Some Mathematical and Geophysical Considerations in Radioisotope Dating Applications

Some quality considerations for use in isotopic dating are presented to identify and correct heretofore unidentified overestimate scenarios. These include to a lesser degree the statistical interpretation issues with linear-least-squares fitting results but more importantly the isotope effect in the individual components of the isochron coefficient ratios. By taking into consideration the isotope effect (differential mass diffusion rates) when measuring isotopic ratios from very old samples, the distribution dependency in the coefficient ratios will cause a bias if isotopic diffusion rates are not identical throughout a sample. The isotope effect is that isotopes having a smaller atomic mass will diffuse faster throughout a medium than will their heavier counterparts causing concentration gradients of their ratios even when there are no contributions from radioactive decay. The application to Rb/Sr dating is evaluated and shown to result in expected age overestimates when isotopic ratios are employed to linearize the isochron. A suggested method to test for this effect is argued to require rigorous statistical analysis. An associated optimal sampling technique would involve using single-grain etching. It is also shown that the only method to fully eliminate the isotope effect is to not use isotopic ratios at all in radioisotopic dating as the physics do not require the use of isotopic ratios for geochronological dating. However, without the ratios, the data are inherently noisy.