The composition of the Earth

Preliminary reference earth model

Geophysical, petrological, and geochemical data provide important clues about the composition of the deep continental crust. On the basis of seismic refraction data, we divide the crust into type sections associated with different tectonic provinces. Each shows a three-layer crust consisting of upper, middle, and lower crust, in which P wave velocities increase progressively with depth. There is large variation in average P wave velocity of the lower crust between different type sections, but in general, lower crustal velocities are high (>6.9 km s−1) and average middle crustal velocities range between 6.3 and 6.7 km s−1. Heat-producing elements decrease with depth in the crust owing to their depletion in felsic rocks caused by granulite facies metamorphism and an increase in the proportion of mafic rocks with depth. Studies of crustal cross sections show that in Archean regions, 50–85% of the heat flowing from the surface of the Earth is generated within the crust. Granulite terrains that experienced isobaric cooling are representative of middle or lower crust and have higher proportions of mafic rocks than do granulite terrains that experienced isothermal decompression. The latter are probably not representative of the deep crust but are merely upper crustal rocks that have been through an orogenic cycle. Granulite xenoliths provide some of the deepest samples of the continental crust and are composed largely of mafic rock types. Ultrasonic velocity measurements for a wide variety of deep crustal rocks provide a link between crustal velocity and lithology. Meta-igneous felsic, intermediate and mafic granulite, and amphibolite facies rocks are distinguishable on the basis of P and S wave velocities, but metamorphosed shales (metapelites) have velocities that overlap the complete velocity range displayed by the meta-igneous lithologies. The high heat production of metapelites, coupled with their generally limited volumetric extent in granulite terrains and xenoliths, suggests they constitute only a small proportion of the lower crust. Using average P wave velocities derived from the crustal type sections, the estimated areal extent of each type of crust, and the average compositions of different types of granulites, we estimate the average lower and middle crust composition. The lower crust is composed of rocks in the granulite facies and is lithologically heterogeneous. Its average composition is mafic, approaching that of a primitive mantle-derived basalt, but it may range to intermediate bulk compositions in some regions. The middle crust is composed of rocks in the amphibolite facies and is intermediate in bulk composition, containing significant K, Th, and U contents. Average continental crust is intermediate in composition and contains a significant proportion of the bulk silicate Earth's incompatible trace element budget (35–55% of Rb, Ba, K, Pb, Th, and U).

Nature and composition of the continental crust: A lower crustal perspective

RECENTLY, Birch1 reported data on the density and composition of the mantle and core. He wrote: “The resulting densities in the lower mantle are found to be in good agreement with shock-wave measurements on rocks having FeO contents in the range 10 ± 2% by weight … except for iron oxide, the chemical composition of the mantle is indeterminate. The density of the outer core is lower than that of iron by about 10%”.

Composition of the Earth

Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

Murnaghan's theory of finite strain is developed for a medium of cubic symmetry subjected to finite hydrostatic compression, plus an arbitrary homogeneous infinitesimal strain. The free energy is developed for cubic symmetry to include terms of the third order in the strain components. The effect of pressure upon the second-order elastic constants is found and compared with experiment, with particular reference to the compressibility; the pressure-volume relation in several approximations is compared with the measurements to 100,000 kg/${\mathrm{cm}}^{2}$. The simplest approximation is shown to give a satisfactory account of most of the experimental data. The results are also compared with some of the calculations based on Born's lattice theory.

Finite Elastic Strain of Cubic Crystals

Ultrasonic, pressure-volume, and shock wave measurements of NaCl are reviewed, with the purpose of representing as much as possible within a single theoretical framework, A large portion of the data is consistent, to within reasonable uncertainties, with the Eulerian formulation of finite strain, in the BE2 form. This contains three parameters, of which two, K0 and K0′, are obtainable from single-crystal ultrasonic measurements, while the third, K0″, may be found with the aid of shock wave data. The combination of the values of Spetzler et al. (1972a) with the isotherm of Fritz et al. (1971) gives an equation of state consistent with the pressure-volume measurements to 300 kbar, to within a kilobar or two. There remain small but possibly significant discrepancies with the high-precision measurements of linear change at low pressures. Various two-parameter isotherms are also examined and found to fail either at low or at high compressions: While other three-parameter forms may be fitted to the data, they do not afford a satisfactory general treatment of wave propagation. Finite strain theory is applied to project the effective elastic coefficients of single-crystal NaCl to 270 kbar. The anisotropy index, 2B44(B11–B12), falls from 0.7 at P = 0 to 0.12 at 270 kbar, and the usual methods of averaging to find the properties of a quasi-isotropic aggregate diverge increasingly as pressure increases. The methods of Kroner and of Peresada give fair agreement with recent measurements of velocities in NaCl aggregates to 270 kbar.

Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300°K

The velocity of compressional waves has been determined by measurement of travel time of pulses in specimens of rock at pressures to 10 kilobars and room temperature. Most of the samples, mainly igneous and metamorphic rocks, furnished three specimens oriented at right angles to one another. The present paper gives experimental details, modal analyses, and numerical tables of velocity as function of direction of propagation, initial density, and pressure. Discussion of various aspects of the measurements is reserved for part 2.

The velocity of compressional waves in rocks to 10 kilobars: 1.

The observed variation of the seismic velocities with depth, below the crust, is examined with reference to the variation to be expected in a homogeneous medium. A general equation is derived for the variation of the quantity, , in a homogeneous gravitating layer with an arbitrary gradient of temperature. The parameters of this equation are then discussed in terms of the experimental and theoretical relations for solids. The principal parameter is (∂KT/∂P)T, the rate of change of isothermal incompressibility with pressure, which can be found for large compressions from Bridgman's measurements. Comparison of observed and expected rates of variation of ϕ throughout the Earth's interior leads to conclusions regarding homogeneity and, with a larger uncertainty, to estimates of temperature.

A shadow zone at a depth of about 100 km, as suggested by Gutenberg, may be accounted for by a gradient of temperature of about 6°/km in a homogeneous layer of ultrabasic rock. Between depths of about 900 and 2,900 km, the mantle appears to be substantially uniform, and at a relatively uniform temperature of the order of several thousand degrees. Between about 200 and 900 km, the rate of rise of velocity is too great for a homogeneous layer, and indicates a gradual change of composition, or of phase, or both. New phases are required to account for the high elasticity of the deeper part of the mantle (below 900 km), and it is suggested that, beginning at about 200 to 300 km, there is a gradual shift toward high-pressure modifications of the ferro-magnesian silicates, probably close-packed oxides, with the transition complete at about 800 to 900 km. There may also be a concentration of alumina, lime, and alkalis toward the upper part of the mantle, in and above the transitional layer but below the crust, existing in minerals of high elasticity such as garnets and jadeites. The transitional layer appears to hold the key to a number of major geophysical problems.

The velocities in the core and inner core are also reviewed. The inner core is most simply interpreted as crystalline iron, the outer part as liquid iron, perhaps alloyed with a small fraction of lighter elements. The density and compressibility of iron at high pressures are estimated with the aid of the experimental compressions of the alkali metals; the central density is found to be about 15. Several other recent proposals regarding the crust are discussed.

Elasticity and constitution of the Earth's interior

Two new density distributions are obtained, closely related to the seismic velocities. In the upper mantle and transition layer, density is assumed to be proportional to the velocity of compressional waves, with ratios consistent with experimental studies of rocks. In the lower mantle and core, the density variation is found by the Adams-Williamson method. The resulting densities in the lower mantle are found to be in good agreement with shock-wave measurements on rocks having FeO contents in the range 10±2% by weight, and may be accounted for in terms of mixtures of close-packed oxides, silica transforming to stishovite in the transition layer. Except for iron oxide, the chemical composition of the mantle is indeterminate. The density of the outer core is lower than that of iron by about 10%. The estimated density of the inner core, based on shock-wave measurements of metals and considerations of abundance, is no higher than 13.5 g/cm3.

Francis Birch

Papers

Finite Elastic Strain of Cubic Crystals

Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300°K

The velocity of compressional waves in rocks to 10 kilobars: 1.

Elasticity and constitution of the Earth's interior

Density and composition of mantle and core