isostasy Isostasy (a word derived from the Greek for ‘equal standing’) is essentially the principle of hydrostatic equilibrium applied to the Earth. In its simplest form, it considers rigid blocks of the Earth (usually taken to be the crust) to be buoyantly supported in an underlying fluid medium (usually taken as the mantle) and free to move vertically. These blocks will then move until their weight is exactly balanced by their buoyancy, at which point they are said to be ‘in isostatic equilibrium’.

The concept was originated by French surveyors in the eighteenth century working around the Andes, who noted that the observed gravitational attraction of the mountains was less than that predicted. They inferred the presence of a low-density ‘root’ that balances the excess weight of the mountain range and also reduces its gravitational attraction. The theory was further developed by the English geodesists Pratt and Airy in the nineteenth century, who have given their names to two forms of the theory.

In both versions, it is assumed that different crustal blocks have different thicknesses. Pratt's hypothesis (Fig. 1a) assumes that the bases of the floating blocks are at a constant depth and that their densities vary inversely with their thickness, so that the total weight of each column, or pressure at its base, is the same everywhere. Nowadays the requirement for constant-depth bases seems arbitrary and contrary to much observation, although some real situations (e.g. the variations in depth, thickness, and density of oceanic lithosphere with age) approximate to the Pratt mechanism.

In Airy's mechanism, the surface layer has a constant density but variable thickness (Fig. 1b). Blocks move so that at a certain constant depth (at or below the deepest base) the weights and pressures are again equalized. The tops of the thicker blocks will then float higher, while their bases sink deeper into the substratum, forming, for example, mountains and their roots. Airy's mechanism is more generally applicable than Pratt's, and is a reasonable model for variations in continental crust. However, it should be realized that both the Airy and Pratt mechanism are particular cases with simplifying assumptions, neither of which is required by the general idea of isostasy. In general, both the thickness and density of blocks vary, and there is usually no reason to assume that their bases lie at a given depth.

The concept of isostasy was originated well before modern ideas of a lithosphere and asthenosphere. When the Mohorovicić discontinuity, separating the light crust from the denser mantle, was discovered by seismology, it was natural for geologists to equate the crust with the solid, floating layer of isostasy and the mantle with the fluid substratum. However, it is now clear that the rheology of the lithosphere is more complex than this. In many applications it is appropriate to consider the lithosphere (crust and uppermost mantle) as the floating layer, while the asthenosphere provides the ‘fluid’ substratum.

In fact, isostasy is not confined to lithospheric-scale blocks, but will apply at any scale where rigid blocks overlie ductile layers. For example, in many places there is a weak, ductile layer in the mid- to lower crust, and fault blocks in the rigid, upper crust can move in this ductile layer to reach equilibrium. It is also often unrealistic to think of free-moving blocks bounded by simple crustal- or lithospheric-scale faults. A more realistic model contains a strong but elastic lithosphere which can flex under applied loads, so that its equilibrium does not depend simply on local hydrostatic equilibrium; instead, the loads are distributed by the strength of the plate and compensated regionally by its flexure.

In any form of the theory, the depth at which pressures are equalized is called the ‘compensation depth’. For ‘pointwise’ isostatic mechanisms, such as Airy's or Pratt's, if the thickness and densities of the blocks or layers are known, it is a matter of simple arithmetic to calculate the expected topography for bodies in isostatic equilibrium. In fact, if one assumes isostatic compensation, then given any two of surface topography, crustal thickness, or crustal density, the third can be calculated. Alternatively, if all three are known, one can estimate the degree to which the observed topography is in isostatic equilibrium. For regional or flexural isostasy this can still be done, but the calculations are more complex.

Areas that have thicker or lower-density roots than are required for equilibrium are said to be ‘overcompensated’, and those that are too thin or too dense are ‘undercompensated’. In either case, the lack of isostatic equilibrium indicates that the topography must be supported either by the finite strength of the lithosphere or by dynamic forces (as, for example, in a tectonically active area).

Many regional-scale geological processes tend to disturb isostatic equilibrium. For example, erosion makes blocks thinner or reduces their weight, so that a mountain being eroded will tend to rise to maintain equilibrium. In contrast, the deposition of sediments represents an added load, so that sedimentary basins tend to sink. Extension of the crust to form rift valleys thins it, while compression in mountain-building thickens it. Loading and unloading by glaciers also affects isostatic equilibrium. In all these cases, the lithosphere will move in order to maintain or regain isostatic equilibrium, and the ductile asthenosphere will flow in response.

Isostatic forces are thus of major importance in controlling the topography of the Earth's surface. For the geologist reconstructing ancient topography (for example, the throw on a fault or the depth of a sedimentary basin or continental margin), it is vital to correct for varying loads and their isostatic effects.

Roger Searle

Bibliography

Kearey, P. and and Vine, F. J. (1996) Global tectonics. Blackwell Science, Oxford.

Isostasy

Isostasy (also spelled Isotacy) is a geophysical phenomenon describing the force of gravity acting on crustal materials of various densities (mass per unit volume) that affects the relative floatation of crustal plates. Isostasy specifically describes the naturally occurring balance of mass in Earth's crust .

Continental crust and oceanic crust exist on lithospheric plates buoyant upon a molten, highly viscous aethenosphere. Within Earth's crustal layers, balancing processes take place to account for differing densities and mass in crustal plates. For example, under mountain ranges, the crust slumps or bows deeper into the upper mantle than where the land mass is thinner across continental plains. Somewhat akin to how icebergs float in seawater, with more of the mass of larger icebergs below the water than smaller ones, this bowing results in a balance of buoyant forces termed isostasy.

Isostasy is not a process or a force. It is simply a natural adjustment or balance maintained by blocks of crust of different mass or density.

Within Earth's interior, thermal energy comes from radioactive energy that causes convection currents in the core and mantle. Opposing convection currents pull the crust down into geosynclines (huge structural depressions). The sediments that have collected (by the processes of deposition that are part of the hydrologic cycle ) are squeezed in the downfolds and fused into magma . The magma rises to the surface through volcanic activity or intrusions of masses of magma as batholiths (massive rock bodies). When the convection currents die out, the crust uplifts and these thickened deposits rise and become subject to erosion again. The crust is moved from one part of the surface to another through a set of very slow processes, including those in Earth's mantle (e.g., convection currents) and those on the surface (e.g. plate tectonics and erosion).

With isostasy, there is a line of equality at which the mass of land above sea level is supported below sea level. Therefore, within the crust, there is a depth where the total weight per unit area is the same all around the earth. This imaginary, mathematical line is called the "depth of compensation" and lies about 70 mi (112.7 km) below the earth's surface.

Isostasy describes vertical movement of land to maintain a balanced crust. It does not explain or include horizontal movements like the compression or folding of rock into mountain ranges.

Greenland is an example of isostasy in action. The Greenland land mass is mostly below sea level because of the weight of the ice cap that covers the island. If the ice cap melted, the water would run off and raise sea level. The land mass would also begin to rise, with its load removed, but it would rise more slowly than the sea level. Long after the ice melted, the land would eventually rise to a level where its surface is well above sea level; the isostatic balance would be reached again, but in a far different environment than the balance that exists with the ice cap weighing down the land.

Scientists and mathematicians began to speculate on the thickness of Earth's crust and distribution of landmasses in the mid-1800s. Sir George Biddell Airy (1801–1892) assumed that the density of the crust is the same throughout. Because the crust is not uniformly thick, however, the Airy hypothesis suggests that the thicker parts of the crust sink down into the mantle while the thinner parts float on it. The Airy hypothesis also describes Earth's crust as a rigid shell that floats on the mantle, which, although it is liquid, is more dense than the crust.

John Henry Pratt (1809–1871) proposed his own hypothesis stating that the mountain ranges (low density masses) extend higher above sea level than other masses of greater density. Pratt's hypothesis rests on his explanation that the low density of mountain ranges resulted from expansion of crust that was heated and kept its volume, but at a loss in density.

Clarence Edward Dutton (1841–1912), an American seismologist and geologist, also studied the tendency of Earth's crustal layers to seek equilibrium. He is credited with naming this phenomenon "isostasy."

A third hypothesis, eventually developed by Finnish scientist Weikko Aleksanteri Heiskanen (1895–1971) was a compromise between the Airy and Pratt models.

The model most accepted by modern geologists is the Hayford-Bowie concept. Advanced by American geodesists John Fillmore Hayford (1868–1925) and John William Bowie (1872–1940), geodesists, or specialists in geodesy, are mathematicians who study the size, shape, and measurement of Earth and of Earth forces (e.g., gravity). Hayford and Bowie were able to prove that the anomalies in gravity relate directly to topographic features. This essentially validated the idea of isostasy, and Hayford and Bowie further established the concept of the depth of isostatic compensation. Both gentlemen published books on isostasy and geodesy. Hayford was the first to estimate the depth of isostatic compensation and to establish that Earth has an oblate spherical shape (a bowed or ellipsoid sphere) rather than a true sphere.

See also Earth, interior structure

isostasy A model for the upper region of the Earth in which differences in elevation are compensated by either low-density roots or lower-density surface rocks. The rigidity of the tectonic plate allows some departure from this model. See ISOSTATIC ANOMALY; AIRY HYPOTHESIS; and PRATT HYPOTHESIS.

isostasy : see continent .