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Isostasy (Greek ''ísos'' "equal", ''stásis'' "standstill") or isostatic equilibrium is the state of
gravitational In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
equilibrium between
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
's crust (or
lithosphere A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the portion of the upper mantle that behaves elastically on time scales of up to thousands of years ...
) and
mantle A mantle is a piece of clothing, a type of cloak. Several other meanings are derived from that. Mantle may refer to: *Mantle (clothing), a cloak-like garment worn mainly by women as fashionable outerwear **Mantle (vesture), an Eastern Orthodox ve ...
such that the crust "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 of
continental crust Continental crust is the layer of igneous, sedimentary, and metamorphic rocks that forms the geological continents and the areas of shallow seabed close to their shores, known as continental shelves. This layer is sometimes called '' sial'' be ...
and mantle, it has subsequently been interpreted in terms of
lithosphere A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the portion of the upper mantle that behaves elastically on time scales of up to thousands of years ...
and
asthenosphere The asthenosphere () is the mechanically weak and ductile region of the upper mantle of Earth. It lies below the lithosphere, at a depth between ~ below the surface, and extends as deep as . However, the lower boundary of the asthenosphere is ...
, particularly with respect to oceanic island
volcanoes A volcano is a rupture in the crust of a planetary-mass object, such as Earth, that allows hot lava, volcanic ash, and gases to escape from a magma chamber below the surface. On Earth, volcanoes are most often found where tectonic plates a ...
, such as the
Hawaiian Islands The Hawaiian Islands ( haw, Nā Mokupuni o Hawai‘i) are an archipelago of eight major islands, several atolls, and numerous smaller islets in the North Pacific Ocean, extending some from the island of Hawaii in the south to northernmost ...
. Although Earth is a dynamic system that responds to loads in many different ways, isostasy describes the important limiting case in which crust and mantle are in static equilibrium. Certain areas (such as the
Himalayas The Himalayas, or Himalaya (; ; ), is a mountain range in Asia, separating the plains of the Indian subcontinent from the Tibetan Plateau. The range has some of the planet's highest peaks, including the very highest, Mount Everest. Over 10 ...
and other convergent margins) are not in isostatic equilibrium and are not well described by isostatic models. The general term 'isostasy' was coined in 1882 by the American geologist Clarence Dutton.


History of the concept

In the 18th century, French
geodesist Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equival ...
s attempted to determine the shape of the Earth (the
geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...
) by measuring the length of a degree of latitude at different latitudes (
arc measurement Arc measurement, sometimes degree measurement (german: Gradmessung), is the astrogeodetic technique of determining of the radius of Earth – more specifically, the local Earth radius of curvature of the figure of the Earth – by relating the la ...
). A party working in
Ecuador Ecuador ( ; ; Quechua: ''Ikwayur''; Shuar: ''Ecuador'' or ''Ekuatur''), officially the Republic of Ecuador ( es, República del Ecuador, which literally translates as "Republic of the Equator"; Quechua: ''Ikwadur Ripuwlika''; Shuar: ' ...
was aware that its
plumb line A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical reference line, or plumb-line. It is a precursor to the spirit level and used to establish a vertic ...
s, used to determine the vertical direction, would be deflected by the gravitational attraction of the nearby
Andes Mountains The Andes, Andes Mountains or Andean Mountains (; ) are the longest continental mountain range in the world, forming a continuous highland along the western edge of South America. The range is long, wide (widest between 18°S – 20°S ...
. 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 in
India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area, the List of countries and dependencies by population, second-most populous ...
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 (the Bouguer 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. The American geologist Clarence Dutton coined the term 'isostasy' in 1882 to describe this general phenomenon. However, two hypotheses to explain the phenomenon had by then already been proposed, in 1855, one by George Airy and the other by John Henry Pratt. The Airy hypothesis was later refined by the Finnish geodesist Veikko Aleksanteri Heiskanen and the Pratt hypothesis by the American geodesist
John Fillmore Hayford John Fillmore Hayford (May 19, 1868 – March 10, 1925) was an eminent United States geodesist. His work involved the study of isostasy and the construction of a reference ellipsoid for approximating the figure of the Earth. The crater Hayford on ...
. Both the Airy-Heiskanen and Pratt-Hayford hypotheses assume that isostacy reflects a local hydrostatic balance. A third hypothesis,
lithospheric flexure Lithospheric flexure (also called regional isostasy) is the process by which the lithosphere (rigid, thin outer layer of the Earth) bends under the action of forces such as the weight of a growing orogeny or changes in ice thickness related to glac ...
, takes into account the rigidity of the Earth's outer shell, the
lithosphere A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the portion of the upper mantle that behaves elastically on time scales of up to thousands of years ...
. Lithospheric flexure was first invoked in the late 19th century to explain the shorelines uplifted in Scandinavia following the melting of continental glaciers at the end of the last glaciation. It was likewise used by American geologist G. K. Gilbert to explain the uplifted shorelines of
Lake Bonneville Lake Bonneville was the largest Late Pleistocene paleolake in the Great Basin of western North America. It was a pluvial lake that formed in response to an increase in precipitation and a decrease in evaporation as a result of cooler temperature ...
. The concept was further developed in the 1950s by the Dutch geodesist Vening Meinesz.


Models

Three principal models of isostasy are used: # The Airy–Heiskanen model – where different topographic heights are accommodated by changes in crustal thickness, in which the crust has a constant density # The Pratt–Hayford model – where different topographic heights are accommodated by lateral changes in rock
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
. # The Vening Meinesz, or flexural isostasy model – where the
lithosphere A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the portion of the upper mantle that behaves elastically on time scales of up to thousands of years ...
acts as an
elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togethe ...
plate and its inherent rigidity distributes local topographic loads over a broad region by bending. 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 Convection (or convective heat transfer) is the transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes o ...
is present in the mantle. This introduces viscous forces that are not accounted for the static theory of isostacy. The isostatic anomaly or IA is defined as the Bouger 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 the free air anomaly. Models such as deep dynamic isostasy (DDI) include such viscous forces and are applicable to a dynamic mantle and lithosphere. Measurements of the rate of isostatic rebound (the return to isostatic equilibrium following a change in crust loading) provide information on the viscosity of the upper mantle.


Airy

The basis of the model is Pascal'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): 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: : (h_1+c+b_1)\rho_c = (c\rho_c)+(b_1\rho_m) : = h_1\rho_c : b_1 = \frac where \rho_m is the density of the mantle (ca. 3,300 kg m−3) and \rho_c is the density of the crust (ca. 2,750 kg m−3). Thus, generally:
:''b''1 ≅ 5⋅''h''1 In the case of negative topography (a marine basin), the balancing of lithospheric columns gives: : c\rho_c = (h_2\rho_w)+(b_2\rho_m)+ c-h_2-b_2)\rho_c : = : b_2 = (\frac) where \rho_m is the density of the mantle (ca. 3,300 kg m−3), \rho_c is the density of the crust (ca. 2,750 kg m−3) and \rho_w is the density of the water (ca. 1,000 kg m−3). Thus, generally:
:''b''2 ≅ 3.2⋅''h''2


Pratt

For the simplified model shown the new density is given by: \rho_1 = \rho_c \frac , where h_1 is the height of the mountain and c the thickness of the crust.


Vening Meinesz / flexural

This hypothesis was suggested to explain how large topographic loads such as
seamounts A seamount is a large geologic landform that rises from the ocean floor that does not reach to the water's surface (sea level), and thus is not an island, islet or cliff-rock. Seamounts are typically formed from extinct volcanoes that rise abru ...
(e.g.
Hawaiian Islands The Hawaiian Islands ( haw, Nā Mokupuni o Hawai‘i) are an archipelago of eight major islands, several atolls, and numerous smaller islets in the North Pacific Ocean, extending some from the island of Hawaii in the south to northernmost ...
) could be compensated by regional rather than local displacement of the lithosphere. This is the more general solution for
lithospheric flexure Lithospheric flexure (also called regional isostasy) is the process by which the lithosphere (rigid, thin outer layer of the Earth) bends under the action of forces such as the weight of a growing orogeny or changes in ice thickness related to glac ...
, 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. For example, the vertical displacement ''z'' of a region of ocean crust would be described by the
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
:D\frac+(\rho_m-\rho_w)zg = P(x) where \rho_m and \rho_w are the densities of the aesthenosphere and ocean water, ''g'' is the acceleration due to gravity, and P(x) is the load on the ocean crust. The parameter ''D'' is the ''flexural rigidity'', defined as :D=ET^3_c/12(1-\sigma^2) where ''E'' is
Young's modulus Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied ...
, \sigma is
Poisson's ratio In materials science and solid mechanics, Poisson's ratio \nu ( nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Po ...
, and T_c is the thickness of the lithosphere. Solutions to this equation have a characteristic wave number :\kappa=\sqrt /math> As the rigid layer becomes weaker, \kappa approaches infinity, and the behavior approaches the pure hydrostatic balance of the Airy-Heiskanen hypothesis.


Depth of compensation

The depth of compensation (also known as the ''compensation level'', ''compensation depth'', or ''level 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. 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.


Implications


Deposition and erosion

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. An analogy may be made with an
iceberg An iceberg is a piece of freshwater ice more than 15 m long that has broken off a glacier or an ice shelf and is floating freely in open (salt) water. Smaller chunks of floating glacially-derived ice are called "growlers" or "bergy bits". The ...
, 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.


Continental collisions

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 thick, versus for average continental crust. As noted above, 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 moves ''downwards'' 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.


Mid-ocean ridges

Mid-ocean ridges are explained by the Pratt hypothesis as overlying regions of unusually low density in the upper mantle. This reflects thermal expansion from the higher temperatures present under the ridges.


Basin and Range

In the
Basin and Range Province The Basin and Range Province is a vast physiographic region covering much of the inland Western United States and northwestern Mexico. It is defined by unique basin and range topography, characterized by abrupt changes in elevation, alternating ...
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.


Ice sheets

The formation of ice 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 the
Baltic Sea The Baltic Sea is an arm of the Atlantic Ocean that is enclosed by Denmark, Estonia, Finland, Germany, Latvia, Lithuania, Poland, Russia, Sweden and the North and Central European Plain. The sea stretches from 53°N to 66°N latitude and from ...
and
Hudson Bay Hudson Bay ( crj, text=ᐐᓂᐯᒄ, translit=Wînipekw; crl, text=ᐐᓂᐹᒄ, translit=Wînipâkw; iu, text=ᑲᖏᖅᓱᐊᓗᒃ ᐃᓗᐊ, translit=Kangiqsualuk ilua or iu, text=ᑕᓯᐅᔭᕐᔪᐊᖅ, translit=Tasiujarjuaq; french: b ...
. As the ice retreats, the load on the
lithosphere A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the portion of the upper mantle that behaves elastically on time scales of up to thousands of years ...
and
asthenosphere The asthenosphere () is the mechanically weak and ductile region of the upper mantle of Earth. It lies below the lithosphere, at a depth between ~ below the surface, and extends as deep as . However, the lower boundary of the asthenosphere is ...
is reduced and they ''rebound'' back towards their equilibrium levels. In this way, it is possible to find former sea cliffs and associated
wave-cut platform A wave-cut platform, shore platform, coastal bench, or wave-cut cliff is the narrow flat area often found at the base of a sea cliff or along the shoreline of a lake, bay, or sea that was created by erosion. Wave-cut platforms are often most o ...
s hundreds of metres above present-day
sea level Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardis ...
. The rebound movements are so slow that the uplift caused by the ending of the last
glacial period A glacial period (alternatively glacial or glaciation) is an interval of time (thousands of years) within an ice age that is marked by colder temperatures and glacier advances. Interglacials, on the other hand, are periods of warmer climate betwe ...
is still continuing. In addition to the vertical movement of the land and sea, isostatic adjustment of the Earth also involves horizontal movements. It can cause changes in Earth's
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational pheno ...
and
rotation rate Rotational frequency (also known as rotational speed or rate of rotation) of an object rotating around an axis is the frequency of rotation of the object. Its unit is revolution per minute (rpm), cycle per second (cps), etc. The symbol for ...
, polar wander, and
earthquake An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, fr ...
s.


Lithosphere-asthenosphere boundary

The hypothesis of isostasy is often used to determine the position of the
lithosphere A lithosphere () is the rigid, outermost rocky shell of a terrestrial planet or natural satellite. On Earth, it is composed of the crust and the portion of the upper mantle that behaves elastically on time scales of up to thousands of years ...
-
asthenosphere The asthenosphere () is the mechanically weak and ductile region of the upper mantle of Earth. It lies below the lithosphere, at a depth between ~ below the surface, and extends as deep as . However, the lower boundary of the asthenosphere is ...
boundary (LAB).


See also

* * * * * * Timeline of the development of tectonophysics (before 1954)


References


Further reading

*


External links

* {{Authority control Geodynamics Geomorphology Buoyancy Earth's crust