1. 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

2.  Oceanic basalts have radiogenic Pb isotopic ratios Increase in Pb isotopes a function of: F 238 U  206 Pb F 235 U  207 Pb F 232 Th  208 Pb Thus, major concerns on the concentrations of U, Th and Pb in the mantle Allegre (2008)

3.  The Pb paradoxes 1 st : long time-integrated high U/Pb 2 nd : long time-integrated low Th/U 3 rd : constant (’canonical’) Ce/Pb & Nb/U

4.  The Pb paradoxes 1 st : long time-integrated high U/Pb 2 nd : long time-integrated low Th/U 3 rd : 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 Th Tatsumoto (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)

5.  2 nd Pb paradox Conventional approach – Th/U (or  = 232 Th/ 238 U) lower than BSE

6.  2 nd Pb paradox Conventional approach – Th/U (or   232 Th/ 238 U) 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/  –  non-conventional) higher than BSE i.e., long time-integrated high U/Th Thus, 1 st and 2 nd paradoxes can be solved through long time-integrated U enrichment !

7.  long time-integrated enrichment in U 1 st : long time-integrated high U/Pb 2 nd : long time-integrated low Th/U 3 rd : constant (’canonical’) Ce/Pb & Nb/U Important implications: o simultaneous solution to 1 st and 2 nd paradoxes o produces Pb* - hence, radiogenic Pb isotopes o inconsistent with proposed solutions to 3 rd paradox (conservation of mass !) o for MORB at least, Th/U is ‘constant’

8.  2 nd Pb paradox Conventional approach – Th/U (or  = 232 Th/ 238 U) lower than BSE (= 3.88) Th/U of MORB (at ~3.1) “remarkably homogeneous” (Elliot et al., 1999)

9.  2 nd Pb paradox Conventional approach – Th/U (or  = 232 Th/ 238 U) 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+/-1.35 Jenner & O’Neil (2012)3.16+/-0.60 Gale 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 !)

10.  If Ce/Pb, Nb/U and Th/U constant (in MORB, at least) (Ratio of constants is also constant) K 1 = (Ce/Pb) / (Th/U) = (U/Pb) * ( Ce/Th) K 2 = (Ce/Pb) / (Nb/U) = (U/Pb) * (Ce/Nb) K 3 = (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)

11.  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)

12.  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)

13.  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)

14.  A conceptual model MORB: binary mixing (enriched melt + DMM) OIB: binary mixing (end-members + FOZO) Modified after Castillo (2015) Castillo (submitted)

15.  subduction of a small amount of marine limestone (natural HIMU) is required  some limestone are being subducted and not being consumed by arc magmatism