An alternative new
approach to the old Pb
paradoxes
P. R. Castillo
Scripps Institution of Oceanography
University of California, San Diego
La Jolla, CA 92093-0212
U.S.A.
Gold2015:abs:1251
 Oceanic basalts have radiogenic Pb isotopic ratios
Allegre (2008)
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
 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
Proposed significant solutions (~40
yrs):
1st : long time-integrated
high U/Pb
- lose Pb
o into core - Allegre et al. (1982)
o into cont. lithosphere/crust – Zartman & Haines (1988)
o
o
2nd : long time-integrated
low Th/U
Chauvel et al. (1992)
into sulfide – Hart & Gaetani (2006)
from early depleted reservoir (EDR)– Jackson et al.
(2010)
- increase U relative to Th
Tatsumoto (1978); Galer and O’Nions (1985); Elliot et al. (1999)
3rd : constant
(’canonical’) Ce/Pb
& Nb/U
- two major ways:
o mantle re-homogenization – Hofmann et al. (1986)
o changing Kd’s for Ce or Pb – Simms & DePaolo (1997)
 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
Important implications:
1st : long time-integrated
high U/Pb
o simultaneous solution to 1st and 2nd paradoxes
o produces Pb* - hence, radiogenic Pb isotopes
2nd : long time-integrated
low Th/U
o inconsistent with proposed solutions to 3rd
paradox
(conservation of mass !)
3rd : constant
(’canonical’) Ce/Pb
& Nb/U
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 Arevalo & McDonough (2010)
Jenner & O’Neil (2012)
Gale et al. (2013)
Th/U of (ALL) MORB
2.87+/- 1.35
3.16+/- 0.60
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
OIB
(Willbold & Stracke, 2010)
-
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’
DMM (Workman & Hart, 2005)
Lucky ? – perhaps…..
Castillo (submitted)
 Nb vs. U, Th vs. Nb (& Th vs. U) plots of MORB (Gale et al., 2013)
OIB
(Willbold & Stracke, 2010)
DMM (Workman & Hart, 2005)
• 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)
OIB
(Willbold & Stracke,
2010)
• All methods produce
the ~same (+/- errors)
constant (‘canonical’) ratios
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