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Equivalence of the time and Laplace domain solutions for the steady state concentration of radiometric tracers and the groundwater age equation
Author(s) -
Engdahl Nicholas B.
Publication year - 2014
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2014wr015413
Subject(s) - tracer , laplace transform , equivalence (formal languages) , radiometric dating , distribution (mathematics) , steady state (chemistry) , inverse laplace transform , range (aeronautics) , mathematics , mathematical analysis , physics , chemistry , geology , materials science , quantum mechanics , paleontology , discrete mathematics , composite material
It has been previously shown that the normalized concentration of a radioactively decaying tracer defines one point on the Laplace transformed age distribution and that point corresponds to the decay rate of the tracer. However, it is unclear how two time domain quantities, the decay rate and normalized concentration, are related to the elements of a Laplace transformed distribution; this note clarifies these relationships mechanistically. It is shown that the Laplace transformed age distribution is equivalent to the late‐time concentration of a radiometric tracer if transport and age are both at steady state. The result is general and may be applied to any age distribution, including non‐Fickian distributions. The significance of the generality is that the steady state concentrations and known decay rates may be used to help constrain the parameters of an unknown age distribution in a wide range of flow systems.