The difference in abundances of lanthanides among terrestrial materials, Norton County achondrite, and chondrites was dealt with mathematically and its implication to the development of the mantle and crust was presented. The difference, d, in relative partition coefficient to that for La was estimated to be 0.296 (see Figs. 3, 4, and 5) by assuming that Norton County achondrite represents the solid-type material corresponding approximately to a certain stage of solidification and by the use of a least square method. By introducing this value of difference in relative partition coefficient, the abundances (CA 18.3 and C°A = 0.32 ÷ 0.832, ppm) of La in Minami's shales and in average chondritic oxide phase (the average percentage of non-oxide components in chondrite was taken as 16.8 %), and the slope coefficient (s = 1.17) of Fig. 1 into Eq. (12), the partition coefficient kA of La was evaluated to be 0.121. If the lanthanide abundances in shales determined by Minami (1935) are assumed to approach the average crustal abundances of lanthanides, the thickness of the crust can be calculated to be 34 km. Thus it could be said that the crust and mantle as a whole originated from chondritic oxide melt, the crust represents the final residual liquid, while the mantle represents the aggregate of crystals separated from the liquid, and the composition of mantle is to vary gradually and steadily with the depth.
Up to the present time, the question of the chemical composition and the isotopic ratios in the interior of the earth has been much debated. It is supposed that the average composition of the interior layers of the earth resembles that of certain types of rocks or meteorites. For example, the mantle may be represented by dunite, eclogite and peridotite. Or it can be represented by chondritic composition. For any theories concerning the model composition of the interior, one might conclude that elements such as Li, Na, Ca, Al and halogens are concentrated toward the earth's surface, while S, Mg, Fe and Ni are enriched in the deeper layers. In the similar way, the isotope ratios of the mantle could be assumed. At first, the geochemical aspects of the isotope ratios are discussed. One general feature of the geochemical cycles of boron and lithium isotopes is discussed by comparing them to the sulfur isotope ratio which has been reported by many individual data. In order to estimate the isotope ratios in the mantle, the following cases are considered. (1) The isotope ratios in the mantle have values similar to the meteoritic values. (2) The isotope ratios in the mantle have values similar to the terrestrial values. And (3) the isotope ratios in the mantle are different from those of either the meteoritic composition or the terrestrial composition. The mean values of isotopic composition for the mantle is important for the estimation of isotope ratios in the nuclear synthesis theory or in cosmochemistry also.
In the past, petrological data have provided the principal contributions towards our knowledge of the constitution of the meteorite. It is now possible to look into the differentiation of the meteorites in which a wide variety of properties are reasonably well specified by the similar way as in petrological studies. If it is possible to establish within reasonable limits the chemical composition of the meteorites, an enormous simplification will be achieved. The systems of (Na2O+K2O) -Fe-OMgO and CaO-FeO-MgO have been studied for meteorites and rocks by means of the three component variation diagrams. The main fractionation trend is continuously shown from chondritic achondrites, H- iron group chondrites, L- iron group chondrites, carbonaceous chondrites, to basaltic achondrites and also from basaltic achondrites to rock variations. From the variation curve of main chemical components against the factor (MgO+FeO +Na2O +K2O), we may see that it is in the main fractionation sequence and is transitional between the meteorite group and the rock group. From this observation, we can assume that the primitive chemical composition of meteorites is rather the chondritic achondrite composition than the carbonaceous chondritic composition and the differentiation system of the appearance of the mineral phase as outlined by geologists on the rock series is consistent with the phase relationships found in the meteorite series. The chemical composition of the mantle could be inferred by these hypotheses.
Olivine-spinel transformation for Ni2SiO4, Fe2SiO4 and Co2SiO4 was examined using a tetrahedral anvil type high pressure apparatus. Tentative phase diagram of olivine-spinel transformation was presented for Ni2SiO4 and Fe2SiO4. Spinel form of Ni2SiO4, Fe2SiO4 and Co2SiO4 shows antiferromagnetic character at the lower temperature below 20°K. Abrupt change in electrical conductivity with olivine-spinel transformation was found for Ni2SiO4.
Observations of relaxation time t of deviation from perfect isostacy as a function of wave length λ will give us viscosity distribution within the earth. Preliminary studies of this kind suggest a low viscosity layer at a depth which coincides with the low velocity layer inferred from surface wave studies.
The elastic anisotropy of rocks is due to the petrofabric structure of anisotropic minerals and/or to the configuration of interface between the constituent mineral grains. With respect to the dilatational wave, the degree of anisotropy of dunite is estimated as follows : 2.5 per cent utmost due to interface configuration and 10 per cent ordinarily due to petrofabric structure of olivine. The origin of the preferred orientation of olivine in massive ultrabasic rocks is discussed based on the nonhydrostatic thermodynamic theory. It is inferred that the olivine crystals in the upper mantle will show a remarkable preferred orientation especially in the tectonically active region where the nonhydrostatic condition prevails. If the peridotite is the main constituent of the upper mantle, its significant anisotropy (about 5 per cent) will be detectable from the analysis of seismic wave propagation. On the other hand eclogitic rocks are considered to be comparatively isotropic. Therefore, it might be possible to determine by seismic prospecting whether the upper mantle is peridotitic or eclogitic.
The deformation and the fracture of rock samples are discussed on the basis of recent experimental results by Griggs, Robertson, Heard and others. The fracture strength of rocks is appreciably influenced by confining pressure, temperature, strain rate, sample size and other factors. From these experimental results and some geodetic data, the strength of the earth's crust is estimated at various depths. According to this estimation, the strength remarkably increases up to the 20-30 km depth and it decreases gradually at deeper regions. It is widely believed among seismologists that earthquakes are caused by brittle fracture of the earth's materials. However, at very high pressure and high temperature, brittle shear fracture cannot occur in rocks. This transition from brittle fracture to ductile fracture in rock samples is very interesting from the seismological point of view. New hypotheses on the earthquake mechanism at deep regions (at very high pressure and temperature) are reviewed.
A few regions for which special crust-mantle system has to be suggested from the observation of surface wave dispersion are given. 1. Group velocity of Rayleigh waves which travelled along East-Pacific Rise shows the maximum value as low as 3.90 km/sec for such a short period as around 25 second. This result indicates the mantle with low shear wave velocity in its upper part overlain by a relatively thin crust. Group velocity dispersion curve of Rayleigh waves along Mid-Atlantic Ridge also shows the similar structure beneath the ridge. 2. Lateral inhomogeneity just below Moho-discontinuity has been discussed from the observation of body waves. Phase velocity dispersion of Rayleigh waves due to a nuclear explosion test has also revealed lateral variation of elastic properties of materials below Moho in Nevada district. 3. Mantle Rayleigh waves passing through the western side of Andesite - line in the western Pacific Ocean show the dispersion character remarkably different from that through other Pacific area. This fact suggests a special upper mantle situation beneath the region in question.
The heat budget of the upper mantle of the earth was recently examined by Tilton and Reed, based on an investigation of the concentration of uranium, thorium and potassium. in ultramafic rocks and eclogites. According to Tilton and Reed, the radioactive heat production rate in ultramafic rocks (olivine nodules from Hualalai, Hawaii; Dreiser Weiher, Germany; Gila, Arizona, USA; and dunite from Twin Sisters Mtn., Washington; St. Pauls Rock, Mid-Atlantic Ridge) and eclogite (from Salt Lake Crater, Hawaii) is 0.38 and 3.25 erg/gr·year respectively. To account for terrestrial heat flow in oceanic areas (50 erg/cm2·sec), the heat production in ultramafic rocks such as peridotite as a constituent of the outer mantle is too low. The same is true for eclogites, if heat transfer takes place in the mantle solely by thermal conduction. Eclogite could provide a satisfactory heat source, if convection currents exist in the outer mantle as an effective mode of heat transfer. Peridotite may be a major constituent of the outer mantle in continental areas or of the deep mantle underlying continental and oceanic regions.