What happens to the mantle in an isostatic adjustment when mountains are eroded?

Consider the theory of isostasy as an explanation for landforms and the geologic cycle

isostasy, ideal theoretical balance of all large portions of Earth’s lithosphere as though they were floating on the denser underlying layer, the asthenosphere, a section of the upper mantle composed of weak, plastic rock that is about 110 km (70 miles) below the surface. Isostasy controls the regional elevations of continents and ocean floors in accordance with the densities of their underlying rocks. Imaginary columns of equal cross-sectional area that rise from the asthenosphere to the surface are assumed to have equal weights everywhere on Earth, even though their constituents and the elevations of their upper surfaces are significantly different. This means that an excess of mass seen as material above sea level, as in a mountain system, is due to a deficit of mass, or low-density roots, below sea level. Therefore, high mountains have low-density roots that extend deep into the underlying mantle. The concept of isostasy played an important role in the development of the theory of plate tectonics.

In 1735, expeditions over the Andes led by Pierre Bouguer, a French photometrist and the first to measure the horizontal gravitational pull of mountains, noted that the Andes could not represent a protuberance of rock sitting on a solid platform. If it did, then a plumb-line should be deflected from the true vertical by an amount proportional to the gravitational attraction of the mountain range. The deflection was less than that which was anticipated. About a century later, similar discrepancies were observed by Sir George Everest, surveyor general of India, in surveys south of the Himalayas, indicating a lack of compensating mass beneath the visible mountain ranges.

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In the theory of isostasy, a mass above sea level is supported below sea level, and there is thus a certain depth at which the total weight per unit area is equal all around the Earth; this is known as the depth of compensation. The depth of compensation was taken to be 113 km (70 miles) according to the Hayford-Bowie concept, named for American geodesists John Fillmore Hayford and William Bowie. Owing to changing tectonic environments, however, perfect isostasy is approached but rarely attained, and some regions, such as oceanic trenches and high plateaus, are not isostatically compensated.

The Airy hypothesis says that Earth’s crust is a more rigid shell floating on a more liquid substratum of greater density. Sir George Biddell Airy, an English mathematician and astronomer, assumed that the crust has a uniform density throughout. The thickness of the crustal layer is not uniform, however, and so this theory supposes that the thicker parts of the crust sink deeper into the substratum, while the thinner parts are buoyed up by it. According to this hypothesis, mountains have roots below the surface that are much larger than their surface expression. This is analogous to an iceberg floating on water, in which the greater part of the iceberg is underwater.

The Pratt hypothesis, developed by John Henry Pratt, English mathematician and Anglican missionary, supposes that Earth’s crust has a uniform thickness below sea level with its base everywhere supporting an equal weight per unit area at a depth of compensation. In essence, this says that areas of the Earth of lesser density, such as mountain ranges, project higher above sea level than do those of greater density. The explanation for this was that the mountains resulted from the upward expansion of locally heated crustal material, which had a larger volume but a lower density after it had cooled.

The Heiskanen hypothesis, developed by Finnish geodesist Weikko Aleksanteri Heiskanen, is an intermediate, or compromise, hypothesis between Airy’s and Pratt’s. This hypothesis says that approximately two-thirds of the topography is compensated by the root formation (the Airy model) and one-third by Earth’s crust above the boundary between the crust and the substratum (the Pratt model).

How does isostasy explain what happens to a mountain range as material is removed by erosion?

How does erosion affect isostasy?

How does isostatic rebound apply to mountains?

How does isostasy relate to mountains?