Isotopic disequilibrium during rapid crustal anatexis: implications for petrogenetic studies of magmatic processes

Abstract

The geochemical consequences of crustal anatexis are investigated over a range of mineral dissolution rates; 10⁻¹⁰ cm/s (Mono Lake, CA), ∼10⁻¹⁶ cm/s (Seram, Indonesia) and <10⁻¹⁶ cm/s (regional migmatite terranes). Isotopic disequilibrium is established in all cases but surprisingly elemental partition coefficients appear close to equilibrium. This observation indicates that the melting and segregation rates are rapid enough to prevent full isotopic equilibration but that diffusion operates over a sub-100-μm length scale. A disequilibrium melting model is proposed in which diffusion maintains chemical equilibrium between the outer portions of minerals and melt but does not achieve full isotopic equilibrium between the entire protolith and melt. Preservation of isotopic disequilibrium in many metamorphic rocks has widespread implications. Dating metamorphic rocks using mineral–whole rock or mineral–mineral pairs may yield erroneous ages, as observed in the metasediments of Seram where ages range from −15 to 201 Ma, despite anatexis at ∼6 Ma. Consequently, some age estimates in the literature may be incorrect. Mono Lake is an example of how rapid melting will produce a sequence of chemically and isotopically distinct melts that are in isotopic disequilibrium with their crustal source. Hence, quantitative prediction of assimilation–fractional crystallisation (AFC) and anatectic processes requires full knowledge of the melting relations of the protolith. The chemical and isotopic disequilibrium associated with anatexis suggests that Nd model ages of granites and their protoliths will be incorrect when garnet and/or minor phases control a significant amount of the REE budget.

Introduction

The composition of an anatectic melt is controlled by the physical conditions of melting and the time scale of the entire thermal event proceeding and associated with melting. At the simplest level, phase relations will result in major element differences between the efficient extraction of small degree, but heterogeneous, melts and the slower extraction of larger degree, more homogeneous, melts. There are two parameters that will determine if anatectic melts and their residua reach trace element and isotopic equilibrium. The first is the prograde history of the protolith. For example rapid heating events in relatively shallow parts of the crust do not allow time for full isotopic equilibration between the minerals of the protolith. In contrast, it could be argued that the higher ambient temperatures of deeper crustal levels would maintain isotopic equilibrium in the protolith prior to anatexis in the lower crust. The observation of numerous disequilibrium and reaction textures in metamorphic rocks seen at the Earth's surface today implies that chemical equilibrium may not be the general rule (Yardley, 1995). Although many of these textures are a consequence of retrograde reactions this is not always the case and hence the possibility of widespread isotopic disequilibrium in protoliths must be assessed. If isotopic equilibrium is not achieved in the protolith then the second parameter, the time scale of melt extraction, will also influence the nature and extent of chemical fractionation between protolith and melt.

In this work, we examine trace element and isotopic evidence to determine which chemical model is most applicable to crustal anatexis and also place constraints on how the time scale of melting and melt extraction affects chemical and isotopic equilibrium. A basic question to be addressed is the extent to which trace elements obey Henry's law: i.e., is partitioning between melt and residue controlled by equilibrium partition coefficients? (e.g., Hart and Allégre, 1980). If trace elements obey Henry's law then melt extraction can be modelled as batch melting, when melt and residue remain in chemical equilibrium throughout the extraction process (e.g., Gast, 1968) or fractional melting where batch melts are immediately extracted from the residue and subsequently accumulated (e.g., Hanson, 1977).

Alternatively, melting may be a disequilibrium process during which chemical equilibrium is not fully maintained between residual phases and the melt. There are two possible scenarios that may operate during disequilibrium melting. The first, in which diffusion is sufficiently slow to prevent inter- and intra-mineral elemental and isotopic equilibration in the residue but chemical equilibrium is preserved between the melt and the portion of phases contributing to the melt. This situation is best envisaged by considering relatively slow mineral dissolution of, for example, a zoned plagioclase. The plagioclase rim alone contributes to the melt and achieves chemical equilibrium so that partition coefficients operate, at least on a sub-grain size scale. The melt will have the ${}^{87}\text{Sr}\text{/}{}^{86}\text{Sr}$ ratio of the plagioclase rim (i.e., not in isotopic equilibrium with the whole grain) and Sr contents will be low because of the high plagioclase–melt Sr partition coefficient. When mineral dissolution rates greatly exceed the rate of element diffusion within minerals, melt–mineral partitioning does not obey Henry's law and equilibrium partition coefficients do not operate: i.e., the effective partition coefficients (K_{d Effective}) are equal to 1. If we again consider a zoned plagioclase, the Sr content and ${}^{87}\text{Sr}\text{/}{}^{86}\text{Sr}$ will simply be the weighted averages of the section of the grain that has been melted. Most previous workers have assumed the first scenario in which equilibrium partition coefficients operate during crustal melting, i.e., K_{d Effective}=K_{d Equilibrium}; K_{d EF}=K_{d EQ} (Allégre and Minster, 1978; Prinzhofer and Allégre, 1985; Barbey et al., 1989; Bédard, 1989). Others have, however, argued that equilibrium partition coefficients do not operate (e.g., Bea, 1996). The aim of this work will be to use well-constrained and rapid melting events to assess if K_{d EF}≠K_{d EQ} and if conditions exist in nature where K_{d EF}=1.

Over the last 2 decades, our understanding of crustal melting has evolved radically, often through the application of models from material sciences. In the 1980s, the use of fluid dynamic concepts led to the conclusion that two phase flow (compaction) was inefficient at the relatively high viscosities of crustal melts (10⁴ to 10¹¹ Pa s). Therefore, over the time scales of most major thermal events (<10 Ma) there would be limited melt–source separation even at large degrees of melting (>10%; McKenzie, 1985; Wickham, 1987a; Miller et al., 1988). Consequently, there was a general consensus that large bodies of relatively homogeneous granitic magma could only form as a consequence of:

• (i) large degrees of melting (30–50%) and/or;

• (ii) hydrous melts with low viscosity.

These conditions would allow convective motion and compaction to operate more efficiently (Wickham, 1987a; Miller et al., 1988). Authors, therefore, favoured extended periods of melt–protolith contact and hence a batch equilibrium melting model. The enigma, however, was the ample evidence that relatively small degree melt fractions can segregate into batholith-sized bodies (e.g., Miller et al., 1988) and that there is no evidence that all granitic magmas have the high water contents to give viscosities of the order of 10² Pa s (see review by Baker (1996)). Although melt extraction due to fracturing was initially dismissed as a local phenomenon (e.g., Miller et al., 1988), more recent numerical analysis implies that melt extraction and migration are most efficient under conditions of fracture propagation (Emerman and Marret, 1990; Clemens and Mawer, 1992; Petford et al., 1993; Sawyer, 1994). This conclusion raises the possibility that coupled rapid rates of melting and extraction may not result in isotopic and chemical equilibration between melts and crustal protoliths.

It is now well-established that the diffusion coefficients of Pb, Sm, Nd and Sr (i.e., elements used in isotopic studies) are low in many minerals at, or close to, anatectic temperatures (<10⁻¹⁶ cm²/s, see review by Brady (1995)). Previous workers have formulated expressions that describe the effective partition coefficient of a mineral as a function of crystal growth/dissolution rate, diffusion coefficient and equilibrium partition coefficient (e.g., see Henderson and Williams, 1979; Hart and Allégre, 1980). When effective diffusion coefficients are <10⁻¹⁶ cm²/s one can predict that full chemical equilibrium will not be maintained during a melting event if mineral dissolution rates exceed 10⁻¹⁸ cm/s. It is, however, difficult to predict the actual elemental diffusion coefficients and diffusive distances within residual minerals. The uncertainty partly comes from the fact that experimental diffusion coefficients are determined on gem quality phases assuming an infinite reservoir. In contrast, minerals in metamorphic rocks have numerous lattice defects (e.g., Watson, 1996) and are involved in multi-component mineral reactions. It is, therefore, to be expected that the effective elemental diffusion length scales in metamorphic minerals are below the observed grain size. This is the reason that many workers assume that chemical disequilibrium is not important during anatexis. Consequently, a goal of this work is to use examples of anatexis to constrain the actual diffusive length scale of elements within residual minerals and so establish if the typical time scale of crustal anatexis and melt extraction will cause the entire process to be in chemical and isotopic equilibrium. Due to the slow diffusion of Sr in feldspars, which are major rock-forming minerals (Giletti, 1991a; Cherniak and Watson, 1992, Cherniak and Watson, 1994; Giletti and Casserly, 1994; Cherniak, 1996), this study will concentrate on the Sr isotope system.

The above discussion is not simply an academic exercise. Crustal anatexis is one of the major processes that control the chemical differentiation of the continental crust, producing an upper crust that is enriched in the heat producing elements U, Th and K (e.g., Fyfe, 1973; Rudnick, 1992). These elements control the thermal budget and the rheology of the upper crust, which in turn may influence near surface tectonics and landform development. It is, therefore, important to establish the details of crustal anatexis to allow realistic quantification of chemical and thermal models of the crust.