Theory of a methodology for initial lead determination, and a procedure to resolve it to some of its stages

Abstract A method for determining the initial Pb of a terrain, on the basis of the measured isotopic compositions of its rocks, is put forward in this report. The method was inspired by the premise that the initial Pb inherited by the rocks from a reservoir from which they were extracted, is immutable and inerasable, irrespective of the multitude of disturbances that may have subsequently been superimposed on the terrain. This is because while these disturbances may have altered the isotopic composition of some or all the rocks, they lacked the vehemence to re-melt the entire terrain or at least a very large portion of it, which is a pre-requisite for altering the isotopic composition of initial Pb. If this rational is valid, then a large Pb isotope database (including data on mineral separates with low affinities for U and Th) that is representative of a terrain, when plotted on any Pb isotope correlation diagram (e.g., the conventional Pb/Pb plot), may define a dispersion field that tapers toward a single spot. That single spot (once unambiguously determined) is the initial Pb isotopic composition. Furthermore, from the equations of radioactive decay as applied in geochronology, the author provides evidence for the potential existence within a Pb isotope dispersion field, of three classes of lines that converge in different types of Pb isotope correlations, to always meet in a point that yields the composition of initial Pb. These lines are: (1) isochron : defined by samples that remained as closed systems since crystallization, (2) transposichrons : each made up of samples that experienced in a disturbance episode, fractionation by the same constant factor F = ( 238 U/ 204 Pb) pc /( 238 U/ 204 Pb) cr , and/or the same constant factor K = ( 232 Th/ 238 U) pc /( 232 Th/ 238 U) cr , where the subscripts stand for post-crystallization and crystallization, and (3) Heterochrons : each defined by samples produced by different evolution scenarios (including different multiple stages with different values for the geochemical parameters F and K), which happen to accidentally have the same average F and/or the same average K. As demonstrated by synthetic examples, heterochrons occur because the production of a Pb isotopic ratio by radioactive decay is controlled by multiple Independent variables. This circumstance allows for various combinations of the parameters, to accidentally produce same radiogenic isotopic ratio. An application to a terrestrial terrain (out of four, discussed in companion paper # 2), further illustrates in this report, the validity of the rational and the practicality of the method. The determination of the initial Pb composition is a necessary step toward elucidation of the early evolution history of a planet, but alone, such a step falls short of reaching the goal. Full chronometric elucidation of a planet's history, requires complete resolution of initial Pb into all the multiple stages that led to its final composition. As this is not readily tenable, a procedure (termed ‘ Congruently Associated Profiles ’, CAPs ) in which initial Pb is partially resolved (into two or three stages) is introduced as an alternative. However, now that initial Pb is shown to be routinely determinable, could resolution of its multi-stages, someday become possible? To some, including the author, even the apparent ‘impossibility’ of an objective neither over rides hope nor stops prospecting for its realization.