Geoscience Reference
In-Depth Information
Cenozoic
1.0
Cretaceous
Jurassic
Triassic
Permian
0.1
0
50
100
150
200
250
300
Age at end of period (Ma)
Figure 6.3
arrangement implies that the sedimentary reservoir is well mixed with a probability of erosion
independent of sediment age. The slope of the line indicates that this type of sediment survives
on average about 150 million years before being eroded.
time here below. However, the average age of the population is much younger, probably
about 30-40 years. Let us imagine now an outbreak of a virus that affects old and young
indiscriminately. The population becomes well mixed in the sense that the probability of
exiting the system is independent of the individual's age. The gravestones would then show
an average age of demise close to the mean age of the population. This latter case is the
one most often considered in the dynamics of natural systems where the probability that
a particle leaves the system does not increase with the particle's age. It can be shown (see
box) that particles in a well-mixed system have an exponential age-group histogram (exit is
a Poisson process). Under such conditions, the proportion of individuals that have resided
in the system for a time in excess of
θ
is
e
−
θ/τ
f
(θ)
=
(6.12)
τ
in which
is the mean residence time of all the individuals in the system. In a well-mixed
reservoir, not all the individuals have the same residence time but they all have the same
probability of exit, regardless of their previous history in the system.
Such an example of age distribution is given by the survival of clastic sediments since
age decreases exponentially with time. The average age of the sediment is equal to its
mean survival time of about 150 million years. This demonstrates the stationary charac-
ter of the total mass of clays, sandstones, etc. Similar ideas may be used for tracers in
the mantle or in the ocean: the “birth” of chemical tracers (e.g. the element Ba or the
