Subduction factory 1. Theoretical mineralogy, densities, seismic wave speeds, and H2O contents

Authors


Abstract

[1] 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.

1. Introduction

[2] 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:

  1. Compile and assess physical properties of minerals relevant to subduction zones.
  2. Construct phase diagrams appropriate for subduction zone rock types and physical conditions.
  3. Compute pressures (P) and temperatures (T) for a specific subduction zone.
  4. Superimpose calculated phase relations onto the P–T model.
  5. Superimpose rock physical properties onto the P–T model.
  6. Compare predictions to observations.

2. Compiling Mineral Properties

[3] 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 [1992], 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 [1998] 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
PhaseGram Formula Weight, g/molMolar Volume, cm3/molρ298, kg/m3Notes and RefsH2O, wt %Expansivity ao, × 105 K−1Notes and RefsKT, × 1010 PaNotes and RefsKT′ = ∂KT/∂PNotes and Refsμ, × 1010 PaNotes and RefsΓ = (∂lnμ/∂lnρ)PNotes and Refsμ′ = ∂μ/∂PNotes and RefsγthNotes and RefsδTNotes and Refs
hab, high albite262.2100.12620[21]04.6[19]5.4D946D942.8[9]13[14]4.26H960.6[20]6.58[18]
lab, low albite262.2100.12620[21]04.6[19]5.4D946D942.8[9]13[16]4.26[17]0.6[20]6.57[18]
an, anorthite278.2100.82760[21]02.4[19]8.4A013.0Apc3.7[9]6.8[14]3.48H960.5[20]3.47[18]
alm, almandine497.7115.14324[21]04.0[19]17.4WJ016.0WJ019.21WJ015.5[16]1.6H961.0[20]5.52H96
grs, grossular450.4125.43593[21]03.9[19]16.8WJ015.5WJ0110.9WJ015.1[14]1.2H961.2AI954.57AI95
prp, pyrope403.1113.13565[21]04.4[19]17.3WJ015.0WJ019.10WJ014.1[14]1.5SB011.3AI955.30AI95
di, diopside216.666.23272[21]05.7[19]11.3K954.8K956.49B956.0[16]2.00H961.2[20]6.04[18]
en, enstatite200.862.63206[21]05.1[19]10.6A018.5A017.68J999.4[16]2.00H960.9[20]9.39[18]
fs, ferrosilite263.965.94003[21]06.3[19]10.0[15]4[13]5.20B955.1[16]2.00H961.1[20]5.05[18]
jd, jadeite202.160.43346[21]04.7[19]13.9K954[13]8.50B955.0[16]1.02H961.0[20]4.99[18]
hed, hedenbergite248.168.03651[21]05.7[19]11.9K954[13]6.1B955.2[16]0.85[17]1.2[20]5.21[18]
clin, clinochlore555.6210.82635[21]134.0[19]7.54WM014HF784.55[7]4.3[16]1.00[17]0.3[20]4.30[18]
daph, daphnite713.5213.43343[21]10.14.0[19]4.58HF784[13]2.76[7]4.3[16]1.00[17]0.3[20]4.29[18]
law, lawsonite314.2101.33101[21]11.53.2C0012.3BA015.4BA016.02L806.3[16]0.82[17]0.9[20]6.25[18]
gl, glaucophane789.4262.43008[21]2.35.3[19]9.6C914C915.6[10]4.8[16]0.97[17]0.8[20]4.81[18]
fgl, ferroglaucophane878.1265.93302[21]2.15.3[19]8.9HP984[13]5.2[10]4.8[16]0.97[17]0.8[20]4.81[18]
tr, tremolite812.4272.72979[21]2.25.3[19]8.5C914C914.9[10]4.7[16]0.97[17]0.7[20]4.74[18]
fact, ferro-actinolite970.1282.83430[21]1.95.3[19]7.6HP984[13]4.4[10]4.7[16]0.97[17]0.7[20]4.73[18]
ts, tschermakite815.4268.03043[21]2.25.3[19]7.6HP984[13]4.4[10]4.7[16]0.97[17]0.7[20]4.71[18]
parg, pargasite835.8271.93074[21]2.25.3[19]9.12HP984[13]5.29[10]4.8[16]0.97[17]0.8[20]4.84[18]
hb, hornblende864.7266.23248[8]2.55.3[19]9.40[8]4C915.45[3]5.1[16]0.97[17]1.1[13]5.10[18]
anth, anthophyllite780.8265.42942[21]2.35.3[19]7.0HP984[13]4.1[10]4.6[16]0.97[17]0.6[20]4.60[18]
pr, prehnite412.4140.32940[21]4.45.1[19]8.35HP984[13]5.03[7]4.8[16]1.00[17]0.8[20]4.77[18]
pm, pumpellyite943295.53191[21]6.75.0[19]16.2HP984[13]7.91L805.3[16]0.82[17]1.3[20]5.30[18]
aqz, alpha quartz60.122.72648[21]00.65[19]3.71A975.99A974.48O9540.1[14]0.46B950.7[20]8.42H96
bqz, beta quartz60.123.72530[21]00.65[19]5.70[15]4[13]4.14B954.1[16]1.21[17]0.1[20]4.11[18]
coe, coesite60.120.62911[21]01.8[19]9.74A014.3A016.16B954.7[16]1.05[17]0.4[20]4.66[18]
zo, zoisite454.4135.83347[21]26.7[19]12.5G004G006.12H965.2[16]0.82[17]1.2[20]5.24[18]
czo, clinozoisite454.4136.33333[21]24.6[19]12.5[22]5[22]6.12L805.9[16]0.82[17]0.9[20]5.94[18]
ep, epidote483.2138.13498[21]1.95.1[19]16.2[15]4[13]6.12B955.1[16]0.63[17]1.1[20]5.11[18]
ms, muscovite398.2140.82828[21]4.56.0[19]6.14K956.9K953.70[3]7.4[16]1.00[17]0.5[20]7.42[18]
phl, phlogopite417.2149.72788[21]4.55.8[19]5.85HF784HF782.70[3]4.6[16]0.77[17]0.6[20]4.55[18]
ann, annite511.9154.33317[21]3.55.8[19]5.04[4]4[13]2.66[4]4.6[16]0.88[17]0.6[20]4.55[18]
atg, antigorite45361754.72585[21]12.34.7[19]6.35T912.77T911.81[1]3.3[16]0.47[17]0.5T913.28[18]
fo, forsterite140.743.73222[21]06.1[19]12.7AI955.37AI958.16AI955.2[14]1.82AI951.2AI955.50AI95
fa, fayalite203.846.34400[21]05.1[19]13.7AI955.16AI955.10AI954.7[14]0.62AI951.1AI955.40AI95
cc, calcite100.136.92713[21]04.4[19]7.35RA994RA993.20B954.7[16]0.73[17]0.7[20]4.69[18]
ar, aragonite100.134.12931[21]012[19]4.60[15]4[13]3.85B955.4[16]1.39[17]1.4[20]5.36[18]
lm, laumontite470.4203.72309[21]15.32.4[19]4.66C964[13]2.80C964.5[16]1.00[17]0.5[20]4.46[18]
wr, wairakite434.4190.52281[21]8.32.4[19]4.66C964[13]2.80C964.5[16]1.00[17]0.5[20]4.52[18]
br, brucite58.324.62368[21]30.913PW963.96X986.7X982.39[7]4.5[16]1.00[17]0.8[20]4.5F95
ta, talc379.7136.42784[21]4.83.7[19]4.16P956.5P952.26BH006.8[16]0.91[17]0.3[20]6.82[18]
chum, chlinohumite621.1197.43146[21]2.95.0[19]12.0HP984[13]7.69[6]4.9[16]1.07[17]0.9[20]4.91[18]
phA, phase A456.3154.42955[21]11.88.3PW969.74RC006.0RC006.24[6]7.8[16]1.07[17]1.8[20]7.79[18]
sil, sillimanite162.049.93249[21]02.2[19]17.1[15]4[13]9.15B954.5[16]0.89[17]0.5[20]4.50[18]
ky, kyanite162.044.13670[21]04.0[19]15.6C975.6C978.37[11]6.6[16]0.89[17]1.0[20]6.56[18]
or, orthoclase278.3108.92555[21]03.4[19]5.83AA974AA972.81B954.4[16]0.80[17]0.4[20]4.44[18]
san, sanidine278.3109.02553[21]03.4[19]6.70A884A883.23[12]4.4[16]0.80[17]0.4[20]4.44[18]
spl, spinel142.339.83575[21]04.3[19]20.8AI953.36AI9510.8AI954.2[14]0.87[17]1.3AI956.5AI95
herc, hercynite173.840.84264[21]04.0[19]20.9[15]4[13]8.45B955.2[16]0.67[17]1.2[20]5.19[18]
magn, magnetite231.544.55201[21]07.0[19]18.1K955.5K9510.2[3]7.5[16]0.94[17]2.0[20]7.45[18]

3. Constructing Phase Diagrams

[4] 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

[5] There are many different ways to construct a phase diagram for mafic rocks. One internally consistent approach, taken by Kerrick and Connolly [2001], 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.

[6] 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 2. Mid-ocean Ridge Basalt Compositionsa
 UnalteredbAlteredc
SiO250.648.9
Al2O315.716.6
TiO21.51.3
FeO*10.69.6
MgO7.67.1
CaO11.113.7
Na2O2.62.2
K2O0.20.6
Table 3. Mineral Modes for MORB at Various Metamorphic Faciesa
 BasaltGabbroZPPPAGSeAgAegAAGgG 
hab, high albite          21  
lab, low albite16101920212220111118 20 
an, anorthite3838     6 182115 
alm, almandine       117  5 
grs, grossular       83  13 
prp, pyrope       31  10 
di, diopside2826        55 
en, enstatite 5        99 
fs, ferrosilite 6        99 
jd, jadeite           2 
hed, hedenbergite96        911 
clin, clinochlore  181611112 4    
daph, daphnite  108683 3    
law, lawsonite    4        
gl, glaucophane        7    
fgl, ferroglaucophane       176    
tr, tremolite    8129185132  
fact, ferro-actinolite    1451653257  
ts, tschermakite      1514 129  
parg, pargasite      10  127  
pr, prehnite   14         
pm, pumpellyite   1318        
qz, quartz  813552251   
coe, coesite             
zo, zoisite       4     
czo, clinozoisite             
ep, epidote    83218 20    
ms, muscovite  22222 15    
phl, phlogopite        2    
fo, forsterite17           
fa, fayalite 2           
cc, calcite  125    4    
lm, laumontite  25          
ta, talc             
sphene + rutile + spinel  2333312    
mt, magnetite8 46    2111 
 
 lBjlBcjlBjltSeBjeBzaEaEzElaEEcEdE
hab, high albite             
lab, low albite10   18        
an, anorthite             
alm, almandine      1717188181819
grs, grossular      71587131314
prp, pyrope      8784111112
di, diopside      1115207242421
en, enstatite        4   1
fs, ferrosilite   3  1 2 443
jd, jadeite 8816 1313121710181818
hed, hedenbergite   21  2351225
clin, clinochlore455588   3   
daph, daphnite544488   2   
law, lawsonite27282828     14   
gl, glaucophane71111 441  5   
fgl, ferroglaucophane966 44510 8   
tr, tremolite171414 1515104 9   
fact, ferro-actinolite131717 5512 10   
ts, tschermakite      3      
parg, pargasite       8 4   
pr, prehnite             
pm, pumpellyite             
qz, quartz32 251073636  
coe, coesite  2        63
zo, zoisite      10 8    
czo, clinozoisite    55       
ep, epidote    2323       
ms, muscovite2222222222222
phl, phlogopite             
fo, forsterite             
fa, fayalite             
cc, calcite             
lm, laumontite             
ta, talc   16         
sphene + rutile + spinel3333332223222
mt, magnetite             
Table 4. Rules for Decomposing Natural Rock/Mineral Compositions Into End-Member Minerals
Rock/MineralComposition
Greenschist and related faciesall 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 faciesall 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.
Garnet-amphibolite faciesall 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 faciesall 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 faciesall 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

[7] 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.

  1. Metamafic rocks have never been recovered from extremely low temperatures (i.e., the “forbidden zone” of Liou et al. [2000]), 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].
  2. 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].
  3. 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 [1997]).
  4. The restricted phase field for lawsonite eclogites is consistent with the extreme rarity of such rocks, but see Okamoto and Maruyama [1999] 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].
Figure 1.

Phase diagram for MORB; abbreviations as in Table 3. Phase relations in the “forbidden zone” (PT conditions not represented by rocks exposed on Earth's surface [Liou et al., 2000]) are poorly known. Solidi and high-pressure phase relations modified per results of Vielzeuf and Schmidt [2001].

[8] 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

[9] 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.

[10] Phase diagrams for lherzolite, depleted lherzolite, harzburgite, and serpentinite (Figures 23,45) 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 25; see Table 5); the lherzolite is from Ernst [1977], the depleted lherzolite and harzburgite are from Lippard et al. [1986], 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 25. 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 [1995], Ulmer and Trommsdorff [1995], Wunder and Schreyer [1997], Bose and Navrotsky [1998], Wunder [1998], and Pawley [2000]. 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.

Figure 2.

Phase diagram for lherzolite. Mineral abbreviations are after Holland and Powell [1998], plus am, amphibole; chl, chlorite; cpx, clinopyroxene, excluding CaTs (Ca tschermak); gar, garnet; ol, olivine; opx, orthopyroxene, excluding MgTs. Mineralogy of each field shown as m%, modal percentage of each mineral; v%, vol % of each mineral; m, moles of each mineral relative to the unaltered “starting composition.” Phase relations at T < 600°C, P > 5 GPa poorly known. Reactions show stoichiometry appropriate for the starting composition. Line weights are proportional to ΔH2O, and show that the H2O is lost between ∼500 and 800°C. Additional reactions are [1] 6en + 6di + 6sp = 12fo + 6an; [2] 12en + 6sp = 6py + 6fo; [3] 1.5 di + 1.5py = 1.5cats + 3en; [4] 2py = 2en + 2mgts; [5] 2en + 2sp = 2fo + 2mgts; [6] 3.8fo + 3.8tr = 9.4en + 7.5di + 2H2O; [7] 6.8fo + 6.8tr = 16.9en + 13.5di + 6.8H2O; [8] 1.5di + 1.5sp = 1.5fo + 1.5cats; [9] 3tr + 6sp = 1.5en + 9fo + 6an + 3H2O; [10] 3.5clin = 3.5en + 3.5fo + 3.5sp + 14H2O; [11] 0.4clin + 0.2tr = 2.2fo + 1.1en + 0.9an + 4H2O; [12] 5.1di + 5.1clin = 15.3fo + 5.1an + 20H2O; [13] 3.1clin = 3.1en + 3.1fo + 3.1sp + 12.4H2O; [14] 6.4clin + 5.1di = 9fo + 2.6tr + 6.4sp + 23H2O; [15] 9.5clin = 9.5en + 9.5fo + 9.5sp + 38H2O; [16] 4.2fo + 4.2tr = 10.5en + 8.4di + 4.2H2O; [17] 19en + 9.5sp = 9.5py + 9.5fo.

Figure 3.

Phase diagram for depleted lherzolite (see notes to Figure 2). Most of the bound H2O is lost at ∼500°C. [1] 4fo + 2an = 2en + 2di + 2sp; [2] 4en + 2sp = 2py + 2fo; [3] 1.5py = 1.5en + 1.5mgts; [4] 1.5en + 1.5sp = 1.5fo + 1.5mgts; [5] tr + 2sp = 0.5en + 3fo + 2an + H2O; [6] 1.5clin = 1.5en + 1.5fo + 1.5sp + 6H2O; [7] 2clin + tr = 5fo + 2.5en + 2an + 9H2O; [8] 3.5clin = 3.5en + 3.5fo + 3.5sp + 14H2O; [8] 2.2fo + 2.2anth = 9.9en + 2.2H2O; [9] 1fo + 1tr = 2.5en + 2di + 1H2O; [10] 4a + 4fo = 10en + 4H2O; [11] 4ta + 1.8fo = 2.2anth + 1.8H2O; [12] atg = 4ta + 18fo + 27H2O.

Figure 4.

Phase diagram for harzburgite (see notes to Figure 2). Most of the bound H2O is lost at ∼500°C. [1] 2en + sp = py + fo; [2] 1.5py = 1.5en + 1.5mgts; [3] 2.8fo + 2.8anth = 12.5en + 2.8H2O; [4] 5ta + 2.2fo = 2.8anth + 2.2H2O; [5] 5ta + 5fo = 12.5en + 5H2O.

Figure 5.

Phase diagram for serpentinite (see notes to Figure 2). [1] 2.2fo + 2.2anth = 9.9en + 2.2H2O; [2] 1.8fo + 4ta = 2.2anth + 1.8H2O; [3] 4fo + 4ta = 10en + 4H2O.

Table 5. Mineral Modes for “Starting Compositions” of Ultramafic Rocksa
 LherzoliteEnriched HarzburgiteHarzburgiteSerpentinite
di, diopside183  
en, enstatite221918 
fs, ferrosilite222 
hed, hedenbergite2   
atg, antigorite   100
fo, forsterite466771 
fa, fayalite578 
spinel + rutile + sphene21  
mt, magnetite21  
Table 6. Activities Used to Construct Ultramafic Phase Diagramsa
PhaseActivity ModelHigh-Pressure ActivityReferenceLow-Pressure ActivityReference
fo, forsteriteideal0.91MR980.80L86, MR98
di, diopsideHP980.75Z950.96L86, P87
mgts, Mg-tschermakHP980.04Z95?L86, P87
en, enstatiteHP980.81C830.79L86, P87
cats, Ca-tschermakHP980.1Z95?L86, P87
py, pyropeHP980.3C83, Z950 
sp, spinelideal0.8C83, MR980.6MR98
clin, clinochloreHP980.7LZ98, Z950.4P87
atg, antigoriteideal0.95 0.95P87
br, bruciteideal1 1 
ta, talcideal0.78LZ980.97P87
an, anorthiteHP980 0.86MR98
anth, anthophylliteideal0 0.5P87
tr, tremoliteHP980.3C83, LZ98, Z950.6P87
phA, phase Aideal0.95 0 
H2OHP980–1 0–1 
Table 7. Compositions Used to Convert Abundances of Minerals With Solid Solutions to Abundances of End-Member Mineralsa
MineralComposition
  • a

    In units of mole percent.

Olivineforsterite90fayalite10
Clinopyroxenediopside90hedenbergite10
Orthopyroxeneenstatite90ferrosilite10
Garnetpyrope66almandine24grossular10
Spinelmagnetite50spinel50
Chloriteclinochlore90daphnite10
Plagioclaseanorthite86albite14
Amphiboletremolite35pargasite60ferro-actinolite05

3.3. Other Compositions

[11] As a basis for comparing the properties of the metamorphosed rocks to unaltered rocks, we used mineral composition and mode data from holocrystalline MORBs [Ayuso et al., 1976; Mazzullo and Bence, 1976; Cann, 1981; Perfit and Fornari, 1983], diabase [Alt et al., 1993], olivine gabbro [Tiezzi and Scott, 1980; Browning, 1984; Lippard et al., 1986; Elthon, 1987; Robinson et al., 1989], wehrlite, and olivine clinopyroxenite [Lippard et al., 1986]. We do not model the physical properties of typical glassy ocean floor basalt because porosity and cracks play a dominant role in such rocks.

4. Computing Subduction Zone Pressures and Temperatures

[12] 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. [2003] 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.

Figure 6.

Calculated properties of the Cascadia subduction zone along a transect through southern Vancouver Island. (a) Geology and isotherms [Hacker et al., 2003]. (b) Calculated phase relations in mafic crust and observed seismicity [Rogers, 1998]. Anhydrous eclogite formation is predicted to occur at 80–90 km depth in the slab. (c) Calculated phase relations in ultramafic rock. Numbers indicate vol % of minerals: anth, anthophyllite (amphibole); atg, antigorite (serpentine); br, brucite; clin, clinochlore (chlorite); en, enstatite (orthopyroxene); fo, forsterite (olivine); sp, spinel; py, pyrope (garnet). (d) Calculated maximum H2O contents. Downgoing, hot slab mantle is nearly anhydrous, and only the tip of the mantle wedge can contain substantial H2O. (e) Calculated densities. Density of mantle wedge is low because of maximum possible hydration is assumed. (f) Calculated P wave speeds. Wave speed of mantle wedge is low because maximum possible hydration is assumed.

5. Superimposing Phase Relations

[13] 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 25) that involve the gain or loss of H2O shift to favor anhydrous minerals.

6. Superimposing Rock Physical Properties

[14] 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 713. 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. [1999] 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 [1974] 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 [1995], 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 [1996] 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.

Figure 7.

P wave speeds (6.x–8.x km/s), densities (3.x g/cm3), and VP/VS (1.xx) of (a) unmetamorphosed MORB and (b) unmetamorphosed gabbro. Differences are due solely to differences in mineralogy. Shading shows PT paths for Tohoku, Nankai, Costa Rica, and Cascadia subducted crust from Peacock and Wang [1999] and Hacker et al. [2003].

Figure 8.

(a) P wave speeds (6.x–8.x km/s) and densities (3.x g/cm3) of metamorphosed MORB. (b) VP/VS (1.xx) and Poisson's ratio (0.xx) of metamorphosed MORB. (c) P wave speeds for a simple, two-part (gabbro and eclogite) mafic rock model; such a simple model obscures most of the important changes seen in the complete model.

Figure 9.

P wave speeds (6.x–8.x km/s), densities (3.x g/cm3), and VP/VS (1.xx) of metamorphosed lherzolite; shading shows PT paths of upper 8 km of subducted mantle in Tohoku, Nankai, Costa Rica, and Cascadia subduction zones. The presence of antigorite (serpentine) causes a marked change in physical properties.

Figure 10.

Properties of metamorphosed depleted lherzolite (see Figure 9 caption). The presence of antigorite (serpentine) causes a marked change in physical properties.

Figure 11.

Properties of unmetamorphosed spinel harzburgite (see Figure 9 caption). Physical properties change monotonically.

Figure 12.

Properties of metamorphosed harzburgite (see Figure 9 caption). The presence of antigorite (serpentine) causes a marked change in physical properties.

Figure 13.

Properties of metamorphosed serpentinite (see Figure 9 caption).

Figure 14.

Rock properties measured in laboratories differ from our calculated properties for the same rocks by 1–2%. We assumed that (1) Mg/(Mg + Fe) = 0.75 for orthopyroxene, clinopyroxene, and biotite; (2) garnet has the composition alm50grs30prp20, (3) all amphibole is hornblende; (4) Mg/(Mg + Fe) = 0.5 for chlorite; and plagioclase is An50Ab50.

[15] 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 [1996]. 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.

[16] Our more detailed treatment of metamorphism results in significantly different predictions than previous studies. For example, Furlong and Fountain [1986] 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 [1986] calculation, extends it to 8 GPa, and emphasizes the resultant simplification of a two- or three-part model for mafic rocks.

7. Uncertainties

[17] 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

[18] 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. [1998] reported KT = 127 ± 4 GPa assuming ∂KT/∂P = 4, Grevel et al. [2000] reported KT = 125.1 ± 2.1 GPa assuming ∂KT/∂P = 4 and KT = 137 GPa if ∂KT/∂P = 0.5, and Comodi and Zanazzi [1997] 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. [2000] argued that none of these studies can distinguish ∂KT/∂P from 4.

[19] 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

[20] Our calculation procedure makes three important assumptions (see Appendix A). We use Holland and Powell's [1998] 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

[21] 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

[22] White et al. [1992] and Mutter and Mutter [1993] 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. [1992] 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. [1992] 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.

Figure 15.

The observed P wave speeds for oceanic lower crust and mantle (triangles, circles, and dots from White et al. [1992]) compared with our calculated P wave speeds for various rocks at 200 MPa and indicated temperatures (gray curves). Subvertical lines connect measured uppermost lower crust, lowermost crust and uppermost mantle velocities at single locations; the temperatures shown for each datum were calculated from the lithosphere age reported by White et al., following Sclater et al. [1980]. Room temperature, 200 MPa measurements of Christensen [1996] shown along right side are slightly slower than our calculated velocities. Most uppermost mantle velocity measurements are best explained as spinel harzburgite. Most lower crust measurements are intermediate between gabbro and amphibolite, indicating partial hydration. Most lowermost crust measurements are consonant with a mixture of gabbro, wehrlite, and olivine clinopyroxenite, or harzburgite containing <20% hydrous minerals.

[23] 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 [1998] and Dilek et al. [1998]. 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.

[24] 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. [1992] 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).

[25] Our approach has some advantages over other techniques. For example, Carlson [2001] 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

[26] 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 16.

Percent differences in velocities between pairs of rocks. Metamorphic facies boundaries as in Figures 1 and 4; gray lines show P–T paths for Moho of Tohoku, Nankai, Costa Rica, and Cascadia subduction zones. (a) VP in unmetamorphosed gabbro relative to VP in unmetamorphosed harzburgite; gabbro is 9–12% slower. (b) VP in metamorphosed, fully hydrated MORB relative to VP in unmetamorphosed harzburgite; metamorphosed MORB ranges from significantly slower (at low P or low T) to indistinguishable from unmetamorphosed harzburgite at eclogite-facies conditions. (c) VP in metamorphosed, fully hydrated MORB relative to VP in metamorphosed, fully hydrated harzburgite; the presence of hydrous minerals in harzburgite means that at low P and high T, metaharzburgite is faster than meta-MORB, and at low T, this situation is reversed. (d) VP in metamorphosed, hydrated MORB relative to VP in unmetamorphosed MORB and VP/VS in metamorphosed, hydrated MORB relative to VP/VS in unmetamorphosed MORB. Metamorphism of MORB changes VP/VS insignificantly. (e) VP in metamorphosed, hydrated harzburgite relative to VP in unmetamorphosed harzburgite, and VP/VS in metamorphosed hydrated harzburgite relative to VP/VS in unmetamorphosed harzburgite. Metamorphism of harzburgite produces large changes in VP/VS due to formation of serpentine, making it a good measure of mantle hydration.

Figure 16.

(continued)

[27] 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.

[28] 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).

[29] 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 [2000] 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].

Table 8. Tohoku at 4 GPa (∼125 km)a
LithologyFigureVPVSVP/VP Dry,bVS/VS DrybVP/VP WetcVS/VS Wetc
  • a

    From Figures 713, calculated at Moho temperatures predicted by Peacock and Wang [1999]. VP and VS in km/s.

  • b

    Velocities relative to anhydrous harzburgite.

  • c

    Velocities relative to fully hydrated harzburgite. Compare with Figure 16.

laE8a7.874.36−9%−10%+29%+56%
Metastable dry gabbro7b7.664.22−11%−13%+26%+51%
Dry MORB7a7.584.15−12%−15%+24%+48%
Dry spinel harzburgite118.634.860%0%+41%+74%
Fully hydrated lherzolite96.423.16−26%−35%+5%+13%
Fully hydrated harzburgite126.102.80−29%−42%0%0%
Serpentinite136.052.68−30%−45%−1%−4%
 
Low-velocity layer observationsVP/VP(mantle)VS/VS(mantle)  
Matsuzawa et al. [1986]−6%/−12%   
Abers [2000]−6 + 2%−4 + 2%  

[30] 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].

[31] In hot subduction zones such as Nankai, little hydration of the mantle is thermodynamically permitted (Figures 24), 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 [1990] 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

[32] As a final example, consider the reports of serpentinization of arc mantle wedges. Graeber and Asch [1999] 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.

[33] Kamiya and Kobayashi [2000] 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 [1972] 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.

9. Conclusions

[34] 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

[35] We calculated the physical properties of minerals at elevated pressure and temperature via the following algorithm, based on Bina and Helffrich [1992]. Holland and Powell [1998] advocated a relationship between expansivity α and temperature T(K), defined by a single constant a° for each mineral:

display math

which gives

display math
display math

where V(T) is the molar volume at temperature, Vo is the molar volume at STP, and To = 298 K.

[36] The density at elevated temperature ρ(T) is related to the density at STP ρo by

display math

[37] The isothermal bulk modulus at elevated temperature KT(T) is related to the isothermal bulk modulus at STP by

display math

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:

display math

where

display math

[38] The finite strain f is calculated recursively from

display math

where

display math

typically evaluated at To (KT′ in Table 1). The density at elevated pressure ρ(P) is then

display math

[39] The bulk modulus at elevated pressure and temperature KT(T,P) is

display math

[40] The expansivity at elevated pressure and temperature α(T,P) is

display math

[41] The isentropic bulk modulus KS is

display math

where γth is the first Grüneisen parameter. The shear modulus at elevated pressure and temperature μ(T,P) is

display math

[42] The density at elevated pressure and temperature ρ(P,T) is

display math

from which the P wave velocity VP, shear wave velocity VS, and Poisson's ratio ν can be calculated:

display math

[43] 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:

display math

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.

Acknowledgments

[44] 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.

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