2.02 Seismological Constraints upon Mantle Composition C. R. Bina Northwestern University, Evanston, IL, USA 2.02.1 INTRODUCTION 39 2.02.1.1 General Considerations 39 2.02.1.2 Bulk Sound Velocity 40 2.02.1.3 Acoustic Methods 40 2.02.2 UPPER-MANTLE BULK COMPOSITION 41 2.02.2.1 Overview 41 2.02.2.2 Velocity Contrasts 42 2.02.2.3 Discontinuity Topography 42 2.02.2.4 Sharpness 43 2.02.2.5 Broadening and Bifurcation 43 2.02.3 UPPER-MANTLE HETEROGENEITY 45 2.02.3.1 Subducted Basalts 45 2.02.3.2 Plume Origins 46 2.02.4 LOWER-MANTLE BULK COMPOSITION 48 2.02.4.1 Bulk Fitting 48 2.02.4.2 Depthwise Fitting 49 2.02.5 LOWER-MANTLE HETEROGENEITY 51 2.02.5.1 Overview 51 2.02.5.2 Subducted Oceanic Crust 52 2.02.6 SUMMARY 54 REFERENCES 56 2.02.1 INTRODUCTION and lower mantle? What light can they shed upon 2.02.1.1 General Considerations the nature of velocity heterogeneities in both the upper and lower mantle? It is these questions that Direct sampling of mantle rocks and minerals is we shall seek to address in this chapter. limited to tectonic slices emplaced at the surface Most seismological constraints on mantle com- (see Chapter 2.04), smaller xenoliths transported position are derived by comparison of values of upwards by magmatic processes (see Chapter seismic wave velocities inferred for particular 2.05), and still smaller inclusions in such far- regions within the Earth to the values measured in traveled natural sample chambers as diamonds the laboratory for particular minerals or mineral (see Chapter 2.05). Because of such limited direct assemblages, with such comparisons being made access to mantle materials, knowledge of mantle under comparable regimes of pressure (P) and structure, composition, and processes must be temperature (T ). The primary parameters of augmented by geophysical remote sensing. What interest, then, are the compressional (or P-) wave can various seismological observations tell us velocities (VP)andtheshear(orS-) wave about the major-element composition of the upper velocities ðVSÞ: These wave velocities are simply mantle? How can they constrain possible differ- related to the density (r) and to the two isotropic ences in chemical composition between the upper elastic moduli, the adiabatic bulk modulus (KS) 39 40 Seismological Constraints upon Mantle Composition 2 and the shear (or “rigidity”) modulus (G), via VP ¼ provide independent constraints upon Vf (Bina = 2 = ; ½KS þð4 3ÞG=r and VS ¼ G r respectively. and Helffrich, 1992). Again, chemical composition in regions of Earth’s interior is primarily constrained by mapping 2.02.1.2 Bulk Sound Velocity values of seismic velocities in those regions and Straightforward measurements of elastic prop- comparing the values to those determined for erties of materials can be made via high-pressure various candidate mineral assemblages. The pri- static compression experiments, in which X-ray mary observables in the seismological studies diffraction (XRD) is used to measure the molar consist of measured travel times of various P-and volume (V), or equivalently the density (r), of a S-waves, some of which can in principle constrain material as a function of pressure (P). The density contrasts (Shearer and Flanagan, 1999)from pressure dependence of volume is expressed a large enough set of which values of VP and VS can by the “incompressibility” or isothermal bulk be determined through mathematical inversion. modulus (K ), where K ¼ 2Vð›P=›VÞ : Secondary observables include the measured ampli- T T T tudes of various arriving P-andS-waves, some of This isothermal bulk modulus ðKT Þ measured by static compression differs slightly from the afore- which can in principle constrain density contrasts mentioned adiabatic bulk modulus ðK Þ defining (Shearer and Flanagan, 1999) but these are much S more sensitive to complex properties such as seismic velocities in that the former ðKT Þ describes resistance to compression at constant temperature, anelasticity than are simple travel times. Seismological observables, then, directly yield VP such as is the case in a laboratory device in which a ; sample is slowly compressed in contact with a and VS but static compression experiments directly large thermal reservoir such as the atmosphere. yield Vf. It is common, therefore, to seek to combine seismological VP and VS models to generate a Vf The latter ðKSÞ; alternatively describes resistance to compression under adiabatic conditions, such as model for a region, for comparison to mineralogi- those pertaining when passage of a seismic wave cally constrained Vf values. Such combinatoric causes compression (and relaxation) on a time- procedures can introduce additional errors, how- scale that is short compared to that of thermal ever, in that the VP and VS profiles used may often conduction. Thus, the adiabatic bulk modulus reflect seismic ray paths or frequency bands that generally exceeds the isothermal value (usually by differ from one another. Indeed, special source– a few percent), because it is more difficult to receiver geometries (such as those whose epicentral compress a material whose temperature rises upon distances are so small as to ensure nearly overlap- compression than one which is allowed to conduct ping ray paths) may be necessary to obtain robust away any such excess heat, as described by a estimates of Vf values (Bina and Silver, 1997). ¼ ð þ Þ Nonetheless, comparisons to Vf, rather than to VP simple multiplicative factor KS KT 1 Tag , ; where a is the volumetric coefficient of thermal and VS are commonly used to constrain compo- expansion and g is the thermodynamic Gru¨neisen sitions in the deep interior, because (as noted below) parameter. mineralogical values for G (and hence for VS) Experimentally, the bulk modulus is the become more problematic with increasing depth. simplest parameter to measure, but the seismo- ; logical parameters of primary interest, VP and VS 2.02.1.3 Acoustic Methods both involve the shear modulus as well. It is convenient, therefore, to define a new parameter, Direct laboratory measurements of VP and VS the “bulk sound velocity” (Vf), which eliminates for materials can be made through acoustic all dependence upon the shear modulus (G) methods, such as Brillouin spectroscopy and through a judicious linear combination of the ultrasonic techniques. Brillouin spectroscopy (or 2 squares of the two seismic wave velocities: Vf ¼ “Brillouin scattering”) determines acoustic velo- = 2 = 2: KS r ¼ VP 2 ð4 3ÞVS This new parameter (some- cities in a single crystal through measurements of times thought of as the P-wave velocity of an the Doppler shifts experienced by visible light “equivalent” fluid, for which G ¼ 0) can be scattering off the faces of a single crystal in which determined directly from static compression thermally induced acoustic waves are propaga- 2 = = data: Vf ¼ KS r ¼ð1 þ TagÞð›P ›rÞT . The bulk ting. Because the technique employs single sound velocity possesses another desirable fea- crystals, full elasticity tensors (rather than just ture, in that it can also be constrained indirectly isotropic VP and VS) can be determined, which are through chemical equilibrium experiments. useful in studies of velocity anisotropy. The Chemical equilibria describe free energy minima; technique requires only small samples, and the pressure dependence of free energy is because visible light is employed, the samples described by the molar volume, and the pressure may be placed in an optically transparent dependence of volume (or density) is described diamond-anvil cell (DAC) in order to make by KT and hence Vf. Thus, experimental deter- measurements at elevated pressures and tempera- minations of equilibrium phase boundaries can tures. DAC studies yielding VP and VS may be Upper-mantle Bulk Composition 41 combined with XRD analyses yielding r, to allow the compositions of mantle-derived melts (see for direct determination of KS and G (and hence Chapter 2.08), various cosmochemical arguments Vf) for single crystals (Zha et al., 1998a). (see Chapters 2.01 and 2.15), and simple geophy- The second group of acoustic methods, the sical considerations, the mineralogy of the upper ultrasonic techniques, require larger samples but mantle is commonly concluded to resemble that of can be performed on either single crystals or some sort of peridotite (McDonough and Rudnick, polycrystalline aggregates. They require experi- 1998). Perhaps the most frequently invoked model mental measurement (via interferometry) of the composition is that of “pyrolite” (Ringwood, travel times of two consecutive ultrasonic echoes 1975, 1989), which contains ,60% olivine by from the ends of a shaped sample, combined with volume, the depth-varying properties of which are measurement of the length of the sample. These dominated by progressive high-pressure phase measurements directly yield VP and VS; rather than transitions from olivine (a) to wadsleyite (b, also full anisotropic elasticity tensors, but this is usually called “modified spinel”) to ringwoodite (g, also sufficient (unless patterns of seismic velocity called “silicate spinel”) and thence to a mixture of anisotropy are to be used to map strain fields in silicate perovskite (pv) and magnesiowu¨stite (mw, the mantle). Samples may be placed in a multi- also called “ferropericlase”). The remaining, anvil cell (MAC) to make measurements at nonolivine, components are orthopyroxene elevated pressures and temperatures, and simul- (opx), clinopyroxene (cpx), and garnet (gt), and taneous (usually synchrotron) XRD analysis can these undergo more gradual high-pressure tran- then be used to keep track of associated changes in sitions as the pyroxenes dissolve into the garnet, sample length. Again, MAC studies yielding VP with the resulting “garnet–majorite” solid solu- and VS may be combined with r measurements tion (gt–mj) eventually transforming to silicate from the XRD analyses to directly yield KS and G perovskite as well (Figure 1).