Jökull - 01.12.1973, Page 34

TABLE 1.
Properties of silicates and oxides.1
Compound Molar Wgt. (X 10-3kg/mole) Molar Vol. (10-G m3/mole) p x 103 (kg/m3)
Mg2Si04 (forsterite) 140.7 43.792 3.213
Mg2Si04 (spinel) 140.7 39.582 3.555
MgO (periclase) 40.32 11.25 3.584
Si02 (stishovite) 60.09 14.02 4.287
2MgO + Si02 140.7 36.50 3.855
Fe2Si04 (fayalite) 203.79 46.392 4.393
Fe2Si04 (spinel) 203.79 42.032 4.849
FeO (wiisdte) 71.9 12.05 5.969
2FeO + Si02 203.79 38.12 5.346
1) After Anderson (1967).
2) Ringwood and Major (1970).
mantle convection. The upper mantle is gener-
ally assumed to contain about 75% olivine with
an Mg/Fe ratio of about 9:1 (Ringwood, 1970).
The lower mantle is probably composed of the
component oxides MgO, FoO, and SÍO2 (Ander-
son and Jordan, 1970). We shall treat the
mantle phase transitions as univariant. More-
over we shall assume that the transition para-
meters can be approximated by the parameters
for transitions occurring in pure Forsterite (Mg2
SÍO4) and pure Fayalite (Fe2Si04). Table 1 and
Table 2 list the pertinent data. We shall take
commonly used values for the average physical
properties of the mantle: c = 103j/kg; ot =
2 x 10-5/°C; a = 2 X 10-6m2/sec. For the aver-
age heat production in the entire mantle, we
take A = 10-12 watts/kg, the same order of
magnitude as the heat production in dunite
(Stacey, 1969).
We first consider convection throughout the
entire mantle and assume = 10-3 °C/m. The
ratio di/h is approximately 0.1 and 0.2 for the
400 km and 650 km transitions respectively.
We have calculated the critical Rayleigh
number for the various transitions from (58).
Table 3 lists the results.
Table 3 shows that the olivine-spinel phase
transition lowers the critical number slightly,
whereas the spinel-oxides transition raises the
cridcal number slightly. Since the effects of
each transition are small, the interaction be-
tween the two transitions should introduce only
a slight error into the critical Rayleigh numb-
ers shown in Table 3. Although there is a fair
amount of uncertainty in the data, Table 3
indicates that the mantle phase transitions
modify tlie critical Rayleigh number by less
than a factor of two from the critical number
for a homogeneous fluid.
To calculate the Rayleigh number for the
entire mantle, we recall that
_ q gAh5
j/a2c
All the needed parameters have been estimated
except tlie kinemadc viscosity. Fennoscandian
uplift data give values from 1015 to 3 X 1017
m2/sec for the asthenosphere (McConnell, 1965,
1968; Lliboutry, 1971). Munk and MacDonald
(1960) have suggested that the non-equilibrium
flattening of the earth requires the viscosity of
tlie lower mantle to be of the order of 1022
m2/sec. Recently Goldreich and Toomre (1969)
have suggested tliat this liigh estimate is un-
realisdc.
32 JÖKULL 23. ÁR