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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

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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

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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.

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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 0C, 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.

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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

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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.

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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

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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

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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.

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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 (udS=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

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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

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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

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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.