Compositional dependence of the elastic wave velocities of mantle minerals: implications for seismic properties of mantle rocks

Using single-crystal elasticity data we constrain the effect of chemical substitutions on the elastic properties of mantle minerals and estimate the consequences for the seismic properties of mantle rocks. At ambient conditions the calculated relative variation of compressional and shear velocities ∂lnv P /∂X Fe and ∂lnv S /∂X Fe due to Fe-Mg substitution, range between -0.05 and -0.46 and between -0.08 and -0.74 respectively in the main mantle minerals. The corresponding heterogeneity ratios R = ∂lnv S /∂lnv P for Fe-Mg substitution range between 0.9 and 1.7 suggesting that the effect of this substitution is very different in different solid solutions systems. More limited experimental results for Ca-Mg substitution and Al enrichment in pyroxenes and garnets were also evaluated. Only Ca-Mg substitution in garnets is found to produce large (>2.0) values of R. Heterogeneity parameters at upper mantle and transition zone conditions can be substantially different from ambient P-T values in some cases. Using a first-order approximation of the effect of Fe-Mg substitution on the elastic properties of the most relevant upper mantle rocks, we find that the sensitivities of seismic velocities to Fe enrichment can vary as much as 2-3 times between the different rock types. We estimate that in the upper mantle the value of ∂lnv S /∂lnv P for pyrolite, piclogite and harzburgite decreases from 1.5 to 1.0 at the base of the transition zone, while it only decreases from 1.5 to 1.3 in mid ocean ridge basalt eclogite, which is enriched in garnet. We also estimate that the seismic effect of lateral changes in lithology from average mantle to subducted slab rocks decreases in intensity at upper mantle and transition zone depths, in agreement with seismic tomographic models. Information about the effects of Ca and Al enrichment are still too incomplete to make predictions of their effects on whole rocks, but they could be relevant based on our limited information. INRTRODUCTION The improvement of seismological models of the Earth mantle in recent years [e.g. Kennett et al., 1998; Masters et al., 2000; Enrichment and depletion in the average Fe content of lithospheric rocks is invoked as a mechanism of compositional stabilization of the thermal heterogeneity between the uppermost subcontinental and suboceanic mantle A major effort has been devoted to the development of in-situ high-pressure and hightemperature measurements of the thermoelastic properties of mantle minerals In this chapter we will evaluate the effect of composition on the elastic properties of upper mantle minerals and model rocks using an elasticity dataset derived solely from single-crystal experimental techniques. We will first calculate 3 the sensitivity of sound wave velocities in olivine and aluminum-bearing garnets to Fe-Mg and CaMg substitutions by combining new experimental results by Brillouin spectroscopy METHODS Elasticity dataset We use an elasticity dataset based on a large number of experimental results from single-crystal techniques (e.g. Brillouin scattering, impulsive stimulated scattering, resonant ultrasound spectroscopy, GHz ultrasonic interferometry) in order to place constraints on the effects of Fe-Mg substitution in different families of mantle minerals. Single-crystal elasticity measurements allow us to determine the whole elastic tensor which completely defines the elastic anisotropy, gives information about interatomic interactions and integrates the information from crystallography. In selecting the database of elastic moduli, we systematically prefer singlecrystal results with respect to measurements on polycrystalline samples (e.g. by ultrasonic techniques), because of potential grain size inhomogeneity, texture effects and porosity in the polycrystalline samples that can affect the validity of these results. Direct results from elasticity measurements are also emphasized over indirect determination of bulk moduli and their pressure derivatives from high-pressure x-ray diffraction because the latter are the results of fitting experimentally measured volumes to a pressure- and for three garnet compositions We first derive the endmember properties of olivine by averaging available data We generate mixture densities for olivine by averaging endmember densities using molar fractions as weighting factors. In the case of the ternary garnet (here treated as a mixture with complete disordered distribution of Fe, Mg, and Ca in the dodecahedral site) the densities are calculated using a regular solution model for volume mixing [Geiger, 1999]. We calculate thermal expansion coefficient, bulk and shear moduli, and their pressure and temperature derivatives by linear combination of the endmember properties using their molar fractions as weighting coefficients. We apply a linear mixing model because the available experimental data, both for natural and synthetic materials, do not show well resolved non-linearities. We then compute acoustic velocities and densities of mixtures with arbitrary compositions along adiabatic pressure-temperatures paths with foot temperature of 1673 K, compatible with model geotherms for a radially averaged mantle. The zero-pressure density, bulk and shear modulus and pressure derivatives of the mixtures at 1673 K are calculated following the procedure outlined by Duffy and Anderson [1989]. Aggregate bulk and 5 shear moduli along the adiabatic profiles are calculated with third order Eulerian finite strain equations [Davies and Dziewonski, 1975; Duffy and Anderson, 1989] except for the case of olivine where we use fourth order Eulerian strain equations Other mineral families In accordance with the philosophy of this study, we also use a dataset based on single-crystal elasticity data for other mantle mineral families. We limit our attention to ambient conditions because the single-crystal elastiticy data at high pressure or high temperature available for these systems are largely incomplete. We calculate the sensitivities of aggregate acoustic velocity to FeMg exchange in orthopyroxens, clinopyroxenes of the diopside-hedenbergite series, periclasewüstite, and in the high-pressure β-and γ-polymorphs of olivine. We determine the sensitivity of acoustic velocity to Al-(Fe,Mg) substitution in orthopyroxenes and in majoritic garnets. We also estimate the effect of incorporation of water in different systems relevant for the Earth's upper mantle. The calculated sensitivities are reported in Average sensitivities of mantle rocks We compute the effect Fe to Mg substitution on the seismic heterogeneity parameters in four relevant mantle rock types, pyrolite We approximate the pressure and temperature effects on seismic heterogeneity induced by MgFe substitution in the system ringwoodite -γ-Fe 2 SiO 4 by combining isobaric temperature dependence and isothermal pressure dependence of the heterogeneity parameters from the available experimental data. Due to the absence of singlecrystal high-pressure data on the effect of Fe-Mg substitution in pyroxenes and β-(Mg,Fe) 2 SiO 4 , we adopt the data available for these minerals groups at ambient conditions. The sensitivity of majoritic garnet to Fe-Mg substitution is assumed to be equivalent to that of Al-garnet. We have first tested our averaging scheme in the case of arbitrary mixtures of olivine and ternary garnets in different proportions by comparing our calculations with heterogeneity parameters calculated as the relative variation of the average of Hashin -Shtrikmann bounds Shtrikman, 1961, 1963] for the velocities of the same mixtures in response to variation of the Fe content of the two component minerals. The parameters calculated at different pressures and different minerals proportions are in agreement between the two methods, within the estimated uncertainties. RESULTS AND DISCUSSION Olivine and ternary aluminum garnets The substitution of Fe for Mg in olivine results in a strong shear modulus weakening [Graham et al., 1988; The compositional effect on both the shear and compressional velocities at constant pressure can be represented by velocity heterogeneity parameters (also referred as compositional heterogeneity parameters in the following discussions) expressed as (∂lnv P,S /∂X i ) P , Heterogeneity parameters for olivine along an adiabatic path starting at 1673 K are presented in The effect of Fe -Ca -Mg substitutions on the elastic velocities of garnets in the pyropealmandine -grossular subsystem is more complex than the simple Fe -Mg substitution in olivine. Substitution of Fe for Mg causes as much as 8.5% and 8.2% decreases of compressional and shear velocity at ambient pressure, and 7.2% and 7.7% respectively, at 14 GPa. Substitution of Ca for Fe produces 10.2% and 14.9% increases of compressional and shear velocity at ambient pressure, and 7.3% and 12% increases at 14 GPa . In the case of ternary garnets we define two heterogeneity parameters X Fe = Fe/(Fe+Mg) and X Ca = Ca/(Ca+Mg) for Fe -Mg and for Ca -Fe substitutions respectively. In addition to the heterogeneity parameter we have to specify a second ratio to completely determine the compositional path along which the heterogeneity parameter is defined. As an example, a mixture of 70% Mg component, 10% Fe component and 20% of Ca component has the same X Fe as a mixture of 77% Mg component, 11% Fe component and 12% Ca component, but it has different mixture properties because it is richer in the Ca component. In fact, the apparent effect of Fe enrichment is different in the case in which we maintain Ca/Fe =1, compatible with the ratio for average peridotitic garnets (see section 2.2), with respect to the case in which Ca/Mg is fixed to the value 0.19 typical of average peridotitic garnets Previous estimates of the effect of Fe to Mg substitution in an average peridotitic mineral assemblage The logarithmic derivatives of shear and compressional elastic wave velocities with respect to density, ∂lnv i /∂lnρ, for Fe to Mg substitution in garnet are systematically smaller than those for olivine We also analyze the effect of Ca enrichment or depletion in garnets at constant Fe/Mg ratio, compatible with that of peridotitic garnets ( Other systems The differences that we observed between the effect of Fe to Mg substitution in olivine and garnets highlight inherent risks involved in gross generalizations of compositional effects on the elastic properties of a limited subset of minerals to those of the rocks of the mantle as a whole [e.g. Karato and Karki, 2001]. Information about the chemical composition of the mantle should be accompanied by a precise petrological and mineralogical model. For this reason we calculate the heterogeneity parameters for Fe -Mg substitution, and where possible for other substitutions, for other minerals of the mantle based on single-crystal elasticity measurement consistent with the strategy adopted for garnet and olivine. Unfortunately, the available elastic data for the members of the different families of mantle minerals are fragmentary. For this reason we limit our calculations to ambient conditions. All the computed logarithmic derivatives of compressional and shear velocity presented for the different systems discussed in the following sections are reported in [McDonough and Rudnick, 1998]. Different studies have been performed to determine the whole elastic tensor of different compositions in the orthoenstatite (MgSiO 3 ) -orthoferrosilite (FeSiO 3 ) solid solution series, at ambient conditions [e.g. Webb and Jackson, 1993; Chai et al. [1997] measured the elastic tensor of an orthorhombic pyroxene containing 2.6 weight% Al. By comparison with the calculated velocity for an Al-free orthopyroxene with the same Fe/Mg ratio, we calculate an average sensitivity of the heterogeneity parameters to Al enrichment in orthorhombic pyroxene: ∂lnv P /∂X Ts = 0.24 ± 0.04, and ∂lnv S /∂X Ts = 0.13 ± 0.04, where Ts = MgAl 2 SiO 6 is the Mg-tschermak component. The presence of Al increases the acoustic velocity of orthorhombic pyroxene, in agreement with the observations for other silicate systems. The effect of Al enrichment on density is smaller than that on velocity, and the logarithmic derivatives ∂lnv i /∂lnρ are larger than unity albeit with large uncertainties Clinopyroxene. A second pyroxene is also present in fertile lherzolites. It is a Ca-rich monoclinic member of the diopside (MgCaSi 2 O 6 ) -hedenbergite (FeCaSi 2 O 6 ) solid solution series. The composition of Ca-rich clinopyroxene in mantle rocks ranges between 88 and 95 mol% diopside component [McDonough and Rudnick, 1998]. Because of the complexity of the monoclinic elastic tensor, only few studies of the singlecrystal elasticity of Ca-rich clinopyroxenes are available in the literature [Kandelin and Weidner, 1988; The seismic heterogeneity parameters for Carich clinopyroxenes are ∂lnv P /∂X Fe = -0.09 ± 0.01, and ∂lnv S /∂X Fe = -0.15 ± 0.02, generally smaller than those of olivine and orthopyroxene and closer to the range of values determined for ternary aluminum garnets. On the other hand, the logarithmic derivatives of velocity with respect to density are in close agreement with those of olivine, once again showing that the relationship between compositional effect on the elastic moduli and on density is structure-specific in the different solid-solution series β-(Mg Majorite -pyrope mixture. Due to the high abundance of garnet-majorite solid solution in the transition zone in mineralogical models of the mantle Recent results on polycrystalline Al-bearing Mg silicate perovskite Periclase -wüstite mixture. Periclase (MgO) -wüstite (FeO) solid solution represents the second most abundant mineral in the lower mantle in the reference mineralogical model of the Earth [e.g. Jackson, 1988]. A study of the singlecrystal elasticity of the complete solid solution series has been performed at ambient conditions by Jacobsen et al. [2002] using GHz-ultrasound interferometry. Periclase has been subject of 13 numerous single-crystal studies at both highpressure and high-temperature [e.g. On balance, we find that the heterogeneity parameter for a single substitution such as Fe-Mg can vary dramatically for different mantle mineral families. The logarithmic compositional heterogeneity parameters for v P and v S can vary by a factor of ~ 10 depending on the mineral structure involved TEMPERATURE VERSUS PRESSURE EFFECTS: EXPERIMENTAL RESULTS Reliable mineralogical models of the Earth interior must integrate high-temperature and highpressure experimental results from mineral physics in a coherent thermodynamic and petrological model in order to compute single phase and rock aggregate properties along pressure / temperature / composition paths relevant to the Earth interior. The available high quality high-temperature elasticity studies performed by resonant ultrasound spectroscopy (see for reference) and by Brillouin spectroscopy [e.g. Sinogeikin et al., 2003] combined with high-pressure results on comparable mineral phases, allow us to separately investigate temperature and pressure effects on the compositional sensitivity of acoustic velocity in three solid solution series: forsterite -fayalite, pyrope -grossular, and ringwoodite -γ-Fe 2 SiO 4 . The average relative uncertainties on the pressure and temperature derivatives of the elastic moduli 14 from selected high quality single-crystal measurements The temperature and pressure effects of FeMg substitution in olivine and ringwoodite -γ-Fe 2 SiO 4 and Ca -Mg substitution in pyropegrossular are plotted in In olivine, the pressure and temperature effects have an opposite sign, suggesting a near cancellation of pressure-temperature effects under mantle conditions In grossular -pyrope solid solutions, temperature increases ∂lnv P /∂X Ca up to 20% at 1800 K and the effect on ∂lnv S /∂X Ca is to decrease its value by 15% at 1800 K with a variation of the heterogeneity ratio R = ∂lnv S /∂lnv P from 2.2 at 300 K to 1.9 at 1800 K. The effect of pressure is that of decreasing both the heterogeneity parameters. However, the effect on the compressional velocity is two times larger than that observed on the shear velocity causing an increase of the heterogeneity ratio R to 2.5 at 10 GPa and 300 K The available data suggest that temperature and pressure dependence of the heterogeneity parameters for the same chemical substitution can be radically different even in closely related systems such as olivine and its high-pressure polymorph γ-phase, suggesting caution in generalizing results obtained at ambient pressure and temperature by direct extrapolation to the 15 conditions and the materials of the deep Earth's interior. The combination of high quality data collected at high temperature and high pressure is the prerequisite to any reliable modeling or even qualitative estimation of the compositional effect on seismic velocity under mantle conditions. However, in general, the effects of P and T at upper mantle conditions on heterogeneity parameters are smaller than the changes in heterogeneity parameters observed across the different structure types. The effect of water The effect of water content on the elastic property of minerals of the mantle is far from being completely explored experimentally. The very few single-crystal elasticity studies of hydrated silicates give us a general idea limited to the olivine system, to γ-phase and grossular [e.g. Wang et al., 2003]. Superhydrous phase B and phase D, two of the high-pressure magnesium silicate hydrous phases which are considered the most probable carriers of water in the deep interior of the Earth, have been subject of single-crystal elasticity measurements by Pacalo and Weidner [1996] and Liu et al. [2004] respectively. Here we report estimates of the average sensitivity of seismic velocity to water content in the cases of γ-phase and grossular, in which water incorporation does not involve structural modifications The softening caused by hydration affects in a similar way both compressional and shear velocity. As a consequence, the value of the ratio R = ∂lnv S /∂lnv P is equal to 1 for ringwooditehydrous ringwoodite, grossular-hydrogrossular, and olivine-humites The results discussed here represent the effect of water content on the heterogeneity parameters in the elastic regime. However, it has been demonstrated that water plays a primary role in enhancing anelastic effects in silicates [e.g. Karato and Jung, 1998], which have to be fully taken into account when laboratory elasticity results (obtained using high frequency spectroscopic methods) are compared with seismological observations. Applications to mineralogical models of the mantle 3.5.1. Overview. In the prospective of understanding the Earth interior, mineral physics furnishes information about the elastic behavior of candidate mantle minerals at high pressures and temperatures in order to construct mineralogical and petrological models of the Earth that can satisfy both geophysical observation and geochemical constraints. In a first-order approximation, the rocks of the upper mantle contain mineral assemblages consistent with those observed in oceanic peridotites, mantle xenoliths and diamond inclusions [e.g. Rocks of different origin and compositions contain substantially different minerals assemblages, which are subject to modifications at depth. For this reason, in absence of reliable mineral physics databases, general correlations between elemental enrichments and average sound velocities [e.g. Lee, 2003] could result in largely inaccurate model velocities, especially if extrapolated to mantle conditions. As an example of the complexity of the effects of variable rock chemistry, in a pyrolitic average mantle, rich in (Mg,Fe) 2 SiO 4 polymorphs, the volume fraction of garnet is 15% in the upper mantle and that of garnet-majorite solid solution is 40% in the transition zone [Fei and Bertka, 1999], a MORB eclogite, corresponding to subducted oceanic crustal material, contains 25% garnet at the top of the upper mantle but about 90% majorite-garnet solid solution in the transition zone . The relative contribution of garnets to the overall thermoelastic properties of 17 the two rock types, will be dramatically different in varying temperature and pressure regimes. To model the behavior of the rock at mantle conditions the chemical composition has to be accompanied by a precise mineralogical and petrological model. Single-crystal elastic properties need to be converted into effective or average elastic properties of mineral aggregates in order to compare mineral physics information with information from seismology. Simple bounding schemes for the elastic moduli of isotropic aggregates 3.5.2. Average heterogeneity parameters. The heterogeneity parameters for Fe-Mg substitution calculated for MORB eclogite, which is strongly enriched in garnet-majorite component at high pressure, are ∂lnv P /∂X Fe = -0.09 ± 0.02 and ∂lnv S /∂X Fe = -0.14 ± 0.02 and they gradually decrease with depth to -0.08 ± 0.02 and -0.10 ± 0.02 at the conditions of the transition zone ( Effect of elemental partitioning. We have carried out simple calculations of the effect of changes in Fe-Mg partitioning between the different minerals on the elastic velocities of these four rock-types at ambient conditions. The computations have been performed using HashinShtrikman bounds to the rock elastic moduli to determine average rock velocities. The relative velocity variations ∆v i /v i , where ∆v i is the velocity difference, caused by enrichment of Mg, up to 4 mol%, in pyroxene, at constant rock bulk composition, in MORB eclogite, are ∆v P /v P = 0.002 and ∆v S /v S = 0.003. Similar en