9.1: The Non-Uniform Distribution of Geothermal Heat Flux
- Page ID
- 85146
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The above example clearly shows that if the total geothermal power were evenly distributed over the Earth surface, there would be no chance of making a ny practical use of it. Fortunately, the geothermal power flux is not evenly distributed over the planets surface and there are areas where the flux density is orders of magnitude higher than the average value of 0.088 W/m2.
To explain what’s going on, for a moment we have to focus our attention on the Earth’s inner structure. With the current advanced drilling technol- ogy, we can probe directly the composition of the rocks to the depth of about 10 km below the Earth surface. But the Earth’s radius is 6371 kilometers. How can we get an insight into the areas at greater depths than 10 km? Well, there is something that can be used for “X-raying” those regions – namely, the seismic waves. Such waves are created by earthquakes. Not only those major catastrophic ones, but also by smaller ones which cannot be felt, but can be detected by instruments called seismographs (there are about 500,000 detectable earthquakes every year). The seismic waves can travel long distances, even across the globe. When passing from one layer to another with different properties, they exhibit the effects of refraction and reflection, in analogy to the known behavior of light. The branch of science focused on investigating the origin and the propagation of seismic waves is referred to as seismology . The foundations of modern instrumental seismology were laid 170 years ago by Robert Mallet. Systematic research on seismic waves continued since then have revealed a clear image of the inner structure of Earth. In short, it consists of several spherical “layers” of different properties, as shown in Fig. \(\PageIndex{1}\).

From the viewpoint of geothermal power, only the properties of the uppermost layer, the lithosphere, are important. The lithosphere is the rigid outermost shell of a planet (the crust and upper mantle, with a combined thickness up to about 100 kilometers.). It is not a uniform spherical shell – it is broken into a number of tectonic plates: there are six major of them, and a number of smaller ones. The most important fact is that the pattern of plates is not static, it’s dynamic. The relative motion of the plates is explained in closer detail in this Web site of the US Geological Service. The regions where there exist the most favorable conditions for harnessing geothermal energy are near the boundaries of the tectonic plates.

The boundaries may be divergent – meaning that the two plates tend to move away from one another. It would create a deep “cleft” between the two plates, reaching down to the upper mantle – yet, the pressure existing in the upper mantle pushes upwards the liquid and semi-liquid rocks it consists of (such mixture is called magma), so that the cleft gets filled

The best known example of such an divergent boundary is the Mid- Atlantic Ridge. The lower end of it is located below the southern tip of Africa, and it runs over the Atlantic Ocean bottom all the way up to the Arctic Ocean. Note that the shape of this boundary closely resembles the contour of the western coastal line of Africa and the contour of the eastern coastal line of South America, indicating that these two continent were once a single larger continent that separated and drifted away, while the magma emerging from the widening cleft gradually formed the entire bottom of the Atlantic in between. Today, Africa and South America still drift away with a rate of 2.5 cm/year. It’s a slow motion, but over a million years it corresponds to 25 kilometers – so, assuming that the drifting rate did not change in time, the creation of the entire part of Atlantic separating the two continents could take about one hundred million years. One more interesting feature of the cleft is that it runs below the island of Iceland. The inhabitants of the island benefit from the presence of a large number of geothermal spots. In Iceland, geothermal energy is used for generating nearly 30% of electric power, and for heating 85% of homes, as well as greenhouses, schools, and a variety of public institutions.

If the plates press on each other, the boundary is convergent. Sometimes one of the plates is the “winner”, the other “sinks” below it, or is subducted. The region where it happens is the subduction zone. One consequence of subduction is that much magma is pushed upwards and if it reaches the surface, it may create hot spot or even a volcano. In fact, most of the existing volcanoes are located close to tectonic plate boundaries. In particular, the boundary of the Pacific Plate is an especially efficient “volcano maker”, about 80% of all active volcanoes on Earth are located close to it, and therefore it is known as the “Ring of Fire”.
Divergent tectonic plate boundaries may also give rise to volcanic activity – as is the case, for example, at Iceland. Sometimes, however, a hot spot or volcano occur in the middle of a tectonic plate, far away from its boundary. Known example are the active volcanoes at Hawaii, or a number of volcanoes in Africa– by the way, the linked site makes it possible to go to a “global tour” and to visit most of the existing volcanoes on Earth, these close to the tectonic plate boundaries as well as those located pretty far from them.
