Before discussing the geochemical techniques applied in the exploration and exploitation of geothermal resources, it is convenient to recall few general concepts.  Geothermal energy is the natural heat of the earth, which is transferred towards the surface through conductive and convective processes. Because of these processes, the temperature within the earth crust generally increases with depth of ∼30 °C/km.

The phase discontinuity that occurs at the mineral-water interface greatly influences the geochemical cycles of many elements. The composition of natural waters and the flux of material through the hydrosphere are largely controlled by the weathering of minerals and the precipitation of new phases -- processes in which the mineral-water interface plays a fundamental role.

In the field of groundwater numerical flow modelling has become a standard tool for scientific and also for most of the practical problems. The modelling software has matured during the past 10 years from being user-unfriendly with complex interfaces to a powerful, easy-to-use, windows-based system. For porous media flow in the saturated zone, the basic principle pertinent to all common programmes like MODLFOW, FEFLOW etc. is the solution of the linear DARCY- and continuity-equations. The numerical problems associated with the limitations in discretisation known in earlier days are not a serious burden any more because of the high-speed PCs with hundreds of Mbytes memory available nowadays.

The disposal of low-level radioactive waste generated by the U.S. Department of Energy (DOE) during the Cold War era has historically involved shallow land burial in unconfined pits and trenches. The lack of physical or chemical barriers to impede waste migration has resulted in the formation of secondary contaminant sources where radionuclides have moved into the surrounding soil and bedrock, as well as groundwater and surface water sources.

Mills, C. F. Geochemical aspects of the aetiology of trace element related diseases
Plant, J. A., Baldock, J. W. & Smith, B. The role of geochemistry in environmental and epidemiological studies in developing countries: a review
Fordyce, F. M., Masara, D. & Appleton, J. D. Stream sediment, soil and forage chemistry as indicators of cattle mineral status in northeast Zimbabwe
Jumba, I. O., Suttle, N. F., Hunter, E. A. & Wandiga, S. O. Effects of botanical composition, soil origin and composition on mineral concentrations in dry season pastures in western Kenya
Maskall, J. & Thornton, I. The distribution of trace and major elements in Kenyan soil profiles and implications for wildlife nutrition

Colloid systems may be defined as systems containing at least two components: 1) a continuous dispersing medium and 2) a disperse phase. For many years the science of colloids was concerned mainly with the description of the behavior of very small particles. The classical definition of a colloid system described the disperse phase as being comprised of particles or macromolecules smaller than 1000 nm in diameter, but larger than 1 nm. Particles smaller than 1 nm do not exist as a discrete phase, and any system containing them cannot be considered as heterogeneous.

A huge amount of data has been accumulated in the field of high-pressure mineralogy to date (Agee 1998; Stachel 2001; Akaogi 2007; Irifune and Tsuchiya 2007; Kaminsky 2012; and others). Direct study of the substance of the Earth’s mantle using data on the minerals of mantle xenolith and inclusions in natural diamonds is significantly restricted. According to the geothermobarometric estimates, most of such minerals are formed at a depth of 150–200 km, i.e., their associations characterize the P–T conditions of the upper mantle (Sobolev 1977; Sobolev et al. 1997; Taylor and Anand 2004).

Let us start with a question here. Which figure in Fig. 1.1 is the most symmetric? Obviously, figure (c) in Fig. 1.1 has less symmetry than (a) and (b); however, it is difficult to compare symmetries of (a) and (b).
One of the basic tools for describing symmetries of crystal structures is space groups, which describe symmetry of atoms (vertices/points) in a crystal structure. For example, the symmetry of a regular hexagonal tiling of R2 is described by the group P6m, and the space group of the symmetry of a regular three-colored hexagonal tiling (see Fig. 1.2b) is P3m1. Similarly, the group P6m describes the symmetry of a regular hexagonal lattice.

The urge to make geology more quantitative has led to the widespread inclusion of chemistry, physics, and mathematics—the so-called "basic" sciences—among the required courses in undergraduate curricula. One can only applaud this practice, for certainly many of the new and exciting ideas in earth science have come from application of quantitative reasoning to geologic problems. It is reasonable to ask. however, if the mere requiring of courses in basic science is an efficient way to give most students facility in handling ideas quantitatively. For the few who take easily to mathematical symbolism, the answer would be "yes":