Isostasy

Isostasy is a principle that describes the vertical positioning of segments of the earth's lithosphere relative to the elevation of the land and depth to the top of the asthenosphere. It is, in effect, a restatement of Archimedes' principle or an application of that principle to the outer layers of the earth.

Archimedes' Principle

Isostasy, sometimes called the doctrine or principle of isostasy, is a fundamental principle of the earth sciences that describes the spatial positioning of lithospheric mass within the earth. Isostasy requires that the total mass of air, water, and rock within any vertical column extending from within the asthenosphere, through the lithosphere, to within the atmosphere is equal to the total mass of any other column in the same area of the earth, extending from the same depth in the asthenosphere to the same elevation in the atmosphere. The concept of isostasy is analogous to the concept of buoyancy in physics. Buoyancy was first explained by Archimedes, who, as legend tells it, lowered himself into the the, observed the level of the water rise against the wall of the bathpool, and thus realized that ships float because they displace a mass of water equal to the mass of the ship. This discovery came to be known as Archimedes' principle.

Many centuries later, scholars realized that Archimedes' principle could be used to explain why the earth has both high mountain ranges and deep ocean basins. The main obstacle to the acceptance of the principle was the belief of early scholars that the earth was a solid, rigid body. The idea that the ground on which they stood could be compared to a boat floating on the sea was totally beyond their comprehension. The knowledge needed to draw that analogy did not become available until the mid-nineteenth century, when British surveyors under the direction of Sir George Everest were engaged in the trigonometrical survey of India near the Himalayas. The surveyors noted that the distance between the towns of Kalianpur and Kaliana, when measured by triangulation methods, differed by 5.236 seconds of arc, or about 160 meters from the distance when measured by astronomical methods. Two British scholars, George Biddell Airy and John Henry Pratt, realized the cause of this apparent error, though each provided different interpretations of the geologic conditions that gave rise to the difference in distances. Their interpretations later came to be known as the Airy hypothesis and the Pratt hypothesis of isostasy.

Airy and Pratt Hypotheses

While both Airy and Pratt applied Archimedes' principle to explain the elevation of the Himalayas and the discrepancy in distance between the two survey methods, their hypotheses differed in the way they explained how the mass is distributed below the mountains. Airy viewed that apparent mass deficiency below the mountains as a result of the mountains having a root of low-density rock that extends well into a lower-lying, denser, fluid layer upon which the mountains and all other surficial rock layers float. This lower-density mountain and mountain root combination were envisioned as being like a boat floating upon a denser fluid, which Airy thought was lava. The “boat” was thus made buoyant by the root's displacing a mass of the fluid equal in mass to the combined mountain and mountain root. To Airy, the higher the mountain, the deeper the root must extend to compensate for the elevated mass. By analogy, of two vessels of the same areal extent, one tall and the other of low profile, the tall vessel projects deeper into and rises higher out of the water.

Pratt saw the situation somewhat differently. He maintained that the position of the base of the solid crust must be the same everywhere. The differences in surficial elevations, Pratt thought, arise from some areas having experienced less “contraction” than other areas during the cooling of the earth. These areas of less contraction are also of less density and float higher in accordance with Archimedes' principle. Regional variations in surface elevation, according to the Airy hypothesis, result from variations in the thickness of the solid outer layer of the earth. Airy thought the density of the outer layer was the same everywhere, but the position of the base varies according to the magnitude of surface elevation. According to the Pratt hypothesis, the regional variations in surface elevation result from variations in density of the solid outer layer, with the base of that layer being of equal position everywhere. The Pratt model has a flat-bottomed crust.

Elevated terrains in both the Airy and the Pratt models have less mass near the surface than low-lying terrains. Therefore, according to these hypotheses, the plumb bob was pulled by gravity away from the area of the mountains and toward the lower-lying plains of India. Clarence Edward Dutton in 1889 recognized the significance of this variation in the amount of mass near the surface and concluded, “Where the lighter matter was accumulated there would be a tendency to bulge, and where the denser matter existed there would be a tendency to flatten or depress the surface.” Dutton coined the term “isostasy” for this definition between land surface elevation and rock mass as mandated by Archimedes' principle. In the twentieth century, Airy's theory was refined by Finnish geodesist Veikko Heiskanen and Pratt's theory was developed by American geodesist John Hayford, giving the Airy-Heiskanen model for the thickness of the crust, and the Pratt-Hayford model for the density of the crust.

Isostatic Compensations

Earth scientists acknowledge the validity of both the Airy and the Pratt hypotheses. They consider large-scale or regional land surface elevation variation to result from variations in density and thickness of the lithosphere and also from variations in density of the asthenosphere. Furthermore, earth scientists recognize that the density and/or thickness of the lithosphere at any particular place can change through time and thus result in vertical movements of lithospheric plates to compensate for these changes. If one were to heat a solid object, such as a steel pipe, it would expand and thus decrease its density and increase its length. If a segment of the lithosphere of the earth were to be heated, the rock within that segment would also become less dense, the thickness of the lithospheric segment would increase, and the elevation of the land surface of that segment would rise in accordance with both the Airy and the Pratt hypotheses. This rising of the land surface is known as uplift. Similarly, if a segment of the lithosphere were to cool, the rock would increase in density, the thickness would be reduced, and the elevation of the surface would be reduced. This reduction of land surface elevation through time is referred to as subsidence. If cargo were added to the deck of a boat, it would be seen to ride lower in the water. The top of the cargo, however, would be at a greater distance above the water. Removing deck cargo has the opposite effect. If a segment of the lithosphere were to have sediment deposited on its surface, its base would project a greater distance into the asthenosphere, and its top would be described as being at a greater elevation. If material is removed from the lithosphere by erosion, the base of the lithosphere rises and the land surface elevation decreases.

The vertical adjustments in the position of the lithosphere to maintain equilibrium are referred to as isostatic compensations. To be in equilibrium, the total amount of mass within a column of the earth that extends from within the atmosphere, through the hydrosphere and lithosphere, and into the asthenosphere must be equal to the total mass of any other column of the same areal range that extends from the same elevation in the atmosphere to the same depth in the asthenosphere. A change in the lithosphere within a column in terms of mass or density will be compensated for by changes in the mass of the atmosphere, hydrosphere, and asthenosphere.

When sediment or rock is deposited or eroded from the top of the lithosphere, mass is added or subtracted from the lithosphere, and isostatic adjustments are made to compensate for this change. If sediment is deposited upon the surface of the lithosphere, the added load displaces some of the asthenosphere; thus, there is less asthenospheric mass in the column. If the top of the lithosphere were below sea level, then hydrospheric mass would also be displaced; if sediment accumulated until it were stacked above sea level, then mass within the atmosphere would be displaced as well. If sediment or rock is eroded from the top of the lithosphere, the base of the lithosphere rises, and mass is added to the asthenospheric portion of the column. If the top of the column were initially above sea level, then the mass of the atmospheric portion of the column would increase; if erosion cut below sea level, then hydrospheric mass would be added to the column. Depositional isostatic subsidence is seen along continental margins such as the Gulf Coast of Texas, where there are great accumulations of sediment. Isostatic rebound is associated with erosion (melting) of the Pleistocene ice sheets. Such glacio-isostatic rebounds have been measured in eastern North America and Northern Europe.

Thermo-isostatic Uplift and Subsidence

When the lithosphere is warmed or cooled, the situation becomes more complex. The warming or cooling of the lithosphere is geologically accomplished by changes in the temperature of the asthenosphere. Therefore, the density of both the lithosphere and the asthenosphere would be expected to vary with temperature changes. If temperature change were the only process operating, then the mass of the lithosphere would have remained constant regardless of its temperature; its thickness and density, however, would have changed. If the lithosphere were warmed, the mass in the hydrosphere and/or atmospheric portions of the column would have decreased in an amount equal to the increase in mass of the asthenospheric portion. The net effect would be an increase in the elevation of the land surface, or thermo-isostatic uplift. If the lithospheric portion of the column were to cool, there would be an increase in the mass of the hydrospheric and/or atmospheric portions of the column and a decrease in the asthenospheric portion. The net effect would be a decrease in land elevation, or thermo-isostatic subsidence.

Isostatic uplift is seen in the area of the Mid-Atlantic Ridge, the greatest mountain range on the surface of the earth. It also may explain why the continent of Africa has such a greater average elevation relative to sea level than do the other continents. Isostatic subsidence has been suggested to be the underlying mechanism for the formation of the thick sediment accumulations within continental areas. The Michigan Basin and the Williston Basin in North America are examples of these accumulations.

The processes that give rise to isostatic adjustments take millions of years. The resulting isostatic adjustments are also very slow to occur. When a person steps onto a boat, it instantly rides lower in the water, because the compensation of the boat for the additional load is immediate. The medium upon which the boat floats, water, has a very low viscosity. If the boat were afloat in a more viscous fluid, such as cold molasses, the adjustment to the added mass would be noticeably slower, perhaps taking a minute or more. The asthenosphere is very viscous. Consequently, isostatic adjustments to lithospheric changes may take tens of thousands of years.

Evaluation of Glacio-isostatic Rebound

Isostasy is a principle or law of the earth sciences, and, as such, it cannot be collected, observed, or quantified. What can be observed or quantified are the results of lithospheric segments satisfying or attempting to establish isostatic equilibrium. If a geologic process changes the mass or density of a segment of the lithosphere, vertical adjustments in the position of the lithosphere are necessary to reestablish the equilibrium. These vertical adjustments are slow; 1 centimeter per year would be considered fast. To measure the changes in lithosphere position caused by isostatic compensation, one needs a hypothetical measuring stick and a clock. The “stick” in nearly all cases measures the distance between the top of the lithospheric segment and sea level. Because the time over which the adjustment process occurs is quite long, the clock that is used is the decay of radioisotopes, such as carbon-14, potassium-40, and uranium-238.

The application of these tools to the study of isostatic compensation can be illustrated with the evaluation of the phenomenon of glacio-isostatic rebound. During the last glaciation, the Wisconsin, vast sheets of ice covered portions of Antarctica, North America, Europe, and the southern tip of South America. That ice constituted a load on the decks of several lithospheric boats. From 18,000 to 6,500 years ago, most of the ice sheets in North America, Europe, and South America melted. The meltwater increased the volume of water in the oceans. Consequently, the level of the oceans rose 100 meters relative to a fixed point on a landmass that was not glaciated, such as the island of Cuba. From 6,500 years ago to the present, little additional ice has melted. Thus, the amount of water in the oceans has been constant. Sea level, therefore, should have been constant worldwide.

During this period of time, however, sea level has not been constant in those areas where glacial ice had once loaded the lithosphere. In those areas, fixed points on the land surface are rising relative to sea level. Some areas are currently rising at the rate of 2 centimeters per year; other areas have already risen nearly 140 meters. Scientists can determine how far and how fast the lithosphere has rebounded or is rebounding by examining the locations of exposed shoreline sediments or marine terraces. The sediments would have been deposited and the terraces formed by waves on a beach when sea level was at that land point. Part of that sediment would have been the remains of plants and animals that were alive at the time of deposition of the sediment. By surveying the current difference in elevation between the ancient shoreline sediments and the present sea level, scientists can determine the amount of vertical uplift since the sediment was deposited. By determining the radiometric age of the remains of organic life using carbon-14 dating methods, scientists can calculate the length of the time over which that amount of rebound occurred. Several different shoreline deposits or terraces in the same region can reveal different land positions relative to sea level and how the rate of rebound has changed with time.

Geologists can therefore determine the viscosity of the asthenosphere, project how much rebound will occur in the future, and estimate how much rebound will have occurred when isostatic equilibrium is established. This estimate can be translated into how thick the ice was when the glaciers were present. Ice thickness equals the product of the total rebound times the ratio of the density of the asthenosphere to the density of the ice.

Interest to Geologists and Historians

The relationship between isostasy and the surface of the land is analogous to the relationship between buoyancy and the deck of a ship. Humans can overload the deck of a ship and sink it into the sea, but they cannot overload the lithosphere and sink it into the asthenosphere. This area of nature is one of the few that is not heavily influenced by human activity. If all the engineers of the world used all the earth-moving equipment in the world to pile soil, sediment, and rock in one huge mound, they could not in their lifetimes cause a segment of the lithosphere to ride 1 millimeter lower in the asthenosphere. Nature, however, in a few hundred millennia can pile enough snow and ice on Antarctica to sink land surface so substantially that most of the subice rock surface (the preglaciation top of the lithosphere) now lies below sea level, several hundred meters below where it originally was. Besides geologists and geophysicists, isostasy touches the lives of very few people directly. The notable exceptions are those historians who ponder why certain Viking harbors in Scandinavia are now situated above sea level: The answer pertains to glacio-isostatic rebound.

Principal Terms

Archimedes' principle: the notion that a solid, floating body displaces a mass of fluid equal to its own mass

asthenosphere: the layer immediately underneath the lithosphere, which acts geologically like a fluid

column: a cylindrical segment of the earth oriented on a line from the center of the earth to any point on its surface, beginning somewhere in the asthenosphere and ending somewhere within the atmosphere

density: the amount of mass per unit volume of a substance

lithosphere: the outermost solid layer of the earth

sea level: the position of the surface of the ocean relative to the surface of land

subsidence: the sinking of the earth's surface or a decrease in the distance between the earth's surface and its center

uplift: the rising of the earth's surface or the increase in distance between the earth's surface and its center

viscosity: the ability of a fluid to flow

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