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Supplementary Text
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Calculating porosity and density of differentiation products
Modeled mineral compositions can be used to calculate the densities of the lithologies
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resulting from the differentiation of the SPA impact melt sheet. These values can be used in
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future studies to compare our model results to the gravity anomalies detected from recent orbital
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missions. The densities of the modeled lithologies change as a function of the composition of
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each crystallizing mineral and the porosity of the rocks. As indicated in the text, crystal densities
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were selected from Barthelmy [2010] based on the relative oxide concentrations, e.g., Mg#, for
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each mineral. The density of each lithology was then calculated by weighting the densities of the
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minerals by their proportion in the rock. This density represents the grain density of the rock
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(Table S2), assuming no porosity.
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The grain density must then be adjusted to account for the porosity of lunar rocks.
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Recent analyses of lunar gravity data returned from the Gravity Recovery and Interior
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Laboratory (GRAIL) mission have estimated the average porosity of the lunar crust to be 12%,
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with regional variations ranging from 4% to 21% [Wieczorek et al., 2013]. These porosities are
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consistent with porosities calculated from analyses of Kaguya orbital data [e.g., Huang and
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Wieczorek, 2012] and measured from Apollo and lunar meteorite samples [e.g., Jeanloz and
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Ahrens, 1978; Kiefer et al., 2012a, 2012b], which have indicated that the lunar crust has an
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average porosity of ~8% with a maximum porosity ranging from 14% to 20%. We use a
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porosity of 12% to represent the porosity of rocks at the lunar surface.
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Porosity is expected to decrease exponentially as a function of depth, as pore spaces close
due to lithostatic pressure [e.g., Binder and Lange, 1980; Abramov and Kring, 2004]. Porosity
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variations with depth can be calculated for the lunar crust using the following equation [Binder
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and Lange, 1980]:
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𝑧
ɸ(𝑧) = ɸ𝑜 exp (− 𝐾) ,
(S1)
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where ɸo is the porosity of surface rocks (12%), z is the depth in the lunar interior, and K is the
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porosity decay constant (~6.5 km for the Moon, [Abramov and Kring, 2005]). Porosities
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expected for the solidified SPA impact melt sheet are shown in Table S2. Note that the final
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compositions noted in the table represent the final reasonable compositions from the model and
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correspond to depths of 3 km and 4 km for scenarios 1a and 3a, respectively.
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These porosities can be used to calculate the density of each lithology, including any pore
space. This density can be calculated with the following equation [e.g., Kiefer et al., 2012a]:
ρgrain+porosity = ρgrain (1 − 𝑃) ,
(S2)
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where P is the porosity. The resulting ρ(grain+porosity) for each lithology is shown in Table S2.
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Results indicate that the basal ultramafic layers of scenario 1a have densities ranging from 3.4–
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3.5 g cm-3 and that the upper gabbroic and noritic layers of scenario 1a have densities ranging
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from 3.1–3.3 g cm-3. Results for scenario 3a indicate densities ranging from 3.4–3.5 g cm-3 for
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the basal ultramafic layers and from 2.9–3.2 g cm-3 for the upper gabbroic and noritic layers.
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The lower dunite and pyroxenite layers had very little porosity (~0.01%) while the porosity
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increased to 3%–12% in the shallower layers.
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Alternatively, the pore spaces may have partially filled with melt if the porosity had
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developed due to crystal settling during melt solidification. Pore spaces completely filled with
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melt represent an upper limit for the density of each lithology. The density of the melt at each
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model step was determined using the CIPW norm calculation [e.g., Hollocher, 2013], and
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resulting melt densities are shown in Table S2. The density of each lithology with melt-filled
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pore spaces can be calculated using the following variation of equation S2:
ρgrain+melt−filled pores = ρgrain (1 − 𝑃) + ρmelt (𝑃) .
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(S3)
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Calculated densities for each lithology with melt-filled pore spaces are shown in Table S2.
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Results for scenario 3a indicate that melt-filled pore spaces yield higher densities for the basalt
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ultramafic layers (3.4–3.6 g cm-3) than for the gabbroic and noritic layers (3.2–3.4 g cm-3),
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though densities do not change significantly throughout the solidified melt sheet for scenario 1a.
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The main text further discusses implications of the differentiation sequence and modeled
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lithologies.
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References
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system at the Sudbury crater, Journal of Geophysical Research, 109(E10007),
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