls (dilates) the rock. P waves, in common with sound waves, can travel through both solid rock and liquid material, such as vulcanic magma or the water of the oceans. The slower body wave is called the secondary, or S. wave, and as it propagates it shears the rock sideways, at right angles to (Indirection of travel. P waves involve change of volume, whereas S waves involve distortion without change of volume. S waves, in common with light waves, are transverse and so are polarized, Vertical (SV) polarization is distinguished from horizontal (SH) polarization.

3.1 : The form of ground motion near the surface of the Earth for four types of earthquake waves: P wave. S wave. Love wave and Rayleigh wave. The motion of Love waves is essentially the same as that of S waves with no vertical displacement. The ground moves from side to side in a horizontal plane parallel to the Earth's surface at right angles to the direction of propagation. Rayleigh waves are like rolling ocean waves, the material disturbed by the wave moving both vertically and horizontally in a vertical plane in the direction in which the waves are travelling

It can be shown that the velocity of P waves is given by:

where p is the density, k the adiabatic incompressibility and µ the rigidity. Both P and S wave velocities depend only on the elastic constants and the density of the medium. In particular, if the rigidity is zero. V_s is zero: ie shear waves cannot be transmitted through a material of zero rigidity, such as the oceans.

If a stone is thrown into a pond, or a strong wind blows across an open stretch of water, the surface of the water is agitated and waves that travel away from the source of disturbance are set up. Such waves are called surface waves and are controlled by gravity. They can also occur in a solid, when they are controlled by elasticity. There are two types of surface waves in solids: Love waves and Rayleigh waves.

Rayleigh waves can be generated oh a uniform solid, whereas Love waves are possible only if the material is non-uniform. Love waves require a surface layer in which the velocity of S waves is less than that below. The velocity of Love waves also depends on the ratio of the wavelength to the thickness of the layer, so that unlike P and S waves Love waves show dispersion. If the velocity is found by observation for a number of wavelengths it is possible to determine the thickness of the layer.

Surface waves travel more slowly than body waves and of the two surface waves. Love waves generally travel faster than Rayleigh waves. Thus as the waves spread out into the Earth's crust from the earthquake source the different types separate out from one another in a predictable pattern (see Figure 3.5).

3.5: Travel time curves for P, S and surface waves. To locate an earthquake epicentre, the time interval observed at a given station is matched against the travel time curves for P and S waves until the distance is found at which the separation between the curves agrees with the observed S-P time difference. If the distance from three stations A. B and C is known, the epicentre can be located

When an elastic wave meets a sharp boundary between two media of different properties part of it will be reflected and part refracted, and laws of reflection and refraction apply, rather like those for light waves. The case of elastic waves, however, is more complicated since waxes of both P and S type may be reflected and refracted. The theory is based on Fermat's principle, according to which an elastic wave takes the quickest path between any two points. This does not imply that there is only one path. There may be a number of alternative paths, but each must involve a minimum transit time.

The basic principle of refraction in optics is Snell's law. which is equally applicable to seismic waves; the angles of reflection and refraction are related to the angle of incidence by the wave velocities V_p and V_s of P and S waves ill the two media. There are two major discontinuities in the Barth, one just below the surface, separating the crust from the mantle, and the other at a depth of about 2900 km. separating the mantle from the core. The core may also be divided into an inner core and an outer core. All these discontinuities may variously reflect or retract seismic waves, leading to a great variety of potential pathways (figure 3.2).

3.2: Some of the many possible reflections and refractions of elastic waves at discontinuities within the Earth, P and S waves reaching the surface directly without refraction are labelled p and s. A P wave re/let ted from the Earth's surface gives rise to both a P Wave and an S wave ((idled PP and PS waves, respectively).

Likewise an s wave reflected from the surface can give both P and S waves (called SP and SS waves respectively). The letters c and i denote reflections from the onto and inner core boundaries respectively, and K and 1 are P waves that have come through the outer and inner core. Thus ScS is an S wave that has travelled down to the core boundary and been reflected as an S wave. Similarly SKP is an S wave that has been refracted into the outer core (necessarily us a P Wave) and refracted back into the mantle as a P wave.