4 Isotope Geochemistry in the Environment
85
A d
v,++ = AT~
ft)
ATs corresponds to the time period during which sedimentation takes place
leading to an increase in the sediment pile thickness equal to ,Sd (Fig. 4.34). In
bed i, the nuclide content present: ar,i sed (Bq/kg dry sample) is considered to be
the result of the influence of the two independent input mechanisms (see above):
~r
st+Je C/~u.~p
ar.i = t~'lr.i "~- ..... t
(H)
The average nuclide content at time Tp in the sediment sample arsed(Tp) can be
calculated as follows after consideration of the appropriate radioactive decay
constant (3,):
aS+a(T ) =
z~d,a:'~ exp[-2(Tv- T=., )]+...Ad.a:,~ exp[-2(T,- T,.. 1]
(m)
i=1
Assuming that the sediment bed thicknesses Adi are the same throughout period
ATs then the sedimentation rate Vse d must also be constant through time.
Therefore:
Act, = Az+l, = .......... Az-/i = Ad
~z3z/i =d
t=l
lad
L - r.,., = i A L = ...
Vsed
(iv)
We can rearrange equation (III), by taking into account equations (II) and (IV) as
follows:
I=+
=:'~(r')--T _ ~'" ~
+E='''.=p-~-. J ,., "
~ ,..,
CV)