Density distribution and constitution of the mantle
Authors: Clark Sydney P. , Ringwood A. E. 
Published: February 2008

Major regions of inhomogeneity are present in the mantle at depths less than 1000 km. The thermal gradient also greatly exceeds its adiabatic value at relatively shallow depths. Hence the Williamson‐Adams equation cannot be used in this part of the earth to derive the density variation from seismic data. In this paper the density in the upper mantle is obtained by explicitly introducing the constitution of the material there. In the lower mantle the extended Williamson‐Adams equation is used, and the constitution of this region is deduced from the density curve.

Recent seismic results for the upper mantle, particularly those relating to low‐velocity zones, are examined. Significant regional differences are present. Beneath the oceans there is a definite LV zone forS, and possibly one forPas well. Beneath Precambrian shields the LV zone forSis less pronounced, and the LV zone forPseems to be absent. Other continental regions are intermediate between these zones. The LV zone is considered to be due to high thermal gradients with mineralogical and chemical heterogeneity superimposed. Differences between the behavior ofPandSare largely due to different temperature coefficients of the two velocities. Regional contrasts arise from regional differences in thermal gradients and mineralogy.

Consideration of temperature‐depth relations leads to the conclusion that the mantle is hottest beneath the oceans because of the absence of a thick, radioactive crust, and coolest beneath Precambrian shields because of low heat flow. A self‐consistent model of the mantle requires that the thermal flux at a depth of 400 km be about 0.5 μcal/cm² sec, because geochemical evidence indicates that the K/U ratio in the upper mantle is much smaller than in chondrites. The self‐consistent model requires very high thermal conductivity at high temperatures, such as would be provided by radiative transfer or possibly by movement of material.

Petrological models of the upper mantle are constructed on the assumptions of an over‐all pyrolite (ultrabasic) composition and an eclogitic composition. Densities in the mantle are then calculated from known densities, thermal expansions, and compressibilities of minerals inferred to be present. Corrections for the effect of pressure on thermal expansion and compressibility are made from results of the theory of finite strain.

The transition zone, at depths between 400 and 1000 km, is the site of a series of major phase transformations leading to close‐packed structures with silicon in sixfold coordination. The density curve in this region is approximated by a linear increase in density with depth. The lower mantle, between 1000 and 2900 km, is considered to be homogeneous, and the density is computed from the Williamson‐Adams equation, modified in some cases to take account of a superadiabatic thermal gradient. The magnitude of the density increase in the transition zone is adjusted to satisfy the restrictions imposed by the total mass and moment of inertia of the earth. A complete density curve for the earth is given for each petrological model of the upper mantle. In constructing them it is assumed that the outer core is homogeneous and adiabatic, and that the inner core is of uniform density.

A density curve derived from the third‐order theory of finite strain is fitted to the densities calculated in the lower mantle by least squares. The density of the lower mantle at low temperature and pressure can then be calculated. The results at 20°C and atmospheric pressure are 4.2–4.3 g/cm³ for the adiabatic pyrolite model, and 4.0–4.1 g/cm³ for the adiabatic eclogite model. These values are in good agreement with estimates for the density of the lower mantle based upon recent investigations of phase transformation in olivines and pyroxenes at very high pressures. A superadiabatic gradient of 1°C/km in the lower mantle produces results inconsistent with a plausible constitution; therefore we conclude that the thermal gradient in this part of the earth is smaller than 1°C/km.

Our models imply that important differences in density persist to depths of 400 km, and it is inferred that isostatic compensation is not complete before that depth. This conclusion is consistent with gravity data, and it leads to crustal densities more plausible, in terms of observed seismic velocities, than those obtained by assuming compensation at the continental M discontinuity. Because of these deep‐seated density contrasts, the position of the present pole of rotation may well be in equilibrium with the present distribution of continents and oceans.

The relatively low temperature beneath the shields could explain their behaving like rigid blocks in Paleozoic and later orogenesis.