Structure of the Earth’s interior

The question of the solution s existence is associated with the mathematical formulation of the inverse problem. From the physical point of view, there should be some certain solution, since we study real geological structures of the earth s interior. However, from the mathematical point of view, there could be no adequate numerical model from the given model set which would fit our observed data. 

Considerable interest centres on the Mantle constituting, as it does, more than half of the Earth by volume and by weight. Attention has been focussed on several problems, including the chemical composition, mineralogy, phase transitions and element partitioning in the Mantle, and the geophysical properties of seismicity, heat transfer by radiation, electrical conductivity and magnetism in the Earth. Many of these properties of the Earth s interior are influenced by the electronic structures of transition metal ions in Mantle minerals at elevated temperatures and pressures. Such effects are amenable to interpretation by crystal field theory based on optical spectral data for minerals measured at elevated temperatures and pressures. 

Liu, L.-G. Bassett, W. A. (1986) Chemical and mineral composition of the Earth s interior. In Elements, Oxides, and Silicates. (Oxford Univ. Press), pp. 234—44. Sherman, D. M. (1988) High-spin to low-spin transition of iron(II) oxides at high pressures possible effects on the physics and chemistry of the Lower Mantle. In Structural and Magnetic Phase Transitions in Minerals. (S. Ghose, J. M. D. 

Matsui, Y., and K. Kawamura (1984). Computer simulation of structures of silicate melts and glasses. In Materials Science of the Earth s Interior (I. Sunagawa, ed.) Tokyo Terra, pp. 3-23. 

The major aim of mantle geochemistry has been, from the beginning, to elucidate the structure and evolution of the Earth s interior, and it was clear that this can only be done in concert with observations and ideas derived from conventional field geology and from geophysics. The discussion here will concentrate on the chemical structure of the recent mantle, because the early mantle evolution and dynamics and history of convective mixing are treated in Chapters 2.12 and 2.13. 

The impact of computers on high-pressure theoretical studies may be compared with that of synchrotron facilities on high-pressure experimental studies. Steady improvements in computational methods have enabled calculations of structure, stability, and elastic properties of simple systems under pressures and temperatures of the Earth s interior (e.g., Stixrude and Brown, 1998 Boness and Brown, 1990 Sherman, 1995, 1997 Steinle-Neumann and Stixrude, 1999 ... 

Yagi T. (1995) Formation of iron hydrides under the condition of the Earth s interior-implication for the core formation process. In The Earth s Central Part Its Structure and Dynamics (ed. T. Yukutake). Terra Scientific Publishing Company, Tokyo, pp. 13-28. 

F. Marumo and M. Okuno, X-ray structural studies of molten silicates Anorthite and albite melts, in Material Science of the Earth s Interior (ed. I. Sunagawa), Terra Scientific Pub. Tokyo, pp. 25-38 (1984). 

Allegre CJ, Staudacher T, Sarda P (1986) Rare gas systematics formation of the atmosphere, evolution and structure of the Earth s mantle. Earth Planet Sci Lett 87 127-150 Allegre CJ, Sarda P, Staudacher T (1993) Speculations about the cosmic origin of He and Ne in the interior of the Earth. Earth Planet Sci Lett 117 229-233... 

Figure 2. The nature of the statistical meehanical problem in the ease of a ciystalline solid. Uppermost is a representation of a perfect one-dimensional monatomie lattiee as would exist imder static conditions. Immediately beneath is an illustration of the effeet of temperature atoms no longer occupy their ideal lattice sites and the symmetry of the strueture at any instant is completely broken. The lowermost graph shows how the energy of the structure depends on the displacement of an atom the dependence is quadratic to first order, but higher order (anharmonie) terms may be important at conditions typicd of the Earth s interior.

The planets nearest the Sun have a high-temperature surface while those further away have a low temperature. The temperature depends on the closeness to the Sun, but it also depends on the chemical composition and zone structures of the individual planets and their sizes. In this respect Earth is a somewhat peculiar planet, we do not know whether it is unique or not in that its core has remained very hot, mainly due to gravitic compression and radioactive decay of some unstable isotopes, and loss of core heat has been restricted by a poorly conducting mainly oxide mantle. This heat still contributes very considerably to the overall temperature of the Earth s surface. The hot core, some of it solid, is composed of metals, mainly iron, while the mantle is largely of molten oxidic rocks until the thin surface of solid rocks of many different compositions, such as silicates, sulfides and carbonates, occurs. This is usually called the crust, below the oceans, and forms the continents of today. Water and the atmosphere are reached in further outward succession. We shall describe the relevant chemistry in more detail later here, we are concerned first with the temperature gradient from the interior to the surface (Figure 1.2). The Earth s surface, i.e. the crust, the sea and the atmosphere, is of... 

Chapter 5 summarizes the crystal field spectra of transition metal ions in common rock-forming minerals and important structure-types that may occur in the Earth s interior. Peak positions and crystal field parameters for the cations in several mineral groups are tabulated. The spectra of ferromagnesian silicates are described in detail and correlated with the symmetries and distortions of the Fe2+ coordination environments in the crystal structures. Estimates are made of the CFSE s provided by each coordination site accommodating the Fe2+ ions. Crystal field splitting parameters and stabilization energies for each of the transition metal ions, which are derived from visible to near-infrared spectra of oxides and silicates, are also tabulated. The CFSE data are used in later chapters to explain the crystal chemistry, thermodynamic properties and geochemical distributions of the first-series transition elements. 

In addition to the contributions to understanding the Earth s interior from geophysical evidence and the geochemistry of solar system materials, and from very high-pressure experiments, an important contribution comes from attempts to calculate the effects of pressure on crystal and electronic structures of appropriate materials using quantum-mechanical methods. Some examples of this approach will now be considered, with reference to the phases thought likely to dominate the interior of the Earth. 

The topography and structure of the ocean floor are highly variable from place to place and reflect tectonic processes within the Earth s interior. These major features are shown in Fig. 9-1. These features have varied in the past so that the ocean bottom of today is undoubtedly not like the ocean bottom of 50 Ma ago. The major topographic systems, common to all oceans, are the continental margins, the ocean-basin floors, and the oceanic ridge systems. Tectonic features such as fracture zones, plateaus, trenches, and mid-ocean ridges act to subdivide the main oceans into a larger number of smaller basins. 

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