The first, titled "Theory of a methodology for initial lead determination," highlights the development of a new method for determination of initial Pb, synthetic examples for applications, application to a terrestrial terrain, and an algebraic resolution of initial Pb to multi 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/204Pb)pc/(238 U/204Pb)cr, and/or the same constant factor K = (232Th/238 U)pc/(232Th/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, some day become possible? To some, including the author, even the apparent ‘impossibility’ of an objective neither over rides hope nor stops prospecting for its realization.
The second, titled "Determination of initial leads of four terrestrial terrains, applying the Tulip methodology," covers the initial leads of four terrestrial terrains, as well as the occurance of first-stage U-Pb fractionation at most 67 Ma after the Earth's accretion.
Abstract: The recently developed TULIP methodology for determining Initial lead, based on the measured Pb isotopic compositions of rocks, was applied to four terrestrial terrains, and the results are shown and discussed in this report. Particular emphasis was given to the determination of initial Pb of the South Of Isua (SOI) terrain, because of the availability of a large high-quality database on its rocks and feldspar separates. The initial Pb results for SOI, are: 206Pb/204Pb = 11.088 ± 0.024, 207Pb/204Pb = 12.983 ± 0.002, and 208Pb/204Pb = 31.196 ± 0.014. Initial Pb was also precisely determined for the Beartooth Mountains, and the results are: 206/204 = 13.571 ± 0.071, 207/204 = 14.891 ± 0.003, and 208/204 = 32.41 ± 0.08. These results demonstrate the feasibility of routine determination of initial Pb by the developed methodology, once large databases for the terrains are established. Extending the methodology to terrains of other planets should be possible.
Projection of initial Pb by a database is caused by Th-U-Pb fractionation, in disturbing events superimposed on the rocks of a terrain. As demonstrated mathematically (in a companion paper), elemental fractionation can induce alignments of the data in linear trends of false ‘ages,’ which together with the rocks' isochron, converge (on various Pb plots) on a point that yields initial Pb. This may result in two counter effects: (1) precise determination of initial Pb, and (2) ambiguity in the exact meaning of an isochron (because of the possibility it was affected by fractionation, like the other lines). Consequently associating a Pb/Pb age with the determined initial may not be meaningful. For SOI, the rocks' age is 3.84 ± 0.05 Ga.
The ability to determine initial Pb opens the possibility for eventual unfolding of details of the evolutionary history of the Earth and other planets. However, that cannot be satisfactorily achieved without additionally developing a methodology for resolving initial Pb to its multi-stages. Because such methodology is still lacking, a procedure of Congruently Associated Profiles (CAPs), for resolving initial Pb to a maximum of three stages was developed and outlined in a companion paper (C, P, # 1, 2016). For SOI, only a two-stage CAP solution is possible. It indicates a U-Pb fractionation event at 67.5 Ma after the Earth's accretion (that is a first stage lasting from 4.563 to 4.496 Ga), with μ = 238 U/204Pb = 0.45 ± 0.25. For the second stage, extending from 4.496 to 3.8 Ga, I obtain μ = 9.25 ± 0.02.
The stated duration of 67.5 Ma for the first stage is an upper limit, and in a multi- stage solution, if and when it becomes possible, the first stage duration would be shorter, and its meaning may be elucidated. For now it remains subject to qualitative speculations including the possibility of being ‘associated’ with core formation, or an early impact (resulting in formation of the moon?), or …or. This ambiguity underlines a crucial need for a methodology to resolve initial Pb to more of its multi stages.