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Sea level variations during snowball Earth formation: 1. A preliminary analysis

A preliminary theoretical estimate of the extent to which the ocean surface could have fallen with respect to the continents during the snowball Earth events of the Late Neoproterozoic is made by solving the Sea Level Equation for a spherically symmetric Maxwell Earth. For a 720 Ma (Sturtian) continental configuration, the ice sheet volume in a snowball state is ~750 m sea level equivalent, but ocean surface lowering (relative to the original surface) is ~525 m due to ocean floor rebounding. Because the land is depressed by ice sheets nonuniformly, the continental freeboard (which may be recorded in the sedimentary record) at the edge of the continents varies between 280 and 520 m. For the 570 Ma (Marinoan) continental configuration, ice volumes are ~1013 m in eustatic sea level equivalent in a “soft snowball” event and ~1047 m in a “hard snowball” event. For this more recent of the two major Neoproterozoic glaciations, the inferred freeboard generally ranges from 530 to 890 m with most probable values around 620 m. The thickness of the elastic lithosphere has more influence on the predicted freeboard values than does the viscosity of the mantle, but the influence is still small (~20 m). We therefore find that the expected continental freeboard during a snowball Earth event is broadly consistent with expectations (~500 m) based upon the inferences from Otavi Group sediments.