At that age the crust has finished cooling and has reached abyssal plain Radiometric dating--this gives the age of igneous and metamorphic.
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Oceanic crust
As an example, he uses Pliocene to Recent lava flows and from lava flows in historical times to illustrate the problem. He says, these flows should have slopes approaching zero less than 1 million years , but they instead appear to be much older million years. Steve Austin has found lava rocks on the Uinkeret Plateau at Grand Canyon with fictitious isochrons dating at 1. Then a mixing of A and B will have the same fixed concentration of N everywhere, but the amount of D will be proportional to the amount of P.
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This produces an isochron yielding the same age as sample A. This is a reasonable scenario, since N is a non-radiogenic isotope not produced by decay such as lead , and it can be assumed to have similar concentrations in many magmas. Magma from the ocean floor has little U and little U and probably little lead byproducts lead and lead Magma from melted continental material probably has more of both U and U and lead and lead Thus we can get an isochron by mixing, that has the age of the younger-looking continental crust.
The age will not even depend on how much crust is incorporated, as long as it is non-zero. However, if the crust is enriched in lead or impoverished in uranium before the mixing, then the age of the isochron will be increased. If the reverse happens before mixing, the age of the isochron will be decreased. Any process that enriches or impoverishes part of the magma in lead or uranium before such a mixing will have a similar effect. So all of the scenarios given before can also yield spurious isochrons.
Dating Oceanic Crust – No Interracial Dating
I hope that this discussion will dispel the idea that there is something magical about isochrons that prevents spurious dates from being obtained by enrichment or depletion of parent or daughter elements as one would expect by common sense reasoning. So all the mechanisms mentioned earlier are capable of producing isochrons with ages that are too old, or that decrease rapidly with time. The conclusion is the same, radiometric dating is in trouble.
I now describe this mixing in more detail. Suppose P p is the concentration of parent at a point p in a rock. The point p specifies x,y, and z co-ordinates. Let D p be the concentration of daughter at the point p. Let N p be the concentration of some non-radiogenic not generated by radioactive decay isotope of D at point p. Suppose this rock is obtained by mixing of two other rocks, A and B. Suppose that A has a for the sake of argument, uniform concentration of P1 of parent, D1 of daughter, and N1 of non-radiogenic isotope of the daughter.
Thus P1, D1, and N1 are numbers between 0 and 1 whose sum adds to less than 1. Suppose B has concentrations P2, D2, and N2. Let r p be the fraction of A at any given point p in the mixture.
So the usual methods for augmenting and depleting parent and daughter substances still work to influence the age of this isochron. More daughter product means an older age, and less daughter product relative to parent means a younger age. In fact, more is true. Any isochron whatever with a positive age and a constant concentration of N can be constructed by such a mixing.
It is only necessary to choose r p and P1, N1, and N2 so as to make P p and D p agree with the observed values, and there is enough freedom to do this. Anyway, to sum up, there are many processes that can produce a rock or magma A having a spurious parent-to-daughter ratio. Then from mixing, one can produce an isochron having a spurious age. This shows that computed radiometric ages, even isochrons, do not have any necessary relation to true geologic ages. Mixing can produce isochrons giving false ages. But anyway, let's suppose we only consider isochrons for which mixing cannot be detected.
How do their ages agree with the assumed ages of their geologic periods? As far as I know, it's anyone's guess, but I'd appreciate more information on this. I believe that the same considerations apply to concordia and discordia, but am not as familiar with them. It's interesting that isochrons depend on chemical fractionation for their validity. They assume that initially the magma was well mixed to assure an even concentration of lead isotopes, but that uranium or thorium were unevenly distributed initially.
So this assumes at the start that chemical fractionation is operating. But these same chemical fractionation processes call radiometric dating into question. The relative concentrations of lead isotopes are measured in the vicinity of a rock. The amount of radiogenic lead is measured by seeing how the lead in the rock differs in isotope composition from the lead around the rock. This is actually a good argument.
But, is this test always done? How often is it done? And what does one mean by the vicinity of the rock? How big is a vicinity? One could say that some of the radiogenic lead has diffused into neighboring rocks, too. Some of the neighboring rocks may have uranium and thorium as well although this can be factored in in an isochron-type manner. Furthermore, I believe that mixing can also invalidate this test, since it is essentially an isochron.
Finally, if one only considers U-Pb and Th-Pb dates for which this test is done, and for which mixing cannot be detected.
Investigations of the oceanic crust
The above two-source mixing scenario is limited, because it can only produce isochrons having a fixed concentration of N p. To produce isochrons having a variable N p , a mixing of three sources would suffice. This could produce an arbitrary isochron, so this mixing could not be detected. Also, it seems unrealistic to say that a geologist would discard any isochron with a constant value of N p , as it seems to be a very natural condition at least for whole rock isochrons , and not necessarily to indicate mixing.
I now show that the mixing of three sources can produce an isochron that could not be detected by the mixing test. First let me note that there is a lot more going on than just mixing. There can also be fractionation that might treat the parent and daughter products identically, and thus preserve the isochron, while changing the concentrations so as to cause the mixing test to fail.
It is not even necessary for the fractionation to treat parent and daughter equally, as long as it has the same preference for one over the other in all minerals examined; this will also preserve the isochron. Now, suppose we have an arbitrary isochron with concentrations of parent, daughter, and non-radiogenic isotope of the daughter as P p , D p , and N p at point p. Suppose that the rock is then diluted with another source which does not contain any of D, P, or N.
Then these concentrations would be reduced by a factor of say r' p at point p, and so the new concentrations would be P p r' p , D p r' p , and N p r' p at point p. Now, earlier I stated that an arbitrary isochron with a fixed concentration of N p could be obtained by mixing of two sources, both having a fixed concentration of N p. With mixing from a third source as indicated above, we obtain an isochron with a variable concentration of N p , and in fact an arbitrary isochron can be obtained in this manner. So we see that it is actually not much harder to get an isochron yielding a given age than it is to get a single rock yielding a given age.
This can happen by mixing scenarios as indicated above. Thus all of our scenarios for producing spurious parent-to-daughter ratios can be extended to yield spurious isochrons. The condition that one of the sources have no P, D, or N is fairly natural, I think, because of the various fractionations that can produce very different kinds of magma, and because of crustal materials of various kinds melting and entering the magma. In fact, considering all of the processes going on in magma, it would seem that such mixing processes and pseudo-isochrons would be guaranteed to occur.
Even if one of the sources has only tiny amounts of P, D, and N, it would still produce a reasonably good isochron as indicated above, and this isochron could not be detected by the mixing test. I now give a more natural three-source mixing scenario that can produce an arbitrary isochron, which could not be detected by a mixing test.
P2 and P3 are small, since some rocks will have little parent substance. Suppose also that N2 and N3 differ significantly. Such mixings can produce arbitrary isochrons, so these cannot be detected by any mixing test. Also, if P1 is reduced by fractionation prior to mixing, this will make the age larger. If P1 is increased, it will make the age smaller. If P1 is not changed, the age will at least have geological significance. But it could be measuring the apparent age of the ocean floor or crustal material rather than the time of the lava flow. I believe that the above shows the 3 source mixing to be natural and likely.
We now show in more detail that we can get an arbitrary isochron by a mixing of three sources. Thus such mixings cannot be detected by a mixing test. Assume D3, P3, and N3 in source 3, all zero. One can get this mixing to work with smaller concentrations, too.
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All the rest of the mixing comes from source 3. Thus we produce the desired isochron. So this is a valid mixing, and we are done. We can get more realistic mixings of three sources with the same result by choosing the sources to be linear combinations of sources 1, 2, and 3 above, with more natural concentrations of D, P, and N. The rest of the mixing comes from source 3. This mixing is more realistic because P1, N1, D2, and N2 are not so large. I did see in one reference the statement that some parent-to-daughter ratio yielded more accurate dates than isochrons.