Isostasy (from Greek ísos 'equal' and stásis 'standstill') orisostatic equilibrium is the state ofgravitationalequilibrium betweenEarth'scrust (orlithosphere) andmantle such that thecrust "floats" at an elevation that depends on its thickness and density. This concept is invoked to explain how different topographic heights can exist at Earth's surface. Although originally defined in terms ofcontinental crust and mantle,[1] it has subsequently been interpreted in terms oflithosphere andasthenosphere, particularly with respect to oceanic islandvolcanoes,[2] such as theHawaiian Islands.
Although Earth is a dynamic system that responds to loads in many different ways,[3] isostasy describes the important limiting case in which crust and mantle are instatic equilibrium. Certain areas (such as theHimalayas and other convergent margins) are not in isostatic equilibrium and are not well described by isostatic models.
The general termisostasy was coined in 1882 by the American geologistClarence Dutton.[4][5][6]
In the 17th and 18th centuries, Frenchgeodesists (for example,Jean Picard) attempted to determine the shape of the Earth (thegeoid) by measuring thelength of a degree of latitude at different latitudes (arc measurement). A party working inEcuador was aware that itsplumb lines, used to determine the vertical direction, wouldbe deflected by the gravitational attraction of the nearbyAndes Mountains. However, the deflection was less than expected, which was attributed to the mountains having low-density roots that compensated for the mass of the mountains. In other words, the low-density mountain roots provided the buoyancy to support the weight of the mountains above the surrounding terrain. Similar observations in the 19th century by British surveyors inIndia showed that this was a widespread phenomenon in mountainous areas. It was later found that the difference between the measured local gravitational field and what was expected for the altitude and local terrain (theBouguer anomaly) is positive over ocean basins and negative over high continental areas. This shows that the low elevation of ocean basins and high elevation of continents is also compensated at depth.[7]
The American geologistClarence Dutton use the word 'isostasy' in 1889 to describe this general phenomenon.[4][5][6] However, two hypotheses to explain the phenomenon had by then already been proposed, in 1855, one byGeorge Airy and the other byJohn Henry Pratt.[8] The Airy hypothesis was later refined by the Finnish geodesistVeikko Aleksanteri Heiskanen and the Pratt hypothesis by the American geodesistJohn Fillmore Hayford.[3]
Both the Airy-Heiskanen and Pratt-Hayford hypotheses assume that isostacy reflects a local hydrostatic balance. A third hypothesis,lithospheric flexure, takes into account the rigidity of the Earth's outer shell, thelithosphere.[9] Lithospheric flexure was first invoked in the late 19th century to explain the shorelines uplifted in Scandinavia following the melting ofcontinental glaciers at the end of thelast glaciation. It was likewise used by American geologistG. K. Gilbert to explain the uplifted shorelines ofLake Bonneville.[10] The concept was further developed in the 1950s by the Dutch geodesistVening Meinesz.[3]
Three principal models of isostasy are used:[3][11]
Airy and Pratt isostasy are statements of buoyancy, but flexural isostasy is a statement of buoyancy when deflecting a sheet of finite elastic strength. In other words, the Airy and Pratt models are purely hydrostatic, taking no account of material strength, while flexural isostacy takes into account elastic forces from the deformation of the rigid crust. These elastic forces can transmit buoyant forces across a large region of deformation to a more concentrated load.
Perfect isostatic equilibrium is possible only if mantle material is in rest. However,thermal convection is present in the mantle. This introduces viscous forces that are not accounted for the static theory of isostacy. Theisostatic anomaly or IA is defined as the Bouguer anomaly minus the gravity anomaly due to the subsurface compensation, and is a measure of the local departure from isostatic equilibrium. At the center of a level plateau, it is approximately equal to thefree air anomaly.[12] Models such as deep dynamic isostasy (DDI) include such viscous forces and are applicable to a dynamic mantle and lithosphere.[13] Measurements of the rate ofisostatic rebound (the return to isostatic equilibrium following a change in crust loading) provide information on the viscosity of the upper mantle.[14]
The basis of the model isPascal's law, and particularly its consequence that, within a fluid in static equilibrium, the hydrostatic pressure is the same on every point at the same elevation (surface of hydrostatic compensation):[3][8]
h1⋅ρ1 = h2⋅ρ2 = h3⋅ρ3 = ... hn⋅ρn
For the simplified picture shown, the depth of the mountain belt roots (b1) is calculated as follows:
where is the density of the mantle (ca. 3,300 kg m−3) and is the density of the crust (ca. 2,750 kg m−3). Thus, generally:
In the case of negative topography (a marine basin), the balancing of lithospheric columns gives:
where is the density of the mantle (ca. 3,300 kg m−3), is the density of the crust (ca. 2,750 kg m−3) and is the density of the water (ca. 1,000 kg m−3). Thus, generally:
For the simplified model shown the new density is given by:, where is the height of the mountain and c the thickness of the crust.[3][15]
This hypothesis was suggested to explain how large topographic loads such asseamounts (e.g.Hawaiian Islands) could be compensated by regional rather than local displacement of the lithosphere. This is the more general solution forlithospheric flexure, as it approaches the locally compensated models above as the load becomes much larger than a flexural wavelength or the flexural rigidity of the lithosphere approaches zero.[3][9]
For example, the vertical displacementz of a region of ocean crust would be described by thedifferential equation
where and are the densities of the aesthenosphere and ocean water,g is the acceleration due to gravity, and is the load on the ocean crust. The parameterD is theflexural rigidity, defined as
whereE isYoung's modulus, isPoisson's ratio, and is the thickness of the lithosphere. Solutions to this equation have a characteristic wave number
As the rigid layer becomes weaker, approaches infinity, and the behavior approaches the pure hydrostatic balance of the Airy-Heiskanen hypothesis.[14]
Thedepth of compensation (also known as thecompensation level,compensation depth, orlevel of compensation) is the depth below which the pressure is identical across any horizontal surface. In stable regions, it lies in the deep crust, but in active regions, it may lie below the base of the lithosphere.[16] In the Pratt model, it is the depth below which all rock has the same density; above this depth, density is lower where topographic elevation is greater.[17]
When large amounts of sediment are deposited on a particular region, the immense weight of the new sediment may cause the crust below to sink. Similarly, when large amounts of material are eroded away from a region, the land may rise to compensate. Therefore, as a mountain range is eroded, the (reduced) range rebounds upwards (to a certain extent) to be eroded further. Some of the rock strata now visible at the ground surface may have spent much of their history at great depths below the surface buried under other strata, to be eventually exposed as those other strata eroded away and the lower layers rebounded upwards.[18]
An analogy may be made with aniceberg, which always floats with a certain proportion of its mass below the surface of the water. If snow falls to the top of the iceberg, the iceberg will sink lower in the water. If a layer of ice melts off the top of the iceberg, the remaining iceberg will rise. Similarly, Earth's lithosphere "floats" in the asthenosphere.[8][19]
When continents collide, the continental crust may thicken at their edges in the collision. It is also very common for one of the plates to be underthrust beneath the other plate. The result is that the crust in the collision zone becomes as much as 80 kilometers (50 mi) thick,[20] versus 40 kilometers (25 mi) for average continental crust.[21] As notedabove, the Airy hypothesis predicts that the resulting mountain roots will be about five times deeper than the height of the mountains, or 32 km versus 8 km. In other words, most of the thickened crust movesdownwards rather than up, just as most of an iceberg is below the surface of the water.
However, convergent plate margins are tectonically highly active, and their surface features are partially supported by dynamic horizontal stresses, so that they are not in complete isostatic equilibrium. These regions show the highest isostatic anomalies on the Earth's surface.[22]
Mid-ocean ridges are explained by the Pratt hypothesis as overlying regions of unusually low density in the upper mantle.[22] This reflects thermal expansion from the higher temperatures present under the ridges.[23]
In theBasin and Range Province of western North America, the isostatic anomaly is small except near the Pacific coast, indicating that the region is generally near isostatic equilibrium. However, the depth to the base of the crust does not strongly correlate with the height of the terrain. This provides evidence (via the Pratt hypothesis) that the upper mantle in this region is inhomogeneous, with significant lateral variations in density.[22]
The formation ofice sheets can cause Earth's surface to sink. Conversely, isostatic post-glacial rebound is observed in areas once covered by ice sheets that have now melted, such as around theBaltic Sea[24] andHudson Bay.[25] As the ice retreats, the load on thelithosphere andasthenosphere is reduced and theyrebound back towards their equilibrium levels. In this way, it is possible to find formersea cliffs and associatedwave-cut platforms hundreds of metres above present-daysea level. The rebound movements are so slow that the uplift caused by the ending of the lastglacial period is still continuing.[18]
In addition to the vertical movement of the land and sea, isostatic adjustment of the Earth also involves horizontal movements.[26] It can cause changes in Earth'sgravitational field[27] androtation rate,polar wander,[28] andearthquakes.[29]
The hypothesis of isostasy is often used to determine the position of thelithosphere-asthenosphere boundary (LAB).[30]
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