The “Best” Straight Line among the Points

Bacon, Ralph Hoyt

doi:10.1119/1.1933485

Cited by 35 publications

(2 citation statements)

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“…The estimated uncertainty in the recent single-crystal acoustic data was assumed to be 1 per cent, and that of the remaining data 3 per cent. The data was weighted using these uncertainties for a least square determination following the method suggested by Bacon (1953). The results for the adiabatic bulk modulus KS and rigidity p as a function of mol per cent fayalite (Fa) are: and KS = 1290-1.679 (Fa),…”

Section: Elastic Properties Of Olivinementioning

confidence: 99%

Elasticity and Composition of the Upper Mantle

Graham

1970

Geophysical Journal International

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This paper is concerned with the elasticity and composition of the upper mantle as inferred from recent laboratory ultra-sonic and phase-stability data. The seismically-determined compressional and shear velocity structure of the upper mantle, as well as the density distribution, is initially discussed in terms of homogeneous olivine models of variable fayalite content. The elastic properties of the olivine solid solution series are defined by a least squares linear fit to existing acoustic and static compression data from several single-crystal and polycrystal specimens of forsterite and fayalite. Compressional and shear velocity profiles are calculated for olivine models of 0, 10 and 20 mol per cent fayalite using geothermal models defined by requiring a satisfactory fit between the model V,, profile and a standard seismic compressional wave profile. The significance of the calculated velocity curves is discussed in terms of the estimated uncertainties in the ultra-sonic input data. On a basis of the elastic and density requirements alone, the 1Omol per cent fayalite model appears to be most satisfactory.In addition to consideration of the elastic requirements, the stability relations of the olivine-spinel phase transformation provide an additional constraint on the proportion of fayalite fraction. At the 370-km seismic discontinuity, assumed to be the change in velocity associated with the olivine-spinel transition, the combined elastic, density, and geochemical requirements are satisfied with an olivine model of composition Foss Falz. Assuming that the olivine approximation is reasonably valid, the Mg/Mg+ Fe ratio at the top of the 370-km discontinuity is 0.88 &0.03, and the temperature is 145O&12O0C. Lastly, the effects of other mineral phases such as pyroxene and garnet are assessed. It is concluded that the addition of relatively minor fractions of other phases, for example, an assemblage of garnet pyrolite, would not significantly alter the present results in terms of presently available data. That is, the elasticity, density, and structure of the upper mantle below the low-velocity zone, are satisfied self-consistently by a peridotite model.

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Section: Elastic Properties Of Olivinementioning

confidence: 99%

Elasticity and Composition of the Upper Mantle

Graham

1970

Geophysical Journal International

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“…Accordingly, the widths at each pressure were extrapolated to zero size (i.e., to vanishing metastable atom, electron, ion, etc., densities) by making a leastsquares straight-line fit to the data. 13 From Eq. (4), the limiting width, A£T^, is given by…”

Section: B Argonmentioning

confidence: 99%

Lifetimes and Alignment Depolarization Cross Sections of the (3p54p)D3
Landman
¹

1968
Phys. Rev.
21
0
0
0
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33 25 In the notation of Paper I, {ll f lG 0(2)~M ZZ'}=-AH zz , ",, and hence wtog/ ={W \G 0 i2) \ll , }Qi 2 (l/r 12 )\ [W']i 2 >, where the diagrammatic expansion of this expression is implicitly given in Paper I. The {a IG* 2 *"" 1 1/3} of Paper I is identical to the negative of the whole two-electron block of AH and substituting G (2) for G 0 (2) above, YJI" >V» x{U'\G i2) \l"r"}Q 12 (l/r 12 )\[l"l"'] 12 )gives the "complete pairs" discussed in Ref. 20, whose diagrammatic expansion in powers of OPT is also given in Paper I. The off-diagonal components of AH connecting cluster functions of say one (or three) and two electrons are just the V (1 » 2) (or V <3 > 2) ) operators of Paper I. The process of obtaining expansions of w (1) , w (2> , • • •, in orders of OPT, therefore, need not be presented here in detail. 26 H. J. Silverstone and O. Sinano^lu, J. Chem. Phys. 44, 1899, 3608 (1966). 27 We could look for the set of localized HF orbitals that reduce the size of higher-order corrections, i 0 e 0 , that make the off-diagonal elements of AH as small as possible.

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