Why do some impact craters have an elevation in the center? Why do some impact craters have an elevation in the center? What processes lead to its formation?
 A: Note that this is almost identical to this previous SE question; the answers on that question however, including the favourite answer with 13 upvotes, are somewhat erroneous (or rather oversimplified).

This is a good question: the exact details of how such elevations, called 'central uplifts', form are not well known. What follows is a brief summary of the crater formation process, and a couple of references for further reading [1,2].
Large impact craters form when a projectile hits the ground with a speed much greater than the sound speed in the surrounding rock; typical speeds on impact are 11 km/s or greater [1]. The following processes may follow the impact, leading to the formation of a crater with a central uplift.


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*In a hypersonic meteorite impact, the projectile launches shock waves into the surrounding medium. Contrary to our day-to-day experience, rock under conditions of extreme temperature and pressure at the front of a shock is rather 'elastic' and can be stretched and squashed by the shock. This is the compression stage.

*The shock wave propagates radially away from the impact site into the surrounding rock. As the shock enters solid, uncompressed rock, it can cause melting, compression and displacement (movement) of the rock. Much of the displacement of rock near the surface is outward and upward, forming the rim of the crater. This is the excavation stage.

*After the initial shock has subsided, the gradual release of stress built up in the compressed rock can cause it to expand into the excavated crater. The release of this stress and the consequent deformation of the surface can, if the crater is sufficiently large, cause a central uplift or even a single or double ring to form in the crater. This is the modification stage.
[1] http://www.lpi.usra.edu/publications/books/CB-954/chapter3.pdf
[2] http://www.impact-structures.com/understanding-the-impact-cratering-process-a-simple-approach/
