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The Vredefort Crater is one of the biggest known impact craters on earth. How deep would it have been, relative to the original ground height, immediately after the dust settled, and before any erosion kicked in?
Is there a general relationship between the diameter of a meteorite crater and it's initial depth?
Therriault et al. (1993) suggest an initial diameter of 192-300km. Turtle & Piarazzo (1998) suggest a smaller initial diameter but make no estimates of the depth; they do, however, suggest an impactor of 10-14km diameter. Dietz (1961) describes the impact crater as "40km across and 16km deep" - i.e. does not take into account the extensive erosion that has occurred in this location. Grieve et al. (2008) also give no estimate of transient depth.
Numerical modelling of the impact diameter-crater depth relationship has been carried out: see e.g. Wünneman & Ivanov (2003), which also discusses crater morphology; meanwhile Turtle et al. (2003) suggest that for an impactor of 10km diameter the maximum transient crater depth will be 24km.
It seems likely that difficulty in estimating transient depth arises due to the 2Ga history of erosion in the area; as such the best option is probably to appeal to uniformitarianism, and assume that the Vredefort-forming impact obeyed the same diameter-depth relationship as has been modelled for the population of recent craters in works cited above.
