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 We present a new compilation of physical properties of minerals relevant to subduction zones and new phase diagrams for mid-ocean ridge basalt, lherzolite, depleted lherzolite, harzburgite, and serpentinite. We use these data to calculate H2O content, density and seismic wave speeds of subduction zone rocks. These calculations provide a new basis for evaluating the subduction factory, including (1) the presence of hydrous phases and the distribution of H2O within a subduction zone; (2) the densification of the subducting slab and resultant effects on measured gravity and slab shape; and (3) the variations in seismic wave speeds resulting from thermal and metamorphic processes at depth. In considering specific examples, we find that for ocean basins worldwide the lower oceanic crust is partially hydrated (<1.3 wt % H2O), and the uppermost mantle ranges from unhydrated to ∼20% serpentinized (∼2.4 wt % H2O). Anhydrous eclogite cannot be distinguished from harzburgite on the basis of wave speeds, but its ∼6% greater density may render it detectable through gravity measurements. Subducted hydrous crust in cold slabs can persist to several gigapascals at seismic velocities that are several percent slower than the surrounding mantle. Seismic velocities and VP/VS ratios indicate that mantle wedges locally reach 60–80% hydration.
 A consistent thermal-petrological-seismological model of subduction zones could be a powerful tool to further our understanding of the subduction process. Even if such a model were incomplete, it might still be a useful means of contrasting one subduction zone against another or for comparing subducted versus unsubducted lithosphere. This paper is our attempt to build a consistent model; the companion paper [Hacker et al., 2003], on the relationship between intermediate-depth seismicity and metamorphism, gives an example of how such a model can be used. Our approach comprises six specific steps:
Compile and assess physical properties of minerals relevant to subduction zones.
Construct phase diagrams appropriate for subduction zone rock types and physical conditions.
Compute pressures (P) and temperatures (T) for a specific subduction zone.
Superimpose calculated phase relations onto the P–T model.
Superimpose rock physical properties onto the P–T model.
Compare predictions to observations.
2. Compiling Mineral Properties
 We performed an extensive literature search to obtain physical properties of minerals relevant to subduction zones. To estimate densities and seismic velocities at elevated P and T, the physical properties that are needed, and known to sufficient degree [e.g., Anderson et al., 1992; Bina and Helffrich, 1992], include formula weight, molar volume, H2O content, expansivity α, ∂α/∂T, isothermal bulk modulus KT, ∂KT/∂P, shear modulus μ, ∂μ/∂P, Γ = (∂lnμ/∂lnρ)P, Grüneisen parameter γth, and second Grüneisen parameter δT = (∂lnKT/∂lnρ)P (Table 1). From these, we calculated the adiabatic bulk modulus, shear modulus, density, seismic wave speeds, and Poisson's ratios for each mineral as a function of P and T, following Bina and Helffrich , ignoring the second pressure derivatives of the moduli, but (1) describing the dependence of μ(T) via Γ [Anderson et al., 1992], and (2) using Holland and Powell's  approximation for α(T) (see Appendix A). Each of these calculated values was examined in detail to ensure agreement with values measured directly on minerals or monomineralic aggregates at elevated P and T, as summarized elsewhere [e.g., Christensen, 1996]. Major deficiencies in this dataset, most notably in the paucity of μ and ∂μ/∂T values, should provide an impetus for mineral physicists to conduct further work.
Table 1. Physical Properties of Subduction Zone Mineralsa
 We chose to model only a restricted set of the most abundant rock compositions relevant to subduction zones: basalt/gabbro, lherzolite, depleted lherzolite, harzburgite, and serpentinite. We treated the entire crust of the overriding and subducting plates as basalt and gabbro of mid-ocean ridge basalt (MORB) composition, and the entire mantle as ultramafic. For each rock composition, we calculated the P–T stability fields of different minerals and the reactions that bound the various fields. We treated each stability field as though it contained a single set of minerals of constant composition and mode, and as though it were bounded by discontinuous reactions. This is a more serious simplification for mafic rocks than for ultramafic rocks.
3.1. Mafic Rocks
 There are many different ways to construct a phase diagram for mafic rocks. One internally consistent approach, taken by Kerrick and Connolly , is to specify the bulk composition in terms of major elements and then calculate phase assemblages based on minimizing Gibbs free energy. A weakness of this approach is the heavy reliance on the thermodynamic properties of minerals, which are known to varying degrees of accuracy and precision. A second approach is to use experimental observations of the stabilities of minerals. The strength of this methodology is that important variables such as pressure, temperature, and bulk composition are specified by the experimentalist. A crucial weakness of using experiments is that it is nearly impossible to reverse reactions at low temperature (typically <600°C), and many experiments conducted at such conditions have yielded metastable minerals.
 We used a third approach, which involved a comprehensive search of the literature to identify petrological field studies that reported bulk rock compositions, mineral modes, and mineral compositions. From these studies we chose only those rocks with bulk compositions that differed from unmetasomatized, anhydrous MORB (Table 2) by less than ∼10% in each oxide. We then compiled the mineral modes and mineral compositions into various metamorphic facies (Table 3). Obvious outliers were discarded, and a mean mineral mode and set of mean mineral compositions were computed for each metamorphic facies. Each mineral composition was then decomposed proportionally into end-member phases listed in Table 1 (e.g., garnets are represented as mixtures of almandine, grossular, and pyrope end-members). Because many natural mineral compositions are not easily decomposed into constituent components for which we have physical property data (e.g., ferric-iron or Ti-bearing amphibole) each mineral mode was adjusted, using rules given in Table 4, to ensure that the bulk composition calculated from the modes and compositions of the end-member mineral components was still within 10% of MORB. The H2O content of each rock thus calculated was not fixed or limited, but determined by the mineral modes. Note that even the least hydrous rocks we calculated for MORB composition contain a tiny fraction of H2O bound in mica.
Table 4. Rules for Decomposing Natural Rock/Mineral Compositions Into End-Member Minerals
Greenschist and related facies
all Na in albite; all K in muscovite; all Ti in sphene; epidote assumed to have Fe3+/(Fe3+ + Al) = 0.33; remaining mineral modes adjusted to fit MORB bulk composition while preserving mineral Fe/Mg ratios
Amphibolite, granulite, and related facies
all Na in albite + pargasite; all K and Ti in hornblende; assumed 1 vol % magnetite; assumed An50 plagioclase; epidote assumed to have Fe3+/(Fe3+ + Al) = 0.33; remaining mineral modes adjusted to fit MORB bulk composition while preserving mineral Fe/Mg ratios.
all Na in albite + ferroglaucophane; all K in hornblende; all Ti in rutile; assumed An35 plagioclase; remaining mineral modes adjusted to fit MORB bulk composition while preserving mineral Fe/Mg ratios
Various blueschist facies
all Na in albite + glaucophane + ferroglaucophane; all K in muscovite; all Ti in sphene; remaining mineral modes adjusted to fit MORB bulk composition while preserving mineral Fe/Mg ratios
Various eclogite facies
all Na in jadeite; all K in muscovite; all Ti in sphene; zoisite assumed to have Fe3+ = 0; remaining mineral modes adjusted to fit MORB bulk composition while preserving mineral Fe/Mg ratios
 Next, the stoichiometries and P–T positions of the reactions that were judged to bound the various mineral assemblages were calculated with the aid of Thermocalc [Powell et al., 1998] in the system K-Na-Ca-Mg-Fe2+-Fe3+-Al-Si-O-H. Most facies boundaries are thus defined by the appearance or disappearance of at least one phase, in addition to changes in the compositions and modes of minerals with solid solutions. The result is shown in Figure 1. Several important observations apply to Figure 1.
Metamafic rocks have never been recovered from extremely low temperatures (i.e., the “forbidden zone” of Liou et al. ), so phase relations in this domain are speculative. However, we calculate assemblages in the forbidden zone because calculated geotherms for cold subduction zones penetrate into this region [Peacock and Wang, 1999].
Our phase diagram is consistent with mineralogies of high-pressure to ultrahigh-pressure rocks; for example, in the ultrahigh-pressure Kokchetav Massif, quartz eclogites contain zoisite and amphibole, coesite eclogites contain rare amphibole, and diamond eclogites contain neither zoisite nor amphibole [Ota et al., 2000].
There is no stability field for chloritoid in Figure 1, consistent with its absence in naturally metamorphosed rocks of MORB composition (but see Poli and Schmidt ).
The restricted phase field for lawsonite eclogites is consistent with the extreme rarity of such rocks, but see Okamoto and Maruyama  for a different interpretation. Specifically, lawsonite eclogites have been reported in mafic bulk compositions from three localities. In one of those [Helmstaedt and Schulze, 1988], lawsonite may not be an eclogite-facies phase. In another locality (Corsica), lawsonite occurs in unusually Fe + Mn-rich eclogites [Caron and Pequignot, 1986]. The third locality is a single boulder [Ghent et al., 1993].
 The strength of our approach is that the mineral parageneses, compositions, and modes that we used to construct Figure 1 actually occur in naturally metamorphosed high-pressure rocks. Some disadvantages include (1) Assuming that the entire crust is of MORB composition is incorrect for the lower oceanic crust, which tends to be more aluminous and more magnesian [Dick et al., 2000]. (2) This assumption is also incorrect for portions of the crust that are altered, which are most notably enriched in Al and Ca relative to MORB (Table 2) [Staudigel et al., 1996] and which would likely stabilize additional hydrous Ca-Al silicates [Pawley and Holloway, 1993; Poli and Schmidt, 1997]. (3) In this paper, we consider only anhydrous and fully hydrated MORB, whereas the oceanic crust is heterogeneously hydrated. The end-member cases that we treat here can be considered to bound all possible hydration states.
3.2. Ultramafic Rocks
 Lherzolite and harzburgite are the common enriched and depleted rock types of the upper mantle; depleted lherzolite is intermediate. Harzburgite (olivine + orthopyroxene) is the dominant rock type in mantle wedges and the uppermost oceanic mantle; the lherzolite (olivine + orthopyroxene + clinopyroxene) models are included for completeness. Because of considerable interest in serpentinization, we model the bulk composition of pure serpentinite, but note that all the other ultramafic bulk compositions we model also are largely serpentine at lower temperature.
 Phase diagrams for lherzolite, depleted lherzolite, harzburgite, and serpentinite (Figures 23,4–5) were constructed with a different technique than that used for mafic rocks. We used four sets of mineral compositions and modes as “starting compositions” (labeled in Figures 2–5; see Table 5); the lherzolite is from Ernst , the depleted lherzolite and harzburgite are from Lippard et al. , and we chose the bulk composition of the serpentinite as Mg95 antigorite. These are typical upper mantle bulk compositions. The volume and molar proportions of each mineral that make up each rock are shown in Figures 2–5. A reaction network was then created around each of these “starting compositions.” Using mineral compositions reported from meta-ultramafic rocks worldwide, we calculated two separate sets of activities for high pressure and low pressure, using either ideal mixing or the program “A-X” by T. Holland and R. Powell (Table 6). The P–T positions of the reactions among the phases were then calculated as Mg-end-member reactions in the Ca-Fe2+-Mg-Al-Si-H-O system, using Thermocalc [Powell et al., 1998]. Thermocalc calculations of phase relations at P > 5 GPa were then modified in light of recent experiments by Luth , Ulmer and Trommsdorff , Wunder and Schreyer , Bose and Navrotsky , Wunder , and Pawley . The calculated mineral abundances were then converted to end-member mineral abundances using the formula in Table 7. Although these phase diagrams are considered to be very reliable, there is still considerable ambiguity regarding the relations among phases in ultramafic rocks at high pressure and low temperature; e.g., the slope of the reaction antigorite + brucite = phase A + H2O is poorly constrained.
Table 5. Mineral Modes for “Starting Compositions” of Ultramafic Rocksa
4. Computing Subduction Zone Pressures and Temperatures
 Temperatures in subduction zones have been calculated using numerical [e.g., Toksöz et al., 1971; Peacock, 1990] and analytical [e.g., Royden, 1993; Davies, 1999] solutions. As an illustration, we show the thermal model of Hacker et al.  for southern Vancouver Island (Figure 6a). Pressures were calculated using fixed densities of 1.0, 2.7, 3.0, and 3.3 g/cm3 for water, continental crust, oceanic crust, and mantle, respectively.
5. Superimposing Phase Relations
 Onto a subduction zone cross section depicting P, T, and rock compositions, we overlayed the different metamorphic mineral assemblages computed in step 2. Figures 6b and 6c show the results for mafic rock and harzburgite, respectively. The diagrams are constructed assuming that the activity of H2O = 1 (or that PH2O = Plithostatic; i.e., rocks are H2O saturated) and that equilibrium obtains; these assumptions cannot be correct everywhere and are addressed partially in a later section. If the activity of H2O < 1, phase boundaries (Figures 2–5) that involve the gain or loss of H2O shift to favor anhydrous minerals.
6. Superimposing Rock Physical Properties
 From the mineral physical properties calculated at elevated P and T in step 1, we derive density and H2O contents using a linear (Voigt) average and derive VP and VS from bulk and shear moduli determined for aggregates using a Voigt-Reuss-Hill average [Hill, 1952], all weighted by mineral proportions determined in step 2. Hashin-Shtrickman bounds on the same rocks reproduce the Voigt-Reuss-Hill averages to ±0.4%, so the simpler averaging method should suffice. The results are shown in Figures 7–13. As a test, we compare our calculated values with laboratory measurements of rocks in Figure 14. We used the measurements of 26 mostly mafic rocks by Kern et al.  because that study also reported the proportions of minerals in the tested samples. At 60 MPa, 20°C (Figure 14b) and 60 MPa, 600°C (Figure 14c), our calculated VP values exceed those of Kern et al. by ∼2 and ∼3%, respectively, likely because 60 MPa may not be sufficient to close microcracks in experimental samples. Christensen  reported VP and mineral modes, but not mineral compositions, for two eclogites, a dunite, and a pyroxenite. Our calculations reproduce his measured 3.0 GPa VP values to better than 1%. We also compared our calculations to rock VP values reported by Christensen and Mooney , even though their mineral modes and compositions are unknown to us (Figures 14d–14f). In spite of this, we reproduce their VP values at elevated P and T to within 2%. Of particular relevance to subduction zones, we calculate ΔVP = −15% and ΔVS = −19% for gabbro relative to dunite, in excellent agreement with Christensen's  measured values of ΔVP = −14% and ΔVS = −18%. We consider all of this to be excellent agreement, considering that the mineral compositions (and in some cases, proportions) of the tested samples are unknown, and that the difference in VP across the compositional ranges of, for example, olivine and plagioclase are 25% and 16%, respectively.
 The values we calculate for MORB composition are significantly different than those for a pure Ca-Mg-Al-Si-H-O system such as that used by Helffrich . One mole of an Fe-bearing mineral requires more wt % Fe than one mole of a Mg-bearing mineral. Thus rocks composed of Fe-bearing minerals contain less weight percent H2O. Also, replacement of Mg by Fe affects density much more than elastic moduli, so seismic velocities correlate negatively with density for such substitutions. Our Fe-bearing rocks are also, as a result, roughly 4% denser and have seismic velocities that are ∼4% slower.
 Our more detailed treatment of metamorphism results in significantly different predictions than previous studies. For example, Furlong and Fountain  calculated the P wave velocities of mafic rocks using a three-part model of gabbro (VP = 7.0–7.2 km/s), garnet granulite (VP = 7.2–7.8 km/s), and eclogite (VP = 7.8–8.2 km/s) (see their Figures 6 and 7). Our Figure 8 shows that metamorphism yields a much broader range of more distinctive velocities, and much slower velocities (6.5 km/s for mafic granulite, for instance). A simple two-part model of gabbro and eclogite (Figure 8c) captures the essence of the Furlong and Fountain  calculation, extends it to 8 GPa, and emphasizes the resultant simplification of a two- or three-part model for mafic rocks.
 There are many sources of uncertainty inherent in calculating rock properties from laboratory physical property measurements. These uncertainties can be grouped into three categories: (1) uncertainty in single-mineral thermoelastic parameters, (2) uncertainty due to calculational approximations, and (3) uncertainty arising from converting single-crystal data to rock properties.
7.1. Single-Mineral Thermoelastic Parameters
 The thermoelastic parameters that most significantly influence single-crystal property calculations are the densities, thermal expansivities and elastic moduli. Densities are generally known to better than 0.15% [Smyth and McCormick, 1995], although minerals with variable structural state (e.g., mica polytypes) have different densities (<3%), an issue that we do not consider. Various investigators have reported thermal expansivities for simple minerals such as olivine that vary by 14% [Fei, 1995], although the precision of individual measurements is better than 2% [Anderson and Isaak, 1995]; for many minerals, including most pyroxenes, ∂α/∂T has not been measured. Bulk and shear moduli measured in different laboratories for simple minerals such as pyrope and diopside differ by 2% and 3%, respectively [Bass, 1995; Knittle, 1995], although the precision of individual measurements is better than 1% [Anderson and Isaak, 1995]. Uncertainties for individual modulus and thermal expansitivity measurements translate to uncertainties of ∼1.5% for individual γth and Γ measurements and determinations from different laboratories should vary no more than ∼10%. Moreover, the general dearth of ∂μ/∂T and ∂KT/∂P determinations mean that Γ for most minerals must be approximated as Γ = δT [Anderson and Isaak, 1995], and δT must be approximated as δT ≈ γth + KT′ [Anderson et al., 1992]. The Grüneisen parameter γth, can be measured to ∼2% [Anderson and Isaak, 1995] but is unmeasured for most minerals. As a single example of the kind of uncertainty inherent in values for specific minerals, consider zoisite. Pawley et al.  reported KT = 127 ± 4 GPa assuming ∂KT/∂P = 4, Grevel et al.  reported KT = 125.1 ± 2.1 GPa assuming ∂KT/∂P = 4 and KT = 137 GPa if ∂KT/∂P = 0.5, and Comodi and Zanazzi  reported K0 = 102.0 ± 6.5 GPa and ∂KT/∂P = 4.8. At 6 GPa, these different values translate into KT values of 151, 149, 140, and 131 GPa, or bulk sound velocity variations of +3%. Grevel et al.  argued that none of these studies can distinguish ∂KT/∂P from 4.
 Monte Carlo simulations indicate that for a simple mineral with a reasonably well-determined set of thermoelastic parameters (e.g., garnet), the uncertainties on single measurements imply <0.5% uncertainty in VP and VS and <1% uncertainty in elastic moduli calculated at elevated pressure and temperature (e.g., 800°C, 4 GPa). If we consider the much larger variation exhibited by measurements from different laboratories, the calculated uncertainties increase to <2% uncertainty in VP and VS and <4% uncertainty in elastic moduli. Fortunately, the polymineralic nature of rocks minimizes sensitivity to error in any single measurement.
7.2. Calculational Approximation
 Our calculation procedure makes three important assumptions (see Appendix A). We use Holland and Powell's  approximation for thermal expansivity, which appears to give excellent fits to the data [Pawley et al., 1996]. We use a third-order finite strain approximation. We ignore the second pressure derivatives of the elastic moduli. Although small uncertainties may arise from these approximations, the general lack of higher-order information on derivatives makes any more exact procedure difficult to verify.
8. Comparing Predictions to Observations
 As a simple example of the use of these calculations, we compare observed and predicted wave speeds for (1) unsubducted oceanic lithosphere, (2) subducting slabs, and (3) the mantle of the overriding plate in a subduction zone.
8.1. Oceanic Lithosphere Velocities and Mineralogy
White et al.  and Mutter and Mutter  summarized the seismic velocity structure of oceanic crust and uppermost mantle obtained from seismic refraction measurements worldwide. Figure 15 compares the inferred lower crust and upper mantle velocities measured in the studies cited by White et al.  with our calculated velocities. Each velocity measurement and calculation is compared at the appropriate in situ temperature and pressure for lower crust and mantle of the ages reported by White et al. The compilation of White et al.  does not, in general, differentiate azimuths, and the upper mantle is known to have substantial anisotropy (e.g., Pn can vary by up to 5% with azimuth [Shearer and Orcutt, 1986]), so some of the observed variation may be due to anisotropy. Our calculated wave speeds represent isotropic averages, so actual measurements from anisotropic peridotites should lie within ∼2.5% (0.2 km/s) of these calculations, and variations smaller than that should not be considered to necessarily reflect differences in composition.
 The observed lower crustal velocities range from 6.5 to 7.8 km/s, with most values in the range of 6.6–7.6 km/s. The velocities we calculate for anhydrous rocks typical of layer 3 (gabbronorite and olivine gabbro) are toward the middle of this range. The speeds slower than 7.0 km/s observed from the lower crust imply alteration or geological heterogeneity of the type described by Karson  and Dilek et al. . If homogeneous alteration of a single rock type is responsible, these velocities are best matched by amphibolite-facies alteration (1.3 wt % H2O); however, in even the most altered sections of the lower crust alteration does not reach 100% [cf. Dick et al., 1991]. If these slow velocities are the result of complex mixtures of mafic rock and serpentinized ultramafic rock [e.g., Karson, 1998], mixtures of gabbro plus 15–30 vol % antigorite can account for the observed velocity shifts of −0.4 to −0.6 km/s because antigorite has velocities of 5.7–5.8 km/s at these conditions. Because serpentine has an unusual Poisson's ratio [Christensen, 1996], better oceanic VS measurements would help resolve these two possibilities. Observed velocities greater than our predicted gabbro speeds are well matched by a mixture of gabbro and wehrlite or olivine clinopyroxenite. Such waves are likely sampling the mafic/ultramafic transition zone, which is petrologically part of the crust, but seismically part of the mantle. Note that there is no persuasive indication that lower crustal wave speeds change with age of the lithosphere in any way other than expected from simple cooling (i.e., the measurements of White et al. track our calculated curves for various rock types), implying that the structure and composition of the lithosphere are determined at or near the ridge axis and not significantly modified thereafter.
 Spinel harzburgite is a good explanation for most of the faster observed upper mantle velocities. The slower velocities could be wehrlite or olivine clinopyroxenite, as suggested above for the lowermost crust, but the summary of White et al.  shows that the thickness of the zones with measured velocities that are faster than gabbro and slower spinel harzburgite velocities is much greater than the typical 500-m thickness of ophiolite transition zones [Coleman, 1977]. Thus these slowest parts of the uppermost mantle are likely harzburgite with up to 20% alteration to serpentine, brucite, and chlorite (∼2.4 wt% H2O).
 Our approach has some advantages over other techniques. For example, Carlson  demonstrated that velocities inferred for end-member rock types from measurements of Ocean Drilling Program (ODP) cores 504B and 735B do not compare well with velocities calculated from single-crystal measurements averaged by the Voigt-Reuss-Hill (VRH) technique or with seismic profiles of the oceanic lithosphere. In contrast, as illustrated in Figure 14, our calculated velocities compare well with rock velocities measured in the laboratory and with those inferred from seismological studies (Figure 15). We suspect that variable degrees of alteration and accessory minerals may be affecting properties of the field samples treated as end-member compositions. Our method permits the calculation of properties of unaltered rocks, whereas many laboratory velocity measurements are on rocks with incompletely described alteration.
8.2. Subducting Slab Velocities and Mineralogy
Figure 16 extends the comparison among calculated wave speeds of rocks to a broader range of bulk compositions and pressures relevant to subducting slabs. Figure 16a shows that anhydrous gabbro is 9–12% slower than anhydrous harzburgite over subduction zone pressures and temperatures. This number is a good match to Figure 15, which shows that the observed velocity difference between typical uppermost mantle and uppermost layer 3 is ∼15%. Figure 16 is a better way to compare crustal and mantle velocities than simply comparing gabbro to dunite [e.g., Christensen, 1996].
Figure 16b shows P wave velocities of the various metamorphic facies for fully hydrated MORB versus anhydrous harzburgite. Metamorphosed, fully hydrated MORB is >15% slower than dry harzburgite at pressures <1.0 GPa, ∼10% slower than harzburgite at temperatures <500°C, and ∼3% slower when at zoisite- or amphibole-bearing eclogite facies. The fact that the P wave speed of anhydrous eclogite is indistinguishable from unaltered harzburgite has important implications for P wave tomography: velocity variations can only reflect differences in temperature. Figure 16c shows P wave velocities of the various metamorphic facies for fully hydrated MORB versus the various metamorphic facies for fully hydrated harzburgite. Velocities of metamorphosed MORB are ∼5–15% slower than metamorphosed harzburgite at T > 450°C and P < 1.5 GPa, 15–30% faster at T < 500°C, ∼3–4% faster at T = 600–800°C and P > 1.5 GPa, and similar at higher temperatures. Figures 16b and 16c thus encompass the entire range of wave speed differences expected between MORB and harzburgite with 0–100% alteration. In principal, one can solve for extent of hydration using the P wave speed.
 These diagrams serve as a useful starting point for interpreting the velocities of subducted slabs. In cold subduction zones such as Tohoku, abundant alteration of the mantle is thermodynamically permitted, leading to the potential for slow mantle wave speeds immediately above and below the slab crust (Figure 16c). If the crust and mantle are completely hydrated, the crust can be up to 22–40% faster than the mantle to great depth (Figure 16c). Most relatively cold subduction zones exhibit seismically slow rather than fast layers: the Mariana, Tohoku, Kurile, Aleutians, and Alaska slabs have 5–8% slow layers that persist to depths of 100–250 km [Abers, 2000]. This is incompatible with extensive alteration of the mantle (Figure 16c) but can be explained as a slab of metamorphosed MORB contained within partially altered harzburgite (i.e., intermediate between Figures 16b and 16c).
 Several seismic signals passing through the Tohoku slab (northern Honshu) have revealed a slow channel, of thickness comparable to subducted crust at the top of the slab [Matsuzawa et al., 1986; Iidaka and Mizoue, 1991; Abers, 2000], potentially explainable in manner just described. The study of Matsuzawa et al. models P-S conversions by a layer 6% slower than the overlying mantle and 12% faster than that underlying it, between 60 and 150 km depth, whereas that of Abers  explains dispersed body waves with a layer 6% slow and 4 km thick, largely between 100 and 150 km depth (Table 8). At these depths, subducted crust beneath Tohoku should be lawsonite-amphibole eclogite with VP = 7.9 km/s if fully hydrated (Figure 8a and Table 8). The presence of a low velocity crust precludes extensive hydration of the mantle above and below, as at these P–T conditions hydrated ultramafic rocks should be 25–29% slower than hydrated gabbro (Figure 16c). By comparison, a hydrated metamorphosed gabbro should be 8% slower than unmetamorphosed mantle (Figure 16b). The slightly lower contrast observed here may reflect incomplete hydration; the difference in mantle wave speed above and below the crust may reflect less mantle hydration in the downgoing plate than within the mantle wedge. Alternatively, a combination of hydrated MORB overlying anhydrous, unmetamorphosed gabbro may explain these observations [Hacker, 1996].
 The Tonga slab appears very different, as high-frequency precursors recorded in New Zealand may require a thin, high-velocity layer embedded in a relatively slow surrounding mantle [Gubbins and Sneider, 1991; van der Hilst and Snieder, 1996]. This inferred velocity profile, if correct, may be explainable as a consequence of extensive hydration of the mantle surrounding the subducted crust. Alternatively, the Tonga observations may be a path effect [Abers, 2000].
 In hot subduction zones such as Nankai, little hydration of the mantle is thermodynamically permitted (Figures 2–4), leading to fast predicted mantle wave speeds (Figures 16a and 16b). Fully hydrated mafic crust will be 16% slower than the mantle down to depths of ∼35 km, ∼4% slower down to ∼70 km, and indistinguishable from the mantle at greater depth (Figure 16b). In contrast, anhydrous mafic crust will remain ∼12% slower than the mantle until transformed to eclogite (Figure 16a). Hori  examined seismic waves coming from the Philippine Sea plate subducting at the eastern end of the Nankai Trough, and noted that waves emanating from depths shallower than 40–60 km show two strong P and S phases each, the second traveling considerably slower than predicted from travel time tables. They interpreted the first P and S arrivals as traveling through the upper mantle of the downgoing plate at velocities of 8.2 and 4.7 km/s, respectively, and modeled the second phases as traveling through the subducted crust at VP = 7.0 and VS = 4.0 km/s at <60 km depth. From these velocities, they infer that the slab crust remains gabbroic and has not yet transformed to eclogite. This 60 km depth corresponds to our modeled [Hacker et al., 2002] transformation from zoisite-bearing eclogite to eclogite. Using our thermal model of the Nankai subduction zone [Hacker et al., 2003], at 40–60 km depth (∼500°C), unaltered harzburgite should have VP = 8.2 km/s, as observed. Our methodology predicts that unaltered gabbro at 40–60 km depth beneath Nankai should have VP = 7.1–7.2 km/s, slightly faster than observed. If the crust is entirely altered to hydrous assemblages, it should have P wave speeds of 7.8–7.9 km/s (zoisite-amphibole eclogite) or 6.7 km/s (epidote blueschist) at these depths. Thus the observation of a slow waveguide to 40–60 km depth beneath Nankai is consistent with the presence of unaltered gabbro or blueschist, but not eclogite (Figure 16b).
8.3. Mantle Wedge Alteration
 As a final example, consider the reports of serpentinization of arc mantle wedges. Graeber and Asch  found by tomographic inversion that the Nazca plate subducting beneath northern Chile is overlain at depths of 50–100 km by a layer with VP/VS ratios of 1.79 to >1.84. Examination of Figure 11b reinforces Graeber and Asch's conclusion that such ratios cannot represent unaltered mantle. Comparison of Figures 11b and 9b, 10, 12, and 13b shows, however, that such VP/VS ratios are easily explained by ∼20% alteration to stable hydrous minerals.
Kamiya and Kobayashi  measured VP ∼ 6.9 km/s, VS ∼ 3.4 km/s, and Poisson's ratio is ∼0.34 at depths of 20–45 km in a small region beneath central Japan. They concluded from the data of Christensen  that these observations are consistent with 50 vol % serpentinized peridotite. Our calculations indicate higher fractions of hydrous minerals, 60–80%, but reinforce the general conclusion that mantle wedges are locally hydrated.
 Our model produces calculated physical properties of MORB, lherzolite, harzburgite, and serpentinite in subduction zones using a compilation of mineral physical property measurements, a new set of phase diagrams, and subduction zone thermal models. These data are used to calculate H2O content, density and seismic wave speeds of subduction zone rocks. New insights are provided into (1) the presence of hydrous phases and the distribution of H2O within a subduction zone; (2) the densification of the subducting slab and resultant effects on measured gravity and slab shape; and (3) the variations in seismic wave speeds resulting from thermal and metamorphic processes at depth.
Appendix A:: Calculation Method
 We calculated the physical properties of minerals at elevated pressure and temperature via the following algorithm, based on Bina and Helffrich . Holland and Powell  advocated a relationship between expansivity α and temperature T(K), defined by a single constant a° for each mineral:
where V(T) is the molar volume at temperature, Vo is the molar volume at STP, and To = 298 K.
 The density at elevated temperature ρ(T) is related to the density at STP ρo by
 The isothermal bulk modulus at elevated temperature KT(T) is related to the isothermal bulk modulus at STP by
where δT is the second Grüneisen parameter. The shear modulus at elevated temperature μ(T) follows in similar fashion from the shear modulus at STP:
 The finite strain f is calculated recursively from
typically evaluated at To (KT′ in Table 1). The density at elevated pressure ρ(P) is then
 The bulk modulus at elevated pressure and temperature KT(T,P) is
 The expansivity at elevated pressure and temperature α(T,P) is
 The isentropic bulk modulus KS is
where γth is the first Grüneisen parameter. The shear modulus at elevated pressure and temperature μ(T,P) is
 The density at elevated pressure and temperature ρ(P,T) is
from which the P wave velocity VP, shear wave velocity VS, and Poisson's ratio ν can be calculated:
 The physical property Ψ of a mineral aggregate is then calculated from the physical property Ψi of n constituent minerals using a Voigt-Reuss-Hill average:
where νi is the volume proportion of each mineral and the first and second terms are ΨV, the Voigt bounds, and ΨR, the Reuss bounds. Because mass in aggregates is a simple sum of component masses, only ΨV is used in calculating ρ for aggregates.
 Supported by grants from the National Science Foundation. Thoughtfully reviewed by W.G. Ernst and two anonymous reviewers. Ross Angel and Nancy Ross provided preprints and helpful reviews of our mineral physical parameter compilation. Stephan Husen provided sundry seismology tutorials to B.R.H.