How do mountains build?

Plate moves around the Earth's surface which exerts powerful lateral forces on rocks. The response of the crust to those forces gives rise to deformation on a large scale, particularly along plate boundaries. For example, dozens or hundreds of large-scale faults can form in zones of plate convergence, resulting in a broad and high mountain belt. The geologic processes that can result in mountain building.

• Crustal shortening/thickening in response to convergence of a subducting plate.
• Continental collision.
• Uplift of sediments accreted by subduction.
• Volcanism.
• "Corner" accretion/uplift due to along-trench rafting of terrain.
• Heating or cooling of lithosphere by the underlying mantle (and hence uplift or subsidence).
• Crustal extension.

Geometrically, if two plates are colliding, they can respond as follows:

• One plate can subduct into the mantle.
• One or both plates can undergo shortening and hence uplift and crustal thickening.
• One or both plates can undergo lateral extrusion (i.e. part of the plate escapes the collision zone by extruding sideways).

Let's consider the first two cases.
Suppose an oceanic plate converges with a continental plate. The oceanic plate, being more dense, subducts into the mantle. If all convergence (100%) is accommodated by subduction, the overlying continent will remain undeformed and should undergo no net uplift (although topography will undoubtedly develop as arc volcanoes appear). Suppose that not all convergence is accommodated by subduction and a few percent of the convergence instead causes the upper plate to shorten. How much uplift is implied?

For 100 millimetres per year of convergence (a typical plate velocity), if 5% is accommodated by long-term shortening of the overlying plate, then the overlying plate will shorten at a rate of roughly 5 millimetres per year.

Geometrically, the 5 mm/yr of horizontal shortening translates into vertical motion as shown above, with the only dependence being on the dip of the fault along which the continent is shortening. For low angle faults (10 degrees), uplift will occur at rates of about 1 mm/yr (1 kilometre per million years). Over 5 million years, this amounts to uplift of 5 kilometres or 3 miles (15,900 feet). Over the same period, the two plates will have converged some 5 million years x 100 kilometres per million years or 500 km. The total uplift then is only a small percentage, 1%, of the total horizontal motion.

Continent-continent collisions are not usually accompanied by subduction because both plates are too buoyant to be thrust deeply into the mantle. The amount of crustal thickening and uplift in such a collision can thus be much greater than for an ocean-continent collision. For example, over the past 40 million years, continental India has driven northward into continental Eurasia across the Himalayas mountain belt at a rate of about 40-50 millimetres per year. If you work it out, this implies that the two plates have somehow shortened by more than 1500 kilometres (about 900 miles) across the Himalayas. Since subduction is not occurring, the shortening has been accommodated by mountain building and lateral escape.

Factors that complicate calculations of total uplift

Plate convergence of hundreds or even a thousand kilometres or more over millions of years might be accompanied by only several kilometres of uplift. This uplift, while spectacular to the eye, is merely a small part of the displacement "budget", which is largely dominated by horizontal motion.

Many important aspects of mountain building are ignored and thus cannot predict total topography given total horizontal motion.

Why is this the case?. It is because of the following:

• Fault dips are rarely well known and faults are often curved, with their dips increasing toward the surface.
• Erosion/mass wasting removes material from the upper reaches of uplifting regions, sometimes nearly as quickly as the region is going up!
• Vertical uplift must fight the downward pull of gravity. In extreme cases, no amount of horizontal convergence is capable of causing further uplift.
• Crustal uplift often coincides with subsidence through a process called isostatic adjustment. This is analogous to climbing into a boat, which sinks lower into the water once your weight is added to that of the boat. Your net height above the water surface is equal to your height on land minus the amount the boat sinks. Continents similarly sink into the underlying mantle when substantial topographic loads are added to their surface.
• Lateral escape of crust sometimes accommodates a significant fraction of plate convergence, leaving less available for inducing vertical uplift.
• Uplift can occur simultaneously or sequentially along many faults that exist in a broad zone of deformation between two converging plates. Relating the total horizontal convergence to the total uplift caused by the convergence then requires measurements across many faults.

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