2. Isotope Geochemistry In isotope geochemistry, our primary interest is not in dating, but using the time-dependent nature of isotope ratios to make inferences about the nature of reservoirs in the Earth and their evolution. Radiogenic isotope ratios, such as 87 Sr/ 86 Sr record the time-integrated parent daughter ratios in a reservoir or reservoirs.

3. Paul Gast Paul Gast was arguably the father of radiogenic mantle isotope geochemistry, being among the first to recognize its potential. Thinking of the above equation, he explained it as follows: In a given chemical system the isotopic abundance of 87 Sr is determined by four parameters: the isotopic abundance at a given initial time, the Rb/Sr ratio of the system, the decay constant of 87 Rb, and the time elapsed since the initial time. The isotopic composition of a particular sample of strontium, whose history may or may not be known, may be the result of time spent in a number of such systems or environments. In any case the isotopic composition is the time-integrated result of the Rb/Sr ratios in all the past environments. Local differences in the Rb/Sr will, in time, result in local differences in the abundance of 87 Sr. Mixing of material during processes will tend to homogenize these local variations. Once homogenization occurs, the isotopic composition is not further affected by these processes. Because of this property and because of the time-integrating effect, isotopic compositions lead to useful inferences concerning the Rb/Sr ratio of the crust and of the upper mantle. It should be noted that similar arguments can be made for the radiogenic isotopes of lead, which are related to the U/Pb ratio and time.

4. Time-Integrated Rb/Sr

5. 87 Sr/ 86 Sr and ε Nd in the Earth

6. 87 Sr/ 86 Sr and ε Nd in Oceanic Basalts

7. Comparing OIB & MORB

8. ε Hf &ε Nd in Oceanic Basalts

9. Summary: Sr, Nd, & Hf Isotope Ratios in Oceanic Basalts Sr, Nd, and Hf isotope ratios in MORB indicate time- integrated low Rb/Sr and high Sm/Nd and Lu/Hf. These indicate time-integrated incompatible element-depletion in the MORB source – a result of partial melt extraction. The ratios in OIB indicate less incompatible element- depleted sources – ranging to incompatible element- enriched sources. OIB and MORB overlap. Far more dispersion in the OIB ratios.

10. Pb Isotope Geochemistry

11. Pb Isotope Evolution

12. Pb isotopes in the silicate Earth

13. Pb Paradox Pb mass balance in the Earth is difficult and suggest the Earth is significantly younger (by 100 Ma) than the solar system. Continental crust does not have higher 206 Pb/ 204 Pb than the mantle (which it should if U is more incompatible than Pb). MORB have, on average, time-integrated U/Pb ratios greater than the silicate Earth

14. Pb in oceanic basalts

15. 208 Pb/ 204 Pb vs 206 Pb/ 204 Pb

17. 208 Pb*/ 206 Pb* 206 Pb/ 204 Pb, 207 Pb/ 204 Pb, and 208 Pb/ 204 Pb don’t correlate well with other isotope ratios globally. This implies the fractionation of U/Pb and Th/Pb is “decoupled” from Rb/Sr, Sm/Nd, and Lu/Hf fractionation. Which element is the outlier? Pb, or U and Th? We can to some degree eliminate Pb and focus on U/Th fractionation by examining the ratio of urogenic Pb to thorogenic Pb: To calculate just the radiogenic component, we subtract our the solar system initial values ( 206 Pb/ 204 Pb i =9.306; 206 Pb/ 204 Pb i = 29.532:

19. Mass Balance From how much of the mantle would we have to extract a partial melt to form the incompatible element-enriched continental crust? This is a mass balance problem. REE geochemistry well understood, so perhaps best addressed with Nd isotope ratios. We consider 3 reservoirs: continental crust, depleted mantle, undepleted mantle. We write a series of mass balance equations: for all mass: for element i: for isotope ratio:

20. Mass Balance Considerations: We know the isotopic ratio of DM, but not concentration We know concentration of Nd and Sm/Nd in crust, but not isotope ratio We know mass fraction of continental crust We simultaneously solve for ratio of mass of 2 reservoirs: We express isotope ratio in crust in terms of Sm/Nd and T – average age of crust. First linearize growth equation: Now express isotope ratio in crust as function of Sm/Nd and T

21. Nd isotope mass balance

22. Depleted Mantle as an Open System

23. Geoneutrinos β – decay produces neutrinos, specifically, electron anti-neutrinos, ν e. 6 are produced by 238 U decay and 4 by 235 U and 232 Th. We could determine U and Th in the Earth by detecting their neutinos. Neutrinos can induce nuclear reactions such as: However, the cross section for this reaction is ~10 –44 cm 2. Flux of geoneutrinos through Earth’s surface is 10 6 cm -2 sec -1 Detectors, consisting of large volumes of hydrocarbon scintillator and many photodetectors capable of detection geoneutrinos have been built in Japan, Italy, and Canada. KAMLAND neutrino detector. 1000 tons of scintillator and 1,879 photdetectors.

24. Summary of geoneutrino results MODELS Cosmochemical: uses meteorites – O’Neill & Palme (’08); Javoy et al (‘10); Warren (‘11) Geochemical: uses terrestrial rocks – McD & Sun ’95; Allegre et al ‘95; Palme O’Neil ‘03 Geodynamical: parameterized convection – Schubert et al; Turcotte et al; Anderson

25. OIB and Mantle Plumes

41. Lower Mantle Structure

42. Heterogeneous Plumes

46. Galapagos

48. Continental Basalts & Subcontinental Lithosphere

52. U-decay series & Melt Generation

53. Th & U Geochemistry Th and U are two highly incompatible elements strongly concentrate in the melt and ultimately in the crust. Th is slightly more incompatible that U. Generally similar geochemical behavior, except under oxidizing conditions where U is in the +6 valance state. Overall, because both are strongly incompatible, fractionation between the two should be small.

54. Th-U Isotopes Th enrichment Amount of U/Th fractionation is surprising given similarity of partition coefficients equiline

55. U and Th Disequilibria in Melting For mantle at equilibrium: ( 230 Th) = ( 238 U) When melting begins, we can write the following mass balance equation: The partition coefficient is defined as: Substituting: Rearranging and noting that activities are proportional to concentration: Concentration (or activity) is inversely proportional to partition coefficient and melt fraction

56. U and Th Disequilibria in Melting Assuming parent and daughter were in radioactive equilibrium before melting, the activity ratio in the melt will be: For a multiphase system, the distribution coefficient is the weighted average of individual mineral partition coefficients: Partition coefficients similar, but U is slightly more compatible in garnet. To produce 38% disequilibrium would require F be ~0.2% - implausibly low.

57. Mantle Melting

58. Spiegelman and Elliot Model Spiegelman and Elliot (1993) showed that large isotopic disequilibrium can result from differences in transport velocities of the elements, that results from continued solid-melt exchange as melt percolates upward through the melting column. In a one-dimension steady-state system, with a constant amount of melt, the melt flux is simply the melt density, ρ, times porosity (we assume melt fills the pores), φ, times velocity, v:

59. Mathematically conservation equation for each parent-daughter pair: subscript i denotes the element, c m is the concentration of the element of interest in the melt, ∇ is the gradient, ρ m is the density of the melt, ρ s is the density of the solid, v is the velocity of the melt, V is the velocity of the solid, D is the partition coefficient, φ is the melt volume fraction, and λ is the decay constant. In English: [change in parent conc. with time] + [transport parent] = [decay of daughter] – [production of daughter] ! Whew!

60. Add in Melting We assume the extent of melting increases linearly with the height, z, above the base of the melting layer of thickness d: Melting rate: (note F max and d depend on T φ and lithospheric thickness Flux of solid is: the melt flux as a function of height is: Velocity of melt:

61. The Usercalc Model Need to make assumptions about relation between porosity and permeability and melt viscosity. Then think about transport of an element through the column rather than bulk melt or solid. Since an element is partitioned between solid and melt, its effective velocity depends on how much is in the melt and how much in the solid: Very incompatible elements travel up through the melting column at near the velocity of the melt; very compatible elements travel upward at velocities near the solid velocity.

62. An example in which F max = 20% melting begins at 4 GPa (123.56 km) and ends at 0 GPa. Bulk partition coefficients for U and Th are 0.0011 and 0.00024 respectively in the garnet peridotite facies, and both are 0.00033 in the spinel peridotite facies. The phase transition occurs at 2 GPa. We set the remaining parameters to their default values (V = 3 cm/yr, f max = 0.008, n = 2). Kinks in the curves reflect the phase change from garnet to spinel peridotite at 20 kb. 230 Th/ 238 U of the melt flowing out the top is 1.113.

63. Melt and Solid Evolution

64. Contour plots illustrating the sensitivity of U-series disequilibria to porosity and upwelling velocity (the latter is in cm/yr). Colored lines show the combination of porosity and upwelling velocity needed to reproduce the “target values”, which are ( 230 Th/ 238 U)=1.15, ( 226 Ra/ 230 Th)=1.15, and ( 231 Pa/ 235 U)=1.5.