An Index of Degree of Chemical Inhomogeneity in the Earth

Summary An index 7 is introduced which, for a region of continuous density variation in the Earth, defines the ratio of the actual density gradient to the gradient which would apply if the region were chemically homogeneous and devoid of phase changes. A formula is derived expressing 7 in terms of the three quantities dkldp, g and dldx (defined in Section I), which are all physically or observationally significant. The formula is applied to examining the density changes in the regions D”, F and G of the Earth, and to apportioning the factors which contribute to uncertainties in the formally computed results. Bolt’s new core-velocity distribution is discussed in the light of the theory given, and it is shown that the estimated central density of the Earth can now be reasonably lowered to about 15 g/cm3, though a value of 18 g/cm3 is still not precluded on the theory given. The argument in the paper shows incidentally that, in the Earth’s deeper interior, seismic velocity gradients in excess of certain values are unlikely, on stability grounds. The values must be such that d/dx is not significantly greater than The paper provides ingredients for constructing Earth models based on seismic data with more ease than hitherto. I. Derivation of formula Let p, k, p, p, a, /3 and g denote the density, adiabatic incompressibility, rigidity, pressure, P velocity, S velocity, and gravitational attraction at depth z below the surface (or distance r from the centre) of the Earth. Deviations from spherical symmetry and adiabatic temperature gradients will be ignored. Previous work of the writer (1956) indicates that the effects of the latter are likely to be small compared with the effects to be here investigated. The argument to follow does not discriminate between changes in chemical composition and changes in phase caused by pressure. For brevity the term chemical inhomogeneity will be used to include inhomogeneity arising from change of phase; a region referred to as chemically homogeneous will be understood to be also devoid of phase transitions.