Download the earth`s mantle elasticity and constitution

DEC
81966
BIRC FS4 0016
(Reprinted in U. S. A. from TransMtioms of the American
GeophysicaZ Union, v. 95, pp. 79-85 and 97-98, 1954)
THE EARTH'S MANTLE
ELASTICITY AND CONSTITUTION
with further discussion by author
FRANCIS BIRCH
79
[Symposium)
THE EARTH'S MANTLE
ELASTICITY AND CONSTITUTION
Francis Birch
Abstract - - The principal facts contributing to modern ideas of the structure of the
mantle will be briefly reviewed. Particular attention will be given to the problem of a
physical interpretation of the seismic velocities and their variations with depth, following a method discussed in detail in a recent paper by the author in the Journal of Geophysical Research (Elasticity and constitution of the Earth's interior). The prir,cipal
conclusions are (1) that the mantle as a whole is not homogeneous; (2) that there may
be a reasonably homogeneous layer between the depths of 900 and 2900 km, consisting
of high - pressure phases, presumably of the composition of a ferro magnesian Silicate;
(3) that gradual changes of composition} of the proportion of high pressure phases, or
both, take place in a transitional layer oetween the depths of 200 to 900 km. Discovery
of the nature of this transitional layer is considered to be of crucial importance for dynamical geology and petrology.
The major problems of geology and geophysics lead us rather quickly to the Earth's interior,
to the problem of its present constitution and of the chemical and physical processes which account
for its activity. No doubt most of you feel, asIdo, that this is a very durable problem; we shall
have to return to it again and again, with new information and with new methods of interpretation.
But, difficult and elusive as this question is. and despite the many valuable lines of evidence provided by other sciences, it presents a scientific commitment for which geophysics is particularly
responsible . The most detailed information is derived from seismology, and it is mainly this information and its possible uses which I shall discuss. The spectacular achievements of Elsasser,
Bullard, Vestine, Runcorn, and others [see note regarding References at end of paper) in finding,
at last, a function for the Earth's central core in the production of the magnetic field and its var iations have already been presented, and I shall speak only of the mantle, so far as is possible.
Most of what I have to say has been published, but I welcome this opportunity for describing briefly
a line of approach which seems most fruitful to me, and the principal conclusions, as of the moment.
It is hardly necessary to mention that these conclusions can, and doubtless will, be questioned on
various grounds .
Until some 50 years ago, the principal sources of information about the Earth's interior were
geodesy and astronomy. The mean density and moment of inertia were known, and there were estimates of the effective rigidity based on the study of Earth tides. Since the mean density is about
5 .5, as compared with values usually less than 3 for surface rocks, and the moment of inertia is
about 1/ 3 MR2, as compared with 2/ 5 MR2 for a sphere of uniform density, it has long been clear
that there must be an increase of density toward the center; these two pieces of information just
determine such two-parameter relations between density and radius as those of Laplace and of
Roche. As calculated by Kelvin, the effective rigidity was somewhat greater than that of steel, a
result in conflict with the prevailing geological concept of his day, which was of a generally liquid
interior covered by a thin crystalline "crust."
The first calculations based on a definite physical picture of the interior seem to be those of
Wiechert, though Dana and others had earlier suggested the main features: Wiechert divided the
interior into two uniform parts, a central sphere of iron, and a shell composed of heavy silicates.
This subdivision was suggested by the most striking fact about meteorites, that they are chiefly
composed of two distinctly different materials: Silicates, and metallic iron . Iron is by far the most
abundant of the heavy elements, not only in surface rocks and meteorites, but also in the outer layers of the Sun and other stars; its existence in the meteorites as free metal is a definite suggestion
for a metallic core in the Earth . Wiechert's model has been greatly modified by later work, but,
in prinCiple, no better solution has been found for the gross chemical composition.
With the development of instrumental seismology, facts began to accumulate regarding definite
levels inside the Earth. The central core postulated by Dana and Wiechert was now discovered to
have physical reality, though its Size, as later determined by Gutenberg, was very different from
that of Wiechert's core. The division, based upon seismic observations, at the Oldham-Gutenberg
discontinuity, is the major feature of the Earth's internal structure. The outer part, the mantle,
is characterized by two distinct velocities of wave propagation, V P and V S, as shown in Figure 20;
these have been identified with the two velocities characteristic of the ideal isotropiC elastic medium. These velocities vary with depth, but throughout the mantle maintain a ratio very similar
to that in familiar materials; the quantity known as Poisson's ratio is always between about 0.27
FRANCIS BIRCH
80
VELOCITY ,
[Trans. AGU, v. 35 - 1]
and 0.30. In the core, on the other hand, a single
velocity is recognized and identified with the V P
of compressional waves; the absence of Vs or of
shear waves is the principal reason for supposing that most of the core is fluid, though this conelusion is supported by studies of Earth tides and
of the variation of latitude.
IUIIIIUC
v.
DEPTH ,
The gradual refinement of the velocity distributions, of which recent versions are shown
in the figure, made it possible to deal with a
point neglected by Wiechert: the effect of pressure in changing the density . In 1923, it was remarked by L. H. Adams and E. D. Williamson,
in the course of their classical studies of the
compressibility of rocks , that the seismic velocities could be used to obtain the change of
density with depth. Their method has been applied by Bullen, with successive recalculations
reflecting improvements of the velocities. Having the density, we can then obtain the distribution of gravity and pressure throughout the interior, as shown in Figure 21, taken from Bullen's
work.
11M •
Fig. 20--Seismic velocities in the Earth's
interior ; solid lines, after Jeffreys;
broken lines, after Gutenberg; designation of layers after Bullen
P
Me
The Adams-Williamson equation is found as
follows: The ratio of incompressibility K to
density p for an isotropic elastic body is
2
PRESSURE
2
K/ p = (dP/ dp) = Vp - 4/ 3 Vs
We suppose that the hydrostatic relation holds
with adequate approximation
dP = - gpdr
.......... -.1000 10p...----_ _ _-
where g is the acceleration at radius r . Combining these relations, we have
G
CM / SEC
g p/ (V 2 - 4/ 3 V 2)
P
S
Once we have the velocities as function of radius ,
it is possible to integrate numerically from surface to center to obtain the whole density distribution ' which must, of course, satisfy also the
conditions on mean denSity and moment of inertia.
dp/ dr
,
500
,
,,
,
DEPT H. IN 10) KM
,,
= -
,
There are two important assumptions implicit in this method: First, it is supposed that the
Fig. 21--Density, pressure, and acceleration
denSity changes only as a result of compreSSion,
within the Earth, after Bullen
with no change of intrinsic density, as by introduction of new material; second , the compression
is supposed to be adiabatic, that is, the rate of change of temperature with depth is taken to be just
the change corresponding to adiabatic compression; this follows from the use of the adiabatic incompressibility given by the seismic velocities. Since there are only two conditions upon the density distribution, we can determine at most two parameters: if we consider that there are only two
distinct uniform regions, mantle and core, in each of which the Adams-Williamson relation applies,
then the problem is just determinate. In this case, for any choice of density at the top of the mantle,
we may solve for the density jump at the boundary of the core ; this seems the natural place to have
a discontinuity of density, since it is also the locus of a discontinuity of velocity. Not all of these
solutions are acceptable, however, if indeed anyone of them is, and I would like to emphasize an
argument due to Bullen which has not been given the attention it deserves.
On Bullen's first application of the Adams-Williamson method in 1936, he began with the assumptions that the mantle was uniform in composition, and that the density at the top of the mantle
[Symposium]
THE EARTH'S MANTLE
81
was 3.32 at a depth of 33 km. A small and conventional correction was applied for the crust, which
is quite unimportant in this problem. There are several reasons for this choice of initial density:
it is close to the density of the magnesium-rich olivines which were believed to constitute the mantle, and to the mean density of the Moon, which is considered by some to be uniform, relatively uncompressed material similar to that of the Earth's mantle. However, on carrying through the computation to the boundary of the core, Bullen found that the remaining mass and moment of inertia to
be attributed to the core alone were such that the ratio I/MR2 for the core had the value 0.57. This
would mean a concentration of mass toward the outer margin of the core, since the value of this
ratio for a thin spherical shell is 2/3, and for a sphere of uniform density, 2/5. Even a uniform
density in the core is inadmissible; there must be compression, and the velocity shows a steady
increase down to the small and relatively unimportant inner core. Consequently it was necessary
to increase the moment of inertia of the mantle, and Bullen met this requirement by introducing a
discontinuous increase of density at a depth of 350 km, at which Jeffreys had introduced a discontinuous increase of velocity for independent reasons. This discontinuity was later changed to a
second-order one, that is, a discontinuity of slope, but the principal conclusion remained the same:
the mantle could not be uniform in composition, with its density determined by compression alone,
as given by the Adams-Williamson method and the velocities now accepted.
0.7,----,----,---.-------,---.-----,-----,
SHELL
"cr"
~
"
-
::~
04
UNIFORM
DENS IT 'I'
-------"'"'<;~::--------1
~
0'
0;L
, __,.L,_ _..J.,.___,L
. __,.L.__.'.7
J.__-=",.L
. _ ----::',..
DENSITY AT DEPTH OF 33 KM
It might be supposed, however, that this conclusion depends upon Bullen's choice of 3.32 for
the initial density. On repeating the calculations,
with some unimportant Simplifications, for initial
densities between 3.2 and 3.9, I find the results
plotted in Figure 22. The curve shows the ratio
I/MR2 for the core, as function of initial density
at the top of the mantle, on the assumption that
the change of density in the mantle is determined
by compreSSion alone, as given by the seismic
velocities. In order to get an acceptable solution,
the initial density would have to be about 3.7.
Allowance for a rate of rise of temperature
with depth greater than the adiabatic gradient
increases the required initial density still further.
Fig. 22--Moment of inertia of the central core,
Now we do not lmow the density below the
as function of density at the top of a uniform crust, but there are reasons for thinking that
mantle; I c ' Mc ' and Hc are the moment of inertia, 3.7 is too high. The seismic velocities just bemass, and radius of the core, respectively
low the crust are about 8.0 to 8.2, and 4.5 to 4.6
km/ sec. Such velocities exclude an olivine rock of density 3.7, whit!h would necessarily be ironrich; a rock containing a large fraction of garnets, such as eclogite, would be a possibility, but
this choice would commit us to an entire mantle of eclogite, which seems improbable in terms of
chemical abundances. It seems highly probable, therefore, that Bullen's conclusion remains valid,
even though we may wish to modify somewhat his original choice of initial density.
Thus we have to face the following question: If the density in the mantle is not determined by
compression alone (with an appropriate correction for temperature effects, if required), what are
the alternatives? There appear to be three: Somewhere in the mantle there must be either (1) a
change of composition, involving a change of intrinsic density; or (2) a change to phases of higher
density, or (3) changes of both of these kinds. A phase change of olivine from its familiar orthorhombic symmetry to a cubiC, spinel structure has been suggested by Bernal and Jeffreys: this
seemed particularly appropriate when it was believed that there was a first-order discontinuity of
velocity at about 400 km. But this has now become at most a second-order discontinuity, and there
are reasons, which I wish now to discuss, for thinking that the required abnormal density increase
is not localized at a single level, but spread over a thick zone.
In principle, at any rate, we may approach this question by setting up an equation giving the
rate of change of velocity or of compressibility in an ideal uniform layer, and comparing this with
the observations. I have taken the quantity K/ p, or .p for short, the ratio of adiabatic incompressibility to density, which is given by the velocity distribution. With the usual assumptions of reversibility of changes of pressure and temperature, it is possible to obtain a relation between the
rate of change of .p with depth in this ideal uniform layer and various parameters of the material,
and this rate of change can be compared with the observed rate of change. The theoretical relation
has been developed for an arbitrary temperature gradient, so that, again in principle, it is possible
to estimate the effect of departure from the adiabatic temperature distribution. The rate of variation of .p with depth in the ideal uniform layer is given in terms of certain dimensionless parameters
FRANCIS BIRCH
82
[Trans . AGU, v. 35 - 1]
of the material, involving chiefly the rate of change of incompressibility with pressure, but also
thermal expansion, specific heat, and their temperature and pressure coefficients. The usefulness of this procedure depends , of course, upon the possibility of estimating these parameters for
a material known only through its seismic velocities.
The examination of these coefficients leads us to a review of the theory of solids and of the
extensive results of high-pressure investigation; ~ can give only the barest summary. One of the
first Points to examine is the characteristic temperature, a concept of fundamental importance in
the theory of solids. This temperature plays an important part in the Oebye theory of specific
heat~ roughly, it separates the classical, or high-temperature, region from the quantum-mechanical, or low-temperature, region. It is related to the vibrational frequencies of the crystalline
lattice, which, in turn, depend upon the velocities of the elastic waves. From these velocities,
with an assumption concerning the mean atomic weight of the material of the mantle which cannot
be far wrong, we can obtain the Oebye temperatures as function of depth in the mantle. These
temperatures are everywhere lower than what seem to be minimum estimates of the temperatures ;
even at the base of the mantle, the Oebye temperature is only about 1000° C. Thus it appears that
we have to do with high-temperature properties, in spite of the marked increase of characteristic
temperature produced by the high pressures of the interior. This means that we are especially
interested in measurements on materials above their Oebye temperatures ; or since most of the
measurements have been made at ordinary temperature, in materials having low Oebye temperatures, such as the alkali metals, the more compressible alkali halides, and the like. Let us notice
also that the Oebye theory of specific heats is based on the idea of corresponding states, or a universal reduced curve of specific heat versus temperature. The difference between materials depends upon the value of a single parameter, the characteristic temperature. This relatively simple theory is successful for a great variety of materials.
We have next to see whether there is any way of getting around the obvious difficulty that our
experiments do not reach suffiCiently high pressures to permit direct investigations with likely
materials. The laboratory pressures are by no means negligible, even on the planetary scale;
Bridgman has measured the change of volume of a large number of materials to pressures as high
as 100,000 bars; this is roughly the pressure at a depth of 300 km in the Earth, or the central
pressure of the planet Mercury, or twice the central pressure of the Moon . What is even more
significant is that many of these materials have been compressed by ratios greater than the compression at the base of the mantle, which is about 1.4; this is the ratio of compressed to uncompressed density. These large compressions show that there is a close approach to a common law
of compression for a wide variety of elements and compounds. Figure 23 shows the measurements
for the most compressible solids, the alkali metals, several of which have been compressed to
twice their initial densities. The pressures
have been reduced by dividing, in each case, by
the appropriate initial incompressibility, Ko
,. ·05
(strictly, by (3/ 2}Kol; this is the only adjustable
/
,·0
2.
2P
2P
3K
3K.
1. 5
~ ·o
5
1.0
0.15
01
• LITHIUM
o
• SOOlUN
• POTASSIUM
o RlI8IOIUM
01.0
1.5
P/ P.
2.0
Fig. 23--Compression of the alkali metals;
experimental points, after Bridgman; the
smooth curves are theoretica\.o with several values of the parameter «;
900'.
!
~.~00;----ol10"5----'-;I+';'0;-----!1.I"5-",-y,,-L-~1.2",0----l
Fig. 24--Compression of several compounds;
experimental pOints, after Bridgman; theoretical curves as in Figure 23
THE EARTH'S MANTLE
[Symposium]
83
parameter. The five metals follow the same reduced law of com~ression, whose theoretical expression is given by the solid curve marked ~ = O. The quantity I; is a second adjustable parameter, not necessarily zero, though evidently it cannot be large for the alkali metals; the theoretical
curves for ~ = 1/ 2 and -172 are also plotted. Figure 24 shows a similar plot for several ionic
compounds, on an enlarged scale; here it appears that for NaCI, the parameter ~ is nearly -1;
while for AgCI and CsI a small or zero value is adequate. These compounds also are of very different compressibilities: CsI is compressed as much at 30,000 bars as is AgCI at 90,000. Nevertheless, the experimental values show a strong similarity when reduced in this way. The compressions in the mantle, if considered uniform, at depths of 400 km and 900 km are indicated at
the bottom of the figure. A great many compounds have been studied by Bridgman to higher compressions than these values. Most of the results, except for the very numerous cases where polymorphic transitions occur, can be represented within the experimental uncertainty by curves of
the type shown here, with the parameter ~ seldom greater in absolute value than about 1/ 2. Thus
we have an indication of what we may take to be the normal value of the parameter dK/ dP, which
is the principal factor governing the rate of variation of rp in a uniform layer. If ~ = 0, dK/ dP=4
at zero pressure, and gradually decreases toward about 3 for the compressions at the base of the
mantle. If ~ = -1/ 2, dK/ dP is 4.7 at zero pressure, and gradually decreases toward about 3.5 at
the base of the mantle.
I.O. . - - - - - - - - - - - r - - - -- -, - - - - - - - - - , -- - - - - - - ,
o LITHIUM
• SODIUM
•
POTASSIUM
0.5
1-4P/K
BASE OF MANTLE
01.0
0 .9
0 .8
0 .7
V/V.
0.6
Fig. 25--Thermal expansion of the alkali metals as function
of compression; experimental values after Bridgman
Another indication that the compression rather than the pressure is the most important variable
for determining the high-pressure properties of solids is shown in Figure 25, where I have plotted
the thermal expansion, relative to the zero-pressure value, versus compression for three alkali
metals. These difficult measurements, by Bridgman, were carried to 20,000 bars in all three
cases. The thermal expansion decreases by very appreciable fractions as the metals are compressed, but the results for all three metals are probably consistent with a single law of variation.
We now proceed to a comparison of the seismiC values for the variation of rp with the theor~
ical curve for an isothermal uniform medium at a moderate temperature; the theoretical curve iE
plotted for ~ = 0 (Fig. 26). The open circles are derived from Jeffreys' 1939 velocities, the solid
dots from Gutenberg's 1948 velocities. This comparison is the basis for several conclusions:
First, we can now identify the region which departs from uniformity as lying between about 300
and 900 km, where the deviations from the theoretical curve are most extreme; second, below
about 900 km, though there is some scatter, the seismic values are everywhere close to the theoretical curve. Not much can be said at present about the region shallower than some 300 km;
there are still some differences of interpretation which affect the velocities. It is possible, however, that this region is nearly uniform.
This approach furnishes independent support for Bullen's conclusion with respect to the departure from uniformity of the mantle as a whole, and it furnishes additional details. We may now
replace the former assumption of uniformity for the deeper part of the mantle with something resembling a demonstration of uniformity. The small discontinuity of velocity formerly placed at
400 km or so now appears as a part of a much larger abnormal increase of velocity, extending
over a depth of 500 or 600 km . From the close agreement between observed and theoretical values
in the lower part of the mantle, we obtain a rough indication that the temperature is not exceSSively
high, perhaps not more than about 4000° C. On the other hand, some may prefer to believe that the
appearance of uniformity arises from a set of compensating factors, such as changes of temperature just offsetting changes of composition; we have no way of demonstrating that this is impossible,
however unlikely it may seem.
FRANCIS BIRCH
84
[Trans. AGU, v. 35 - 1]
10
~
KII , IN (KM/SEC)'
.
B
10C
.
. ..
/0:6
~
~
5C
0
0.31
.'
~.~;::
o
2
DEPTH .IN 10' KM
o
1 2 3
Fig. 26--The function, 1 - g-1 t:.cpl t:.r, for the
mantle, versus depth; the circles are obtained from the seismic velocities; open
circles, after Jeffreys; solid circles, after
Gutenberg; the smooth curve is the theoretical value of (dK/ dP), for ~ = 0
I
2
3
Fig. 27--The variation of K/p, (K/p)o' and
Poisson's ratio (T, in the mantle; the solid
curve at the top gives Kip formed from
Jeffreys' seismic velocities; the dashed
curve from Gutenberg's velocities; the
open circles show (K/p)o (the value at zero
pressure) derived from the observed K/ p
at the corresponding depth; the lowermost
curve shows (T, after Jeffreys
Accepting these results as indicating uniformity of the deeper mantle, we can draw some
further consequences regarding the properties
of this material. A point-by-point calculation
leads from the observed values of K/p, plotted
as a solid curve in Figure 27, to the zero-pressure values of K/p, plotted as circles. Thesevalues
are closely the same below 900 km, since this is another test of uniformity, and give for this ratio
at zero pressure the value 51 (km/sec)2. This figure also shows the curve of Poisson's ratio. The
reversal of trend between 400 and 900 km seems to support the conclusion already reached on other
evidence concerning the departure from uniformity in this region. Let us now examine the zeropressure values of K/p for some familiar materials (Table 3). The experimental values are all 2
for ordinary temperature; the comparable value for the deep mantle might be close to 60 (km/sec)
The values for the common silicates are much lower than this; the olivines are far too low. There
appears to be no known material with a plausible composition which has also the required value for
this ratio.
Table 3--Properties at one atmosphere
Material
Corundum
Beryl
Rutile
Periclase
Garnets
Jadeite
Forsterite
Anorthite
. Fayalite
Iron
Albite
Quartz
Density
Po
4
2.8
4.2
3.6
3.5-4.2
3.3
3.3
2.8
4.1
7·.9
2.6
2.7
(km/ sec) 2
69
67
50
47
40-45
39
36
33
26
21
20
14
We are thus brought back to the idea of highpressure modifications, of which so many have
been discovered by Bridgman. The hypothetical
spinel form of olivine has been mentioned; its
properties are still unknown. There is no convincing reason for supposing that the whole mantle has the composition of olivine, however; if
we are to be guided by the che'm ical composition
of the stony meteorites, we should take roughly
equal parts of olivine and pyroxene. More generally, we probably ought to think of a system
with at least three major components, say MgO,
FeO, and Si0 2 , with the possibility of forming,
at high pressure, compounds or structures with
quite different properties from the known representatives of this system. Since corundum, periclase, and rutile do possess elastic properties
of about the right magnitude, it is atleast plausible
[Symposium]
THE EARTH'S MANTLE
85
that there may be phases in the magnesia - iron oxide - silica system with the required properties.
Here we encounter a most promising area for both theoretical and experimental chemical physics,
or high-pressure mineralogy, which evidently needs further study.
IT this deep layer below 900 km is uniform in compOSition and phase, as these considerations
suggest, how might it have reached such a condition? There are at least two possibilities: It
might haVe been unifor.m initially, and stayed uniform, differentiation having affected only the
shallower levels; or it may be a uniform product of a process of differentiation which has affected
the whole mantle. For several reasons, all inconclusive, I incline toward the second alternative,
but I shall not attempt to go further into this question at present.
With high :pressure phases required for the deeper part of the mantle, the region between
about 300 and 800 km is most naturally interpreted as transitional between the region of familiar,
low-pressure phases, just below the crust, and the deep region where the transformation to highpressure phases has become complete. The present analysis indicates that chemical change alone
is not adequate to explain the properties of the deeper part of the mantle, but chemical change in
the transitional layer can evidently not be excluded, and almost any theory of the transitional layer
seems to lead to a compositional gradient in this region. It seems most likely to me that we shall
have to face the complex problem of a multicomponent system with pressure, temperature, and
compositional gradients, as well as high-pressure phases.
There are additional reasons for looking upon the region in which this transitional layer has
been found as the seat of important geophysical or geochemical processes. Earthquakes originate
as far down as 700 km, deep in the transitional layer ; it seems natural to associate these deep
shocks with the postulated phase changes, and to predict that about 800 km will prove to be the
upper limit of focal depth. It is perhaps more than a coincidence that the rate of cooling by conduction to the surface is expected to be most rapid at present between about 400 and 600 km. The
formation of denser phases may be dependent upon such cooling, with the result that the amount of
contraction available for "shortening the crust" may be appreciably greater than is usually estimated in terms of the classical thermal contraction process. Deep-seated fracturing associated
with these density changes, and expressed as deep-focus shocks, may provide a mechanism for the
extrusion of material from deep to shallow levels. These are all no more than suggestions ; they
require more serious examination, but they indicate a few of the possible implications of this conception of the structure of the mantle. In my opinion, the transitional layer is the key to the problem of what is going on in the mantle; when we understand its nature, we shall be well on the way
to a grasp of the dynamics of the Earth's interior.
References
For additional details and complete bibliography, see J. Geophys. Res., v. 57, pp. 227-286;
1952 ; also Bull. Geol. Soc. Amer., v. 64, pp. 601-602, 1953 .
Dunbar Laboratory,
Harvard University,
Cambridge 38, Massachusetts
(Manuscript received May 20, 1953; presented at the Thirty-Fourth Annual Meeting,
Washington, D. C., May 5, 1953; open for formal discussion until July 1,1954.)
PETROLOGICAL EVIDENCE ON TEMPERATURE DISTRIBUTION
IN THE MANTLE OF THE EARTH
[Symposium]
THE EARTH'S MANTLE
97
DISCUSSION
Francis Birch (Harvard University, Cambridge 38, Mass.)--Let me remind you again that the
conclusion that the mantle is not homogeneous in both phase and composition does not depend upon
a particular equation of state, but, as explained above, upon the assumptions that (1) the seismic
velocities are approximately correct, (2) the ratio I/MR2 for the core cannot exceed 0.4, and (3)
the density at the top of the mantle is less than 3.7. If these very plausible assumptions are accepted, then we must conclude that the mantle departs from homogeneity, and the next question is
to find where it does so and why . The analysis employing an equation of state is directed to this
second objective, not to the basic question of homogeneity which has already been decided by
Bullen's method.
It now appears likely that the flow of heat to the surface is about the same in continents and
oceans; following Bullard, we may explain this by supposing that the total radioactive content per
unit of surface is everywhere roughly the same. But the relatively high concentration of radioactivity in typically continental rocks is, at least qualitatively, one of the best-established geochemical facts. Thus we are led to the conclusion that the radioactive content of the suboceanic rocks is
greater than that of the rocks below the Mohorovicic discontinuity below the continents. Such a
horizontal difference is inconsistent with the movements of material postulated by convectionists.
Alternatively, if convection is invoked to account for the oceanic heat flow, then the rough equality
with continental heat flow and the absence of thermal anomalies on a scale corresponding with cell
dimensions require fut;ther explanation. The measurements of heat flow at sea, as they now stand,
seem to me to constitute our most definite evidence against convection currents affecting the shallow levels of the mantle.