This is a place for all questions about Geology (not only related to Petroleum exploration and production). You can also ask our experts to determine rock types from photographs in this forum.
Wed Dec 17, 2014 8:12 pm
I am very interested in dating rocks and am about to read the book of Gunter Faure, Principles of Isotope Geology. I came across the linear equation below, which I understand well.
(87Sr/86Sr)t = (87Sr/86Sr)i + (87Rb/86Sr)t * lambda * t
where the index t after the parenthesis refers to time dependency and i to the initial value, lambda is the decay constant.
However, I don't understand the interpretation that is given in the book, that is, the claim that (87Rb/86Sr)t * lambda is the slope. How can this be since a slope in linear equation must be independent of the variable t, which is not the case. In fact rubidium 87 decays to stable strontium 87 so (87Rb/86Sr)t is decreasing over time since strontium 86 is stable as well. Can someone explain this oddity?
Thu Dec 18, 2014 8:41 am
Interesting question. I'm just thinking out liud here.
Isn't (87Rb/86Sr)t the ratio at a certain time 't'. I interpret it as the t not being a variable but rather a indication of the time dependancy of the ratio.
The (87Rb/86Sr)t is thus a given if you measure it, but you don't know t.
The 'constant' in the formula is then multiplied with Lambda to get the slope of the function as in y=ax+b a is the slope.
Thu Dec 18, 2014 9:02 pm
Yes, (87Rb/86Sr)t is the ratio at a certain time t. If for instance a rock is very old, you can take an initial value (87Sr/86Sr)i as it is found in meteorites. The other ratios you measure and then you can solve the equation for t and determine how old a rock is. But in Faure's book there is an illustration (see below).
The straight lines there have presumably constant slopes (87Rb/86Sr)t * lambda. But these ratios are certainly not constant over a time of 800 million years like in the illustration, unless I am missing something. But what?
Tue Dec 23, 2014 12:18 pm
The solution is that the ratio 87Rb/86Sr can be interpreted both as time dependent and as the initial ratio when the rock was formed. Because the number of daughter atoms can both be:
D = D0 + N(t) (Exp[lambda * t] - 1)
or:
D = D0 + N0 (1 - Exp[-lambda * t])
where N(t) is the number of parent atoms at time t, D0 the initial number of daughter atoms and correspondingly N0 the initial number of parent atoms.
So approximating Exp[±lambda * t] = 1 ± lambda * t for small lambda * t, we get what we are looking for. Unfortunately, only the first equation is explicitly discussed in the book...
Tue Dec 23, 2014 3:54 pm
Thanks for sharing. I wouldn‘t have come up with that...
Powered by phpBB © phpBB Group.
phpBB Mobile / SEO by Artodia.