Download 12.710: Introduction to Marine Geology and Geophysics Solutions to

12.710: Introduction to Marine Geology and Geophysics
Solutions to Midterm (Questions 1-8)
1) Nucleosynthesis: What is the fundamental building block (i.e. the starting point) from
which all elements are formed during nucleosynthesis? [5 pts]
The proton, hydrogen nucleus, 1H.
2) Radioactive decay:
a) ...What is the atomic number of 143Nd? [5 pts]
60.
b) ...What is the atomic number of 87Sr? [5 pts]
38.
3) Earth Accretion and Differentiation:
a) Briefly describe the Chondritic Earth model. [5 pts]
In this model, it is assumed that the bulk composition of the Earth
is equivalent to that measured in [generally CI] chondrites, whose
composition closely resembles that of the solar photosphere and which are
thought to represent the early composition of the solar system.
b) Define the Bulk Silicate Earth (BSE) in terms of the Chondritic Earth
and the Core. [5 pts]
The BSE is defined as the silicate part of the Earth, i.e. the crust +
silicate upper and lower mantles. In a Chondritic Earth model, the BSE is
what remains after core formation, so BSE = Chondritic Earth – Core.
c) Define the BSE in terms of the Depleted Mantle and Continental Crust.
[5 pts]
The Depleted Mantle is thought to be the remnant from early
Continental Crust extraction from an upper mantle with BSE composition,
so BSE = DM + CC.
4) Earth Accretion and Differentiation: ...If 129Xe is measured in samples from deep in
the Earth’s mantle, what constraint does this place on the formation interval/accretion
time of the Earth?
Xe’s volatility means that were accretion to occur after all of the 129I had decayed, all of
the daughter 129Xe would have degassed and been lost from the Earth during accretion.
Likewise, were accretion to happen before the 129I in the solar system decayed to
extinction, the remaining 129I in the earth would ingrow 129Xe, which would not be lost
and would remain in the mantle. Thus, any 129Xe in the mantle implies that some 129I
must have been present in the solar system after accretion. Any 129Xe in the mantle limits
accretion to earlier than the life of 129I in the solar system (determined by our ability to
resolve small differences in Xe isotopes – e.g. if that limit is 5 half-lives of 129I, accretion
must have occurred within the first 82 Ma of the solar system. In this case we can resolve
this to maybe ~50Ma). If we know the amount of 129I present initially, we can also
calculate a time of accretion and Xe degassing, but this is not easily known – in this case
we can determine an age window or age limit but not a precise age.
If the earth inherited one thousand moles of 129I, how many moles would be left after one
half-life?
500 moles.
After 3 half-lives? [10 pts]
125 moles.
5) Geological time scale: [10 pts]
Missing blanks: Mesozoic era, Cambrian, Devonian, and Triassic periods, and
Paleocene, Pliocene, and Pleistocene epochs (all in chronological order).
6) Interpreting the rock record: Describe the sequence of events for fault A, dike B, and
dike C. [10 pts]
Sequence of events: Dike C, Fault A, Dike B.
7) Petrogenesis: Briefly describe the three primary different tectonic settings where
volcanism occurs and discuss how differences in these settings result in different melting
conditions, styles of volcanism and resulting melt compositions. [10 pts]
Volcanism occurs at divergent margins (spreading ridges), convergent margins
(subduction zones or arcs), and intraplate settings (“hot spots”). Melts at
spreading centers form by decompression melting of upwelling solids in the
convecting mantle; most of the lavas erupted on earth erupt at ridges, the extent of
melting is relatively high, lavas are low in volatiles, and lavas undergo moderate
fractionation in magma chambers so that they are basaltic (tholeiitic) in
composition. The basalts have relatively low viscosity and cool rapidly under the
oceans. They show some isotopic and trace element variability, but not nearly as
much as ocean island basalts. Melts at convergent margins are produced by “wet
melting” of the mantle wedge due to the addition of water and other volatiles to
the wedge overlying the wet subducting slab of crust. They can experience a lot of
fractionation in the overlying crust, leading to differentiated melts ranging from
basalts to rhyolites, and they are high in volatiles that can exsolve suddenly and
generate explosive eruptions. Finally, intraplate or hot-spot volcanoes form
seemingly independent of plate tectonics; some of these are probably formed by
plumes of upwelling material from the mantle, while others may formed by some
other process (this is hotly debated). They are generally low in volatiles and erupt
as low-viscosity basalts. Their isotopic and trace element compositions are
extremely variable and help us fingerprint heterogeneous mantle reservoirs.
8) Petrogenesis:
A) Derive the batch melting expression for the ratio of two elements. [5 pts]
CAl / CBl = (CAs / CBs) * (F + (1 – F)*DB) / (F + (1 – F)*DA)
B) Given the bulk partition coefficients for Sr, Rb, Nd, Sm, which is the most
compatible element? What is the relative order of compatibility? [5 pts]
Rb is most incompatible. In order of relative compatibility, from least to
most compatible: Rb, Sr, Nd, Sm.
C) For a mantle source ratio with Rb/Sr = 10 and Sm/Nd = 1, what is the Rb/Sr
and Sm/Nd in a partial melt of that source if the total melt fraction is 1 and 0? [5
pts]
For F = 1, Rb/Sr = 10, Sm/Nd = 1 in the melt
For F = 0, Rb/Sr = 100, Sm/Nd = 0.5 in the melt
D) Describe why this makes sense given the relative compatibility of the element
pairs. [5 pts]
This makes sense because Rb is less compatible than Sr, so at low degrees
of melting (i.e. approaching F = 0), liquid Rb/Sr ratios are elevated. On the other
hand, Nd is less compatible than Sm, causing the opposite sense of fractionation:
for small F, Sm/Nd in the melt is less than one.