410 km discontinuity sharpness and the form of the olivine - phase diagram: Resolution of apparent seismic contradictions

George R. Helffrich, Bernard J. Wood

Geology Department, University of Bristol, Wills Memorial Building, Queens Road, Bristol BS8 1RJ, UK

Accepted 1996 June 17, Received 1996 June 12; in original form 1996 March 27.

SUMMARY
Estimates of the thickness of the 410 km seismic discontinuity, believed to be due to the olivine -> modified spinel transformation in olivine, are as low as 4 km based on discontinuity reflectivity. The seismically estimated thickness is however biased to values narrower than the true transformation interval if linear interpolation of properties is used for modelling. A 5 km linear velocity gradient yields an average reflection coefficient identical to that of a 10 km transition interval based on olivine phase diagram features. Moreover, alternative forms of the phase diagram, equally consistent with experimentally determined iron-magnesium partitioning, can yield true transition intervals as narrow as 4 km. This reconciles a discrepancy between phase equilibrium and seismic measures of discontinuity thickness in two ways: 1) seismic thickness estimates are too narrow; and 2) narrow transition intervals are permissible given existing phase equilibrium constraints. Incorporating recent results on the influence of on discontinuity properties, it appears that 410 km discontinuity reflectivity is much more sensitive to varying concentration than to temperature, suggesting that discontinuity reflectivity variations reflect changes in mantle chemistry.

Key words: Mantle discontinuities, phase transitions, seismology.

1 INTRODUCTION

Upper mantle peridotite consists of about 70% olivine with smaller amounts of pyroxene and garnet phases in which the molar iron concentration (Fe/Fe+Mg) is about 0.1. At a pressure of approximately 14 GPa, corresponding in depth to the 410 km seismic discontinuity, the major phase is observed to transform to - (Fig. 1), with an increase in density of approximately 5.5%. Revenaugh and Jordan's (1991) demonstration that the depths of the earth's major seismic discontinuities, at 410 and 660 km, are anticorrelated strongly supports the hypothesis that they are due to phase changes in mantle minerals (Bernal 1936; Ringwood 1969). Multivariant mineral reactions such as the olivine -> modified spinel transformation (->) are, however, gradual rather than discontinuous with the two phases coexisting over a finite depth interval. This feature is difficult to reconcile with seismic observations indicating an abrupt change in elastic properties with depth. Reported discontinuity thicknesses are in some cases 4 km or less (Benz and Vidale 1993; Yamazaki and Hirahara 1994; Neele 1996) based on the size of the reflection coefficient computed for linear velocity gradients. This is much narrower than the accepted -> transformation interval of 11-19 km (Katsura and Ito 1989; Akaogi et al. 1989), which suggests that some reassessment is warranted. The focus of this paper is to examine two possible explanations for the discrepant transformation interval sizes. The first is that the accepted phase equilibrium transformation interval is too large and the second that seismic results underestimate interval thickness. By exploring plausible limits on the phase transformation interval obtained from high pressure (Fe,Mg) partitioning between the and phases, we find that in the absence of and other trace components a range of transition thicknesses from 4-12 km is possible. This is clearly consistent with the seismic data. Furthermore, 0.5-1 Hz seismic wave reflection coefficients are higher for realistic transition profiles than they are for the linear gradients with which they are typically approximated. Thus, thicker transition intervals may be compatible with short period seismic observations because their equivalent reflectivity approaches that of thinner linear gradients. Finally, by comparing transition interval broadening due to lateral variations in temperature with those due to bulk composition, we find broadening more sensitive to content than temperature. The most likely cause of the observed variability in thickness of the 410 discontinuity is, therefore, bulk compositional fluctuations.

2 PHASE DIAGRAM PROPERTIES

Conservation of mass in a system of fixed bulk composition results in the so-called "lever rule" where the molar proportions of the coexisting phases and are given by the relative lengths of the tie lines lying to either side of the system bulk composition (Fig. 1). Approximating the boundaries and of the two-phase region on a pressure-composition (P-X) phase diagram with straight lines that share a common intercept at and slopes and respectively,

revealing a fundamental dependence of phase proportion on pressure. The constants and describe the width and slope of the transition profile. Since the proportion of phases through a transition interval is not linear, as seismic modelling typically assumes (Richards 1972; Lees et al. 1983; Benz and Vidale 1993; Vidale et al. 1995), it is, as shown below, likely that seismic reflectivity is underestimated for a phase transition such as .

3 THE OLIVINE PHASE DIAGRAM

3.1 Shape effect. The boundaries of the two-phase region are generally curves rather than the straight lines assumed above, tending to enhance nonlinearities in the elastic property profiles through the transition interval (Meijering and Rooymans 1958). To demonstrate the importance of curvature on reflectivity, we show schematic phase diagrams of fixed, 10 km transition width with different curvatures broadly consistent with the experimental Fe-Mg partitioning data obtained at 1600°C by Katsura and Ito (1989). P-X diagrams and their phase proportions through the transition interval are shown in Figure 2. From these phase diagrams we compute short period reflectivity profiles using a Haskell propagator methodology (Aki and Richards 1980). The velocities and densities used in these calculations are proportional combinations of properties from the IASP91 earth model (Kennett and Engdahl 1991) based on for each profile. Olivine properties are approximated by the IASP91 values above the discontinuity at 410 km and -modified spinel below it, extrapolated in depth as necessary using the gradients above and below the discontinuity. This approximation is justified because the elastic properties of the inert (non-) mineral components in the mantle increase roughly linearly through the 10 km intervals of interest. Figure 3 shows underside P reflectivity profiles for the phase diagrams as a function of frequency from 0-2 Hz and averaged over 0.5-1 Hz. Though the transition intervals are equally thick, their reflectivities differ. Between 0.5-1 Hz, the reflectivity derived from the more strongly curved phase boundary with a 10 km transition interval approximates that of a 5 km linear profile. It is clear therefore that comparison of transition reflectivities to linear profiles generally underestimates transition interval thicknesses.

3.2 Feasible alternative forms. Whether the - transition interval is indeed 10 km, or whether a strong curvature for the phase diagram is thermochemically plausible, may be assessed by examining the solid solution properties of olivine and modified spinel, which control the shape of the two-phase loop. Our goal here is not to present a definitive + thermodynamic model, but to show that alternative forms are feasible given phase equilibrium constraints. Both solid solutions may be modelled as binary subregular solutions (Thompson 1967) where the excess free energy of solution = , but recent data suggest olivine solutions are essentially regular (Wiser and Wood 1991), with . Adopting an interaction parameter of 1770 cal (Wiser and Wood 1991) and the end-member solid solution properties listed in Table 1, we explored about 1000 different subregular interaction parameter combinations by grid search in the range ±30 kcal in 1 kcal increments and computed phase diagrams to determine both two-phase loop shape and transition interval thicknesses. We also explored models which incorporate the internal (Fe,Mg) ordering in found in a single-crystal structure refinement of synthesized at high pressure and temperature (Sawamoto and Horiuchi 1990). Only those diagrams compatible with (Fe,Mg) partitioning data (Katsura and Ito 1989; B.J.W. unpubl. data 1996) were considered to be acceptable. Element partitioning data provide the best constraint on the shape of the two-phase loop principally because they are only weakly sensitive to pressure and thus largely independent of experimental pressure uncertainties, which may be 5-10% in multi-anvil apparatus. The end-member properties we used (Table 1) are within the uncertainties of the experimentally constrained 1 bar enthalpies and entropies reported by Akaogi et al. (1989). The diagrams consistent with (Fe,Mg) partitioning data encompass transition intervals ranging from 4-12 km thick (0.15-0.4 GPa in pressure). Three typical diagrams with transition intervals between 4 and 7 km are shown in Fig. 4. Their transition intervals are centred above the 13.6 GPa pressure at 410 km depth but are within the joint experimental and pressure scale uncertainties and thus are plausible models for the 410 seismic discontinuity. We find that by modelling modfied spinel as a subregular (Fe,Mg) solution, thin, 5-6 km transition intervals are feasible, but transitions more curved than those shown in Figure 4 are not. Taking explicit account of Mg preference for the M2 site in - yields transition intervals as narrow as 4 km (Fig. 4). The principal reasons our results differ from those of Katsura and Ito (1989)and Akaogi et al. (1989) is that we take explicit account of pressure uncertainty in multianvil apparatus allowing the composition brackets to shift in pressure (due to P uncertainty), which permits compatibility with narrower phase loops.

3.3 Effect of and temperature. Both temperature and bulk compositional differences affect the form of the two-phase + region in the olivine phase diagram. Wood (1995) showed how water, a minor mantle constituent incorporated into the structure of nominally anhydrous minerals, influences the properties of the - transition. Because strongly prefers the phase to , presence of stabilizes over a wider range of pressure and temperature, broadening the transition interval. Figure 5 shows calculated 410 reflectivity for varying concentrations of in mantle olivine using data from Wood (1995) to provide phase proportions through the transition interval. Compared to anhydrous mantle, the 0.2-0.5 Hz RMS reflection coefficient is halved if 600 ppm water is present, and ~1/3 at 1000 ppm concentration. Thus lateral variations in mantle water content can significantly affect 410 reflectivity.

      By comparison, temperature effects are smaller. Though Fe-Mg partitioning between and depends on temperature (Bina and Wood 1987; Katsura and Ito 1989), the overall effect on reflectivity is weak but frequency dependent (Bina and Helffrich 1994). Averaging reflectivity between 0.2-0.5 Hz yields a change of about ±10% over ±400°C (Fig. 5). The full 800°C range approaches or exceeds the largest thermal perturbations anticipated at transition zone depths, the temperature difference between subducted lithospheric slabs and ambient mantle (Helffrich et al. 1989), and excess plume temperatures (Sleep 1992). The maximum plausible thermal effects are equivalent to a 100 ppm change in mantle olivine content, underscoring the stronger sensitivity to chemical rather than temperature differences.

4 DISCUSSION

In the 0.5-1 Hz band, the underside P reflectivities of the thinner profiles (Fig. 4) are comparable to those of a linear, 4 km gradient against which Benz and Vidale's (1993) observations of underside reflections of P'P' from the 410 km discontinuity were compared. Notwithstanding their claims to the contrary, as well as others (Yamazaki and Hirahara 1994), these observations are quite compatible with olivine -> modified spinel phase transition intervals up to 10 km thick (Fig. 3b), as also shown by Neele (1996). Our results indicate that even 4 km thick transition profiles are feasible given the available (Fe,Mg) partitioning data between and phases (Fig. 4). Thus, the phase transition model for the 410 km discontinuity may not be ruled out simply on the basis of transition thickness.

      Of additional interest is the apparent variability in 410 km discontinuity thickness estimates, ranging from 4 to 35 km (Sobel 1978; Benz and Vidale 1993; Priestley et al. 1994; Yamazaki and Hirahara 1994; Vidale et al. 1995; Neele 1996). Bina and Helffrich (1994) attributed this variability to temperature differences in the mantle. Fig. 5 indicates a significantly greater sensitivity to concentration between 0.2-0.5 Hz. Regionally, the contents of MORB glasses, derived by melting of the mantle, varies by a factor of 4 (Michael 1994). Thus lateral variations in or other minor constituents such as Mn and Ni, which in general also broaden the transition interval (Wood 1995), may be a major source of reflectivity variation. The fact that the 410 km discontinuity is visible at all at short periods suggests that it provides a useful constraint on bulk mantle water content.

      While significantly affects 410 reflectivity, it does not significantly change the apparent depth. This is in contrast to the effect of increasing temperature which both narrows and deepens the discontinuity. If the principal reason for variability in transformation width is lateral temperature variation, then substantial `410' depth variations should be seen because the P-T slope of the - transformation is large (Bina and Helffrich 1994). The 410 is however less variable in depth as well as less frequently seen than the 660. These characteristics are more compatible with a response to variations in mantle content which affects reflectivity (Fig. 5a) but not the apparent depth of the discontinuity.

ACKNOWLEDGMENTS

We thank D. Rubie and H. Paulssen for thoughtful reviews and John Vidale for 410 reflectivity information and for comments on an earlier version of the manuscript.

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Source: Bina and Wood (1987), with and adjusted to yield -> transition pressures reported by Katsura and Ito (1989). Olivine regular solution = 1770 cal + 0.006 P for mixing on two sites. non-convergent ordering model recognizes 1 M1, 1 M2 and 2 M3 sites in the phase (Sawamoto and Horiuchi 1990) with equivalent mixing properties on the M1 and M3 sites. Internal regular solution mixing and are 1500 cal, -6200 cal for mixing on two sites and of the ordered and anti-ordered phases and are 700 and 3300 cal higher than a mechanical mixture of the and end-members, respectively.

Figure 1. 1600°C isothermal phase diagram in the system after Katsura and Ito (1989). Single phase regions are those marked , and and two phase regions are identified with , and . Fe concentration in mantle olivines shown by dashed line. Where this intersects the two phase loops determines the pressure interval of two phase coexistence. Relative lengths of line segments marked and to + field width denote proportions of and phases at a position in the transition interval.

Figure 2. a) Schematic phase diagrams consistent with experimetally determined (Fe,Mg) partitioning between and (Katsura and Ito 1989) having equivalent transition interval thicknesses, 0.3 GPa (10 km). The pressure scale is relative because the diagrams are shifted to emphasize their identical transition intervals for mantle composition (Jeanloz and Thompson 1983) (dashed line). b) Molar proportions of coexisting and phases through the transition intervals for the two profiles in a, compared to a linear gradient. For the sharply curved phase diagram, half of the transition occurs in the final 25% of the depth interval.

Figure 3. Underside P reflection coefficients for 4, 6, and 10 km linear gradients and for the schematic profiles in Fig. 2, simulating reflectivity at 72° (18° vertical incidence angle) (Benz and Vidale 1993). a) Frequency dependent reflection coefficients, showing the slower decay of high frequency reflected energy from realistic transformation profiles compared to linear ones. b) Dependence of the RMS reflection coefficient between 0.5-1 Hz on transformation interval thickness. The sharply curved phase diagram, with a 10 km transition interval, yields reflectivity equivalent to a ~5 km linear gradient. The more gently curved phase boundaries lead to reflectivities equivalent to 7 km, thinner than the full 10 km transition interval in each case.

Figure 4. Calculated phase diagrams compatible with (Fe,Mg) partitioning at 1600°C. The experimentally determined coexisting and Fe contents (Katsura and Ito 1989) are linked with dotted tie lines, with open symbols denoting partitioning determined by B.J.W. at the Bayerisches Geoinstitut. Uncertainties are ±1 mol% in composition and ±1.5 GPa in pressure. Heading each panel are the subregular interaction parameters ( and for mixing on two sites, in cal.) pertaining to each diagram. See Table 1 for ordering model parameters.

Figure 5. a) Frequency dependent reflection coefficients for for varying concentrations. b) Dependence of 0.2-0.5 Hz RMS reflection coefficients on concentration (solid line) and temperature changes (dashed line). The reflection coefficient change relative to `normal' conditions is shown in each case: anhydrous conditions and along a 1350°C adiabat (Bina and Helffrich 1994). A 400°C change in temperature yields a 10% reflectivity change, equivalent to the effect of 50 ppm added to anyhdrous mantle. Thus discontinuity reflectivity is much more sensitive to concentration than temperature.