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Gravimetry is the science that studies the gravity. In Geomorphology interests the gravity and, particularly, the free fall and terrestrial isostasy .

isostasy was enunciated like principle at the end of century XIX. It is the condition of I balance that densidad presents/displays the terrestrial surface due to the difference of of its parts. It is solved in heaves ( epirogénicos ) and is based on Principle of Archimedes .

### Basic principle

terrestrial Crust floats on Mantle like Iceberg in the ocean; or, Sial floats on Sima like a iceberg in the ocean. The basic principle is that so that a body floats on another one, this one must be denser, and so it is placed underneath. The material that floats, sinks in a variable percentage, but always it has part of emerged him. Thus, the condition of bouyancy does not depend on the size, and when the emerged part loses volume and weight, the submerged part ascends to compensate it. Each individual block, or this one plate or a block delimited by Faults tend to reach this balance. The collapse produced in a river basin where they are settling material receives the name of Subsidence

The isostatic balance can break by a tectonic movement or the defrosting of Inlandsis . The isostasy is fundamental for the relief of Earth . The continents are less dense than the mantle, and also that oceanic Crust . When continental Crust is folded accumulates great amount of materials in a concrete region. Finished the ascent, the erosion begins. material deposits, in the long run, outside the mountainous chain, and so this one loses weight and volume. The roots ascend to compensate this loss leaving in surface the materials that been have put under a greater metamórfico process, and which they have become Granite . This promoted granite, forms rigid old massive Shields or, and that does not fold before new orogenia, but it is broken forming failed Relief . Each one of the blocks in which is broken Shield, of different sizes, also tend to reach the isostatic balance. The readjustments, ascents and collapses of blocks with respect to the other, generate small Earthquakes

## Isostatic models

In 1735, in a scientific expedition in Peru, Pierre Bouguer observed that Deflection of the vertical one was smaller to the awaited one being based on the visible topography of Andes . The same phenomenon was observed in a relief in India in charge of George Everest . From these observations the idea that arises certain compensation, with a negative resistance of densidad, must exist underneath the topography. This lead to the isostasy concept, that assumes balance of each certain Earth column until compensation level . The isostatic equilibrium condition considers like:

$\ int_ \left\{- T\right\} ^ \left\{H\right\} \ rho dz.$

Where $T$ is the depth of compensation, $H$ the height of the topography and $\ rho$ the densidad.

Since the densidades of the terrestrial interior are not known, two models were developed of almost simultaneous way. Henry Pratt proposed a depth of constant compensation $T_0$, consequently, the variations of the topography are associate to lateral changes in the densidad. On the other hand, George Airy assumed a constant densidad, which implies a depth of variable compensation.

At the moment three isostatic models exist:

### Model of Pratt-Hayford

The model of Pratt was developed for geodesic intentions by Hayford . The model assumes a depth of consante compensation $T_0$. The densidad in the absence of topography would be $\ rho_0$. The isostásico equilibrium condition for one given to column i will be:

In the continents:

$\ rho_i \left(T_0+H_i\right) = \ rho_0 T_0$

In the oceans:

$\ rho_i \left(T_0-d_i\right) + \ rho_w d_i= \ rho_0 T_0$

Where $\ rho_w$ is the densidad of the water of sea: $\rho_w=1030 kg/m^3$

### Model of Airy-Heiskanen

The model of Airy was developed for geodesic applications by Heiskanen . The Airy-Heiskanen model is similar to the one of a iceberg floating. Instead of ice we have cortical material of densidad $\ rho_c$ and instead of water of greater densidad we have material of the densidad mantle $\ rho_m$. If an elevation exists (like a mountain) on the surface, must exist corresponding root that is introduced within the mantle. As the cortical material is of smaller densidad than the material of the mantle, a towing traction force will exist that balances the gravitational attractive force of mountains. A similar mechanism takes place below the oceans. As the water of sea has minor densidad will induce a negative root, that is to say, one more a finer crust below the oceans.

In the continents:

$\left(\ rho_m- \ rho_c\right) t_i= \ rho_c H_i$

In the oceans:

$\left(\ rho_m- \ rho_c\right) t_i= \left(\ rho_c- \ rho_w\right) d_i$

### Model of Vening Meinesz

This model is more recent than the previous ones and was proposed in the decade of 1950 . The theory arises from studies that Vening Meinesz realizes in the Himalayas and from which it discovers that these mountains do not have roots of 80 km as it predicted the theory of Airy.

According to this theory, the crust acts as an elastic plate and its inherent rigidity distribute the topographic loads on a greater region.

## Local isostasy versus. regional isostasy

Ever since the isostasy concept extended, the predominant idea was that the isostatic balance was reached locally, in each column of terrestrial Crust, as if the bouyancy in each point of the crust was independent of the contiguous columns. That is to say, as if the movements necessary to readjust the isostatic balance were independent between two points any and they would not be transmitted laterally. Although in the decade of 1880 Grove Karl Gilbert proposed a rigid behavior of the crust in response to the disappearance of Bonneville Lake, the force and simplicity of the isostatic model local era like lasted until the works of Felix Andries Vening Meinesz in the decade of 1950, when Tectonic of plates mainly began to be adopted. Vening Meinesz showed that the oceanic crust is flexionada or doubled under the weight of marine volcanos of form similar to a thin plate, transmitting the collapse due to its weight beyond the own volcanic building.

Although the local isostatic model continues being used like first approach the calculation of isostatic movements in response to deglaciaciones, vulcanism or orogénesis, now is commonly accepted that the external Earth layer has certain rigidity and that behaves like a thin plate, elastic in first approach. To this process is called to him litosférica Flection . The flexural behavior of the lithospere essentially depends on elastic Thickness of the lithospere .

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