<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>In a single decaying system, the age determined from the exponential decay law is directly related to its linear Maclaurin approximation. This relationship can be additively extended to several decaying systems resulting in the same daughter element, by using proportionality functions, thus allowing an explicit formulation of the age as a function of element concentrations. The values of the binary proportionality function for the 238U-235U-Pb system and the ternary proportionality function for the 232Th-238U-235U-Pb system were determined by iterations of the exponential decay formula up to 4 Ga, with a step of 10 Ma, for a set of 24 different U/Th ratios. From the iteration data, the expressions of the two functions and the associated coefficients were determined by polynomial regression and mathematical programing on conveniently separated time and compositional intervals.</p><p>Additional time- and composition-dependent age corrections optimized by mathematical programming of the residuals lead to an accuracy of 0.005 Ma of the resulting age. The error propagation can be traced through all the operations defined by explicit formulas according to simple error propagation rules, finally allowing the calculation of the standard error of the result. The formulas and parameters derived can be used in a calculation spreadsheet.</p></abstract>

In a single decaying system, the age determined from the exponential decay law is directly related to its linear Maclaurin approximation. This relationship can be additively extended to several decaying systems resulting in the same daughter element, by using proportionality functions, thus allowing an explicit formulation of the age as a function of element concentrations. The values of the binary proportionality function for the 238U-235U-Pb system and the ternary proportionality function for the 232Th-238U-235U-Pb system were determined by iterations of the exponential decay formula up to 4 Ga, with a step of 10 Ma, for a set of 24 different U/Th ratios. From the iteration data, the expressions of the two functions and the associated coefficients were determined by polynomial regression and mathematical programing on conveniently separated time and compositional intervals.Additional time- and composition-dependent age corrections optimized by mathematical programming of the residuals lead to an accuracy of 0.005 Ma of the resulting age. The error propagation can be traced through all the operations defined by explicit formulas according to simple error propagation rules, finally allowing the calculation of the standard error of the result. The formulas and parameters derived can be used in a calculation spreadsheet.

Chemical U-Th-Pb geochronology: A precise explicit approximation of the age equation and associated errors

Geological Institute of Romania, 1 Caransebeş st., RO-012271, Bucharest 32, Romania

Geochronometria

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In a single decaying system, the age determined from the exponential decay law is directly related to its linear Maclaurin approximation. This relationship can...

Chemical U-Th-Pb geochronology: A precise explicit approximation of the age equation and associated errors

Published Online: Jun 19, 2012

Page range: 167 - 179

DOI: https://doi.org/10.2478/s13386-012-0007-3

Keywords
U-Th-Pb chemical dating, age equation, explicit approximation

© 2012 Silesian University of Technology, Gliwice, Poland

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Chemical U-Th-Pb geochronology: A precise explicit approximation of the age equation and associated errors

Published Online: Jun 19, 2012

Page range: 167 - 179

DOI: https://doi.org/10.2478/s13386-012-0007-3

KeywordsU-Th-Pb chemical dating, age equation, explicit approximation

© 2012 Silesian University of Technology, Gliwice, Poland

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
U-Th-Pb chemical dating, age equation, explicit approximation