Ge192
Homework Assignment #1. Topics 1-3
You may use class notes and library materials and may work in groups among
yourselves. Due on April 29 (either hand in to Margarita or put into an envelope
and place in my mailbox in North Mudd).
1. Although a number of different detrital minerals have been employed for provenance analysis
through 40Ar/39Ar dating of individual grains, hornblende is most commonly used. Why is that?
(2 points)
2. Because K-feldspar tends to exclude U, their Pb isotope ratios reflect the source composition at the
time of crystallization, making Pb isotopic compositions of detrital K-feldspar grains useful as
provenance indicators. Why might this approach not be useful for Mars? Suggest alternative
Martian detrital grain(s) that might be amenable to comparable Pb isotope analyses, and why that
might be the case?
(3 points)
3. In the following table are two isotope dilution (ID) rare earth element analyses, one for an Archean
sedimentary rock (derived from tonalities) and the second for an ocean basalt (ID cannot provide
data for mono-isotopic elements and Lu commonly is not determined). Also given is an estimate of
average chondritic meteorites. On the attached graph paper, carefully plot the sediment and basalt as
chondrite-normalized patterns. Calculate or estimate the following: REE, LaN/SmN and LaN/YbN,
and the likely concentrations of Y in ppm (Y has 2.1ppm in average chondrites). Eu-anomalies
(Eu/Eu*) are defined as the ratio between measured Eu and the value expected for Eu on a smooth
chondrite-normalized plot. In the literature, you will find people calculate Eu-anomalies (Eu/Eu*)
using either geometric ( (SmN  GdN ) or arithmetric ((SmN+GdN)/2) means to estimate Eu*.
Calculate Eu-anomalies for the two patterns using both formulas. Referring to the REE diagrams,
explain which is correct, why and describe the nature of the error if you calculate it the wrong way.

La
Ce
Pr
Nd
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
Archean Sediment
(ppm)
160
345
128
16.2
1.31
6.12
3.05
1.25
1.00
-
(15 points)
Ocean Basalt
(ppm)
1.45
4.79
5.68
2.30
0.44
3.01
3.89
2.59
2.62
-
Average Chondrite
(ppm)
0.367
0.957
0.137
0.711
0.231
0.087
0.306
0.058
0.381
0.0851
0.249
0.0356
0.248
0.0381
4. For the three samples listed in the table below, calculate fSm/Nd, Nd(0), TCHUR and TDM. On a
diagram of Nd versus Time, plot the evolution paths of CHUR, the depleted mantle and the three
samples (HINT: you don’t have to calculate the slopes (but can if you want) but can infer them
graphically). Assume that each of the samples is modern unconsolidated sediment taken from
widely separated locations. From these data, what can you say about the REE pattern of each of the
samples? Referring to the diagram and considering what you have learned so far, what can you say
about the provenance of each of the samples from the Nd-isotopic data?
(20 points)
Assume the depleted mantle (DM) evolves in a linear fashion, with the following present-day values:
(143Nd/144Nd)CHUR = 0.512636
(147Sm/144Nd)CHUR = 0.1966
(143Nd/144Nd)DM = 0.513149
(147Sm/144Nd)DM = 0.2138
Sample 1
Sample 2
Sample 3
147Sm/144Nd
143Nd/144Nd
0.1130
0.1041
0.1975
0.511381
0.512429
0.513064
5. In the table below are six highly precise analyses (~±2%) of fine-grained sedimentary rocks from
adjacent beds in a single stratigraphic section. Only 4 elements have been obtained in preparation
for isotopic analyses; all concentrations in parts per million. Carry out the following analysis:
(30 points)
(a) Tabulate Rb/Sr and Sm/Nd ratios. (To carry out analyses, you will need to calculate at least one
and perhaps more ratios – blank columns are for this purpose.)
(b) Construct a plot of Rb/Sr versus Sm/Nd. Identify the two extreme samples in terms of these
ratios and from these two samples, solve the equation of mixing (i.e., Ax+Bxy+Cy+D=0) and the
r-value. Plot the mixing line on the diagram (this can be done either from the mixing equation or
a mass balance calculation using the extreme sample compositions).
(c) Evaluate the overall data set to see if the chemical variation can be explained by simple two
component mixing. You will likely need at least 1 and probably 2 or more additional diagrams
in order to do this.
(d) If you conclude that these data are consistent with simple two component mixing, describe in as
much detail as you can the nature of the end member compositions. If you conclude that these
data are not consistent with two component mixing, describe in as much detail as you can the
nature of the controls on geochemical variation among the samples.
Lithology
Rb
Sr
Sm
Nd
Sample A
Silty shale
54.5
16.1
2.86
17.5
Sample B
Shale
99.0
19.8
4.99
29.9
Sample C
Silty shale
10.4
20.7
1.01
7.30
Sample D
Shale
5.01
30.1
0.99
7.99
Sample E
Silty shale
32.8
15.6
1.88
11.9
Sample F
Shale
27.4
26.2
1.90
12.9
Rb/Sr Sm/Nd