Geochemical modeling of mantle differentiation and crustal growth

Abstract

In a recent publication, O'Nions et al. [1979] used geochemical constraints to solve transport equations describing the evolution of the outer 50 km of the earth. The paper includes a very helpful compilation of the available data useful in such a solution and provides a valuable overview of the problem. However, it can be shown that the paper contains serious computational errors which put in question a number of the quantitative conclusions. The analysis is based on transport equations of the form dni•/dt = a(t)niM-13(t)ni• (1) dniM/dt = 13(t)ni • -a(t)ni M The symbols n• and n• represent the total number of atoms of element i in the 50-km layer and in that part of the mantle with which it interacts, respectively. The symbols a and/3 are first-order transport coefficients. For potassium, for the O'Nions model II, the transport coefficients are stated to be time-dependent quantities of the form a(t) = 2.6 exp (-2.0t) /3(0 = 20.0 exp (-0.65t) (2) where the numerical quantities are in units or reciprocal gigayears (Ga-•). The computational difficulties of the O'Nions solution are immediately evident from a consideration of these equations.It is not explicitly stated in the reference cited whether the authors considered a crustal layer of constant dimensions with composition evolving from an initial value equal to that of the mantle, or whether the crustal layer was assumed to evolve from zero initial size. Because they criticize earlier models for starting with a finite crustal size, there is a strong implication that their model starts with zero crustal size. (Incidentally, so do the models of Russell [ 1972] and Russell and Birnie [1973], which were included in the criticism.) Therefore, this present comment will proceed on the basis of assumed zero initial layer thickness. The other asumption was examined and shown to lead to substantially similar conclusions. At t = 0 (corresponding to the origin of the earth 4560 Ma ago) n/c • is zero and n•/w is equal to n/c ø, the total number of potassium atoms in the differentiating system. Thus, the initial rate of transport to the outer layer was, according to the equations, dn•/dt = 2.6 rtK ø atoms per Ga This quantity is not zero, and as will be shown below, is about 14 times as great as the corresponding value at any later transport maximum. This clearly violates an initial constraint of O'Nions et al. [1979] that requires the rate of crustal development to peak between 3500 and 2500 Ga ago. Geochronologicai studies suggest that the net rate of crustal growth should be close to zero, initially, as suggested by the illustrations of O'Nions et al. [1979]. Apparently, the illustrations were arbitrarily drawn to zero initial rate. It seems likely that the difficulty can be attributed to the use of a finite number of 50-Ma stages to represent the continuous evolution, but it is not immediately evident what consequences this would have on the various numerical conclusions. To determine this, equations (1) and (2) were solved with careful attention to the computational pro...

Small‐scale convection in the D″ layer

“…The heat flux from the core can probably be as high as 100 mW m À2 , which is one third of the total heat loss from the planet, which is $4.4 Â 10 1 3 W [Pollack et al, 1993]. This value would still be consistent with the constraints on the radiogenic heating in the crust and the mantle [O'Nions et al, 1979] and on the secular cooling of the planet [Abbot et al, 1994]. For example, this value would explain the high total heat flux compared to the heating rate due to radioactive isotopes.…”

Role of recycled oceanic crust in the potassium and argon budget of the Earth: Toward a resolution of the “missing argon” problem

“…Christensen and Yuen, 1985;Weinstein, 1992]. In addition, many geochemical models require a mantle reservoir (presumably the lower mantle) that is significantly less depleted (in terms of its isotopic composition and trace element abundances) than the upper mantle sampled by typical mid-ocean ridge basalts (MORB) [DePaolo and Wasserburg, 1976;O'Nions et al, 1979]. This coincidence between geochemical and geophysical arguments for strong mantle layering historically led to broad acceptance of the layered mantle model.…”

Crustal redistribution, crust–mantle recycling and Phanerozoic evolution of the continental crust

“…Although it is clear that the continental crust was formed as a result of differentiation from the mantle there continues to be debate as to how this was generated and exactly when the bulk of the crust was formed. In some models the volume of continental crust has remained essentially unchanged since the earliest Archean (Fyfe, 1978;Armstrong and Harmon, 1981;Phipps Morgan and Morgan, 1999), while others have argued that the volume of crust has grown through time (Hurley and Rand, 1969;Moorbath, 1978;O'Nions et al, 1979;Albarède and Brouxel, 1987;Kramers and Tolstikhin, 1997). Dating studies of zircons from continental cratons now argue for much of the crust being generated in a series of pulses timed at approximately 1.2, 1.9, 2.7 and 3.3 Ga (Gastil, 1960;Hurley and Rand, 1969;Kemp et al, 2006), a fact consistent with 187 Re/ 187 Os isotope data that imply mantle depletion events at 1.2, 1.9, 2.7 Ga (Parman, 2007;Pearson et al, 2007).…”