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An alternative new approach to the old Pb paradoxes
P. R. CastilloScripps Institution of OceanographyUniversity of California, San Diego
La Jolla, CA 92093-0212U.S.A.
Gold2015:abs:1251
Oceanic basalts have radiogenic Pb isotopic ratios
Increase in Pb isotopes a function of: 238U 206Pb 235U 207Pb 232Th 208Pb
Thus, major concerns on the concentrations of U, Th and Pb in the mantle
Allegre (2008)
The Pb paradoxes
1st : long time-integrated high U/Pb
2nd : long time-integrated low Th/U
3rd : constant (’canonical’) Ce/Pb & Nb/U
The Pb paradoxes
1st : long time-integrated high U/Pb
2nd : long time-integrated low Th/U
3rd : constant (’canonical’) Ce/Pb & Nb/U
Proposed significant solutions (~40 yrs):
- lose Pb o into core - Allegre et al. (1982)
o into cont. lithosphere/crust – Zartman & Haines (1988) Chauvel et al. (1992)
o into sulfide – Hart & Gaetani (2006)
o from early depleted reservoir (EDR)– Jackson et al. (2010)
- increase U relative to ThTatsumoto (1978); Galer and O’Nions (1985); Elliot et al.
(1999)
- two major ways:
o mantle re-homogenization – Hofmann et al. (1986)
o changing Kd’s for Ce or Pb – Simms & DePaolo (1997) Hart & Gaetani (2006)
2nd Pb paradox• Conventional approach – Th/U (or k = 232Th/238U) lower than BSE
2nd Pb paradox• Conventional approach – Th/U (or k = 232Th/238U) lower than BSE
e.g.,Tatsumoto (1978) Galer and O’Nions (1985) Elliot et al. (1999)
• But it can also be expressed as - U/Th ( or 1/ – k non-conventional) higher than BSE
i.e., long time-integrated
high U/Th
• Thus, 1st and 2nd paradoxes can be solved through long time-integrated U enrichment !
long time-integrated enrichment in U
1st : long time-integrated high U/Pb
2nd : long time-integrated low Th/U
3rd : constant (’canonical’) Ce/Pb & Nb/U
Important implications:
o simultaneous solution to 1st and 2nd paradoxes
o produces Pb* - hence, radiogenic Pb isotopes
o inconsistent with proposed solutions to 3rd paradox (conservation of mass !)
o for MORB at least, Th/U is ‘constant’
2nd Pb paradox
• Conventional approach – Th/U (or k = 232Th/238U) lower than BSE (= 3.88)
Th/U of MORB (at ~3.1)
“remarkably homogeneous”
(Elliot et al., 1999)
2nd Pb paradox
• Conventional approach – Th/U (or k = 232Th/238U) lower than BSE (= 3.88)
Th/U of MORB (at ~3.1) “remarkably homogeneous” (Elliot et al., 1999)
• Later studies -Th/U of (ALL) MORB
Arevalo & McDonough (2010) 2.87 +/- 1.35Jenner & O’Neil (2012) 3.16 +/- 0.60Gale et al. (2013) 3.16 +/- 0.11
• Thus, Th/U of MORB is also “constant”
• (Th/U of OIB is only between 3.16 and 3.88 !)
If Ce/Pb, Nb/U and Th/U constant (in MORB, at least)
(Ratio of constants is also constant)
• K1 = (Ce/Pb) / (Th/U)
= (U/Pb) * ( Ce/Th)
• K2 = (Ce/Pb) / (Nb/U)
= (U/Pb) * (Ce/Nb)
• K3 = (Th/U) / (Nb/U)
= (Th/Nb)
Trivial ? = Yes, but important because these also show close relationships among Pb paradoxes
More relevant question = why are Ce/Pb, Nb/U, Th/U, Th/Nb constant?
Castillo (submitted)
Basic principle – two component mixing in a binary element plot generates a line, y = mx + b
- Binary mixing line is special when b = 0, making y/x = m (= constant)
- in Ce vs. Nb plot (MORB – Gale et al.,
2013), mixing between enriched OIB and DMM generates a line with b ~ 0, hence Ce/Pb ‘constant’
Lucky ? – perhaps…..
OIB (Willbold & Stracke, 2010)
DMM (Workman & Hart, 2005)
Castillo (submitted)
Nb vs. U, Th vs. Nb (& Th vs. U) plots of MORB (Gale et al., 2013)
• 1) mixing OIB + DMM also generates binary mixing lines with b ~ 0 in Nb vs. U, Th vs. Nb (& U vs Th) plots
• Other methods: 2) by finding average ratios (b = 0)
3) Least-squares method (b ~0)
• All methods produce the ~same (+/- errors) constant (‘canonical’) ratios
OIB (Willbold & Stracke, 2010)
DMM (Workman & Hart, 2005)
OIB (Willbold & Stracke, 2010)
DMM (Workman & Hart, 2005)
Castillo (submitted)
Summary and conclusions
• The radiogenic Pb isotopes of oceanic basalts create the Pb paradoxes – many excellent solutions proposed, but mainly individualized
• Paradoxes are inter-related, comprising a “system of equations” that should be solved altogether or simultaneously as solution to each equation should also be consistent to solutions to other equations
• Systems of equations require linear or non-linear solutions. Pb paradoxes can be simply solved through linear, binary mixing solutions
Castillo (submitted)
A conceptual model
MORB: binary mixing
(enriched melt + DMM)
OIB: binary mixing
(end-members + FOZO)
Modified after Castillo (2015)Castillo (submitted)
subduction of a small amount of marine limestone (natural HIMU) is required
some limestone are being subducted and not being consumed by arc magmatism
