Mantle models

Figure 1 Depth-varying phase proportions in a pyrolite model mantle after the manner of Ringwood (1989), Ita and Stixmde (1992), and Bina (1998h). Phases are (a) ohvine, (fi) wadsleyite, (y) ringwoodite, (opx) orthopyroxene, (cpx) clinopyroxene, (gt-mj) garnet-majorite, (mw) magnesiowiistite, ((Mg,Fe)-pv) ferromagnesian sihcate perovskite, and (Ca-pv) calcium silicate perovskite. Patterned region at base denotes likely heterogeneity near core-mantle boundary.

Figure 9 Examples of models proposed for the chemical structure of the terrestrial mantle, (a) Whole mantle convection with depletion of the entire mantle. Some subducted slabs pass through the transition zone to the coremantle boundary. Plumes arise from both the core-mantle boundary and the transition zone. This model is not in agreement with isotopic and chemical mass balances, (b) Two-layer mantle convection, with the depleted mantle above the 660 km transition zone and the lower mantle retaining a primitive composition, (c) Blob model mantle where regions of more primitive mantle are preserved within a variously depleted and enriched lower mantle, (d) Chemically layered mantle with lower third above the core comprising a heterogeneous mixture of enriched (mafic slabs) and more primitive mantle components, and the upper two-thirds of the mantle is depleted in incompatible elements (see text) (after Albarede and van der Hilst, 1999).

Machetel P. and Weber P. (1991) Intermittant layered convection in a model mantle with an endothermic phase change at 670 km. Nature 350, 55-57. 

Composition of the lower mantle A variety of compositions have been proposed for the lower mantle including almost pure perovskite, chondrite, and pyrolite. However, most models of the Earth assume that the upper and lower mantle have the same composition. Recent attempts to directly estimate the composition of the lower mantle have used best-fit curves of the thermoelastic properties of the Earth to a PREM model mantle made up of the phases Mg-perovskite, Ca-perovskite, and magnesiowustite. The recent calculations by Li and Zhang (2005) indicate a pyrolitic composition for the lower mantle, with Mg/Si atomic ratios between 1.29 and 1.39, slightly higher than those for the pyrolite models in Table 3.1 (Mg/Siatomic = 1.24—1.25). 

Figure 23. Abundance pattern of primordial noble gases in model mantle sources for MORBs and OIBs, calculated as outlined in the text. The ratios are normalized to the solar pattern and to Ar = 1. The pattern for the atmosphere is shown for comparison.

PHYSICAL CONSTRAINTS ON MANTLE MODELS Mantle reservoirs... 

Albarede (1998) argued that the model mantle cannot be in steady state due to the progressive decay of the parent elements in the upper mantle, and so is selfcontradictory. However, the notion of steady state upper mantle conditions clearly is an approximation. While a strict steady state does not hold, the deviation from this due to decay of the very long-lived parent nuclides over the residence time of upper mantle noble gases is minor. 

These model mantle extraction ages can be interpreted either as a minimum age at which the material separated from the depleted mantle or chondrite uniform... 

The bubble model (Kunii and Levenspiel, Fluidization Engineering, Wiley, New York, 1969 Fig. 17-14) assumes constant-sized bubbles (effective bubble size d ) rising through the suspension phase. Gas is transferred from the bubble void to the mantle and wake at... 

To avoid confusion with the shells of the shell model of the nucleus we shall refer to the layers of spherons by special names the mantle for the surface layer, and the outer core and inner core for the two other layers of a three-layer nucleus. 

The close-packed-spheron theory8 incorporates some of the features of the shell model, the alpha-particle model, and the liquid-drop model. Nuclei are considered to be close-packed aggregates of spherons (helicons, tritons, and dineutrons), arranged in spherical or ellipsoidal layers, which are called the mantle, the outer core, and the inner core. The assignment of spherons, and hence nucleons, to the layers is made in a straightforward way on... 

An ellipsoidal nucleus with two spherons in the inner core has major radius greater than the minor radii by the radius of a spheron. about 1.5 f, which is about 25 percent of the mean radius. The amount of deformation given by this model is accordingly in rough agreement with that observed (18). In a detailed treatment it would be necessary to take into account the effect of electrostatic repulsion in causing the helions to tend to occupy the poles of the prolate mantle, with tritons tending to the equator. 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

The globally S5mchronous development of erosion surfaces and slow uplift rates of shields indicates that models based on localized heating of the crust and mantle are not adequate to explain the uplift process. To produce near simultaneous surfaces on separate continents. King (1967) invoked global epeirogeny - uplift... 

Typical Mossbauer spectra for the fresh, reduced, carblded and used Fe/ZSM-5 system are shown in a composite Fig. 5. Similar spectra were obtained for the Fe-Co/ZSM-5 system. The product distribution for the F-T reaction, using the Fe and Fe-Co systems, are shown in Table 1. The gasoline range hydrocarbon yield increased from 75 to 94%, when the Fe-Co clusters were used in place of Fe only. In a typical CEMS (Conversion Electron Mossbauer Spectroscopy) of the Fe-Co system, no spectrum for 57pg vas observed even after one week from this. It was concluded that in the Fe-Co clusters Co was predominantly in the "mantle" and Fe species were In their "core," in the parlance of metallurgy/geophysics. This model Is sometimes referred to as the cherry model. 

Model I shown in Fig. 1.163 is a slab-induced upwelling model. Upwelling generated along the down going slab-mantle boundary (Karig, 1971) or by secondary convection that is introduced by the slab (Sleep and Toksoz, 1971) causes back-arc formation (Karig, 1971). 

Fig. 4.10. Atmo.spheric CO2 variation estimated by modified BLAG model including CO2 flux related to mantle plume activity (Ishikawa, 1996). t c02 = 202/ 002 - prescut-day PcOi)-...

Landwehr et al. (2001) extended the model of Wood and Blundy (1997) to include and Th". They measured experimentally Aj and Z)xh in a wide variety of synthetic clinopyroxene compositions in order to evaluate the crystal compositional dependence of U-Th fractionation. Their observations confirm the predictions of Wood et al. (1999), namely that as the M2 site becomes smaller, so D-m becomes smaller than Du (Figs. 1 and 11). The M2 site becomes smaller as the enstatite component of the clinopyroxene increases and Ca on M2 is replaced by Mg. Enstatite solubility in clinopyroxene increases with increasing temperature, consequently clinopyroxene coexisting with orthopyroxene will show higher Du/Dih at higher temperature. For this reason, DuIDjb increases with increasing pressure along the mantle solidus, as discussed above. 

There is only one determination of Z)pb in orthopyroxene, that of Salters et al. (2002) at the mantle solidus at 2.8 GPa. This value (0.009 0.006) is within error of that calculated from the Dsr value of McDade et al. (2003a) under similar conditions, using the lattice strain model, i.e., 0.0024 0.0012. However, the uncertainties on both measurements should not be taken as strong support for the potential of Sr as a proxy for Pb. Still, there is no evidence for the anomalously low Z)pb values observed in clinopyroxene. 

Dm (and Du) vary inversely with reciprocal temperature (Fig. 15). For mantle solidus garnets the correlation is reasonably good and can be used to make a first-order estimate of Dm- A more comprehensive model for Du and Dm, as a function of pressure, temperature and melt composition is provided by Salters et al. (2002). Their full expressions (for the molar partition coefficients, D ) are ... 

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