Paleoclimatology
In ice cores, mainly Arctic and Antarctic, the ratio O-18/O-16 (δ18O) can be used to determine the temperature of precipitation through time. Assuming that atmospheric circulation and elevation has not changed significantly over the poles, the temperature of ice formation can be calculated as equilibrium fractionation between phases of water that is known for different temperatures. Water molecules are also subject to Rayleigh fractionation as atmospheric water moves from the equator poleward which results in progressive depletion of O-18, or lower δ18O values. In the 1950s, Harold Urey performed an experiment in which he mixed both normal water and water with oxygen-18 in a barrel, and then partially froze the barrel's contents.
The ratio O-18/O-16 (δ18O) can also be used to determine paleothermometry in certain types of fossils. The fossils in question have to show progressive growth in the animal or plant that the fossil represents. The fossil material used is generally calcite or aragonite, however oxygen isotope paleothermometry has also been done of phosphatic fossils using SHRIMP. For example, seasonal temperature variations may be determined from a single sea shell from a scallop. As the scallop grows, an extension is seen on the surface of the shell. Each growth band can be measured, and a calculation is used to determine the probable sea water temperature in comparison to each growth. The equation for this is:
Where T is temperature in Celsius and A and B are constants.
For determination of ocean temperatures over geologic time, multiple fossils of the same species in different stratigraphic layers would be measured, and the difference between them would indicate long term changes.
Read more about this topic: Oxygen-18