Geoscience Reference
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Figure 6.10
One thousand grains of rice randomly thrown on a square table. The distribution is not regular, as
each small square received a variable number of grains (2-20), but is perceived as random: a
grain lands anywhere on the table with equal probability. The number of grains in any patch
drawn on the table is proportional to the surface area of the patch (Poisson distribution).
Likewise, the mantle is well mixed when the distribution of heterogeneities achieves maximum
randomness. A regular distribution of heterogeneities is totally unlikely. Complex patterns of
isotopic and chemical heterogeneities are no indication that the mantle is not well stirred.
One more time, we meet our old friend the Poisson distribution. As long as the mutual
distance between chemically or isotopically identifiable heterogeneities exceeds the mean
diffusion length, vigorous mantle mixing will tend to produce a distribution of chemical
and isotopic anomalies that resembles a Poisson distribution. Complex heterogeneity pat-
terns in the mantle do not necessarily indicate imperfect mantle or ocean mixing but are a
straightforward consequence of random redistribution of material by mantle convection.
Exercises
1. What is the average time spent (1) by water in the ocean before being renewed by
the rivers, and (2) by material in the mantle before being extracted into the oceanic
lithosphere? Use the data of Appendix F and neglect density differences.
 
 
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