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7 Energy
Sinks
Every geological process involves exchange or transfer of energy in one
form or another. Intrusion of a platonic body causes heat to be trans-
ferred to the wall rock and carried down the temperature gradient,
away from the intrusive body; work must be done to strain rocks or to
uplift a mountain; heat must be applied to rocks undergoing meta-
morphism; and so on. Much of this energy is eventually discharged as
heat into the oceans and atmosphere, whence it is radiated out into
space. Most geological processes thus entail a loss of energy from the
earth into what we shall think of as a heat sink.
There is no great difficulty in imagining where this energy could come
from. We could, for instance, suppose that the earth was originally
endowed with it in the form of the "original heat" of an initially very
hot earth. This is essentially the point of view that prevailed throughout
the nineteenth century, up to the discovery of radioactivity. We now
know that there are other possible sources of energy (e.g., radio-
activity, gravitational energy) in addition to the original heat; as we
shall see in Chapter 2, there is in fact an almost embarrassing abun-
dance of riches. Our problem is thus a little more subtle. What we want
to find out is how the energy gets where we observe it and in its proper
form, whether kinetic, potential, chemical, magnetic, or just plain heat.
Let us elaborate for a moment on this last point. Although all forms
of energy (e.g., kinetic) are readily transformed into heat, the converse
is not true. Heat can never be totally converted to mechanical work; the
efficiency of the conversion- that is, the ratio of work output to heat
input-depends on, among other things, the temperature differences
OCR for page 2
2 ENERGETICS OF THE EARTH
that must exist for there to be any conversion at all. Regardless of the
amount of heat an isolated body may initially contain, very little can
happen if the temperature inside it is uniform. To account for geological
behavior of the earth, it is necessary to postulate not only adequate heat
sources, but also a "structure" of some kind. A structureless, formless,
isotropic sea of heat is geologically useless. Much of the inquiry we are
now embarking on will center on the manner in which appropriate
structures can develop in the spontaneous evolution of a body such as
the earth; as we shall see, it is the earth's gravitational field that pro-
vides most of the desired structure. Much of the following discussion
relates to the interaction of gravitational and thermal fields.
But first we wish to make a brief inventory of the energy require-
ments of geological (in the broad sense) phenomena, which for present
purposes we classify as follows:
1. Heat
(a) Surface heat flow
(b) Volcanic heat
(c) Metamorphic heat
2. Mechanical energy
(a) Strain energy
(b) Uplift of mountains
(c) Motion of plates
(d) Kinetic energy of rotation
3. Magnetic energy
Item 3, although not very significant in magnitude, will be examined
in some detail in Chapter 4 because of its bearing on the nature of the
earth's core.
HEAT FLOW
Surface heat flow, or heat flow for short, refers to the rate at which heat
flows out across the interface between the solid earth and the atmo-
sphere or oceans. The heat flow q is determined by measuring the
temperature gradient VT in near-surface rocks and their thermal con-
ductivity k; by Fourier's law of heat conduction
q =-k VT,
(1.1)
where the minus sign reminds us that heat flows spontaneously down
the temperature gradient, from a hot point to a colder one. The average
OCR for page 3
Energy Sinks 3
of several thousand measurements on land and on the seafloor is about
1.5 x 10-6 cal/cm2 s, or 1.5 heat flow units (HFU); 1 HFU is approxi-
mately equal to 40 mW/m2.
The heat flow determined from (1.1) is a lower bound for its actual
value, for in porous and permeable rocks heat may also be carried by
convective flow of interstitial fluid (water). This convection lowers the
temperature gradient below the value it would have if the rocks were
dry or impervious to water. For this reason Williams and von Herzen
(1974) have proposed a somewhat higher mean heat flow value of 80
mW/m2 (~2 HFU), corresponding to a heat loss for the whole earth
(area = 5.1 x 10~4 m2) of about 4 x 10~3 W.
Heat flow is observed to vary locally within rather broad limits, so
that an arithmetic mean of all observations is not very suitable; ideally,
each measurement should be weighted according to the size of the area
it represents. The difficulty is that no measurements at all are available
in some areas. Chapman and Pollack (1975) have attempted to remedy
this lack of data by observing that in many regions heat flow is found
to be related to the geologic age of the region (see below); conversely,
heat flow values can be predicted in regions where they have not been
measured if the geologic age is known. Chapman and Pollack determine
in this manner a mean heat flow of 50 mW/m2, or 3 x 10~2 W for the
whole earth; these data, however, are not corrected for convective
transport by pore fluids.
A most interesting feature of the heat flow is its regional "structure. "
It is generally observed on land that local values of heat flow tend to
decrease with increasing geologic age of the province, that is, time
elapsed since the last magmatic or metamorphic event. Thus the heat
flow is usually lower in Archean shield areas (~40 mW/m2) than in
regions of Cenozoic tectonic activity and volcanism (~80 mW/m21. This
regional variation may be related to the uneven vertical distribution in
the crust of radioactive heat sources that will be discussed in Chapter
2. Heat flow on oceanic plates also varies with local age, defined
(through magnetic lineations) as distance from the ridge axis divided by
the plate velocity. Heat flow near a ridge axis may be typically about
100 mW/m2, twice its value on portions of a plate that are older than 100
million years. Both the heat flow data and the topography of the ocean
floor can be explained (McKenzie, 1967; Sclater and Francheteau,
1970; Parker and Oldenburg, 1973; Chapman and Pollock, 1977) by
gradual cooling and contraction of a plate as it moves away from the
ridge where it formed by upwelling of hot mantle material. Conversely,
the age-heat flow relationship provides rather convincing evidence as
to the role of mantle convection in heat transport.
OCR for page 4
4 ENERGETICS OF THE EARTH
VOLCANIC HEAT
By volcanic heat we mean the heat that is brought to the surface (ocean
or atmosphere) by volcanic activity, mainly the outpouring of lava. For
each gram of lava that cools from 1000° to 0°C, crystallizing as it cools,
about 400 cat (~1600 J) are released. The average annual rate of out-
pouring is not exactly known. A single eruption may produce several
cubic kilometers of lava and pyroclasts, but such large eruptions are
infrequent. From 1952 to 1971, Kilauea volcano on the island of Hawaii
produced about 0.11 km3/yr. Rates of accumulation of plateau basalts
seem to be of the same order. It may be surmised that the average rate
of eruption on land is less than 1 km3/yr.
The rate of eruption on the ocean floor is even less well known. Most
of the submarine volcanic activity probably occurs in the crestal area
of ridges where new oceanic crust is formed. Following Christensen
and Salisbury (1975), we assume that the total thickness of lava flows
comprising the upper part of the oceanic crust is about 1.5 km. Taking
the total length of ridges to be 5 x 104 km and the average plate velocity
to be 2.5 crn/yr, the rate of production of crust at a symmetric ridge is
5 cm/yr. The erupted volume of lava then comes out close to 4 km3/yr.
The total volume (land plus ocean) is thus somewhat less than 5 km3/yr,
and the corresponding heat loss is about 8 x 10~ W. a few percent of
the heat flow.
This estimate does not include, of course, the heat brought up
through the crust, but not quite to the surface, by bodies of magma that
cool at depth. This heat will presumably be included in the heat flow.
Thus, for instance, the very high heat flow (about 600 mW/m2, 10 times
normal) measured in the Yellowstone caldera beneath Yellowstone
Lake (Morgan et al., 1977), which almost certainly comes from a sub-
jacent body of magma, need not be counted as volcanic heat since it is
presumably already included in the heat flow data. Similarly, any heat
released by cooling of the intrusive gabbros that may form a large part
of layer 3 of the oceanic crust is included in the seafloor heat flow
measurements.
Thus it would seem that the rate of heat lost to the atmosphere and
oceans by surface volcanic activity, on land and on the seafloor, may
be about 8 x 10~ W. less than the uncertainty affecting the global heat
flow, which, as we have just seen, is variously estimated as 3 x 10~3 or
4 x 10~3 W. It follows that there should be no great difficulty in finding
adequate sources of volcanic energy if we can find adequate sources for
the global heat flow. The volcanic problem is again a "structural" one;
what is to be explained is why volcanoes are located where they are.
OCR for page 5
Energy Sinks 5
Nothing has been said so far of the energy transferred to the atmo-
sphere through volcanic explosions. A single major explosion, such as
occurred at Krakatoa in 1883, might release some 1025 ergs, but since
such explosions do not occur very frequently (fewer than 10 per cen-
tury, if that), the total power involved is probably not much greater than
109 W. which is negligible.
METAMORPHIC HEAT
By metamorphic heat we mean the heat required to transform sedimen-
tary and volcanic rocks into their recrystallized metamorphic
equivalents- greenstones, amphibolites, gneisses, granulites, and so
forth. Many metamorphic reactions involve dehydration (e.g., mus-
covite + quartz ~ orthoclase + sillimanite + water) or decarbonation,
and are endothermic. Thus heat must be applied to heat cold sediments
to the reaction temperature and then to make the reaction go. We count
the heat of an endothermic reaction as a sink because it effectively
remains locked in the metamorphic rock until surface weathering and
accompanying hydration and carbonation return a metamorphic rock to
its original condition, releasing the heat of reaction into the atmo-
sphere.
When it is possible to reconstruct from the mineralogy of a meta-
morphic rock the precise conditions of pressure and temperature under
which it recrystallized, it rather frequently appears that metamorphic
temperatures must have exceeded, perhaps by as much as 100° or 200°,
the temperature one would normally expect to prevail at the corre-
sponding pressure or depth. It is difficult to make very precise state-
ments regarding this temperature excess because, in the first place,
metamorphic temperatures are not all that easy to determine, as they
depend on such things as the difference between the lithostatic pressure
to which the solid part of the system is subjected and the pressure of the
gas or fluid phase; they may also depend on the composition (e.g., the
H2O/CO2 ratio) in the fluid phase. It is also difficult to define a
"normal" expected temperature since continental geotherms vary ac-
cording to the surface heat flow and to the vertical distribution of
radioactive heat sources. The impression nevertheless remains that
some types of high-grade metamorphic rocks, particularly granulites or
rocks associated with migmatites and granitic melts, form only when
there is an abnormally high rate of heat influx rising into the continental
crust from below.
Such surges of heat would probably still be required for endothermic
metamorphism even if no "excess" temperature were required. This is
OCR for page 6
6 ENERGETICS OF THE EARTH
seen by refemng to Figure 1-1, which represents possible temperature
profiles (geotherms) in a homogeneous crust of thickness H to which a
constant heat flux qO is applied from below. If the crust contains neither
sources nor sinks of heat, the steady-state temperature distribution is
linear with a slope (gradient) dT/dz = qO/k, where k is the thermal
conductivity. If the crust contains heat sources (e.g., radioactivity or
exothermic reactions) of intensity ~ >, O. the steady-state geotherm will
be as shown by the upper curve. The gradient at the base of the crust
(z = H) is the same as before if qO is the same, but the gradient at the
surface (z = 0) is now (qO + cH)/k; the surface heat flow equals the heat
supplied at the bottom plus the heat generated in the crust itself. If, on
tlie contrary, endothermic reactions are taking place, ~ is negative, and
the steady-state temperature is given by the lower curve, whose slope
at the surface is less than that of the two other curves. Note that the
effect of the endothermic reactions is to lower the temperature below
that of the other curves. Thus endothermic reactions will run at tem-
peratures equal to or greater than the normal temperatures only if the
heat flow q O is increased by an amount that depends on c, a quantity that
is difficult to evaluate because of our total ignorance of the rate at
CL
LL
llJ
a/ ~
/~=/
/~W
H
DEPTH-
FIGURE 1-1 Effect of exothermic reactions
(e > 0) or endothermic reactions (e < 0) on tempera-
ture in a plate of thickness H heated from below.
The rate of heating from below is the same in all
cases, and a steady state is assumed. Temperatures
are lower when c<0 than when c_O.
OCR for page 7
Energy Sinks 7
which metamorphic reactions proceed. As a guideline, a reaction re-
quiring 50 cal/g of rock and running to completion in 106 yr is equivalent
to a heat sink of 16 x 1O-~3 cal/g s or roughly 44 x 10-~3 cal/cm3 s,
assuming a density of 2.75 g/cm3. By comparison, radioactive heat
generation in granites is only about 6 x 10-~3 cal/cm3 s.
The problem is actually much more complicated than Figure 1-1
suggests. In the first place, it is unlikely that anything like a steady state
is ever reached, since the characteristic thermal diffusion time for the
crust (~107 yr) is of the same order as the duration of a metamorphic
episode. Secondly, much heat may be carried connectively rather than
conductively by fluids (e.g., water released by dehydration). Finally,
the assumption of uniform ~ on which the curves of Figure 1-1 are
based is certainly incorrect: radioactivity is not uniformly distributed,
and both the heat and the rate of reaction depend critically on tempera-
ture. Yet it remains almost certainly true that in a region undergoing
regional metamorphism of the high-temperature, low-pressure type, the
rate of heat input into the crust at the time of metamorphism may be
several times larger than it is now in old continental platforms or shield
areas. As deformation and orogeny are commonly associated with
regional metamorphism, orogeny should perhaps be described as a
thermal disturbance rather than a mechanical one. But since the frac-
tion of the earth's surface undergoing orogeny and regional meta-
morphism at any time is small, metamorphic heat as defined here is
probably but a small fraction of the global heat flow, of the same order
perhaps as volcanic heat, and will not be further considered.
STRAIN ENERGY; EARTHQUAKES
In broad terms an earthquake is believed to occur when sudden yielding
or fracturing releases strain energy that has slowly accumulated in the
neighborhood of the focus. At the time of fracture, some or all of that
strain energy Es is converted to kinetic and potential energy Er of the
radiated seismic waves. Er can be determined from the amplitude and
frequency of these waves, from which a number called the magnitude
M of the earthquake is also calculated. The relation between Er and M
is often taken to be
log Er = 11.3 + 1.8M,
where ET is expressed in ergs and the log is to base 10. From a statistical
determination of the average number of earthquakes of given magni-
tude occurring each year, the average total rate of release of seismic
OCR for page 8
8 ENERGETICS OF THE EARTH
energy is of the order of 1026 ergs/yr, or about 3 x 10~i W. This does not
represent the whole of Es' as it does not include the strain energy
accumulated in irreversible deformation (e.g., folding) or that part of
the reversible strain energy that is not converted to seismic energy
(e.g., heat generated by friction along the fault surface). Thus Es might
perhaps be as high as 10~2 W. roughly 2 or 3 percent of the global heat
flux.
POTENTIAL ENERGY; UPLIFT OF MOUNTAINS
To raise a body of sedimentary rocks from below sea level to form a
mountain range, work must be done against gravity. Work must also be
done to form the root of the mountain by displacing heavier mantle
material. The rate at which work is thus converted into potential energy
is not easily calculated in the absence of detailed information on the
density structure of the crust and mantle prior to and after formation of
the mountain; yet a rough average estimate may be obtained if one is
willing to assume that the average height of land has remained roughly
constant through more recent geologic times. This constancy requires
that rates of uplift equal, on the average, rates of erosion. If so, the rate
of increase of potential energy must balance, on the average, the rate
at which this potential energy is degraded to heat during erosion. A
mass m falling through a vertical distance h releases an amount of
potential energy gmh, where g is the acceleration of gravity. Let h =
1 km be the average height of land, with total area 1.5 x 10~8 cm2. Let
the average rate of erosion (thickness removed in 1 year) be about 5 x
1~3 cm (a rough guess). The volume eroded per year is then = 7.5 x
10~5 cm3 and its mass is roughly 2 x 10~6 g, assuming a density of 2.5
g/cm3. This mass, falling a vertical distance of 1 km = 105 cm, will
release 2 x 1~4 ergs, since g-1~ cm/s2. The corresponding input of
potential energy to balance this loss is then 2 x 1~4 ergs/yr, or 7 x 1~
W. This is negligibly small in comparison with the global heat flux of
3_4 x 10~3 W.
PLATE TECTONICS
Since earthquakes, faulting, and deformation in general are now gener-
ally considered to be part of the broader phenomenon of plate motion,
it may be appropriate to disregard for the moment the strain energy and
look instead at the energy required to drive plates. There seems to be
much unnecessary confusion as to what the driving forces are. Some
authors have suggested that oceanic plates are pulled by the negative
OCR for page 9
Energy Sinks 9
buoyancy of their subducted slabs, which are colder and denser than
the surrounding mantle; gravity then pulls them down. Others imagine
plates to be driven by the viscous drag of the fluid in the underlying
asthenosphere, while still others think of plates as simply sliding down
the flanks of oceanic ridges. All three suggestions take only a limited
view of the phenomenon.
To illustrate this point, suppose that we ask a proponent of negative
buoyancy what causes rain to fall on land. "Well, of course," he will
say, "it is negative buoyancy. Liquid water being denser than the
surrounding air, gravity must necessarily pull raindrops down." While
this is true, it neglects four other essential features of the process,
namely (1) the input of solar heat that evaporates water over the ocean,
(2) the positive buoyancy of water vapor, which gravity forces to rise
into the atmosphere, (3) pressure gradients in the atmosphere that move
masses of air from ocean toward land, and (4) cooling that causes water
vapor to condense into raindrops. Clearly, without all these factors we
would have no rain on land. Plates are moved as much by the positive
buoyancy of hot material rising at a ridge as by the negative buoyancy
of the downgoing subducted slab, both of which are elements of a single
convectional process. Plates move for the same reason the rest of the
mantle does. The lithosphere is nothing but a portion of the general flow
that has acquired by cooling somewhat different mechanical properties
(Figure 1-21. Its thickness, which increases with age or distance from
the ridge (Chapman and Pollack, 1977), is a measure of the cooling that
has taken place because of heat loss through the oceanic floor.
The forces that determine the flow velocity at any point in a convec-
tive system are (1) buoyancy or gravitational forces arising from density
differences brought about mainly by temperature differences, (2) a
| RIDGE AXIS
~-
-_ _
LITHOSPHERE
ASTHENOSPHERE
FIGURE 1-2 A spreading ridge. The oceanic lithosphere is part of the mantle; its
motion is caused by the same forces that cause the rest of the mantles flow.
OCR for page 10
10 ENERGETICS OF THE EARTH
pressure gradient, and (3) viscous forces that can only redistribute
momentum and convert kinetic energy to heat and that cannot drive the
motion in the absence of other driving mechanisms. It is important to
remember that the pressure gradients cannot be calculated by looking
at the buoyancy at only one point. The horizontal pressure gradient that
drives horizontal flow in the upper level of a conventional Benard
convection cell is the result of both the negative buoyancy in the cold
descending flow and the positive buoyancy of the ascending flow. It
arises essentially from the vertical gravity forces because of the re-
quirement of conservation of matter, which dictates that matter cannot
indefinitely accumulate at the top of a rising column, or at the bottom
of a sinking one, but must move sideways.
To summarize, the energy that drives plates is the same gravitational
energy that drives all the rest of the convective flow. It is measured by
the integral .(v pg u dV, where p is density, g is the acceleration of
gravity, u is velocity, and integration is done over the whole volume of
the convecting fluid. For convection to occur, this integral must exceed
the sum of the viscous dissipation plus the work done by the system on
its surroundings (for instance, the work of deformation done on passive
continental plates that are being rafted along). The gravitational integral
would be zero if the density were uniform so that div u = 0. Indeed, if
is the gravitational potential such that g = Vie and div u = 0:
JV pg u dV = PJv u · Vie dV = p jv div Bulb dV-P TV ~ div u dV
=
p (¢u·dS=0
since the normal component of the velocity must vanish on the bound-
ing surface S. In thermal convection, nonuniformity of p is maintained
by temperature differences that in turn require heat sources to be main-
tained against the tendency for conduction and convection to equalize
both temperature and density. Clearly, for the fluid to expand when
heated, work must be done against the prevailing pressure, and this
work must come from the heat supply. But in the steady state, exactly
the same amount of heat comes out of the system at the top as goes into
it at the bottom. The heat that comes out is what we have called the
global heat flow, or, more precisely, the global heat flow minus the heat
generated in the continental crust. Plate tectonics does not therefore
require consideration of an additional energy sink.
As noted above, the continental crust and, to some extent, the thick
OCR for page 11
Energy Sinks 11
lithosphere under it must be considered separately, because they are
not integral parts of the convective system. Because of its low density,
continental crust is not easily subducted, and there is some evidence
that very little mixing occurs between continental lithosphere and the
rest of the mantle. Continents and their lithosphere both appear to be
passively pushed or rafted along on the main mantle flow. Yet work is
done on the continental crust, as when mountains form when conti-
nents collide. We shall examine briefly in Chapter 5 conditions under
which mantle convection can do work on its surroundings.
KINETIC ENERGY OF ROTATION
The kinetic energy of rotation is EK = ~/2Ico2, where co is the angular
velocity of rotation and I is the moment of inertia about the rotation
axis. EK, which is about 2 x 1029 J. changes as either I or co changes.
In the absence of external torques, the angular momentum In must
remain constant. Thus changes in I and co are related as I dco + co dI =
0. The kinetic energy change corresponding to a change dI is then
dEK =-i/2 co2 dI.
Thus, if gravitational separation occurs in the earth, with denser matter
moving toward the center, I will decrease and the kinetic energy will
increase at the expense of part of the gravitational energy released by
the condensation. Conversely, if the earth were to expand because of
internal heating, its moment of inertia would increase and its kinetic
energy would decrease.
The rate ~ is measured by astronomical observations made in observ-
atories fixed on the crust and mantle. What is measured is (am' the
angular velocity of the mantle, which may differ from coo, the rate of
rotation of the core. If total angular momentum (mantle + core) re-
mains constant (no external torque), while the moments of inertia of the
mantle, Im, and of the core, Ic ~ also remain constant, the kinetic energy
of the whole earth changes as
~ d (~m
dt ~ m <(~)m-tt)cJ 4,
.
Suppose tom-~; _ 10-l°/s, corresponding to a mantle that makes one
extra turn with respect to the core every 2000 years, a figure suggested
by the rate of westward drift of the magnetic secular variation. Changes
OCR for page 12
12 ENERGETICS OF THE EARTH
in the length of the day amounting to a few milliseconds have been
observed to occur in the course of a few, say 10, years. The correspond-
ing acceleration dcom/dt- 10-20/s2, and dEK/dt _ 108 W. Since the
acceleration of Com is presumably caused by an electromagnetic internal
torque exerted by the core on the mantle, the corresponding change in
kinetic energy must come from the core. Conversely, when the mantle
decelerates, energy flows back into the core. The power involved
(108 W) is negligible in the present context.
Tidal torques of external origin (sun, moon) cause a secular decelera-
tion of the earth of about 5 x 10-22/s2. Kinetic energy of rotation
is dissipated by friction (viscosity of the oceans, anelasticity of the
mantle) and reappears as heat (see Chapter 21. Heat generated by
viscous dissipation in the oceans is rapidly lost to the earth and must be
counted as a sink; heat generated by tidal deformation of the mantle
appears there as a source.
An input of energy is also needed to displace the instantaneous axis
of rotation away from the principal axis of figure, as happens when the
amplitude of the Chandler wobble increases. Excitation of the wobble
alternates, however, with episodes of damping, during which the stored
kinetic energy is again dissipated as heat in a matter of a few decades.
The energy involved is i/2~2~2A (C - A)/C, where A and C are respec-
tively the minimum and maximum principal moments of inertia of the
earth, and ~ is the small angular separation between C and the rotation
axis. Since ~ is at most about 0.2 arc see = 10-6 red, the power involved
in the Chandler wobble is negligible in the present context.
In addition to its quasi-periodic wobble (annual + Chandler), the pole
of rotation moves secularly at a rate of about 3.4 x 10-3 arc sec/yr, or
10 crn/yr (Dickman, 19771. This motion, if continued over a few million
years, could amount to a polar displacement of large amplitude.
Whether this occurs or not is not clear; most analyses of geomagnetic
polar wander do not reveal much of a component that could be ascribed
to large secular displacements of the rotational pole. But even if such
large angular displacements did occur, it seems unlikely that they
would require much energy. At constant angular momentum, it takes an
amount of kinetic energy ]/~2C (C - A)/A _ 1027 J to displace the axis
of rotation from the maximum to the minimum principal axis, for
an undeformable earth. Since a major portion of the difference C - A
arises from the equatorial bulge that is itself an effect of rotation, it
seems much more likely that in a deformable earth polar wander would
be caused by incremental displacements of the principal axes of inertia,
the pole of rotation remaining at all times very close to the axis of figure
OCR for page 13
Energy Sinks 13
C. Thus, polar wander, if it occurs, is unlikely to be an important
energy sink.
SUMMARY
The earth is losing heat into space ("global heat flow") at a rate of 3 x
10~3 - x 10~3 W. the higher figure being now generally preferred. The
heat flux across the earth's surface varies regionally by a factor of 2-3.
Generally, heat flux is low in old continental shields and near oceanic
trenches; it is high in continental regions of Cenozoic tectonic or vol-
canic activity and near oceanic ridges.
Heat is also brought to the earth's surface by lava, on land and on the
oceanic floor. The total amount of the "volcanic" heat so carried is not
precisely known, but is probably less than 8 x 10~ W. A certain amount
of heat ("metamorphic heat") remains locked in those metamorphic
rocks that form by endothermic reactions such as dehydration. It is
estimated that in regions undergoing such metamorphism the heat flux
rising into the crust from below may be at least twice normal; but since
the area undergoing metamorphism at any one time is probably very
small compared to the earth's surface area, metamorphic heat, like
volcanic heat, is at most only a few percent of the global heat flow.
Tectonic phenomena, such as deformation and fracturing of rocks
and uplift of mountains, require an input of mechanical energy. The rate
at which potential energy must be supplied to uplift mountains is small
(~7 x 109 W). Strain energy is converted to seismic energy at a rate
probably less than about 1 x 10~2 W. Since some strain energy is not
released by faulting (e.g., the strain energy that goes into folding rather
than into fracturing rocks), the rate at which strain energy accumulates
is somewhat larger than 1 x 10~2 W. but still probably constitutes no
more than a few percent of the global heat.
Changes in the kinetic energy of rotation of the earth, from the
secular tidal deceleration, are quite small. Tidal friction in the earth is
a source of heat, not an energy sink.
Motion of plates requires no energy not already included in the global
heat flux.
It would thus appear that we may not be grossly in error in assuming
that the total power needed to drive all geological and geophysical
processes is of the same order as the global heat flux, say 4 x 10~3 W.
But the energetic problem of the earth will not be solved by just pin-
pointing a heat source or sources capable of delivering 4 x 10~3 W. This
is where the concept of "structure," alluded to earlier, comes in. Sup
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14 ENERGETICS OF THE EARTH
pose, for instance, that heat transfer in the earth is by conduction only,
as for a long time it was assumed to be. Then, as is well known, the low
thermal conductivity of rocks combined with the large dimensions of
the earth makes it impossible for any large amount of heat to travel
more than a few hundred kilometers in the earth's lifetime; thus a
source of heat of the required intensity, but located in the core, could
not account for the surface heat flow. On the other hand, for convection
to occur certain conditions must be met, and in particular, the tempera-
ture gradient must exceed a certain critical value; this again places
constraints on the location and distribution of heat sources. Finally, no
heat source can account for the expenditure of strain energy, or for the
motion of plates, without a suitable mechanism for converting heat into
other forms of mechanical or potential energy. If that mechanism turns
out to be convection, heat sources will have to be distributed so as to
create the observed patterns of surface heat flow distribution and of
plate motion.
We turn first to an examination of possible energy sources in the
earth.
Representative terms from entire chapter:
kinetic energy
