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I am wondering how accurate such an approximation would be. I wish to take a current height map of the earth (including the ocean floor) and approximate the form of ancient landmasses by changing the sea level height.

I suppose this question could be answered by how much the ocean floor changes over time.

Timescales: Preferably over the last 200 000 - 300 000 years, but depending on the error of such an approximation, I am willing to settle for the last 10 000 - 15 000 years.

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over that short a time there would be very little change in the land itself, all you really get is a sea level change due to changes in the ice sheets, continental movement is barely noticeable.

such measurements and maps already exist.

here is the earth 12,000 years ago. enter image description here

Here is the same map with the changes highlighted. enter image description here

sources for other maps https://www.fieldmuseum.org/pleistocene-sea-level-maps

http://antiquity.ac.uk/projgall/sakellariou334/

Or you can even use this interactive map, which already does what you want to do, and compare it to past sea level.

As for why projecting backwards is easy, you may want to look up the term "continental shelf".

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