Accurate dating by measurement of ionium alone requires that the rate of sedimentation of ionium be constant with time, an assumption that does not hold for many sediments; any thorium-232 present in seawater will also precipitate, and the decay of the ratio of ionium to thorium-232 can be used as a measure of time.
This method does not require a constant rate of sedimentation of ionium but simply that the two isotopes are precipitated in a constant proportion.
Anna Frebel as a post-baccalaureate research fellow at the Harvard-Smithsonian Center for Astrophysics, before bringing her happy intern pants to GE where she worked as a Software Engineer designing mobile apps.
Nor can the measured Pb isotope ratios be used to somehow decide what proportions of them are the initial Pb without recourse to unprovable assumptions about the mineral or rock’s history or their interpreted U-Th-Pb ages within an assumed deep time history.
Nevertheless, the ultimate foundation of this U-Pb dating methodology is the assumption that the earth formed from the solar nebula.
Various methods have been devised to determine this initial or common Pb, but all involve making unprovable assumptions.
Zircon does incorporate initial Pb when it crystallizes. It cannot be proven that the Pb in apparently cogenetic U- or Th-free minerals is only initial Pb, and that it is identical to the initial Pb in the mineral being dated.
Once radioactive decay of U and Th started after creation, daughter Pb isotopes were added inside the earth.