Some geophysical constraints on the chemical composition of the earth's lower mantle

Earth and Planetary Science Letters, 62 (1983) 91-103 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

91

[3]

Some geophysical constraints on the chemical composition of the earth's lower mantle Ian Jackson Research School of Earth Sciences, Australian National University, P.O. Box 4, Canberra, A.C.T. 2600 (.4 ustralia)

Received May 26, 1982 Revised version received August 30, 1982

The physical properties (p, K, K') of the adiabatically decompressed lower mantle are interpreted in terms of an (Mg,Fe)SiO a perovskite + magnesiowtistite mineralogy. The approach employed in this paper involves the removal of the relatively better characterised magnesiowiistite component from the two-phase mixture in order to highlight the physical properties required of the perovskite phase for consistency between the seismological data and any proposed compositional model. It is concluded that a wide tradeoff (emphasized by Davies [1]) between composition, temperature and the physical properties (especially thermal expansion) of the perovskite phase accommodates most recently proposed compositional models including Ringwood's [2] pyrolite and the more silicic models of Burdick and Anderson [3], Anderson [4], Sawamoto [5], Butler and Anderson [6], Liu [7,8] and Watt and Ahrens [9].

1. Introduction

Compelling indications that phase transformations might play an important role in explaining the velocity structure of the transition zone date from the analysis by Birch [10] who showed that the extrapolated lower mantle seismic parameter dp (V 2 - 4V2/3 - 50 km2 s -2 at STP) was comparable only with elasticity data for close-packed oxides such as MgO and A1203. Early indications, deriving mainly from studies by Ringwood and coworkers of germanate and other structural analogues, that most, if not all, of the relatively openpacked silicates of the upper mantle might transform to much denser polymorphs under high-pressure conditions [11], were reinforced by the results of shock-wave experiments reported in the mid1960's by Trunin et al. [12] and McQueen et al. [13], and have since been overwhelmingly confirmed by direct static high-pressure experimentation (recent reviews by Ringwood [14,15], Liu [16] and Akaogi and Akimoto [17]). Furthermore, the major phase transformations in the SiO2-MgOFeO-A1203-CaO system occur in the 10-30 GPa 0012-821X/83/0000-0000/$03.00

pressure interval which corresponds well with the depth interval over which the seismic wave velocities increase so discontinuously in the transition zone of the Earth's mantle. Accordingly, material of upper mantle chemical composition would crystallise in the uppermost lower mantle as a mixture primarily of (Mg, Fe)SiO3 perovskite and (Mg,Fe)O magnesiowiistite [15,16] along with lesser proportions of the dense Ca2A12SiO7, MgA1204 and NaA1SiO4 high-pressure phases discovered by Liu [18-20]. The adequacy (or otherwise) of this isochemical phase transformation model of the transition zone has always been controversial. Analysis of the early shock-wave data of Trunin et al. [12] and McQueen et al. [13] provided a clear indication that most, if not all, of the increase in density and incompressibility across the transition zone of the Earth's mantle could be attributed to isochemical phase transformation of the major upper mantle minerals (e.g. the studies of Birch [21], McQueen et al. [13], Wang [22] and Ringwood [2]). Others argued that consistency between laboratory data and lower mantle seismological models required,

© 1983 Elsevier Scientific Publishing Company

92 in addition to phase transformations, enrichment, relative to the upper mantle, in FeO [12], SiO 2 [3] or both FeO and SiO 2 [4,23,24]. Davies [1] explored the tradeoff between assumed lower mantle mineralogy and inferred chemical composition and temperature, concluding that "an isentropic temperature gradient, chemical homogeneity, or some iron enrichment in the lower mantle relative to the upper mantle" are allowed but not required by the data. This conclusion was reinforced by the analyses of Watt et al. [25] and Graham and Dobrzykowski [26]. Liu's [27-29] discovery of the orthorhombic (Mg,Fe)SiO 3 perovskite phase, and subsequent studies of the elasticity of MgSiO 3 by Yagi et al. [30] and of related perovskites by Liebermann et al. [31], provided a much firmer basis for interpretation of lower mantle seismological models. Watt and Ahrens [9] have recently revised an earlier analysis by Watt and O'Connell [32] concluding that the lower mantle is enriched in SiO 2 but somewhat depleted in FeO relative to the upper mantle. Butler and Anderson [6], Sawamoto [5], and Liu [7] have also argued that the seismological data require a lower mantle which approaches pyroxene stoichiometry. It is the purpose of this paper to re-examine the extent to which lower mantle seismological models constrain the chemical composition and temperature of an assumed perovskite + magnesiowiistite mineralogy. Other data which have a bearing on this issue such as shock compression data for relevant rocks and minerals, cosmochemical elemental abundances, the ratio of velocity and density increments across the 650-km discontinuity, and the inferred sharpness of at least part of this discontinuity are not considered here but will be discussed in a later more comprehensive review.

2. Seismological models for the lower mantle and their extrapolation to zero pressure

The lower mantle is distinguished from the overlying transition zone by relatively uniform variation of the seismic wave velocities with depth. Although there are strong indications of further minor velocity discontinuities in the uppermost

lower mantle [33,34], the relatively smooth variation of seismic velocities and the magnitude of the Bullen parameter B = 1 - g - 1 dq~/dr suggest (but do not demand) a close approach to conditions of homogeneous adiabatic compression [10,35,36]. The fact that density models, constructed from the velocity models on this basis, have required very little perturbation in order to satisfy free oscillation eigenperiods (e.g. [37-39]) indicates that a homogeneous adiabatic lower mantle is at least an approximate solution to the seismological inverse problem. The suggestion that it may not be the only solution (e.g. [40]) is taken up later in this paper in discussion of the sensitivity of compositional inferences to possible lower mantle superadiabaticity. It has therefore been common practice to fit lower mantle elasticity-density-pressure models with adiabatic equations of state which allow extrapolation of density and incompressibifity to zero pressure [6,10,21,38,41-43]. The possibility of significant shear modulus dispersion between seismic and ultrasonic frequencies (e.g. [44]) means that inferences concerning chemical composition, temperature and phase are most reliably drawn from analysis of bulk elasticity data. The zero-pressure density p, bulk modulus K, and its pressure derivatives (K', K " ) obtained from such extrapolations, pertain to some unknown high temperature TOof the adiabatically decompressed lower mantle, but are insensitive to the choice of equation of state because of the relatively short extrapolation involved. This fact along with insensitivity of p, K, etc., to choice of recent earth model is evident from the analyses of Dziewonski et al. [38] and Davies and Dziewonski [43], which would suggest uncertainties in the extrapolated p, K and K ' of order +0.02 g cm -3, ___10 GPa and +0.3, respectively. From a third-order Eulerian fit to their complete parametric earth model, Dziewonski et al. [38] obtained the following parameters for the adiabatically decompressed lower mantle: p = 3.99 g cm -3, K = 219 GPa, K ' = 3.7 If only the bulk elasticity data (p(P), K(P)) are considered, K ' = 3.8 yields a better fit, and this latter value will be used in subsequent discussion.

93

These data for the extrapolated lower mantle will be analysed in terms of the properties of (Mg,Fe)SiO 3 perovskite + (Mg,Fe)O magnesiowtistite mixtures.

3. Perovskite+ magnesiowiistite models for the lower mantle Candidate lower mantle compositions in the three-component system SiO2-MgO-FeO will be the subject of the following analysis. Such compositions will be parameterized by the molar ratios: S = (MgO + FeO - SiO2)/SiO 2 and: XMs = M g O / ( M g O + FeO) In the perovskite + magnesiowi~stite mineralogy, S is the molar abundance of magnesiowiistite per

mole of perovskite. S thus ranges from 0 for pyroxene stoichiometry to 1 for olivine stoichiometry. Most proposed compositional models for both the upper and lower mantle contain more than 90 wt.% SiO 2 + MgO + FeO, and are therefore well approximated by compositions within this threecomponent system. Representative among such models (Tables 1 and 2) are pyrolite [2,45] approximated by S - 0.5, XMg = 0.89, and the much more silicic lower mantle model of Liu [8], based upon a C1 chondritic bulk earth and a pyrolite upper mantle, with S - 0.1, XMg = 0.89. The sensitivity of the conclusions of the present analysis to the inclusion of the next most abundant oxides A1203 and CaO will be briefly discussed later in this paper. The partition coefficient determined by Bell et al. [46]: k = ( X F e / / X M g )pv//( g F e / / X M g )mw = 0 . 0 8

TABLE 1 Representative lower mantle compositional models Composition (wt.% oxides)

Pyrolite a

Simplified pyrolite b

"Chondritic" c

SiO 2 MgO FeO

45.0 38.8 7.6

45.36 39.11 7.66

51.84 34.10 7.29

Total A1203 CaO

91.4 4.4 3.4

Total

92.1 4.44 3.43

99.2

Cr203 Na20 NiO TiO 2 MnO K20

0.45 0.4 0.26 0.17 0.11 0.003

M g / ( M g + Fe) d M g / ( M g + Fe + Cr + Ni + Ti + Mn) d

0.90 0.89

93.2 3.45 3.32

100.0

0.90

100.0

0.89

a Green et al. [45], cf. Ringwood [2]. b Five-component (SiO2-MgO-FeO-AI203-CaO) approximation. c Composition obtained by Liu [8] by subtraction of core and pyrolite upper mantle from a bulk earth of Cl carbonaceous chondrite composition. d Atomic ratios which suggest an effective XMg of 0.89 for pyrolite.

94 TABLE 2 Lower mantle mineralogies for the representative compositions of Table 1 Phase

Pyrolite model molar abundance a

"Chondritic" model composition X~,lg

mass fraction

density (g cm 3)

m i

Pi

s, (Mg, Fe)SiO3(pv ) (Mg, Fe)O(mw)

1 0.469

pv + mw Ca2AI2SiO 7 (h.p.p.) b MgAI204 (h.p.p.) b pv+mw+ Ca2A12SiO 7, MgAI204 h.p.p.'s

molar abundance

a

composition

mass fraction

density (g c m - 3 )

X~4g

m i

Pi

0.936 0.540

0.853 0.060

4.17 4.63

0.89

0.913

4.20

0.081 0.006

4.43 b 4.31 b

1

4.22

si 0.973 0.743

0.733 0.164

4.13 4.17

0.90

0.897

4.14

0.084 0.018

4.43 b 4.31 b

1

4.16

0.042 0.018 0.90

1 0.132

0.036 0.005 0.89

a Molar abundances of phases per mole of (Mg,Fe)SiO 3 perovskite. b Na2Ti3Oy_type Ca2A12SiO7 and c-MgAl204 phases described by Liu [19,20]. For more complex compositions containing N a 2 0 , the calcium ferrite-type NaA1SiO 4 [18] will form at the expense of the other aluminous phases.

will be used to model the compositions of coexisting perovskite (pv) and magnesiowtistite (mw) phases. The possible effect of pressure and temperature upon the partition coefficient [9], nonstoichiometry in magnesiowtistite, and high-pressure polymorphism in FeO [47-49] are all neglected in the following analysis. The sensitivity of the conclusions to the assumed strong partitioning of iron between coexisting phases was explored by performing a parallel series of calculations in which the partition coefficient was set at unity. The object of the exercise is the interpretation of the parameters ( 0 0 = 3 . 9 9 g cm -3, K 0 = 2 1 9 GPa, K~ = 3.8) of the adiabatically decompressed lower mantle, which is at some unknown high temperature (To). Since the high-temperature properties of magnesiowiistite (Table 3) are far better constrained than those of the perovskite phase, it is instructive to remove magnesiowtistite from the model mixture in order to deduce the high-temperature density, bulk modulus and OK/OP required of the perovskite phase. Preferred values of the required perovskite bulk modulus and OK/OP are obtained by inversion of the Voigt-Reuss-Hill (VRH) model for the elasticity of a two-phase aggregate [50]. Uncertainties inherent

in this procedure are estimated by parallel inversion of the Voigt and Reuss averaging schemes. The high-temperature density, bulk modulus and 3K/3P required of the perovskite phase are thus calculated for trial values of the parameters S, XMg and TO which are systematically varied within the limits 0 < S < 1, 0.8 <)(Ms < 1.0 and 1100 < To < 2000°C. The resulting high-temperature densities and bulk moduli of the perovskite phase for silica stoichiometries S of 0.25, 0.50 and 0.75 are represented by the labelled quadrilaterals of Fig. 1. The grid superimposed upon each quadrilateral describes the variation of inferred high-temperature density and bulk modulus of the perovskite phase with choice of bulk magnesium fraction XMg and the temperature To at the foot of the adiabat. For example, the high-temperature perovskite density and bulk modulus, corresponding to S = 0.50, XMg=0.90 (which approximates pyrolite composition) (see Tables 1 and 2) and To = 1400°C, are indicated by the small filled circle at the intersection of the XMg = 0.9 and To = 1400°C grid lines within the S = 0.50 quadrilateral. Partitioning of iron and magnesium between the coexisting perovskite and magnesiowiastite phases, results in respective compositions XP~ = 0.974 and

95 TABLE 3 Physical properties of magnesiowiistite and perovskite phases MagnesiowiJstite

p (g cm -3) K s (GPa)

Perovskite

MgO

FeO

MgSiO 3

3.584 a 162.5 a

5.865 b (182) b

4.10 c

(o~Ks/OP)s

4.09 d 4.5X10 - s f -0.022 g - 0.46 X l0 -3 h

(K - l )

(~gKs/OT)p (GPa K - 1 ) (O(OKs/tgP)s/OT)p ( K - l )

FeSiO 3 5.22 c 2553 --+25 (5-6) e (-0.02) i (--0.46 X 10-3) i

" Jackson and Niesler [60]. b Jackson et al. [61], cf. Sumino et al. [62], Bonczar and Graham [63]. c Yagi et al. [30,64,65]; K s = 255 GPa for aK/aP = 5. Density is assumed to vary linearly with composition for both phases. d Jackson and Niesler [60] data for MgO. Generally similar values are reported by Bonczar and Graham [63] for magnesiowiistite with )(Ms > 0.75. Bulk modulus is assumed to vary linearly with composition for magnesiowtistite. e Jones [53]. f Mean thermal expansion coefficient for MgO between 30 and 1400°C, i.e. ~ = ( p ( 3 0 ) / p ( 1 4 0 0 ) - 1 ) / 1 3 7 0 [66] not likely to be in error by more than 10% for (Mg, Fe)O for 1000 < TO < 2000°C. Approximate mean (OKs/aT)e for MgO for the 25-1400°C temperature interval [67]. Generally comparable values for magnesiowtistite ( a K s / a T ) e near room temperature have been reported by Bonczar and Graham [63]. h Derived from the 300 and 800 K MgO data of Spetzler [68] using the identity (3Ks/OP)s = (OKs/3P)T + 3,T(OKs/OT)p/K s (e.g. [60]) and y = y(T) = 1.54 [59]. i By analogy with data for MgO and other close-packed oxides [59].

I

c~ Q.. (_9

280

-

270

-

I

[

1

I

260

-~ 250 o

Toi

E

X ~ = 0.752. The density and bulk modulus of this magnesiowOstite phase at 1400°C are 3.91 g cm -3 and 137 GPa which are lower than the corresponding parameters (3.99 g cm -3 and 219 GPa) for the adiabatically decompressed lower mantle, also plotted in Fig. 1. As a direct consequence, the inferred high-temperature density and bulk modulus of the perovskite phase (p(T0)= 4.01 g c m -3, K ( T 0 ) = 246 G P a - - t h e filled circle within the S = 0.50 quadrilateral) are correspondingly greater than those of the decompressed lower mantle.

I II

133 2 4 0

O.B

~ - L ~ g ,Fe)Si© ----~--=Per°vkite

~~_z

( 2 5 °C)

230

220

-

-

-

S=0

----~-

ADIABATICALLYDECOMPRESSED LOWER MANTLE (T o )

I

I

I

I

I

3.9

4.0

4.1

4.2

4.3

Density, g / c m 3

Fig. 1. A comparison of 25°C and inferred high-temperature ( T0) density and bulk modulus of (Mg,Fe)SiO 3 perovskite for a variety of (S, XMg, To) models. For example, the filled circles at Xu~ = 0.90, TO= 1400°C within the S = 0.50 quadrilateral and at X ~ = 0.974 within the shaded region denote, respectively, 1400 and 25°C properties of perovskite of the same composition (see text for detailed explanation). The long arrow from the point corresponding to the adiabatically decompressed lower mantle corresponds to correction to 25°C of the high-temperature density and bulk modulus for TO= 2000°C, ~ = 3 x 10 -5 K - I and ( a K s / a T ) p = - 0 . 0 2 GPa K -1.

96 The increase of inferred high-temperature density of the perovskite phase with increasing XM~ is a direct consequence of the removal from the lower mantle aggregate (P(T0)= 3.99 g cm -3) of progressively less dense magnesiowiistite. The increase of inferred perovskite density and bulk modulus with increasing TO are similarly due to removal of progressively less dense and more compressible magnesiowiistite. The modest increase of inferred perovskite bulk modulus with increasing XMg is a consequence of the assumption that the bulk modulus of the magnesiowtistite phase decreases linearly with XM~ from 182 GPa for XM~ = 0 to 162.5 GPa for XM~ = 1 (Table 3). Whether or not the inferred high-temperature perovskite density and bulk modulus deriving from a particular (S, XMg, To) composition-temperature model are reasonable may be assessed by comparison with corresponding 25°C data for the perovskite phase plotted as the shaded region in Fig. 1. Comparison of the inferred high-temperature (To) density of the perovskite phase with the known density for perovskite of the same composition of 25°C yields a value of the mean thermal expansion ~ = ( p ( 2 5 ) / p ( T o ) - 1 ) / ( T 0 - 2 5 ) required of the perovskite phase for consistency between the extrapolated seismological and laboratory data. For the ( S = 0 . 5 0 , XM~=0.90, To= 1400°C) model, the 25°C density of the perovskite phase ( X ~ = 0.974) is 4.13 g c m - 3 (filled circle within the shaded region of Fig. 1), which may be compared with the inferred high-temperature (1400°C) density of the same phase (4.01 g cm-3), yielding the rather low of 2.2X 10 -5 K -1. The tradeoff between calculated in this way, and TOis displayed in Fig. 2 for a variety of interesting compositions. In principle, the inferred high-temperature perovskite bulk modulus and the corresponding 25°C bulk modulus may be similarly compared. However, the large uncertainty ( + 25 GPa) in the perovskite bulk modulus deriving from the static compression measurements of Yagi et al. [30] means that implied values of (aK/OT)p are very poorly constrained. It is therefore considered preferable to employ a plausible assumed value of (aK/aT)p ( - 0 . 0 2 GPa K - t ; Table 3) to extrapolate the high-temperature perovskite bulk modulus to 25 oC. Implied values of the 25°C bulk modulus K(25)

i 2000

i

S=0.50 Pyrolit~

\ \ • \ \\ \\ NN

.

1500

I000

'~o~

I

I

s :o2t

2000

,~¢.'x \\

x

,,.

1500

_

".. \ "t~"

~" 0 . ~

E I000

"1

2000

t ,\, .') ," ,N

I

%~"0. 90

I

I s--o

\ q'\\,x(\\\~Xx ,,\ X
Pyroxene-

\% 1500

" ","< 4": "-"~ I

I000

,_

" -',~

;"o..9~

o

I

1

I

I

2

3

4

5

MeoR4qhermol exponsion coefficient (unit : i0 "s K -I)

Fig. 2. I n f e r r e d ( M g , F e ) S i O 3 p e r o v s k i t e m e a n t h e r m a l e x p a n s i o n parameter ~ for a variety of (S, Xus, To) models. The

filled circle in the upper part of this figure indicates the virtually simultaneousintersectionof the (~, T0) tradeoff curve for pyrolite composition (S = 0.50, Xug = 0.89) with reasonable lower bounds on both ~ and To.

may then be compared with the static compression datum, 255 _+ 25 GPa. This comparison is insensitive to variation of the parameter XMg, and accordingly, implied values of K are plotted in Fig. 3 for a range of the variables S and To, with XMg fixed at 0.90. Also plotted in Figs. 2 and 3 are lines corresponding to TO= 1400°C and To = 2000°C. The significance of To = 1400°C lies in the fact that this adiabat is characterised by an uppermost lower

97

2000 o o

1500

d

_.O/

j

I000

240

250

260

270

-

280

Bulk Modulus, GPo

Fig. 3. Inferred (Mg, Fe)SiO3 perovskite bulk modulus for a range of (S, To) models for XMg = 0.9 and (3Ks/aT)p= - 0.02 GPa K - i (see text for explanation). The filled circle on the S = 0.5 curve indicates the implied perovskite bulk modulus for consistency between the seismological data and the pyrolite model.

mantle temperature of about 1600°C which is compatible according to Jeanloz and Richter [51] and Brown and Shankland [52] with interpretation of the 400-km seismic discontinuity in terms of o l i v i n e ~ spinel equilibria, and with reasonable estimates of temperature gradients within the transition zone. TO- 1400°C may therefore be an appropriate lower mantle adiabat for a chemically homogeneous mantle involving no thermal boundary layer at the base of the transition zone.

In the event of a significant chemical contrast between upper and lower mantles, a substantial thermal boundary layer ( A T - 5 0 0 - 7 0 0 ° C [51]) may exist, and TO- 2 0 0 0 ° C may be a more appropriate choice. The lines ~ = 2 . 5 × 1 0 -5 K -~ and ~ = 3 . 5 × 10 -5 K-1 in Fig. 2 represent what are considered to be realistic lower and upper bounds on the mean thermal expansion of (Mg,Fe)SiO 3 perovskite between 25 and - 1400°C on the basis of data for a variety of closely-packed oxide phases. With reference to Figs. 1-3, it is possible to explore the trade-off between chemical composition and temperature for models which qualify for consideration on the basis of reasonable implied values of mean thermal expansion ((3.0 + 0.5)x 10 -5 K - l ) and bulk modulus (255 + 25 GPa) for the perovskite phase. A representative set of successful (S, X u v To) models is displayed in Table 4. The extent of the possible covariation of XMg and TO at fixed S is clearly a strong function of S and is discussed below. 3.1. S = 0 (pyroxene stoichiometry)

For S = 0, the high-temperature density and bulk modulus of the decompressed lower mantle are also those of the perovskite phase. Extrapola-

TABLE 4 The composition-temperature tradeoff for a perovskite + magnesiowiistite mineralogical model for the lower mantle (units for mean thermal expansion fi, temperature T0, and implied perovskite bulk modulus K, are respectively K - i, oC and GPa) XMs

S = 0.50

~ = 3.0X 10 -5

0.85 0.86 0.87 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95

fi= 2.5× 10 -5

To

K

1620 1520 1420

280 277 274

TO

1620 1500 1390

K

280 277 273

S = 0.25

S = 0.0

~ = 3.0:< 10 -5

f i = 3.0× 10 -5

TO

K

TO

K

1920 1830 1740 1640 1540 1430

272 270 268 265 263 260

2350 2260 2170 2080 1980 1880 1790 1690 1600 1510 1420

266 264 262 260 258 256 254 252 251 249 247

98 tion of these properties such that the 25°C density and bulk modulus lie within the shaded rectangle of Fig. 1 is obviously possible for a wide range of XMg, ~ and (OK/aT)?. The arrow in Fig. 1 shows one such extrapolation for ~ = 3 × 10 -5 K - l , ( a K / O T ) ? = - 0 . 0 2 G P a K - l and T 0 = 2 0 0 0 ° C which corresponds approximately to XMg = 0.89 and falls near the centre of the range of uncertainty in bulk modulus. From Fig. 2 it is apparent that a wide covariation of XMg and TO is allowed for any reasonable value of ~, and from Fig. 3 it is clear that the implied bulk modulus values for almost any choice of TO lie within the allowed range. For ~ = 3 × 10 -5 K-1, it is evident from Table 4, that allowed XMg values vary from - 0 . 9 5 for minimal TO to X M g - 0 . 9 for TO 2000°C, and beyond if higher temperatures are contemplated. In summary, p e r o v s k i t e - - o n l y lower mantle models satisfy the seismological and laboratory data for a wide covariation of M g O / ( M g O + FeO) and temperature, and place few constraints upon the physical properties (~, K, ( 3 K / 3 T ) ? ) required of the perovskite phase.

3.2. S = 0.50 (pyrolite stoichiometry) Partitioning of iron and magnesium between coexisting magnesiowiistite and perovskite phases for 0.85 ~< XMg ~< 0.95 results in perovskite compositions (0.95 ~< XMg ~< 0.99) which correspond to the left-hand quarter of the shaded rectangle in Fig. 1. The inferred thermal expansion between 2 5 o c and T0, i.e. ~(To - 25), is therefore generally much smaller than for S = 0. Similarly, the fact that inferred high-temperature bulk moduli for the perovskite phase (S = 0.50 quadrilateral) plot not far below the preferred 25oc value, constrains the product ( 3 K / 3 T ) p . ( TO- 25). The severity of such constraints is more clearly seen in Figs. 2 and 3. For XMg = 0.89 (pyrolite composition), both ~ and TO are constrained to adopt minimal plausible values - 2.5 x 10 -5 K and - 1400°C, respectively--as indicated by the filled circle in the upper part of Fig. 2. These parameters, together with the use of ( a K / a T ) ? = - 0 . 0 2 GPa K -1, imply a 25°C bulk modulus of - 2 7 3 G P a indicated by a filled circle on the S = 0.50 line in Fig. 3. The restricted range of

successful S = 0.50 models is further emphasized in Table 4. It is therefore concluded that a perovskite + magnesiowiistite model mantle of approximately pyrolite composition can provide an adequate explanation of seismological models for the lower mantle. However, consistency between the seismological data and the model imposes strong constraints upon the mantle geotherm and upon the physical properties of the perovskite phase. Specifically, it is required that: TO- 1400°C and and

- 2.5 × 10 -5 K -1 K - 270 G P a (for (OK/OT)e = - 0.02 GPa K - 1)

The required values for ~ and ( 3 K / 3 T ) p are comparable with data for other close-packed oxide phases, and the value of K, while higher than the static compression datum of Yagi et al. [30], lies within the experimental uncertainties. Parallel calculations in which the F e / M g partition coefficient was set at unity indicated that these conclusions are quantitatively insensitive to the assumed partitioning behaviour in accord with the observation of Watt and Ahrens [9]. Separate inversion of the Voigt and Reuss averaging schemes suggests an uncertainty of order _+ 10 G P a in the quoted bulk modulus inferred by inversion of the V R H scheme. The conclusion that TO- 1 4 0 0 ° C for model mantles of approximately uniform chemical composition is in accord with the expectation, under these circumstances, of single-cell convection throughout the mantle and the concomitant absence of a thermal boundary layer in the uppermost lower mantle (e.g. [51]).

3.3. Other compositional models, S > 0.50 and 0.50 >S>O Compositional models significantly less silicic (i.e. more olivine-like) than pyrolite require absolutely implausibly low temperatures and can be dismissed. Models with silica stoichiometries intermediate between pyrolite and pyroxene (i.e. 0.50

99 > S > 0) span an intermediate range of XM~ and TO. For example, for S = 0 . 2 5 , f i = 3 × 10 -5 K - t and (OK/OT) e = - 0.02 G P a K - 1, XMg varies from - 0.90 for TO- 1400°C to - 0.85 for TO= 2000°C with required values of K between 260 and 272 G P a (see Table 4). Liu's [8] recent lower mantle compositional model, derived by subtraction of a pyrolite upper mantle from a type C1 chondritic bulk earth, is of interest as a specific example of models significantly more silicic than pyrolite. For this composition, approximated by S = 0.1, XMg = 0.89 (Tables 1 and 2), and for ~ = 3 . 0 × 10 -5 K -1, interpolation between the S = 0.25 and S = 0 entries in Table 4 yields TO - 1 8 0 0 ° C and K - 2 6 0 GPa. Choice of a smaller value for ~, say 2.5 × 10-5 K - 1 , would result in a substantial increase in TO to about 2200°C, and a modest increase in K to - 267 GPa. The conclusion that TO- 1800-2200°C for this much more silicic model of the lower mantle is consistent with the scenario of separate convection of chemically distinct upper and lower mantles, separated by a conductive boundary layer with a steep temperature gradient (e.g. [50]).

3K/OP are required of the perovskite phase, especially for the pyrolite model. 4. Qualifications of the applicability of the model

4.1. Sensitivity of conclusions concerning possible chemical uniformity of the mantle to the neglect of the Al203 and CaO components The simple perovskite + magnesiowiistite mineralogical model for the lower mantle does not provide for the incorporation of A1203 and CaO, which together constitute about 8 wt.% of compositional models for the mantle (Tables 1 and 2). Enough is known, however, about phase transformations in A1- and Ca-bearing minerals to estimate the effect of their inclusion, at least upon inferred high-temperature densities of the perovskite phase. The calculations presented in Table 2 suggest a lower mantle mineralogy for the simplified (5component) pyrolite of approximately: 74 wt.% (Mg0.97Fe0.03)SiO 3 perovskite 16 wt.% (Mg0.TaFe0.26)O magnesiowOstite

3.4. OK~ OPfor the (Mg, Fe)SiO~ perovskite phase The above discussion has centred upon interpretation of the density and bulk modulus of adiabatically decompressed lower mantle. The (dKs/dP)s value (3.8) at the foot of the PEM lower mantle adiabat may be similarly inverted for (OK/OP) of the perovskite phase. For a model of approximate pyrolite composition (S = 0.5, XMg = 0.89 and TO - 1 4 0 0 ° C ) , and an assumed [3(3Ks/OP)s/OT]e of - 0 . 4 6 X 10 -3 K -1 (Table 3) for both phases, the inferred (OKs/OP) for the perovskite phase at 25°C is approximately 4.3. For models of pyroxene stoichiometry (S = 0), use of the same value of [ 0 ( O K s / 0 P ) s / O T ] p yields a 25°C perovskite OKs/OP of about 4.7 for To 2000°C. These are to be compared with the range 5 - 6 for (Mg,Fe)SiO 3 perovskite estimated by Jones [53] on the basis of data for structural analogues. There is thus a weak suggestion, given all the uncertainties involved, that somewhat larger values of IOEK/OTOP[ or somewhat smaller values of

8 wt.% Ca2A12SiO 7 h.p.p. 2 wt.% MgA1204 h.p.p. with a calculated zero-pressure density of 4.16 g cm -3 compared with 4.14g cm -3 for the perovskite + magnesiowiistite mixture. The estimated zero-pressure densities for both the pyrolite and chondritic models increase by about 0.02 g c m - 3 with the inclusion of the super-dense Ca- and Al-bearing phases. It may be concluded that neglect of these phases in the foregoing analysis will have resulted in overestimation of the inferred high-temperature densities of the perovskite phase by about the same amount, and consequent underestimation of the product fi(To - 2 5 ) by about 10-15%. In the absence of data concerning the compressibilities of the gehlenite and spinel high-pressure phases, quantitative assessment of the implications of CaO and A1203 inclusion upon inferred perovskite bulk moduli is impossible. It seems probable, however, that these ultradense phases would be at least as

100

incompressible as (Mg,Fe)SiO 3 perovskite. If so, inferred bulk moduli for the latter phase migth be reduced. Accordingly, the probable effect of inclusion of CaO and AI203 in upper mantle proportions, would be to slightly weaken the constraints on implied perovskite fi and K, and To, in the sense of less restrictive viability of the model of uniform chemical composition.

4.2. Possible superadiabaticity of the lower mantle As discussed in section 2, it is possible that density distributions genuinely independent of the Adams-Williamson hypothesis may exist, which also satisfy the free oscillation data. It is therefore of interest to assess the sensitivity of the foregoing analysis to relaxation of the adiabaticity assumption. The effect of possible departures from adiabaticity is well illustrated by a comparison of density models derived by Clark and Ringwood [41] for both adiabatic and superadiabatic temperature gradients. The effect of a I°C km -~ superadiabatic temperature gradient was to alter the extrapolated zero-pressure high-temperature density, bulk modulus, and aK/aP for the lower mantle by - 0.02 g c m - 3, _ 35 GPa and + 0.7 respectively. Appreciable superadiabaticity of the lower mantle (say ~"- 0.3-0.5°/km) would, accordingly, result in a slight increase ( - 5%) in ~, a significant decrease ( - - 10 GPa) in K, and a significant increase ( - 0 . 3 ) in aK/aP required of the perovskite phase for consistency of a given (S, Xug, To) model with seismological data. These changes correspond to less restrictive viability of the model of uniform chemical composition.

4.3. Possible radial heterogeneity of the lower mantle Early indications of minor discontinuities in seismic wave velocities in the lower mantle (e.g. [54,55]) have recently been reinforced by both d t / d A [33,56] and travel-time studies [34], which suggest that at least the upper few hundred kilometres of the lower mantle may contain zones of high velocity gradient--centred near 770, 980 and 1080 km depth. It should be emphasized that these

are minor features when compared with the major velocity discontinuities at depths near 400 and 650 km in the transition zone. Such discontinuities are beyond the resolution of inversions of gross earth data, but would result in increased average compressibility for the uppermost lower mantle. The extrapolation of the smoothed gross earth model back to zero pressure might therefore significantly underestimate the zero-pressure density and bulk modulus and significantly overestimate aK/aP appropriate for the deep mantle. Under these circumstances, it may no longer be possible to explain deep mantle properties in terms of an upper mantle composition with a perovskite + magnesiowiistite mineralogy. This would be consistent with the possibility that the minor velocity discontinuities in the uppermost lower mantle are associated with recombination of perovskite and magnesiowiistite to yield even denser perovskite-related structures similar to that inferred for Ca2A12SiO 7 [19].

5. Comparison with other studies involving perovskite + magnesiowiistite model mantles On the basis of an analysis, similar to the foregoing, in which laboratory data were extrapolated to mantle pressures for comparison with seismological data, Watt and O'Connell [32] concluded that perovskite+ magnesiowiistite lower mantle models of olivine (S = 1.0) and peridotite (S = 0.67) stoichiometries are acceptable but that the densities of pyroxene stoichiometry (S = 0) models are too large by 1-2.5%. The difference between these results and those of the present study is a consequence of an error [9] resulting in the use of an unrealistically low thermal expansion parameter (1 x 10 -5 K - l) for the perovskite phase. More recently, Watt and Ahrens [9] have revised these earlier calculations using a perovskite thermal expansion parameter of 3.5 x 10 -5 K -I and concluded that the lower mantle is probably more silicic (S ~<0.25) than the upper mantle, for which they suggest that a peridotite (S = 0.67) stoichiometry is appropriate. It has been concluded in the present study, that lower values of than the 3.5 x 10 -5 K - 1 used by Watt and Ahrens

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are required for consistency with the pyrolite (S 0.5) model. A similar conclusion concerning the requirement of a relatively small perovskite thermal expansion coefficient for mantle chemical uniformity has recently been reached by Jeanloz and Thompson [57]. Liu's [7] analysis of lower mantle densities and bulk sound velocities in terms of the properties of perovskite + magnesiowiJstite models demonstrated that the seismological data could be explained in terms of an S = 0.5, )(Ms = 0.9 composition (labelled " 2 " in his figs. 2 and 3) provided that a marginally low thermal expansion parameter and a marginally high bulk modulus were assumed for the perovskite phase. This result is in accord with those of the more comprehensive study presented here, from which it is clear that Liu's conclusion that the lower mantle is far more silicic than the upper mantle is allowed but not required by the relevant density and elasticity data. The iron-depleted pyroxene stoichiometry model (S = 0, 1.0 > Xr, g > 0.9) advanced by Sawamoto [5] and Butler and Anderson [6] is similarly allowed but not required by the data. The concept of a lower mantle enriched in both SiO 2 and FeO [4,24] is also allowed by the present analysis but requires relatively high lower mantle t e m p e r a t u r e - - T0 - 1 9 0 0 ° C for ( S = 0.25, XM~ = 0.85) or TO- 2400°C for (S = 0, XM~ = 0.85)--see Table 4. It is also of interest to compare the results of the present analysis with that of Brennan and Stacey [58], who extrapolated the same seismological model (PEM [38]) to zero temperature via the Mie-Grtineisen equation, and then fitted the resuiting zero-temperature model to an isothermal equation of state. The equation of state was based on the assumptions that (OKr/OT)v = 0 and that the thermodynamic Grtineisen parameter is given by the Vashchenko-Zubarev formulation. Extrapolation of the best-fitting isothermal equation of state back to zero pressure yielded P0 = 4.18 + 0.03 g cm -3, g 0 = 242 + 5 GPa, and TO= 1900 _ 400°C. Comparison of these parameters with those of the adiabatically decompressed lower mantle (p = 3.99 g cm -3, K = 219 GPa) yields mean values of the thermal expansion coefficient and (OKs/OT)? for lower mantle material of (2.5 -04) +0.7

X 10 -5 K -1 and - ( 0 . 0 12+0.003 -0.002) GPa K -l, where the calculated uncertainties reflect the quoted uncertainty in TO. This thermal expansion coefficient is comparable with minimal plausible values for (Mg,Fe)SiO 3 perovskite, whereas the temperature derivative of the bulk modulus is lower than even the low-temperature (OKs/OT)e values for closepacked oxides [59] which cluster about - 0 . 0 1 5 G P a K - l - - p r e s u m a b l y as a consequence of the thermodynamic assumptions upon which the Brennan and Stacey approach is based.

6. Conclusions An attempt has been made at an objective and balanced assessment of the elasticity and constitution of the lower mantle in terms of a perovskite + magnesiowtistite mineralogy. The wide tradeoff between composition and temperature and assumed physical properties (especially thermal expansion) of the perovskite phase accommodates most of the compositional models which have been proposed. Included among those which satisfy seismological data for the lower mantle are the pyrolite model [2] along with the more silicic models of Anderson [4], Sawamoto [5], Liu [8] and Watt and Ahrens [9]. Models significantly less silicic (more olivine-rich) than pyrolite require implausibly low temperatures and may be eliminated. For consistency between the pyrolite model and seismological data for the lower mantle, it is required that the mean (volumetric) thermal expansion parameter for the perovskite phase (~), and the temperature of the adiabatically decompressed lower mantle (To), both adopt minimal plausible values of - 2 . 5 x 10 -5 K -~ and - 1 4 0 0 ° C , respectively. The required perovskite bulk modulus ( K ) , - 2 7 0 GPa, is somewhat higher than the measured value, but within experimental error. Allowance for the incorporation of the neglected A1203 and CaO components and for the effects of possible lower mantle superadiabaticity may result in some relaxation of these constraints in the sense of allowing somewhat higher values of ~ and TO (by perhaps 10-20%) and somewhat lower values of K. For more silicic models, of which the

102 " c h o n d r i t i c " m o d e l r e c e n t l y p r o p o s e d b y L i u [8] is representative, consistency with the seismological d a t a r e q u i r e s g e n e r a l l y h i g h e r TO o r ~ a n d l o w e r K t h a n t h e a b o v e v a l u e s e.g., ~ - ( 2 . 5 - 3 . 5 ) x 10 - 5 K -1, TO - 2 2 0 0 - 1 5 0 0 ° C a n d K - 2 7 0 - 2 5 0 G P a . This study underlines the urgent need for further studies of the physical properties (especially thermal expansion) of (Mg,Fe)SiO 3 perovskite and its close structural analogues.

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Acknowledgements I wish to acknowledge the valuable assistance of H. Niesler with the computational component of t h i s s t u d y a n d t o t h a n k T.J. A h r e n s , A . L . H a l e s , R . J e a n l o z , S. K a r a t o , C . A . M c C a m m o n , R.T. M e r r i l l , E. O h t a n i , H . S t . C . O ' N e i l l , a n d A . E . Ringwood, and two anonymous reviewers for constructive comments on an earlier version of this paper.

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