How personal degrees of belief can be represented numerically by using imaginary gambles.

How do you choose among possible acts? The most common decision rule is an obvious one. Perform the action with the highest expected value. There are, however, a few more paradoxes connected with this simple rule.

One of the most important natural resources is fresh water, essential for growing crops, for many industries, and of course for drinking and other personal uses; it is also the basis of many leisure activities, from fishing to water sports. In many parts of the world demand now rivals the natural supply of water, leading to a need for better understanding of aquifers, as well as for building dams and for more recycling. A separate problem is pollution, which has many causes, ranging from influx of saline water due to excessive extraction of fresh water, to contamination by sewage, agricultural and industrial chemicals, or leachate from landfill sites. Hydrogeology is concerned with these problems, and geophysics is an increasingly valuable aid.

In the 1960s the theories of continental drift and sea floor spreading (hitherto largely regarded with scepticism) fused to give birth to plate tectonics, the idea that the surface of the Earth consists of huge rigid pieces that move independently, with most tectonic and igneous activity taking place at their margins as a consequence of their relative movements. Plate tectonics provides a framework for much of geology, being relevant to topics as diverse as continent formation, orogenesis, earthquakes, volcanoes, past climates, and palaeontology. It has been particularly successful when applied to oceans and their margins, but less so at explaining tectonic processes within continents, where deformation extends far from the plate margins.

The success of plate tectonics posed further questions: How deep do plates extend, and what moves them? How does intracontinental tectonics relate to plate collisions? What causes the volcanism – sometimes very extensive – found far from plate margins? This has led enquiry deeper within the earth, particularly to convective flows within the mantle, and this larger framework can be termed global tectonics.

This chapter is mainly concerned with the basic concepts of plate tectonics, which were established largely by geophysical evidence, and geophysics, with its ability to investigate the deep Earth, continues to play a major part in extending our understanding of its processes.

Geophysical techniques employed: Many geophysical techniques have played a part, but seismology, seismicity, magnetics, palaeomagnetism, gravity, radiometric dating, and heat flow have had the major roles.

Many of the minerals of economic importance are ores of various metals, particularly sulphides. Traditionally, they have been discovered from their surface outcrops, but more recently geochemical surveys have been used to detect above-average concentrations of relevant elements in near-surface samples. However, as shallow deposits are extracted there is a need to explore to greater depths. Geophysical surveying potentially can be used because many ores have sufficiently different properties from their surroundings – particularly electrical and magnetic ones – to be detectable.

This chapter gives an outline of the different ways in which orebodies originate and the role of geophysics in exploring for them. Much of the chapter describes the exploration and evaluation of the Elura orebody in Australia, a massive sulphide body upon which many geophysical methods have been employed.

At intervals in the Earth's history there have been mass extinctions, when the number of species of animals and plants was drastically reduced in a time that was geologically short. There has been little agreement about their cause, with suggestions ranging from catastrophes to the cumulative effect of changes in factors such as temperature. It is accepted that abrupt and violent processes, such as meteorite impacts and great volcanic eruptions, do occur from time to time, but it is also being appreciated that the environment, particularly the climate, is less stable than had been thought, so that the cumulative effect of comparatively small, steady changes may have large and abrupt consequences. Therefore, an appreciation of the environmental effects of impacts and volcanism will increase our understanding of the processes at work in the world we inhabit today, as well as possibly accounting for some extinctions in the past.

This chapter examines some of the evidence that the K/T (end-of-Cretaceous) extinction was due to the impact of an extraterrestrial body that produced the Chicxulub structure, and looks briefly at the competing theory that volcanism was responsible.

Most electromagnetic (e-m) methods of surveying are used for targets similar to those of resistivity surveys, because both respond to variations in the resistivity (or conductivity) of the subsurface. The main difference is that e-m methods ‘induce’ current flows in the subsurface, usually without using electrodes. Many e-m methods can therefore be used in aerial as well as ground surveys.

E-m methods are particularly useful for ground surveys where the surface layer has a very high resistivity – such as dry sand or frozen ground – which prevents resistivity electrodes making electrical connection with more conductive layers below; conversely, a very conductive surface layer limits penetration more severely for e-m methods than it does for resistivity ones. A further limitation of e-m surveying is that generally it maps the subsurface less precisely than resistivity surveying. Smaller e-m instruments are quick to use on the ground because there are no electrodes and wires to set out.

Magnetotelluric, MT, surveying relies on naturally induced currents and can investigate down to tens, or even hundreds, of kilometres. Ground-penetrating radar, GPR, operates quite differently, by reflecting radar waves from subhorizontal interfaces, and so has similarities with seismic reflection, except that the discontinuities are of electrical rather than seismic properties. Like seismic reflection, it can provide high-resolution sections, but penetration is limited to a few metres, which limits its use to shallow targets, which include engineering, hydrogeological, and archaeological as well as some geological ones.