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Earth and Space Sciences · 术语表

什么是 Isochron, initial ratio？

又称： isochron · initial ratio

Definition 25.4 University Earth and Space Sciences — Year 1 · 第 25 章 — Radiometric Dating Methods

Let $S$ be a stable isotope of the daughter element that no decay produces ( $^{86}\mathrm{Sr}$ for strontium, $^{144}\mathrm{Nd}$ for neodymium). An isochron is the straight line on which plot, in a graph of $y = D/S$ against $x = P/S$ , samples that formed at the same time with the same value of $D/S$ and have been closed systems since. That shared starting value $y_0 = (D/S)_0$ is the initial ratio.

A rubidium–strontium isochron of six whole-rock samples of an invented rhyolite (exercise data). The points scatter slightly about the least-squares line, which passes through their centroid; the dotted line is where all of them lay when the lavas formed.

示例

Example 25.8 (An invented rhyolite)

Six whole-rock samples of a series of rhyolite lavas (exercise data) give:

$x = {}^{87}\mathrm{Rb}/^{86}\mathrm{Sr}$	1.85	4.62	9.30	14.75	21.20	27.60
$y = {}^{87}\mathrm{Sr}/^{86}\mathrm{Sr}$	0.71732	0.73332	0.76164	0.79420	0.83226	0.87028

Here $\bar x = 13.22$ , $\bar y = 0.784837$ , $S_{xx} = 491.41$ and $S_{xy} = 2.92308$ , so $m = 0.0059484$ and $b = 0.70620$ . The residuals give $s = 0.00024$ , $\sigma_m = 1.10 \times 10^{-5}$ and $\sigma_b = 0.00018$ . The age is $t = \ln(1.0059484)/1.3972 \times 10^{-11} = 424.5\,\mathrm{Ma}$ , with $\sigma_t = 1.10 \times 10^{-5}/(1.3972 \times 10^{-11} \times 1.0059) = 0.8\,\mathrm{Myr}$ : $(424.5 \pm 0.8)\,\mathrm{Ma}$ , initial ratio $0.706\,20 \pm 0.000\,18$ (figure below).

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