Isostasy
Isostasy (Greek
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 in static equilibrium. Certain areas (such as the Himalayas 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.[4][5][6]
History of the concept
In the 17th and 18th centuries, French
The American geologist
Both the Airy-Heiskanen and Pratt-Hayford hypotheses assume that isostacy reflects a local hydrostatic balance. A third hypothesis,
Models
Three principal models of isostasy are used:[3][11]
- 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.
- The Vening Meinesz, or flexural isostasy model – where the lithosphere acts as an elastic 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 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
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):[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:
- b1 ≅ 5⋅h1
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:
- b2 ≅ 3.2⋅h2
Pratt
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]
Vening Meinesz / flexural
This hypothesis was suggested to explain how large topographic loads such as
For example, the vertical displacement z of a region of ocean crust would be described by the differential 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 parameter D is the flexural rigidity, defined as
where E is Young's modulus, is Poisson'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]
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.[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]
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.[18]
An analogy may be made with an iceberg, 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]
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 80 kilometers (50 mi) thick,[20] versus 40 kilometers (25 mi) for average continental crust.[21] 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.[22]
Mid-ocean ridges
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]
Basin and Range
In the Basin 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]
Ice sheets
The formation of
In addition to the vertical movement of the land and sea, isostatic adjustment of the Earth also involves horizontal movements.
Lithosphere-asthenosphere boundary
The hypothesis of isostasy is often used to determine the position of the lithosphere-asthenosphere boundary (LAB).[30]
See also
- Archimedes' principle – Buoyancy principle in fluid dynamics
- William Bowie (engineer) – American geodetic engineer
- Lau, Gotland – District of the island of Gotland, Sweden
- Marine terrace– Emergent coastal landform
- Gravity anomaly – Difference between ideal and observed gravitational acceleration at a location
- Timeline of the development of tectonophysics (before 1954)
References
- ^ 33.Spasojevic, S., and Gurnis, M., 2012, Sea level and vertical motion of continents from dynamic Earth models since the Late Cretaceous: American Association of Petroleum Geologists Bulletin, v. 96, no. 11, p. 2037–2064.
- ^ 13. Foulger, G.R., Pritchard, M.J., Julian, B.R., Evans, J.R., Allen, R.M., Nolet, G., Morgan, W.J., Bergsson, B.H., Erlendsson, P., Jakobsdottir, S., Ragnarsson, S., Stefansson, R., Vogfjord, K., 2000. The seismic anomaly beneath Iceland extends down to the mantle transition zone and no deeper. Geophys. J. Int. 142, F1–F5.
- ^ ISBN 0521622727.
- ^ S2CID 128904689.
- ^ S2CID 128576633.
- ^ a b Longwell, Chester R. (1958). "Clarence Edward Dutton" (PDF). Washington D.C.: National Academy of Sciences. Retrieved 24 March 2022.
- ISBN 9781405107778.
- ^ a b c Kearey, Klepeis & Vine 2009, p. 43.
- ^ a b Kearey, Klepeis & Vine 2009, pp. 44–45.
- doi:10.3133/m1.
- ^ Kearey, Klepeis & Vine 2009, pp. 42–45.
- ^ Kearey, Klepeis & Vine 2009, pp. 45–48.
- .
- ^ a b Kearey, Klepeis & Vine 2009, p. 45.
- ^ Kearey, Klepeis & Vine 2009, pp. 43–44.
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- ISBN 9780199653065.
- ^ a b Kearey, Klepeis & Vine 2009, pp. 45–46.
- ISBN 0314921958.
- ^ Kearey, Klepeis & Vine 2009, p. 322.
- ^ Kearey, Klepeis & Vine 2009, p. 19.
- ^ a b c Kearey, Klepeis & Vine 2009, p. 48.
- ISBN 9780521880060.
- S2CID 54582233. Retrieved 15 November 2022.
- . Retrieved 15 November 2022.
- .
- .
- .
- ISBN 978-94-010-7538-1.
- S2CID 129497623. Retrieved 13 December 2021.
Further reading
- ISBN 9780080870441. Retrieved 23 March 2022.
External links
- Oldham, Richard Dixon (1922). . Encyclopædia Britannica (12th ed.).