Geoscience Reference
In-Depth Information
2. Why can oxygen isotope abundances in carbonate sections and ice cores change
abruptly over time scales much sorter than the residence time of water in the ocean
(e.g. during the Younger Dryas)? Why do you not expect such abrupt changes to be
observed for
87
Sr/
86
Sr records?
3. Using the data of
Appendix A
and
F
and assuming a steady state, calculate the resi-
dence times of the following elements in the ocean: Br, Rb, Mg, Fe, Sr, and Pb. Which
elements do you expect to be homogeneously distributed across the ocean? Which ele-
ments should show regional or vertical variations? Do you expect the fluctuations of
the seawater
87
Sr/
86
Sr ratio to be modulated by glacial-interglacial cycles? Why?
4. The composition of the mean mantle can be calculated by removing the amount of
elements hosted in continental crust (see exercise in
Chapter 1
). Using the data of
Table 1.4
for the composition of MORB and the appropriate data from
Appendix F
,
calculate the mean residence times of K, Sr, Zr, La, Yb, Th, and U in the man-
tle before they are extracted into the oceanic crust. Discuss mantle homogeneity vs.
heterogeneity for these elements.
5. The diameter of a nearly circular lagoon on a Pacific atoll is 3.5 km and its mean depth
500m. Water flows through the inlet at a rate
Q
10
8
m
3
y
−
1
.
(i) What is the residence time of water in the lagoon?
(ii) The lagoon is accidentally contaminated by strontium 90, which has a half-life of
29.1 y. If sedimentation could be ignored, what would be the residence time of
this nuclide in the water of the lagoon?
(iii) Reef growth leaves carbonated sediment on the floor of the lagoon. We assume
a sediment density of 2000 kg m
−
3
and a sedimentation rate
=
of 1 mm y
−
1
.
Calculate the sediment flux
P
in kg y
−
1
. Strontium is scavenged by the sediment
with a carbonate-seawater partition coefficient
D
of 25 m
3
kg
−
1
.
(iv) What is the residence time of
90
Sr in the lagoon in the presence of sedimentation?
(v) Give an alternative theory in which you replace the residence times by probabili-
ties.
6. Show that, if Sr concentrations do not change very significantly through a sequence
of volcanic eruptions, the resorption of a pulse in the
87
Sr/
86
Sr ratio can be used to
estimate the residence of Sr in the magma chamber (discuss the potential importance
of plagioclase on the liquidus). Show that, if the eruption rate is known, the volume of
the magma chamber can be calculated. In 1880, an unusual change of
87
Sr/
86
Sr of a
Hawaiian volcano was resorbed in about 30 years. What was the approximate volume
of the magma chamber if the eruption rate was 0.05 km
3
y
−
1
?
7. Strontium has a residence time in the ocean of about 4 My. What is the proportion of
Sr atoms that have been in the ocean for more than 20 My? For less than 100 ky?
8. A global hydrogen cycle: we assume that H and D are distributed among two reser-
voirs, a deep reservoir (the mantle) and a shallow reservoir (the hydrosphere). Use
ual water left upon melting of the mantle at mid-ocean ridges to demonstrate how the
mantle
v
) relates to the D/H fractionation coefficient at subduction zones.
9. If the mean residence time of Nd in the mantle is 6 Ga, what is the proportion of Nd
atoms in the mantle that have never been extracted into the ridges?
δ
D(
≈−
85
