Elasticity and Constitution of the Earth's Interior

  1. Thomas J. Shankland and
  2. Jay D. Bass
  1. Francis Birch

Published Online: 21 MAR 2013

DOI: 10.1029/SP026p0031

Elastic Properties and Equations of State

Elastic Properties and Equations of State

How to Cite

Birch, F. (1988) Elasticity and Constitution of the Earth's Interior, in Elastic Properties and Equations of State (eds T. J. Shankland and J. D. Bass), American Geophysical Union, Washington, D. C.. doi: 10.1029/SP026p0031

Author Information

  1. Harvard University, Cambridge, Massachusetts

Publication History

  1. Published Online: 21 MAR 2013
  2. Published Print: 1 JAN 1988

ISBN Information

Print ISBN: 9780875902401

Online ISBN: 9781118664971



  • Alkali metals;
  • Earth's interior;
  • Homogeneous layer;
  • Internal layers;
  • Isothermal and adiabatic compressibilities;
  • Murnaghan's theory;
  • Thermal expansion and Gru̇neisen's ratio;
  • Thermodynamic relations


The observed variation of the seismic velocities with depth, below the crust, is examinedwith reference to the variation to be expected in a homogeneous medium. A general equation is derived for the variation of the quantity, $$/phi = V_P2 – 4/3 V_S2 $$, 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 $$(/partial K_{T} //partial P)_T $$, 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.