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Volume 67, 1938
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Note on the Density and Pressure Inside the Earth

[Read before the Auckland Institute, April 21, 1937; received by the Editor, May 5, 1937; issued separately, September, 1937.]

The writer recently (1936) carried out an investigation of the variation of density and pressure within the earth. Since the publication of results, however, there have been certain significant improvements to the data used, and it has become desirable to recalculate the figures previously obtained. As was anticipated in the previous paper, the corrections lead to no general disturbance of the former results, but merely to improved numerical values. In particular, the evidence for an appreciable density increase at the new discontinuity remains.

The most important of the improvements to the data is concerned with Jeffreys's more exact determination (1936) of the depth of the new discontinuity within the earth as 481 ± 21 km., instead of 350 km. as previously taken by the writer. The second improvement is the use of more recent values of the velocities of P and S seismic waves in the earth's interior. These include the results of Jeffreys down to a depth of 800 km. and the latest results of Gutenberg and Richter (1935) at greater depths. The latter differ from those previously used chiefly in involving a greater range of variation of velocity within the earth's central core. In addition, the depth of the boundary of the central core has been taken as 2920 km. in conformity with the results of Gutenberg and Richter, while the thickness of the granitic and “intermediate” layers have been taken as 14 and 28 km., in order to be consistent with Jeffreys's investigation.

The recalculation of the density and pressure has been carried out exactly after the manner described in the previous paper. In the absence of precise knowledge of the temperature variation at considerable depths below the earth's surface, no allowance has been made for the possible influence of this factor. Its effect would be to reduce slightly the rate of increase of density with depth in any particular layer, but the consequent alterations to the following figures would be very small.

The new figures for the density ρ (in grm./cm.3) and the pressure p (in dynes/cm.2) at various depths d km. below the earth's surface are as follows:—

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[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

d p p×10−12
42 3.32 0.011
100 3.37 0.030
200 3.46 0.064
300 3.55 0.099
400 3.63 0.134
481 3.69
4.23 0.164
500 4.25 0.172
600 4.32 0.215
800 4.45 0.302
1000 4.57 0.391
1200 4.69 0.481
1400 4.80 0.575
1600 4.91 0.669
1800 5.01 0.767
2000 5.12 0.866
2200 5.21 0.968
2400 5.31 1.072
2600 5.40 1.179
2800 5.50 1.290
2920 5.56
9.69 1.359
3000 9.82 1.44
3200 10.13 1.64
3400 10.41 1.84
3600 10.66 2.03
3800 10.89 2.22
4000 11.10 2.39
4200 11.30 2.56
4400 11.47 2.73
4600 11.62 2.87
4800 11.75 3.00
5000 11.86 3.12
5200 11.95 3.22
5400 12.02 3.31
5600 12.08 3.38
5800 12.13 3.44
6000 12.15 3.48
6200 12.17 3.50
6371 12.17 3.51

The values of the ellipticities of internal strata of equal density as calculated in the earlier paper are not affected by the changes by more than 0.00001 down to depth of 2600 km. Inside the central core the values are slightly lower than those found previously, varying from 0.00258 at the boundary to 0.00250 at the centre.

The mean density, mass, and moment of inertia of the earth's central core are now 10.76, 185.3 × 1025 grm., and 8.58 × 1043 grm. cm.2, respectively. The mean density of the shell is 4.49.

It is of interest to refer to the relation between density and pressure of the material of the earth's central core. This is indicated in the accompanying diagram, in which the dotted part of the curve corresponds to an extrapolation for pressures less than that at the core's boundary. Although the extrapolation is liable to some uncertainty, it appears that at zero pressure the density would probably be fairly near 7.0. Recent investigations give the density of molten iron at its melting point at 6.92 ± 0.07. Although temperature effects have of course been ignored, the diagram appears to support reasonably well the suggestion made in the earlier paper that the earth's core consists very largely of iron without appreciable quantities of heavier metal.

References.

Bullen, K. E., 1936. The Variation of Density and the Ellipticities of Strata of Equal Density within the Earth, M.N.R.A.S., Geophysical Supplement, vol. 3, no. 9, pp. 395–401.

Gutenberg, B., and Righter, C. F., 1935. On Seismic Waves (Second Paper), Gerlands Beiträge zur Geophysik, vol. 45, pp. 280–360.

Jeffreys, H., 1936. The Structure of the Earth down to the 20° Discontinuity, M.N.R.A.S., Geophysical Supplement, vol. 3, no. 9, pp. 401–422.

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Graph of the relation between the density and pressure of the material of the Earth's central core.