they are trivially simple but they do give some interesting results if you ask the right questions The Physical Principal Conservation of Mass Bulk Silicate Earth the hypothetical homogeneous composition of the solid silicate Earth after core formation but before any other differenti ID: 261256
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Slide1
The Embarrassing Details about Geochemical Mass Balance Models for Calculating Mantle Composition
(they are trivially simple, but they do give some interesting results if you ask the right questions)Slide2
The Physical Principal – Conservation of Mass
Bulk Silicate Earth
(the hypothetical homogeneous composition of the solid silicate Earth after core formation, but before any other differentiation process)
[a] (mg/g)MassBSEMass of “a” = MassBSE x [a]BSE
Melt or Crust
Residue or Depleted Mantle
Mass of element “a” =
Mass
DM
x [a]
DM
+
Mass
C
x [a]
C
+ Mass
(BSE-DM-C)
x [a]
BSESlide3
The Physical Principal – Conservation of Mass
Bulk Earth
(the hypothetical average homogeneous composition of the Earth)
[a] (mg/g)MassBEMass of “a” = MassBE x [a]BE
Mass of “a” =
Mass
A x [a]A + MassCC x [a]
CC + MassOC x [a]OC +
Mass
DM
x [a]
DM
+
MassCore x [a]Core + MassBSE x [a]BSE + MassMoon x [a]Moon + etc., etc. etc.
Reservoir A (atmosphere)
Reservoir CC (Cont. Crust)
Reservoir OC (Oceanic Crust)
Reservoir DM (Depleted Mantle)
Reservoir BSE
Reservoir Core
Reservoir MoonSlide4
The Necessary Inputs
Mass and composition of (n-1) reservoirs
If interested only in composition, then all that matters is the mass balance, not the rates of exchange (unless you are interested in how a given reservoir changed in composition with time)
If interested in the radiogenic isotope compositions (e.g. 87Sr/86Sr), then how and when the various reservoirs formed is criticalSlide5
Some Examples of The Questions You Can Ask
If the BSE differentiates into continental crust and depleted mantle, given the mass and composition of the continental crust, what portion of the mantle can be as depleted as the source of MORB? How does this change with different estimates of the BSE composition? Do you get the same answer when you use a highly incompatible element (e.g. Ba) and a moderately incompatible element (e.g.
Sm
)?If the continental crust has the average composition given in the program, could it be 5 times its current size at the same composition? If not, why not?How much Nb must be in the core to explain the non-chondritic Nb/U ratio of the mantle?How does the composition of the EER vary as a function of its size?Can the Moon be the EER? What would its composition be? The mass of the Moon is approximately twice the mass of the continental crust.The mass of the atmosphere is 5 x 1021g of which 0.93% is argon, and most of that argon is 40Ar produced by the decay of 40K over Earth history. 40K decays to 40Ar and
40Ca with a decay constant of 5.54 x 10-10 yr-1, with 11 % of the decay going to 40
Ar. The BSE has 240 ppm of K, only 0.012% currently of which is 40K. If all of the 40Ar in the atmosphere came from 40K decay, how much
40Ar remains in the mantle? If all the radiogenic 40Ar is in the atmosphere, what is the K content of the BSE?