Heat sources and heat flow

Several significant sources contribute to the internal heat of the earth. Radioactive decay of isotopes of thorium, uranium, and potassium in the crust produces most of the heat observed at the surface of the continents. Terrestrial heat flow is readily observed in deep wells, mines, and tunnels that penetrate below the narrow zone on the surface, which is heated by daily and seasonal radiation changes. Another major source is heat convected outward from the earth's core and through the mantle. This heat produces the majority of the heat flow measured in the oceans, especially at the mid-oceanic ridges.

Terrestrial Heat Flow

The surface of the earth receives heat from several different sources. Solar radiation provides the largest amount of heat—an amount that is approximately five thousand times greater than that moving outward from the subsurface. However, solar radiation is almost all reradiated into space, so it has very little effect on the earth's temperature deeper than a few meters. The amount of terrestrial heat flow is so small that it would take several months for a dish of water placed on the surface to heat up by an additional 1 degree Celsius. During that period of time, the surface temperature on the earth could easily fluctuate 20 to 30 degrees Celsius, depending on the time of year. Because of the large variation in surface temperatures, it is necessary to measure terrestrial heat flow at depths that lie well below those that are affected by these relatively short-term changes.

The fact that subsurface temperatures increase with depth has been known from deep mines and wells that penetrate several kilometers into the earth's crust. The temperature at a given depth cannot be determined with the degree of accuracy that pressures at depth can be calculated. Variations in temperature are attributable to several important variables, particularly radioactive heat production and the coefficient of heat transfer. Our inability to measure these parameters at great depths within the crust makes it difficult to establish a well-defined temperature versus depth graph.

In general, the amount of outward heat flow on the surface is small. The mean heat flow for the earth ranges between 60 and 70 milliwatts per square meter. Average values for oceanic and continental areas are essentially equal. Significant differences for values measured in the two general areas depend on the specific geologic setting within the oceanic or continental area. Observed values also differ significantly for measurements taken at specific locations in either the oceans or the continents. Heat-flow measurements in continental regions vary from 41 milliwatts per square meter in Precambrian shields (large masses of igneous and/or metamorphic rock) to 74 milliwatts per square meter for more active, younger Mesozoic and Cenozoic areas. Within the ocean basins, heat-flow values range from 49 to 80 milliwatts per square meter or more. Many researchers provide a multitude of different values for the various geologic regions.

Oceanic Heat Flow

Molten basaltic rock formed by extrusion at the mid-oceanic ridges cools as it moves out from this primary heat source. This heat is being transferred by both convection from the mantle and conduction of heat produced by radioactive isotopes within the rocks in the oceanic layer. As the molten basalt cools, it contracts and undergoes a small density increase, which allows the newly formed layer to sink deeper into the asthenosphere. The depth to which the cooler basaltic layer sinks has been shown to be roughly proportional to the square root of its age. Oceanic crust that is 2 million years old is covered by about 1.5 kilometers of water, whereas crust that is 20 million years old would be located at a considerably greater depth below the ocean surface.

Subduction trenches have the lowest heat-flow values among measurement sites in the oceans. These trenches are deep depressions on the ocean floor usually adjacent to the boundary of continental-oceanic or oceanic-oceanic plate collisions. The lower values in those regions arise for several reasons. As discussed earlier, most of the heat observed in the oceans results from volcanic activity associated with the mid-oceanic ridges. This heat is lost once the hotter volcanic material moves away from the ridge. Trenches are very distant from the ridges, so the oceanic floor in the trench areas has long since been removed from the heat source as the floor has spread outward.

Trenches associated with continental-oceanic plate collisions are also areas that receive large volumes of sediment that are shed from the continents through normal erosion processes. In addition, the deposition of organic and fine-grained clastic material from seawater fills the trenches. All these sediments produce an insulating blanket that can be as thick as 1 kilometer overlying the basaltic oceanic floor. Any heat produced by the basalts is held in by this sedimentary layer. Heat-flow measurements taken in the oceans are made in this soft sediment layer, not in the underlying basalt.

Radioactive Decay of Isotopes

Heat is produced by the natural radioactive decay of isotopes of thorium, uranium, and potassium. The long-lived radioactive isotopes that contribute most to the overall heat production are thorium-232, uranium-238, potassium-40, and uranium-235 (listed in order of decreasing importance). All these isotopes have half-lives roughly the same as the age of the earth. These isotopes are not readily incorporated into the internal structure of the most common minerals. They do tend to become concentrated in minerals that have lower melting points, such as those occurring in granites. A granitic crust 20-25 kilometers thick can produce the amount of terrestrial heat flow observed over these areas. If a more intermediate composition for the continental crust is used, it is still possible to account for at least two-thirds of the heat flux of the continents as being generated from the crust. The remaining heat flow (about 20 milliwatts per square meter) is assumed to come from the mantle.

Oceanic crust, which has an average thickness of 5 kilometers, produces less than 3 percent of the heat flow observed in oceanic measurements. As previously mentioned, the oceans and continents exhibit near-equality in their total heat-flow measurements. The implication is that the mantle underlying oceanic rocks has a higher temperature and greater amounts of radioactive elements than the continental mantle and thus serves as the primary heat source in the oceans. This higher heat flow is conducted through the basaltic layer and also convected upward at the mid-oceanic ridges. It must be remembered, however, that, as a result of the mobility of the lithosphere, this higher-temperature mantle material underneath the oceans eventually moves under the continents and helps compound the interpretation of actual heat flow being produced by the mantle. Almost 75 percent of the earth's total heat loss occurs through the ocean floors, a percentage similar to the amount of surface covered by the oceans (70 percent). The vast percentage of this oceanic heat loss is related to the formation of new oceanic crust at the mid-oceanic ridges.

Heat Flow Variables

The amount of heat flow observed in the oceans and on the continents is dependent on a number of variables. The age of the rock is of primary importance in that older rocks produce less heat, because the radioactive isotopes in the rocks have had a longer time to break down and hence less of the original heat-producing parent isotope is present. Older basalts on the ocean floor are also farther removed from their primary heat source associated with volcanism along the mid-oceanic ridge, where they were first extruded.

Continental heat-flow values are dependent on this same concept of age of the parent rock. On the continents, the lowest heat-flow values are associated with Precambrian shield areas, those portions of the continents that represent the most stable and oldest central core of the landmasses. These areas have also been subjected to the most erosion, which has removed a significant portion of the rocks and minerals containing the radioactive constituents. Some portions of the continents have undergone extensional stresses, which have pulled the landmasses apart and thus thinned the continents. In these places, such as the Basin and Range area of Nevada, the crust has been thinned just as a rubber band becomes thinner when it is extended. The result is that the mantle is much closer to the surface and its influence is enhanced with respect to the amount of heat being moved upward toward the surface. Areas on the continents that have experienced Mesozoic and Cenozoic mountain-building activity also show high levels of heat flow, yet display the greatest amount of variation in observed values. However, these areas of tensional tectonics and mountain-building activity make up a small percentage of the continents and thus do not contribute much to the average values observed on land.

Surface temperatures can also be affected by groundwater flow, soil moisture, slope orientation, vegetative cover, topography, and sun angle. These contributing factors must be removed to obtain heat-flow readings that are representative of rocks at depth.

Heat-Flow Conduction and Transfer

Scientists have found that the earth is losing heat. The heat that is being lost is produced partly by higher rates of radioactive heat production in the past and partly by heat generated by the formation of the earth. The inner core of the earth has a temperature estimated to be between 4,000 and 5,000 degrees Celsius. If the earth were a perfect conductor of heat, the rate of heat loss would offset the rate of heat generation. The mantle is a poor conductor of heat, however, so it stores heat, which is slowly released as the core and lower mantle cool. Calculations have shown that heat in the lower mantle is not completely transferred to the upper mantle and later to the surface. If large-scale convection cells existed within the mantle, there would be a more efficient transfer of this deep-seated heat; this is not observed, however. The best models of the internal transfer of heat seem to point to two levels of convection cells, one lying in the lower mantle and a second, separate level in the upper mantle. This latter level serves as an additional insulator from the deeper heat, which is trying to rise to the surface. The lateral motion of these convection cells in the upper mantle also serves as the primary mechanism to move the continental masses around. The continents are of a lower density than the underlying material; hence they “float” on the lithosphere and asthenosphere. These convection cells raft the continents around on the earth's surface, albeit at a slow rate (several centimeters per year). It must be remembered that heat-transfer processes in the mantle and core are not directly observable. Therefore, geophysicists do not totally agree on the mechanisms that explain the production and transfer of heat at great depth.

Heat flow itself is controlled by the second law of thermodynamics. This law states that for thermal equilibrium to be attained, heat must move from warmer to colder material. This means that in the earth heat flows from the warmer interior to the colder lithosphere and crustal-atmosphere boundary. Heat produced within the earth is transferred in two ways. Deep-seated sources in the mantle and core transfer heat to the upper mantle and crust by convection. Heat rises slowly up through the mantle until it encounters the base of the lithosphere. Some heat is conducted into the relatively cooler lithosphere, while the remainder moves laterally along the boundary of the lithosphere and mantle. As it does so, the temperature of the upper mantle lessens and eventually the cooler rock material sinks back into the mantle, where it is reheated and returned into the convective cycle. Within the oceanic and continental masses, heat is also conducted by the rock. Although rocks are generally poor conductors of heat, the vast quantities being generated by radioactive decay and moved by convection are conducted toward the surface.

Hot Spots

Heat sources mentioned so far are large, often extending hundreds or thousands of kilometers across and through the earth and displaying a broad horizontal and vertical expanse within the crust and mantle. Mantle plumes or hot spots represent much more localized heat sources. Only several dozen of these features have been recognized to date. Their spatial distribution is widespread and generally dispersed, with a slight concentration located along portions of the mid-oceanic ridges. Hot spots are usually only several tens of kilometers in diameter. They are thought to be conduits of heat rising from the mantle and intersecting the earth's surface. Several well-known examples include Iceland, the Hawaiian Islands, and Yellowstone National Park in Wyoming.

Iceland is the result of a hot spot that lies directly on the Mid-Atlantic Ridge. Its volcanic nature is direct evidence of the heat and type of rock produced by the upward movement of heat from beneath the ocean floor. Geothermal energy produced by the volcanism is used as the primary heat source for the island. An obvious hazard of the geologic setting of the island is that volcanic eruptions can adversely affect everyday life in the area.

The Hawaiian Islands are volcanic mountains that rise from the deep ocean floor to elevations of more than 4,200 meters above sea level. When considered in total, they are the highest mountains on earth. The entire string of islands in the Hawaiian Islands chain formed as the result of the Pacific plate having moved in two separate stages in a northwesterly direction over a hot spot. The present position of the Pacific plate has the hot spot centered on the southeastern corner of the island of Hawaii. This area has experienced very active volcanism in the past few centuries and has been the site of numerous eruptions since 1983. Ocean-floor reconnaissance has detected the formation of a new island to the southeast of the island of Hawaii. This submarine volcanic feature has been named Loihi, and it will continue to grow until it breaks through the ocean surface to produce another major island in the chain.

The Yellowstone caldera, located in and around Yellowstone National Park in the western United States, is an excellent example of a hot spot that has risen through the continental lithosphere. A topographic high is centered on the caldera. Elevations decrease as the cooler lithosphere moves out from the center of the hot spot. Evidence for the heat exists in geologically recent volcanic activity and the present-day hot springs and geysers found in the park.

Heat-Flow Measurement

Heat-flow determinations depend on two separate measurements: the rate of increase of temperature with depth (which is termed the vertical temperature gradient, r) and the thermal conductivity (K) of the rocks in which the temperatures are being measured. The flux, or rate, of heat flow (q) is calculated using the formula q = GKr. The units of q are watts per square meter, those of K are watts per meter per degree, and those of r are per degree per meter (deg C⁻¹m⁻¹). Absolute temperatures (in kelvins) can also be used to express these parameters. The minus sign denotes the fact that heat flows down the temperature gradient, from the warmer spots to the colder ones. It must be noted that it is standard practice to consider heat-flow values as positive numbers even though the values obtained from the equation are indeed negative.

The temperature gradient is fairly linear within certain depth ranges in the earth. The rate of increase of the temperature gradient, which is also referred to as the geothermal gradient, is greatest in the outer 1,500 kilometers. The rate of increase decreases significantly at a depth of 2,900 kilometers, where the core-mantle boundary exists. This is attributable to a change in the state of the minerals present at that depth.

From the above equation, it is clear that two variables must be measured to determine the rate of heat flow. The thermal conductivity (K) is usually measured at discrete points along a core sample taken from the borehole. Errors can be introduced because of temperature contamination as the cores are brought to the surface. Average values are obtained by taking a series of measurements along the retrieved core. Measurements of the temperature gradient (r) are obtained by placing a probe into the borehole (or driving it into the ocean sediment). The probe has a series of thermal sensors attached to it that record the temperatures at various distances along the probe. The gradient is calculated by dividing the temperature differences by the known distance of separation between the respective probes.

Observed heat-flow values of ocean bottoms are much less variable than those measured on the continents. In water depths exceeding several hundred meters, it is necessary only to measure temperatures in the upper few meters of the sediments and to establish the thermal conductivity over this same interval. These shallower probe depths in the oceans are permitted because of the more stable heat regime at the boundary of the cold seawater and the ocean sediments. On the continents, however, seasonal variations resulting from solar radiation can affect heat-flow measurements to varying depths. For an average continental rock, the daily change in temperature affects rocks only to a depth of about 15 centimeters; annual variations extend down about 3 meters, while longer-term variations can reach to more than 8 meters. In addition, the flow of groundwater in the upper 50-100 meters alters the heat regime in the subsurface. In some areas, such as highly fractured rocks, groundwater effects can penetrate to depths of as much as 1 kilometer. Therefore, heat-flow measurements must be taken at depths great enough to remove these effects.

Principal Terms

asthenosphere: the semi-molten portion of the outer mantle (ranging to a depth of 250 kilometers) that lies at the base of the lithosphere

basalt: a fine-grained, dark extrusive igneous rock

conduction: the transfer of heat caused by temperature differences

convection: the transfer of heat by the movement or circulation of the heated parts of a liquid or gas

core: the center portion of the earth that is divided into a liquid outer portion and a solid, denser inner section

crust: the outermost layer of the earth, ranging in thickness from 5 to 60 kilometers; it consists of rocky material that is less dense than the mantle

lithosphere: the outer, rigid portion of the earth that extends to a depth of 100 kilometers; it includes the crust and uppermost portion of the mantle

mantle: the portion of the earth's interior extending from about 60 kilometers in depth to 2,900 kilometers; it consists of relatively high-density minerals that are made primarily of silicates

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