GEOPHYSICS AND GEOCHEMISTRY – Vol.

I - Terrestrial Heat Flow - Vladimir Cermak

TERRESTRIAL HEAT FLOW

Vladimir Cermak
Geophysical Institute, Czech Academy of Sciences, Prague, Czech Republic

Keywords:Heatflow,thermalconductivity,heatproduction,radioactivity,Earth’s structure,
lithosphere temperatures, subsurface record of climate change

Contents

1. Introduction
2. History
3. Heat Flow
3.1 Thermal conductivity
3.2 Heat Production

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4. Measurements of Heat Flow

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5. Geothermal Maps
6. Heat Flow—Age Relationships
7. Heat Flow and Heat Generation
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8. Global Heat Flow Representation
9. Mantle Heat Flow
10. Lithosphere Temperatures
11. Geothermics and Deep Drilling
12. Borehole and Climate
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Glossary
Bibliography
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Biographical Sketch
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Summary

Practically any geophysical phenomenon is connected in some way to the thermal

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physics of Earth. The principal method used to study the subsurface temperature field is
to measure heat flow on the Earth’s surface.
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This paper briefly reviews the relatively young history of geothermal research, and
describes the major milestones from the first heat flow measurements, techniques to
measure heat flow on land and on the sea bottom, and laboratory determinations of the
thermal properties of rock material.

Heat flow data can be related to the tectonothermal evolution, and to the distribution of
radiogenic heat sources. Heat flow maps and regional heat flow patterns are not only
useful in regional and global studies, but also can serve in many applied aspects of
hydrogeology, in surveys for geothermal energy, and in a number of problems of
engineering geology.

One quite modern application of precise temperature logging is the possibility of

inverting the present-day temperature-versus-depth profiles into the ground surface
temperature history, and to interpret this in terms of the paleoclimate reconstruction.

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GEOPHYSICS AND GEOCHEMISTRY – Vol.I - Terrestrial Heat Flow - Vladimir Cermak

1. Introduction

The study of the thermal structure of Earth, generally referred to as geothermics, has a
long history, even though modern geothermics, one of the fundamental geophysical
disciplines, is relatively young. Geothermics is closely related to a number of other
geological, hydrological, and geochemical disciplines, and in its practical applications
heat flow studies are related to the search for and use of geothermal energy.

Most of our knowledge of contemporary geothermics was formulated only in the last
third of the twentieth century. The basic ideas of the thermal structure and thermal
history of Earth, based on measurements of borehole temperatures on land and
measurements of heat flow through the ocean floor, together with determinations of the
thermal properties of rock material, were enabled by the rapid development of
measurement techniques in the 1960s. Geothermal modeling, the assessment of the deep
lithosphere temperature, and evaluations of the thermal regimes of geological processes

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on local, regional, and global scales were made possible by the recent massive

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advancement of computer techniques.

2. History
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The idea of enormous amounts heat coming from the deep subsurface has a long
history, closely related to the ancient occurrence of volcanic eruptions accompanied
with hot lava outflow. Ancient Greeks thought of the underground as an imagined abode
of gods and the souls of the dead. Many other religions, including Christianity, further
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adopted this conception. The extreme temperatures coincided with the hell-fires
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destined to punish the deadly sins. More serious ideas of the general increase of
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temperature with depth would only be discovered when deeper mines were dug much
later, in medieval times.
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It took, however, several more centuries before a modern scientific approach really
started. In 1867, the British Association for the Advancement of Science formed a
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committee “.. to investigate the rate of increase of underground temperature in various

locations of dry land and under water.” Multiplying the temperature gradient and the
mean thermal conductivity of rocks, the first value of the heat flow density was
estimated to be 1.3 x 10-6 cal cm-2 sec-1, that is, approximately 54 m W m-2 in SI units.
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This value is in surprisingly good agreement with the present observations.

At the time, the data acquired by the Commission of the British Association represented
stupendous progress, but their further interpretation produced an enigma. If an observed
temperature gradient of about 30 mK m-1 is to continue downwards, high temperatures
sufficient to melt rocks must exist at relatively shallow depth, a fact that clearly
contradicted the geological evidence. The solution of the dilemma came only later, with
the discovery of radioactivity. It was pointed out that heat is generated within rocks by
the decay of radiogenic elements present in small quantities in the earth material. It had
to be proved that crustal rocks are more radioactive than rocks forming Earth’s interior,
and that the heat production sharply decreases with depth. Solving the thermal history of
Earth played a central role in the development of geophysics for almost fifty years since
then.

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GEOPHYSICS AND GEOCHEMISTRY – Vol.I - Terrestrial Heat Flow - Vladimir Cermak

All models somehow reflected the cosmogenic origin of Earth, either:

• the primitive Earth originating from a filament of hot gaseous material drawn out of
the Sun, and later cooling down from the originally fluid state (see Solar System); or
• the early Earth, heated up from the originally cold body due to excess heat that
could not be conducted away, because of the relatively low thermal conductivity of
the crustal rocks.

The deeper layers become molten and structurally unstable, and a large movement of
the material occurs, carrying the excess heat to the surface. It was suggested that this
convection is the “engine" of geological evolution, producing metamorphism and
periodic tectonic change. A long time scale associated with the diffusion of heat within
the earth, and the enormous thermal inertia of the earth, were common to all these ideas.

The very first assessment of the heat flow density was done in the 1980s, but it was

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about 50 years before that when the first practical heat flow measurements really

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started. The first heat flow data measured in boreholes were reported from Great Britain
in the late 1930s, and similar studies were initiated in the USA and in Canada a decade
later. The first heat flow data measured in the Atlantic Ocean came in the 1950s, when
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Sir Edward Bullard pioneered marine investigations. The international geophysical
community soon realized that knowledge of the heat flow provides a useful tool for
studying crustal structure, and helps to understand Earth’s evolution.

The year 1963 represented an important milestone in the development of the

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international cooperation in geothermal research. At the thirteenth General Assembly of

the International Union of Geodesy and Geophysics at Berkeley, the International Heat
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Flow Committee (later Commission, IHFC) was formed under the chairmanship of
Francis Birch.
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New data on heat flow density then accumulated quickly, and in 1964, about 2000
individual heat flow values from all over the world were available. Such remarkable
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progress in a relatively short time allowed us to draw the first basic conclusions:

(a) It was proved that regional heat flow variations greater than 8 m W m-2 were
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significant.
(b) Spherical harmonic analysis revealed a representative global mean value of 62 m W
m-2, with little difference between land and sea. If heat flow observed on the surface
is produced by radioactivity within the earth, this equality suggests compositional
differences between the upper mantle under the continents and that under the
oceans. However, later, more numerous measurements increased the value of the
global mean, and showed that the characteristic marine heat flow is 20 % to 30 %
higher than on continents.
(c) Heat flow values could have been well correlated with major geological features; on
land, heat flow is higher and more variable in tectonically younger and active
geological units; at sea heat flow increases from trenches to ocean basins, and is
very high on ocean ridges.

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GEOPHYSICS AND GEOCHEMISTRY – Vol.I - Terrestrial Heat Flow - Vladimir Cermak

For borehole temperature logging, a high precision (thermistor-type) thermoprobe was

introduced. For laboratory thermal conductivity determinations of rock samples, a
steady-state “divide-bar" apparatus was proposed. For unconsolidated rock samples, and
especially for the ocean bottom sediments, a transient “needle-probe" device was
constructed.
The real boom for geothermal research was in the 1970s. It was generally understood
that the outflow of heat from Earth’s interior by conduction is, energy-wise, the most
impressive terrestrial phenomena. Knowledge of the heat flow was indispensable for
any extrapolation of the near surface temperature data to greater depth. As almost all
physical properties of rocks are temperature and pressure dependent, and most
geological processes need their energy, the new heat flow measurements accumulated
quickly. The oil crisis, and the sharply increasing prices of oil, initiated an
unprecedented interest in all practical solutions to harness geothermal energy.

3. Heat Flow

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Heat transfer occurs from points at higher temperature to points at lower temperature in
three distinct ways: conduction, convection, and radiation. In fluids, convection and
radiation are of great importance, but in solids, convection is usually absent and
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radiation is negligible at ordinary temperature. Almost all Earth’s lithosphere is solid
and at a rather low temperature, so the heat flow near the surface is essentially by
conduction. Deeper in the earth, convection and radiation may be more important
because of the higher temperature and the probably non-solid behavior of Earth’s
interior. Since the temperature increases downwards, heat is flowing from Earth’s
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interior to the surface.

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As already stated, the outflow of heat from Earth’s interior by conduction (heat flow),
is, energy wise, the most impressive terrestrial phenomena. Its present rate of about 40
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million megawatts is orders of magnitude greater than the energy dissipation of

earthquakes or heat loss from volcanic eruptions. The study of the terrestrial heat flow is
fundamental in earth sciences. It is the most direct observation of the thermal state of
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the earth, and geothermal processes play an important role in all theories of Earth’s
origin, constitution, and behavior.
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By definition, the surface (terrestrial) heat flow at a given locality is the rate of heat
transferred across Earth’s surface at that place per unit area per unit time. It is
determined as the product of the thermal conductivity and the vertical gradient of
temperature. It is given in units of watts per square meter (W m-2).

Heat flow by conduction, q, in a solid is found experimentally to be proportional to the

temperature difference, where the coefficient of proportionality is the so-called thermal
conductivity (k). In general, thermal conductivity is a tensor, but for a homogeneous and
isotropic solid, it is a constant. For practical measurements of the surface heat flow, q is
thus the product of the mean conductivity of the rocks from the borehole and the
measured temperature gradient in that hole, q = k(dT/dz), where the flow is vertically
outward.

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GEOPHYSICS AND GEOCHEMISTRY – Vol.I - Terrestrial Heat Flow - Vladimir Cermak

3.1Thermal conductivity

Thermal conductivity is thus the ability of the material to conduct heat, and in SI units it
is expressed in watts per meter kelvin (W/(m K)). Generally, most rocks are rather poor
conductors, and their conductivity varies in an interval of less than 1 W/(m K) to 10
W/m K (Figure 1). In geothermics, the related investigations have to consider the effect
of temperature, pressure, mineral composition, and water content on the conductivity.
Thermal conductivity is related to the thermal diffusivity (κ), the ability to equalize the
temperature differences, κ = k/(c ρ), where c is the specific heat (the heat capacity per
weight unit) and ρ is the density.

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Figure 1. Range and mean thermal conductivity for several characteristic rock types
(after Cermak and Rybach, 1982)

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Bibliography

Cermak V. and Rybach L., eds. (1979). Terrestrial Heat Flow in Europe, 328 pp. Berlin, Heidelberg, and
New York: Springer-Verlag. [Summary of heat flow studies in Europe covering both general papers plus
national reports from the individual countries. Attached is the heat flow map of Europe 1:5 000 000.]

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GEOPHYSICS AND GEOCHEMISTRY – Vol.I - Terrestrial Heat Flow - Vladimir Cermak

Cermak V. and Rybach L., eds. (1991). Terrestrial Heat Flow and the Lithosphere Structure, 507 pp.
Berlin and Heidelberg: Springer-Verlag. [Proceedings volume of international conference at Bechyne,
Czechoslovakia, June 1-6, 1987 giving a good overview of the interpretation of heat flow data in terms of
the continental lithosphere structure.]
Haenel R., Rybach L., Stegena L., eds. (1988). Handbook of Terrestrial Heat-Flow Density
Determination, 486 pp. Dordrecht, Boston, London: Kluwer Academic Publishers. [More recent summary
describing all aspects of both academic and applied geothermics.]
Hurtig E., Cermak V., Haenel R., Zui V. I., eds. (1991). Geothermal Atlas of Europe, 156 pp, 36 maps.
Gotha: Hermann Haack Verlagsgesellschaft. [Set of 1;5 000 000 and 1;2 500 000 maps of heat flow and
subsurface temperature in Europe with a brief explanatory text.]
Jessop A. M. (1990). Thermal Geophysics, 306 pp. Amsterdam, Oxford, New York, Tokyo: Elsevier.
[Well written monograph explaining what geothermics really is.]
Lee W. H. K., ed. (1965). Terrestrial Heat Flow. Geophysical Monograph Series. 8, 276 pp. Washington:
American Geophysical Union. [The first comprehensive summaries on various aspects of heat flow
studies, still extremely useful.]

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Lewis T., ed. (1992). Climatic Changes Inferred from Underground Temperatures. Global Planet. Change
6(2-4), 71-281. [Series of papers describing the inversion of borehole temperature data and their use in

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climate reconstruction.]
Rybach L. and Muffler L. J. P., eds. (1980). Geothermal Systems: Principles and Case Histories, 336 pp.
Chichester: J. Wiley. [Series of papers addressing various aspects of search and use of the geothermal
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energy.]

Biographical Sketch

Vladimir Cermak ,graduated from the Charles University in Prague in 1960, obtained his PhD in 1965
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and his DrSc-title from the Czechoslovak Academy of Sciences in 1982. From 1968 to 1970 he was a
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post-doctoral fellow at the Dominion Observatory in Ottawa, Canada. He maintained his interest in
various aspects of geothermics, established the Heat Flow Laboratory in the Geophysical Institute in the
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1960s, and started routine heat flow measurements in the country. From 1990 to 1998 he served the
director of the Geophysical Institute, and since 1999 he has been the Chairman of the Czech National
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Commission for Geodesy and Geophysics.Vladimír Čermák always played an important role in
international cooperation. In the 1970s he initiated the preparation of the first heat flow map on the
continental scale in Europe, and together with Professor Ladislaus Rybach from the ETH Zurich,
published a corresponding monograph in 1979. He joined the International Heat Flow Commission of the
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International Association of Seismology and Physics of the Earth Interior in 1971, serving as its secretary
from 1987 to 1991, and its chairman from 1995-1999. From 1992 to 1996 he was the principle
investigator of the project “Borehole and Climate” under the Czech–US cooperation program. From 1994
to 1998 he was the Vice-President of the European Geophysical Society. Presently he is a member of the
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American Geophysical Union, Deutsche Geophysikalische Gesselschaft, and since 1991, also a member
of the Academia Europea. From 1995 to 1999 he was a member of the Board of Directors of the
International Geothermal Association. He has organized a number of international workshops and
conferences, edited a number of special issues of internationally recognized journals, and published over
250 scientific papers, over 30 of them with Dr. Louise Bodri from the Geophysical Department of the
L.Eotvos University, Budapest. Since 1998 he has been leading one of the UNESCO projects under the
International Geological Correlation Program “Borehole and Climate.” The author’s contributions have
been acknowledged internationally. In 1995 he was awarded the AGU Edward Flinn medal and the
O.Yu.Schmidt medal of the Institute of Earth Physics of the Russian Academy of Sciences, and in 1998
the Patricius Plakette of the Deutsche Geothermische Vereinigung.

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