# How fast does isostatic depression occur?

**URL:** <https://boards.straightdope.com/t/how-fast-does-isostatic-depression-occur/747729>\
**Category:** Factual Questions\
**Created:** [March 2, 2016, 12:20pm UTC](https://boards.straightdope.com/t/how-fast-does-isostatic-depression-occur/747729 "2016-03-02T12:20:48Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\
**Post date:** [March 2, 2016, 12:20pm UTC](https://boards.straightdope.com/t/how-fast-does-isostatic-depression-occur/747729/1 "2016-03-02T12:20:48Z")

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Imagine a mile-thick sheet of ice instantaneously appears over a mountain chain. How soon will the chain sink? Around 1 cm a year? How far will it sink?

I almost put this into Cafe Society, because this question came about because supposedly the Misty Mountains in Tolkien’s Legendarium are visibly shorter than they used to be. I wonder, if they had been magically raised in a very short time from close to sea level to around 20,000 feet, if they would visibly sink over a span of millennia. Of course, if it would not be that deep or quick on Earth, one can fanwank that the asthenosphere is weaker in Middle Earth 🙂

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**Author:** ![Grey](https://avatars.discourse-cdn.com/v4/letter/g/b782af/32.png) [@Grey](https://boards.straightdope.com/u/Grey)\
**Post date:** [March 2, 2016, 1:07pm UTC](https://boards.straightdope.com/t/how-fast-does-isostatic-depression-occur/747729/2 "2016-03-02T13:07:11Z")

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> [@http://www.umich.edu/~gs265/isost.html](#):
>
> Assuming that the system had reached isostatic equilibrium when loaded with ice, the buoyancy pressure on the continent would equal the pressure that had been imposed by the ice sheet (equal but opposite forces in order to be in equilibrium). The buoyancy pressure is therefore equal to the weight of the column of asthenosphere that was displaced (density around 3300 kg/m3). The pressure imposed by the ice sheet equals the ice density (about 1000 kg/m3) multiplied by the thickness of the ice sheet.
> 
> ```
> (ice thickness)(density of ice) = (displacement of asthen.)(density of asthen.)
> 
> ```

Now this is continental and not linked to a mountain range but (displacement of asthen.) given ice thickness of 1.5 km would be 454m.

As for the Misty Mountains, they existed as a mountain range before being raised even higher up by Melkor. Given they existed as a continental mountain range we could assume they’re located on a continental plate convergence and are continually being raised up as the plates move past each other. Now continental drift really only became accepted in the 1940s, well after Tolkien’s original conception of the range existed, so I don’t think we should take my had waving too seriously.

Finally Tolkien’s Middle Earth is ours just placed far back in time with the actions shown taking placed in roughly northwestern Europe.

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**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\
**Post date:** [March 2, 2016, 2:22pm UTC](https://boards.straightdope.com/t/how-fast-does-isostatic-depression-occur/747729/3 "2016-03-02T14:22:17Z")

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Grey’s right about how far it’ll settle. The rate would likely be in the same ballpark as the isostatic rebound rate (since both are dependent on the same factors like mantle viscosity etc) which, yes, is around 1cm/yr. Possibly a bit faster us it’s sinking under load, but not likely by much. The mantle isn’t that fluid.

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**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\
**Post date:** [March 2, 2016, 3:31pm UTC](https://boards.straightdope.com/t/how-fast-does-isostatic-depression-occur/747729/4 "2016-03-02T15:31:29Z")

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\<nitpick\> … asthenoplain … Middle Earth is flat. \</nitpick\>

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**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\
**Post date:** [March 2, 2016, 3:40pm UTC](https://boards.straightdope.com/t/how-fast-does-isostatic-depression-occur/747729/5 "2016-03-02T15:40:53Z")

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> [@watchwolf49](#):
>
> \<nitpick\> … asthenoplain … Middle Earth is flat. \</nitpick\>

Not after the destruction of Numenor.