The inversion of lead isotope data

Summary. Lead isotope ratios have been inverted to obtain information about the movement of U, Th, and/or Pb into or out of a source region. Unique time averages of μ( t ) = U 238 ( t )/Pb 204 and ξ( t )= Th 232 ( t )/Pb 204 (both normalized to the present) have been recovered by using the appraisal method of Backus & Gilbert and the corresponding averaging functions codify the resolving power of the isotopic data. In addition, this paper shows how to construct different types of models [μ( t ), or ξ( t )] which reproduce the observations. The techniques have been used to invert lead isotope data from worldwide deposits in the hope of obtaining information about a global μ( t ) and ξ( t ). Assuming that such data can be meaningfully inverted, the results showed that the average value of μ( t ) in the first billion years after Earth formation is 8.0 ± 0.3 while the average value between 2.0 and 3.0 Ga is 9.8 ± 0.3. Similarly, averages for ξ( t ) increase from 35 to 38 in those same time intervals. Whether these increases occurred smoothly or whether the higher values were achieved in one or more discrete jumps cannot be determined because the best time resolution available is 0.5 Ga. This lack of resolution is verified by algorithms which construct continuous and episodic models that reproduce the data. The fact that models exist which satisfactorily reproduce the observations shows that the lead ores used here are compatible with the concept of a single primary growth curve for those isotopes. Moreover, the younger leads, those deposited within the last 1.0 Ga, are compatible with models generated from data on older samples, and this suggests that time‐developing heterogeneity in the source region may not be as severe as initially supposed. Some reference primary growth curves are computed and compared with that generated by Stacey & Kramers.