Reply to comment by R. Bousquet et al. on “Subduction factory: 1. Theoretical mineralogy, densities, seismic wave speeds and H2O contents”

Abstract

[1] Steady increases in the mineral physical property database, new methods of calculating the physical properties of rocks, and the growing understanding of ultrahighpressure rocks [e.g., Liou et al., 2000] has stimulated considerable effort in recent years to calculate rock physical properties at high to ultrahigh pressure. One approach [e.g., Hacker et al., 2003] is to use the mineral abundances and mineral compositions of natural rocks determined in the field and in experiments. Another approach [e.g., Kerrick and Connolly, 2001] uses the thermodynamic properties of minerals to calculate mineral abundances and mineral compositions. Both approaches have strengths and weaknesses [Hacker et al., 2003]: the former is grounded in the reality that the mineral abundances and mineral compositions actually exist in natural rocks, the latter has the internal consistency and elegance that comes from a purely theoretical approach. Between these two end-member methodologies lie a range of approaches, including that presented by Bousquet et al. [1997]. Hacker et al. [2003] and Bousquet et al. [1997] both used metamorphic facies determined from a combination of natural and experimental studies; the boundaries of the facies fields are relatively similar but differ in key areas where temperatures are low (and thus equilibrium is often not attained) or pressures are unusually high (an area of active research). Hacker et al. [2003] used natural mineral abundances and compositions to calculate rock physical properties from a mineral equation of state that uses a third-order finite strain approximation with full consideration of the effects of changes in pressure and temperature. Bousquet et al. [1997] calculated mineral abundances from assumed mineral compositions and calculated rock densities at 1 bar and 25 C [Goffe et al., 2003] using an unspecified procedure. Because the thermal expansivities and compressibilities of key minerals such as feldspar translate into density changes of 15% over the 800 C to 3 GPa pressure range of interest [Hacker and Abers, 2004], the differences in these approaches will necessarily lead to different calculated densities. [2] Our calculated densities do not violate thermodynamics as implied by Bousquet et al. [2005]. With increasing temperature, thermodynamics requires the entropy of a system to increase whereas the density of the system may increase or decrease. With increasing pressure, thermodynamics requires the density of a system to increase, but we and Bousquet et al. [1997, 2005] present calculated densities for the solid minerals, not the whole system which includes H2O in addition to the solid minerals. The specific example cited, of a temperature-dependent increase in density at 800 C and 1.0–1.5 GPa, is caused by the dehydration of amphibole. Our new results ‘‘contradict’’ our previous results [Hacker, 1996] because our new calculations explicitly consider the effect of Fe. [3] We are perplexed by Bousquet et al.’s [2005] suggestion that our density calculations contradict densities of natural rocks measured by Austrheim [1987]. Austrheim [1987] measured granulite facies anorthositic rocks with densities of 2.79–3.21 g/cm and mafic eclogites of 3.5– 3.6 g/cm but did not specify mineral abundances or compositions, precluding a direct comparison. If, however, we use mineral compositions from Austrheim and Griffin [1985] and assume mineral abundances typical for granulites (50% plagioclase, 25% garnet, and 25% pyroxene) and eclogites (50% garnet and 50% pyroxene), we calculate STP densities of 3.20 and 3.61 g/cm, in agreement with those measured by Austrheim, who noted that the presence of microcracks and alteration in his rocks would lower the density measurements. It is even more difficult to make comparisons between our calculated densities and the other papers cited by Bousquet et al. [2005]. Green and Ringwood [1967] did not measure the densities of their experimental rocks. Ito and Kennedy [1971] did not measure garnet compositions and reported only a single pyroxene composition. Bousquet et al. [2005] are correct to note that within individual facies fields our calculated densities depend only on the formula weight, molar volume, expansivity a, @a/@T, isothermal bulk modulus KT, @KT/@P, shear modulus m, @m/@P, G = (@lnm/@lnr)P, Gruneisen parameter gth, and the second Gruneisen parameter dT = (@lnKT/@lnr)P; we do not model the changes in mineral composition and abundance within those individual fields. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, B02207, doi:10.1029/2004JB003490, 2005