Dependence of compressibility and compression on chemical composition in finite-strain theory

Physics

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Scientific paper

Although Birch's adaptation of finite-strain theory leads to estimates of the incompressibility k at depth in the Earth which agree to a fair first approximation with results inferred by the writer using, inter alia, data from seismology, the agreement is by no means complete. This applies especially in the vicinity of the mantle-core boundary and in the lower part of the outer core. The present paper is a first step toward exploring the possibility of removing the discrepancies in the two approaches, and so leading to finer knowledge of the distribution of k inside the Earth. Most of the work here reported is formal and consists of deductive inferences from the finite-strain theory and numerical calculations connected with the effect of increasing pressure on the ratios of the values, k1 and k2 say, of k for any pair of materials of different chemical composition. This work is a necessary preliminary to assessing the reliability of Birch's approach. The results are considered in relation to questions of compressibility and composition in the vicinity of the mantle-core boundary and to the question of rigidity in the inner core. In the course of the work, a remarkably simple approximate formula energed, (14) below, through which the ratio k1/k2 for any two materials in the Earth at a given pressure p can be rapidly estimated knowing p and the values of k1 and k2 at zero pressure.

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