جریان گرما در زمین-heat flow in Earth
heat flow in Earth
The Earth's heat flow is defined as the
amount of heat escaping per unit time from the interior across each unit area of
the Earth's solid surface. The movement of heat within the Earth and its
eventual loss through the surface are central elements in the modern theory of
plate tectonics. The plate movements over the surface of the Earth are seen as
one manifestation of a heat engine at work in the interior, and the heat flow at
the surface as the exhaust from the engine. See also: Earth interior; Plate
tectonics
That the interior of the Earth is a great
reservoir of heat is a fact known from antiquity. The eruption of molten rock
from volcanoes and the egress of thermal waters and steam from subterranean
regions in the form of
Because heat flows from the warmer to the
cooler parts of a body, the observation that the Earth's temperature increases
with depth clearly implies that heat is escaping from the interior by conduction
through the rocky crust. William Thomson (Lord Kelvin) used the heat flow in
estimating the age of the Earth. He argued that as the Earth cooled, following
its formation and solidification from molten rock, the rate at which the
temperature increased with depth (the geothermal gradient) lessened over time,
and thus by measuring the geothermal gradient the length of time that the Earth
had been cooling could be estimated. Such an estimate is based on the assumption
that all the heat being lost is drawn from the endowment of heat that the Earth
possessed at the time of its initially molten condition. This assumption was
later shown to be untenable because a significant fraction of the Earth's heat
flow is derived not from the initial heat but from the decay of radioactive
elements present in trace amounts within the Earth. Thus the Earth's heat should
be thought of not as a finite quantity acquired at the time of formation and
gradually dissipated over time, but as a quantity that in large part has been
continually produced, albeit in diminishing amounts throughout the history of
the Earth. See also: Earth, age of;
Earth, convection in
Measurement
The quantitative measure of heat flow, q, is
obtained as the product of the geothermal gradient, grad T, multiplied by the
thermal conductivity, K, of the material through which the heat is passing: q =
K grad T. The determination of the gradient and conductivity differs in
continental and oceanic settings.
See also: Conduction (heat); Heat radiation; Heat transfer
Continents
On continents the geothermal gradient, that
is, the rate of increase of temperature downward, is ordinarily obtained by
measuring the temperature at several points (or continuously) down a borehole.
Most measurements are obtained in mineral exploration boreholes in the depth
range 100–500 m (330–1650 ft); at shallower depths there are disturbances to the
borehole temperature profile, principally due to circulating ground water, but
also arising from the daily and annual temperature variations, irregular
distributions of vegetation, topographic relief, erosion and deposition,
climatic variations, and other causes. Holes of greater depth, while generally
freer of disturbances in the deeper parts, are only infrequently available.
Occasionally temperature measurements can be obtained in horizontal borings at
different levels of an underground mine, and a geothermal gradient thereby
determined. The thermal conductivity is measured on samples of rock obtained
from the borehole as it was drilled. The conductivity is usually determined by a
laboratory instrument in which a known quantity of heat is conducted through the
sample and the temperature gradient established across the sample is measured.
Other approaches to the determination of conductivity involve heating the
surface of the rock sample with a heating wire or laser for a short time, and
monitoring the rise and subsequent fall of the temperature of the rock. See also: Drilling, geotechnical
Oceans
In oceanic measurements, a hollow probe
several meters long equipped with temperature sensors at intervals along the
length is allowed to plunge into the soft sediment of the ocean bottom. The
temperature of the sediment is thus obtained at several depths, and the
geothermal gradient established. As the probe plunges into the soft ocean
sediment, a core is collected in the interior cavity and is brought to the
surface when the probe is retrieved. The conductivity of the soft sediment is
obtained by inserting a heating needle into it and monitoring the rise of
temperature with time as heat is supplied to the core. Some oceanic heat flow
probes contain the heating needle internally and allow the direct measurement of
conductivity in place while the probe is immersed in the ocean bottom.
The deep ocean floor is a thermally stable
environment, generally free from diurnal and seasonal temperature variations
that disturb equally shallow temperature measurements on continents. However, it
is not free of temperature disturbances arising from the circulation of water
through the fractures in the volcanic rock of the oceanic crust. This
circulation, actually observed as ocean-bottom
Global data
set
In the first review of heat flow
measurements in 1954, the total count of measurements both on continents and in
oceans numbered only in a few tens. Subsequently, the data set has grown
substantially, principally because of the recognition of the role of the Earth's
heat in the internal dynamics and surficial tectonics of the planet.
Measurements have been made at more than 20,000 sites around the globe in both
continental and oceanic settings (Fig. 1). On a 5 × 5° grid, the observations
cover 62% of the Earth's surface. The most intensive continental coverage has
been in the
Fig. 1 Geographic distribution of heat flow
measurement sites. (After H. N. Pollack, S. J. Hurter, and J. R. Johnson, Heat
flow from the Earth's interior: Analysis of the global data set, Rev. Geophys.,
31(3):267–280, 1993)
Heat flow and
age relationships
The most significant empirical relationship
to emerge from the data studies is that heat flow generally decreases with
increasing crustal age at the site of the measurement (Fig. 2). In the oceans
the significant age is the time of magmatic emplacement of the basaltic crust at
a mid-ocean ridge. On the continents it is usually the age of the last major
tectonic, magmatic, or thermal metamorphic event to have affected the
measurement site. The pattern of the decrease in heat flow with age differs from
ocean to continent. While both settings show a heat flow in the older segments
of about 40–45 milliwatts per square meter, the oceanic heat flow shows a
greater range over a shorter time interval than does the continental heat flow.
Fig. 2 Heat flow–versus–age relationships for
continents and oceans. (After D. Sprague and H. N. Pollack, Heat flow in the
Mesozoic and Cenozoic, Nature, 285:393–395,
1980)
The oceanic heat flow–versus–age curve is
somewhat obscured in the younger oceanic crust because of seawater circulating
through the basalt; however, measurements at sites where sediments have sealed
the crust and prevented seawater penetration verify that the inverse square-root
dependence on crustal age is valid in the younger crust. The decay of
continental heat flow with age extends over a much longer period of time and is
more complex than that of the oceans. The continental heat flow principally
comprises (1) a radiogenic component derived from the enrichment of the
continental crust in heat-producing radioactive isotopes, (2) a component
derived from the cooling of tectonothermally mobilized lithosphere, and (3) a
background heat flow of probable deep origin. See also: Radioisotope (geochemistry)
Radiogenic heat
in Earth's crust
The heat production from radioactive decay
contributes significantly to the heat flow from the Earth's interior. In fact,
the entire surface heat flow on continents could arise within the crust if the
surface concentrations of the important heat-producing isotopes such as are
found in granites and gneisses persisted throughout the full thickness of the
crust. However, probable lower crustal rocks such as granulites and migmatites
have lesser concentrations of these isotopes, and so radiogenic heat production
apparently decreases with depth in some manner. The existence of radiogenic heat
and its generation throughout the history of the Earth proved to be the weak
link in the Kelvin theory of the age of the Earth.
Radioisotopes
The principal heat-producing isotopes are
thorium-232 (232Th), uranium-238 (238U), potassium-40 (40K), and uranium-235
(235U) with respective half-lives of 14.0, 4.47, 1.25, and 0.70 × 109 years.
Other radioactive isotopes do not presently contribute significant heat because
their decay chains are not sufficiently energetic, or their abundances are
insignificant, or their half-lives are too short. The concentrations of uranium
and thorium in rocks are generally in trace amounts measured in parts per
million, while potassium is much more abundant, in the range of a few percent,
of which a small but well-known fraction is 40K (see table). A range of values
for the upper mantle is characteristic of various possible mantle rocks as
inferred from xenoliths brought to the surface by igneous and tectonic
processes. If the entire mantle had the lesser concentrations, then crustal and
mantle radiogenic heat production would be less than half the present-day heat
loss; whereas if the greater concentrations were representative of the mantle as
a whole, radiogenic heat production would be about equal to the present-day heat
loss.
The abundances of these isotopes are
commonly obtained from a multichannel gamma-ray spectrometer, which separates
and counts the gamma-ray emissions on the basis of energy. Certain steps in the
decay scheme of each isotope involve gamma radiation with characteristic
energies, and thus the number of counts at certain levels of the energy spectrum
is indicative of the isotopic abundance in the sample. Atomic absorption
spectrometry can also be used to determine the amounts of the more abundant
potassium, and mass spectrometry to determine the much smaller abundances of
uranium and thorium. See also:
Atomic spectrometry; Mass spectrometry
The explanation for the relatively higher
concentrations of uranium, thorium, and potassium in the continental crust
resides in the relatively large ionic radii of these isotopes compared to the
size of silicon, aluminum, magnesium, calcium, and iron, which combined with
oxygen make up the bulk of the Earth's mantle as oxide minerals. The larger ions
fit less easily into the compact crystal lattices of the mantle oxides, and in
magmatic and metamorphic events they are more easily mobilized and tend to
follow the magmatic products and metasomatic volatiles upward into the crust,
where they are more easily incorporated in the more open crystal structures
characteristic of the lower-pressure environment of the crust.
Heat flow
province
The crustal radiogenic component of
continental heat flow has been studied extensively. The principal observation is
that, within a heat flow province, the regional variation in heat flow is well
correlated with the heat production of the surface rocks. The relationship is
expressed as q0 = qr + bA0, where q0 is the surface heat flow, A0 is the heat
production of the surface rocks, qr is the reduced heat flow (the heat flow
intercept for zero heat production), and b (the slope of the line) is a quantity
with dimension of length that historically has been interpreted as a vertical
scale length which characterizes the distribution of the heat sources with
depth. The reduced heat flow is then interpreted as that flux that arises below
the depth range defined by the empirical scale length. A heat flow province
comprises a geographic area in which the heat flow and heat production are
linearly related (Fig. 3); each heat flow province displays a characteristic
reduced heat flow and scale length parameter. However, the traditional
one-dimensional (vertical) interpretations have been questioned by investigators
who argue that two- and three-dimensional heat transfer can also give rise to an
apparent linear heat flow–heat production relationship, depending on both the
horizontal and vertical scale lengths of crustal heterogeneities. In the
multidimensional interpretations the linear relationship reveals more about the
characteristic dimensions of the crustal heterogeneity than it does about the
distribution of heat sources with depth.
Fig. 3 Geographic distribution of 17 heat flow
provinces where the linear relationship between measured heat flow and
radiogenic heat production from near-surface rocks has been empirically
determined. (After I. Vitorello and H. N. Pollack, On the variation of
continental heat flow with age and the thermal evolution of continents, J.
Geophys. Res., 85(B2):983–995, 1980)
Global heat
loss
The heat flow–versus–age relationships (Fig.
2) that provide the critical constraints for thermal history models of the crust
and upper mantle of both oceans and continents can be put to another useful
purpose: estimating the heat flow in areas where no measurements have been made
but for which the age of the crust is known. In a general way, the distribution
of ages in the continental crust has been known for some time, and with the
advent of the geomagnetic reversal time scale, large areas of the oceanic crust
have been dated on the basis of their magnetic signatures. Thus it has become
possible to estimate the heat flow in unsurveyed areas and map the heat flow
over the entire surface of the Earth (Fig. 4).
Fig. 4 Present-day global heat flow (degree 12
spherical harmonic representation). Contours are in milliwatts per square meter.
(After H. N. Pollack, S. J. Hurter, and J. R. Johnson, Heat flow from the
Earth's interior: Analysis of the global data set, Rev. Geophys., 31(3):267–280,
1993)
The oceanic ridge system, where new oceanic
lithosphere is produced, is important in delivering internal heat to the
surface; fully half the Earth's current heat loss comes from oceanic lithosphere
produced in the last 66 million years, representing only 31% of the Earth's
surface. Other regions of above-average heat flow include the cordillera of
western North America, alpine
The average heat flow over the entire Earth
is 87 mW · m−2 and is comparatively a trickle; it is sufficient to bring a
thimbleful of water to a boil in about 2 years, or if collected over the area of
a football field, would be adequate to light four 100-watt incandescent bulbs.
The radiant energy from the Sun intercepted by the Earth is some 4000 times
greater than the geothermal flux. The absorption and reradiation of the incident
solar energy are the principal processes that determine the surface temperature
of the Earth. The geothermal energy is of little significance to the surface
temperature but is of paramount importance in considering the Earth's internal
thermal condition. See also:
Geologic thermometry; Geothermal power
Heat flow in the
past
The present-day heat flow from the Earth has
commonly been considered a useful if not precise upper bound on the quantity of
heat being produced radiogenically in the interior. However, if the heat flow
has a temporal variability on a scale that is short compared to the half-lives
of the principal heat-producing isotopes, the present-day heat flow must be seen
as a much coarser constraint on the Earth's internal heat generation.
Just as the present-day heat loss can be
determined from the heat flow–versus–age relationships and the present-day
distribution of crustal ages, so can the heat loss at a past time be calculated,
provided the age distribution of the crust at that time can be estimated. For
the past 180 million years, the age distribution of the oceanic crust at a given
time can be determined by subtracting from the present-day distribution all
oceanic crust produced from that time to the present and resurrecting and
reinstating crust which has been subducted in the interval from that time to the
present. The age distribution of the restored lithosphere can be estimated from
the present-day age distribution, and the probability that crust produced at an
earlier time will have survived to the present day. Continents can be treated
similarly, but with different survival probabilities which reflect the longevity
of the continents. This method has yielded estimates of the mean heat flow in
oceans and continents and the global flux for the past 180 million years. The
global mean heat flux, presently 87 mW · m−2, has fluctuated in a range of −5%
to +15% around the present-day value. The mean heat flow exceeded the
present-day flux in the interval 60–100 million years before present, when the
rate of production of oceanic crust was high. The mean age of the ocean floor,
presently 62 million years, has ranged between 45 and 65 million years,
accounting for most of the variation in the global heat loss.
For times earlier than 180 million years
ago, an analysis based on the present-day age distribution and survival
probabilities becomes unfeasible because in the oceans, where 70% of the global
heat loss takes place, there is no oceanic crust surviving with which to
estimate past rates of production of the sea floor. Moreover, in studying the
Earth's heat loss over intervals of several hundred million to billions of years
before the present, it is necessary to consider the half-lives and relative
abundances of the principal heat-producing isotopes and the loss of primordial
heat acquired during planetary accretion and core segregation. The isotopic
endowment of the bulk Earth is unknown but is sometimes assumed to be similar to
the chondritic meteorites (see table), which are thought to be representative of
the primitive material from which the Earth differentiated. However, the rocks
of the Earth's crust have a lower potassium-uranium ratio than do the
chondrites. Because of the relatively short half-life of 40K, the heat
production 3 billion years ago from a chrondritic composition would have been
more than four times the present-day heat production, while a terrestrial
composition, based on observed potassium-uranium ratios of crustal rocks, would
yield heat at only somewhat more than twice the present rate. See also: Meteorite
Generalized model calculations of the
thermal history of the Earth using the potassium-uranium ratio of terrestrial
crustal rocks show that the present-day heat production replaces much but not
all of the present-day heat loss. The inequality between heat production and
heat loss arises because a finite transit time is required between the time when
heat is produced within the body of the Earth and when it escapes across the
outer surface, during which interval the heat sources have decayed. The
present-day heat loss thus can be seen as older radiogenic heat, delayed in its
escape from the Earth's interior by the heat transfer process. Because the
replacement heat production is less than the heat loss, the Earth is necessarily
cooling. In spite of the various uncertainties about the blend of the nuclear
fuel, the thermal history calculations indicate that the heat loss from the
Earth 3 billion years ago was at least twice as great as the present-day heat
loss. However, the augmented heat flow may not have been distributed uniformly
over the Earth. Rather, the increased heat loss may have been best accommodated
by a more rapid rate of production of oceanic crust, with only a modest increase
of heat flow through the continents. This latter speculation derives from
crustal temperatures inferred from metamorphic rocks in ancient continental
terrains, which suggest that the heat flow entering the base of the continental
lithosphere was approximately the same as today.
Henry N. Pollack
Bibliography
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H. N. Pollack, S. J. Hurter, and J. R. Johnson, Heat flow from the Earth's interior: Analysis of the global data set, Rev. Geophys., 31(3):267–280, 1993
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