Evaporites form in shallow marine environments or on land in playa lakes in hot deserts. Normal sea water contains a variety of ions in solutions, giving it a salinity of about 35 parts per thousand or 3.5%. As sea water evaporates, the brine first becomes more saturated, then supersaturated, at which point crystals of evaporite minerals being to crystalilise in the reverse order of solubility:

small quantities of calite and dolomite (carbonates) are precipitated (<1%)
followed by gypsm and ahydrite (3%)
then a large quantity of halite (78%)
finally k salts

Formation of Evaporites in barred basins
The basin is a bay with a restricted entrance. In hot arid conditions, water evaporates from the basin, causing lowering of the surface, drawing more water in through the narrow channel at the entrance.
Evaporation of surface water increases the salt concentration, especially at the end of the basin, away from the normal sea water entering over the bar:

carbonates are precipitated near to the entrance due to their low solubility
further away from the entrance, gypsum crystals precipitate at the surface due to evaporation and dissolve as they fall through the water below, increasing the density of the water at the bottom of the basin
dense brine sinks from the surface to the bottom of the basin and concentrated of gypsum is increased further as crystals fall from the surface and dissolve. Eventually the water in the basin is saturated in gypsum. When this occurs, gypsum crystals can form and sink to the sea floor without dissolving.
The process is repeated for the other evaporite minerals.

Permian salt deposits in Europe contain 490m of evaporites, and in some places more. This would mean evaporating a 29km high column of sea water. Obviously these thicknesses could not have built up by evaporating a fixed volume of sea water because there are no ocean basins 29km deep. Instead, if the water supply is regularly topped up within a shallow barred basin, large volumes of evaporties could build up over time. Repeated evaporite cycles are recorded from some deposits, meaning that a basin evaporated then was flooded and evaporated again. Incomplete cycles are formed when normal sea water floods into the basin before complete evaporation has taken place.

Formation fo Evaporites in Sabkhas
Sabkhas are low lying coastal sand flats in hot arid regions. Very gentle slopes mean that during extreme high tides the whole coastline is under water.

Process Operating in a Sabkha Environment

very strong evaporation occurs so that as the sea water approaches the coast salinity increases
much of the calcium carbonate in the sea water is removed by shelled organisms living offshore
evaporation of groundwater from the supertidal area draws sea water into the sediment along the shore
evaporites develop above the high water line as groundwater is evaporated. Algae grow on the short between high and low tide levels and are preserved as stromatolites. Evaporite minerals are found above the stromatolites in sabkha sequences
the first mineral to crystallise out within the sediment is gypsum
Anhydrite crystallises out next, forming nodules in the sediment.

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Undergraduate Geology - Part 2 (Sedimentary Processes and Products) Notiz am Marine Evaporites, erstellt von siobhan.quirk am 19/05/2013.

Marine Evaporites