Case studies Homework
Because the ‘non-Geologists’ are at a slight disadvantage, these questions can be
discussed with anyone. However, formulate your own answers, and be concise. The
due date for this homework set is 11/03/06. Please type and email your answers to me
as a PDF at [email protected].
A. 182Hf-182W:
1) Describe the isotope systematics of the 182Hf-182W chronometer. In other words:
What nucleosynthetic process produces the relevant Hf and W nuclides? What is
the decay scheme? What is the half-life of the parent isotope? What is the decay
equation?
2) What are the characteristics of the Hf-W isotopic system that make it ideal for
addressing the timing of core formation early in the Earths history?
3) What has recently changed in mass spectrometry that has enhanced our
capabilities to measure this isotope system?
4) Define the eW notation used in the Halliday and Lee (1999) paper. Define BSE.
5) What do Halliday and Lee (1999) conclude from their data about the timing of
core formation in the Earth? What do Yin et al 2002 and Kliene et al., 2002
conclude about this timing? What is different about the Haliday and Lee 1999
data from Yin et al 2002 and Kliene et al., 2002.
6) Why is W the chemical symbol for Tungsten?
B. 147Sm-143Nd and 87Rb-86Sr:
1) What is CHUR? How is this different than the Bulk Silicate Earth (BSE)?
2) CHUR currently has a Sm/Nd ratio of 0.3252. What is the current 147Sm/144Nd of
CHUR ? Plot CHUR on a 147Sm/144Nd – Nd isochron plot? Calculate and plot a
1.7Ga isochron through CHUR.
3) Assuming that the ‘continental crust’ and ‘depleted mantle’ are complementary
reservoirs of the Bulk Silicate Earth (or for the Sm-Nd system- CHUR; where Nd
~ 0) and that the average age of the crust and mantle is ca. 1.7Ga, locate the
depleted mantle reservoir (Nd ~ +10) and continental crustal reservoirs (Nd ~ 15) on this isochron.
4) What is the Sm/Nd ratio of the Depleted Mantle reservoir and continental crustal
reservoir? Why are these ratios different? Which reservoir is enriched in the light
Rare Earth Element (REE) Nd? In this model, when did this enrichment of Nd
over Sm occur?
C. U-series disequilibria:
Melting Basics:
1) The batch melting equation is:
CAl =
1
CAs
F + (1 F)DA
(Schilling 1966) where ClA and CSA is the concentration of element A in the
liguid/melt and solid mantle respectively, F is the total melt fraction and DA is the
bulk mineral/melt partition coefficient for the element A, which is the sum of the
individual mineral partition coefficients weighted by the proportion of the minerals in
the melting solid (i.e. DA = wKolA + xKopxA + yKcpxA+ zKgtA where w, x, y and z are
the relative portions of the different minerals and sum to 1).
Olivine (ol)
KU
KTh
1e-5
1e-5
Orthopyroxene
(opx)
1E-5
1E-5
Clinopyroxene
(cpx)
1.0E-02
1.5E-02
Garnet (gt)
1.3E-02
3.5E-03
Given the individual U and Th mineral/melt partition coefficients above, determine
the bulk partition coefficients for U and Th (i.e. DTh and DU) for a “garnet lherzolite”
mantle composed of garnet (12%), olivine (59%), orthopyxone (21%) and
clinopyroxene (8%).
Derive the batch melting expression for the ratio of two elements (i.e. ClA/ ClB = ?).
For a Th/U source ratio (CsTh/ CsU) of 3.9, what is the Th/U in the melt (ClTh/ ClU) if the
total melt fraction (F) is 100%, 0%, 10%, 1%, 0.1%, and 0.001%? Make a plot of
[Th/U]melt/[Th/U]source versus total melt fraction (F).
Considering the relationship shown on this plot what is the maximum melt fraction
capable of fractionating Th from U during batch melting?
Which of the above minerals is responsible for the observed fractionation of Th from
U during melting? What would be different about the direction of Th/U fractionation
(i.e. change during melting) if the solid mantle undergoing melting was composed of
only olivine, orthopyroxene and clinopyroxene (i.e. no garnet)?
2) The decay expressions governing U-Th disequilibria is:
230Th 230Th 238U 230 t
t
e
+
=
232 232 232 (1 e 230 )
Th
Th
Th
initial
a) Derive an expression for time (t), which allows you to calculate the age of a sample as
a function of the current/measured and initial values for (230Th/232Th) and the measured
(238U/232Th).
In the table below is the distance from the axis (in kms), (230Th/238U), (230Th/232Th) and
(238U/232Th) for several mid-ocean ridge basalt (MORB) samples collected off-axis along
the East Pacific Rise.
Sample
2737-8
2746-9
2768-3
2772-1
2772-2
Distance
from axis
(kms)
1.85 west
0.74 west
3.75 east
2.28 east
1.44 west
(230Th/238U)
(230Th/232Th)
(238U/232Th)
1.127
1.120
1.065
1.153
1.148
1.375
1.356
1.322
1.422
1.412
1.219
1.210
1.241
1.233
1.230
b) Determine the ages of these samples assuming that the initial (230Th/232Th) value is
1.36 in “zero-age” lava erupted at the ridge axis.
c) Assuming a spreading rate of 5.5 cm/yr, calculate the spreading rate age of these lavas
assuming they originated in the axis.
d) Is there is a difference between the calculated spreading rate ages and the U-series
ages? If so speculate why.
D. Isotopic Evolution:
Draw the isotopic evolution diagrams for the 238U-206Pb system in the Earth as it has
evolved from the Hadean (presolar formation/condensation) to present. Be sure to
show how major processes such as accretion, core formation, and BSE differentation
(into an enriched crustal reservoir and depleted mantle reservoir) would influence the
resulting Pb isotopic compositions.