## The crustal age distribution function

The present-day continental crust consists of crustal domains of different ages. The masses of crustal domains Mdom that formed at time 6 and were preserved until time t are expressed by the age distribution function AGE(6, t).

The age distribution function relates to the total crustal mass at time t as follows:

and the difference between AGE(6, t) for 6 = t and the crustal mass derivative (or

qi q2 q3

Fig. 26.9 Crustal-age distribution: masses and mass fluxes. Qualitative graph showing the principle of relationships between the crustal-growth curve, the crustal-age distribution and mass fluxes AM into and from the crust. All masses are shown as portions of the present-day continental crust mass. The crustal-growth curve defines the mass of the crust at any time t. The crustal-age distribution shows the masses of blocks of different age for any t. For example, at time t3 the crust consists of only three blocks with ages 01 (old), 02 (intermediate) and 03 (young) = t3. The mass flux into the crust during the interval (t2, t3) is then AM(03, t3)/(t3 - t2). The flux out of the continental crust is the difference between the flux into the crust and the real increase in mass of the continent during the time interval (t2, t3), AMccR(t2, t3). Adapted from Azbel and Tolstikhin (1988, 1990).

 |am(&3, t3) |am(02, t3)

qi q2 q3

Fig. 26.9 Crustal-age distribution: masses and mass fluxes. Qualitative graph showing the principle of relationships between the crustal-growth curve, the crustal-age distribution and mass fluxes AM into and from the crust. All masses are shown as portions of the present-day continental crust mass. The crustal-growth curve defines the mass of the crust at any time t. The crustal-age distribution shows the masses of blocks of different age for any t. For example, at time t3 the crust consists of only three blocks with ages 01 (old), 02 (intermediate) and 03 (young) = t3. The mass flux into the crust during the interval (t2, t3) is then AM(03, t3)/(t3 - t2). The flux out of the continental crust is the difference between the flux into the crust and the real increase in mass of the continent during the time interval (t2, t3), AMccR(t2, t3). Adapted from Azbel and Tolstikhin (1988, 1990).

crustal growth rate) AMCCR(t)/At determines the bulk erosion flux EROSION(t) from the crust (Fig. 26.9):

Here AGE(t = 0, t)isthe mass AM of the new crustal domain added in a given time interval At. Also AGE(0, t) determines another important parameter, the mean age of the continental crust at time t, TCCR(t):

<Wt)} = [MccR(t)]-1 £ (t - 0) x AGE(0, t) (26.3)

where t - 0 is the age. For example, if the masses of the three crustal domains, which have different mean ages as shown in Fig. 26.9, are equal at time t = t3 then Eqn (26.3) gives 2 Gyr as the mean age of the crust at t = t3. For the present time,

370 The Evolution of Matter 20 -

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Age, Gyr

Fig. 26.10 Crustal-age distribution: zircon ages. The distribution of U/Pb zircon ages recalculated as the relative abundance of the crustal domains. Note that the largest portion of the continents appears to have originated at ~ 2.7 Gyr ago. From Condie (2000), © Elsevier Science 2000, reproduced by permission.

for instance, careful analysis of the Nd model ages (Fig. 21.5) gives <rCCR) ~ 1.8 Gyr for a large part of North America (DePaolo et al., 1991) and a similar value, ~ 2 Gyr, is generally assumed for the bulk continental crust and used for modelling crustal evolution (Chapter 28).

Further, Eqn (26.3) may be modified to express the mean age (or residence time) l TCCR(t) of species i in a reservoir, e.g. in the continental crust as a whole or in crustal subreservoirs. Assuming for simplicity that matter with a concentration lC(6) of the stable species i was added to the crust at time 6 and retained this concentration unchanged till time t; then

<lTccR(t)) = [lCccR(t)MccR(t)]~1 £(t - 6) x lC(6) x AGE(6, t). (26.4)

The concepts of AGE(6, t) and the mean-age/residence-time ratio reflect the dynamics of the formation and destruction of a given reservoir and therefore give important constraints on evolutionary models. Age density as a function of age is used as a first-order proxy for the present-day value, AGE(tnN = 6, tnN). Along with progress in geochronology, an increasing amount of dates constrain this function further. If the difference in erosion rate between crustal domains of different ages is known (the so-called erosion law, Allegre and Rousseau, 1984), then the present-day AGE(tFIN = 6, tfiN) can be extrapolated into the geological past.

An episodic history of crustal growth has been inferred by a number of authors (e.g. Condie, 1998,2000; Albarede, 1998b) from the clustering of U-Pb zircon dates in specific, relatively narrow, age intervals: 2.6 to 2.8 and 1.7 to 1.9 Gyr (Fig. 26.10).

This may have implications for models of crustal-growth mechanisms, as will be discussed in Section 26.7 below. However, it should be noted that U-Pb zircon ages, on which this inferred age distribution rests, may be minimum ages for the crustal provinces in which they occur, as many granites result from the remelting of earlier crust. It is expected that future Hf-isotope studies on dated zircon populations will establish whether the age distribution of the latter truly reflects crustal-growth rates.

In Section 26.2 we have discussed the contrasting chemical compositions of crustal domains of different age. Such comparisons are important because they shed light on major changes in crust-feeding materials and processes through time (see e.g. Condie, 1994, 2005; Rudnick and Fountain, 1995; Hawkesworth and Kemp, 2006 for more detailed discussions of this problem). It is of equal importance that they provide the key to a more accurate estimate of the bulk chemical composition of the continental crust, via AGE(tFIN = 0, tnN).

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