The Flow of Heat through the Floor of the Atlantic
Ocean
E. C. Bullard and A. Day
..
“In his master’s steps he trod .
Heat was in the very sod”-Traditional
Summary
Fifteen measurements of the heat flow through the ocean floor
have been made in the Atlantic and one in the Mediterranean. One
measurement in the central valley of the Mid-Atlantic Ridge gives a
heat flow of 6.5 pcal/cmZs. Similar very high values have been found
by others on the crest of the East Pacific Rise. The possibility that these
high values represent the rising limb of a convection current is discussed. The mean of the remaining fifteen values and of five from a
previous investigation, give a mean heat flow of I -06& 0.055 pcal/cm2 s
which is very close to the mean for all measurements in the Pacific
excluding those on the East Pacific Rise.
The equipment has been modified so that the temperature gradients
in the whole probe and in its lower half can be determined separately.
The lower half gives a value 8.8 per cent above that for the whole
probe, the reason for this is not known.
The thermal resistivity of ocean sediment, R,is found to be a linear
function of the water content, w (in per cent water of the wet weight).
At the temperature of the ocean floor the relation is
R(cms degC/cal) = (168i- 14)+(6.78+0-31)~.
Introduction
Five measurements of the flow of heat through the floor of the Atlantic Ocean
obtained in 1952 have been described in a previous paper (Bullard 1954). This
work has been continued by the same methods during voyages in Discooery 11in
1954,1956and 1958. Sixteen further measurements have been made. The purpose of this paper is to describe this work.
I.
Measurement of the temperature gradient
As before the temperature gradient in the sediment beneath the ocean floor
was measured by a probe 4.6 m long and 2.7 cm in diameter. The probe used in
1954had two sets of junctions, each set having three pairs of junctions in series.
One set measured the temperature difference between points near the top and
bottom of the probe and the other that between the top and a point about half-way
2.
282
The flow of heat through the floor of the Atlantic Ocean
283
down. In 1956 and 1958 the second set of junctions measured the temperature
difference between the bottom of the probe and a point 276cm higher up. The
latter arrangement is much to be preferred since a set of junctions in the lower
half of the probe will give a satisfactory measurement even if the probe does not
penetrate completely. If penetration is complete a check is obtained both on the
linearity of the relation between temperature and depth and on the functioning of
the apparatus. The two sets of junctions will be called the long and the short
junctions.
An attempt was made to reduce the time needed to attain equilibrium by
putting the junctions at the lower end of the probe in a tube 4mm in diameter
extending 13 cm beyond the end of the 2.7 cm tube and the top junctions in a
similar tube running parallel to the upper part of the probe and distant ~ o c m
from it. This arrangement was not satisfactory since one or both of the narrow
tubes was always broken, probably when pulling the probe out of the sediment.
Also the temperature rise due to friction while the tube was penetrating the sediment was much greater than with a larger tube. In one lowering the initial rise
obtained by extrapolation back to the instant of penetration as previously described
(Bullard 1954) was 9.1 deg C compared to a mean of 0.8 deg C and a maximum of
1-6degC for the 2-7cm probe. If the friction is proportional to the circumference of the probe and all the heat went into the probe, the temperature rise
would be inversely proportional to the probe diameter; a large rise is therefore to
be expected for the 4mm tube. In view of the difficulties experienced, the use
of this type of probe was abandoned. All the results given in this paper have
been obtained with the probe 2.7cm in diameter.
Wind tunnel tests at the National Physical Laboratory on a twice full size model
of the probe showed that in free fall in water it is stable for inclinations up to 10'
from the vertical; at inclinations beyond this it becomes unstable and sets itself
broad-side on to the direction of motion. In practice the probe is attached to a
cable at its upper end which will increase its stability. Although there seems
little risk of it overturning, fins have been added above the recording case which
render it completely stable. A device that released the probe when its lower end
was from o to 4 m above the sea floor and allowed it to fall freely was used at five
of the stations in 1956.
The recorder was similar to that previously described except that an additional relay switched the recording galvanometer from the long to the short set of
junctions and back again about once every two minutes. An inclinometer, recording on the same film as the galvanometer, recorded the inclination about one horizontal axis as a function of time. This showed that the difference between the attitude of the probe when hanging in the water and when in the sediment averaged
4 O , the largest inclination observed was 9O.
This has a negligible effect on the
measurements and there is little to be gained by fitting a second inclinometer to
record tilts about an axis perpendicular to the first.
3. Thermal conductivity
Mr D. W. Butler and Mr E. H. Ratcliffe of the National Physical Laboratory
have made 44 determinations of the thermal conductivity and water content of
ocean sediments; 15 of these values for globigerina ooze have previously been
published (Bullard 1954, Table 4), the remaining 29 are given in Table I. The
specimens of red clay are from Revelle and Maxwell's (1952) stations, the first
E. C. Bullard and A. Day
284
3 specimens of mud are from Mission Bay, a tidal mud flat near San Diego, the
next 2 from the San Diego trough and the remaining 8 specimens are of a black
mud from our Mediterranean station 8 (Table 2). The specimens of impure
globigerina ooze are from our stations 6, 7 and 8. The water contents vary from
20 to 69 per cent, the extreme values having been obtained by drying and adding
water to the material from the cores.
Table
I
Thermal conductivity of sediments
Water content
(yowet wt)
Density
g/cm3
Thermal
conductivity
cal/cm s"C
x 10-4
Globigerina ooze
37.8
43.8
43 '4
36.9
38.5
1-54
1 '47
1 '47
23 '3
20.7
22 '2
1'55
25 '5
1'54
25 '2
19'3
19'3
19'3
2 1 '7
52
1'43
1'39
I .38
1 '47
1 '47
I .58
1'57
I '41
I '40
69.5
61-8
1'20
I -27
Red Clay
52
54
56.5
50
50
42'5
43 '5
52'5
22 '0
23 '7
24'3
19.1
19.6
16.8
17'3
Dark grey mud
55
52'5
56.5
51.5
46
46 *8
45 '7
44'4
44.6
42.6
38.0
37 *8
38.9
1'32
I .36
1.31
1'37
1.47
1-43
1 '45
1 '47
1 '47
1 '49
1'57
1'57
I -56
19.1
19.0
18.8
'9'4
20.6
20.8
21.7
22 '4
22 '4
22'4
23 '9
23 '0
24'4
The ditto marks in column 2 indicate that a single determination of the CaCOs content is
believed to represent two or more specimens used for the determination of conductivity.
A theoretical expression for the variation of conductivity with water content
has been compared with these observations (Bullard, Maxwell and Revelle, 1956)
and a straight line fitted over the range of practical interest. It has been found,
The flow of heat through the floor of the Atlantic Ocean
285
however, that the reciprocal of the conductivity (the resistivity) gives a straight
line over a larger range of water content (Figure I). A least squares fit gives
R
=
(161 k 14)+ (6.5 I k 0.30)~
where w is the water content in per cent of water on the wet weight and R is the resistivity in deg C cm s/caI. T h e standard deviation of one measurement is 17 deg C cm s/
cal or 4 per cent. The residuals show no significant curvature in the relation
between w and R .
I
0
I
40
1
20
I
60
I
80
J
100
Water content (per cent wet weight)
FIG.I .-Relation between thermal resistivity (laboratory conditions) and
water content (per cent of water on the wet weight). 0 red clay,
A globigerina ooze,+ mud.
An examination of the residuals from ( I ) shows that the resistivity of red clay
and globigerina ooze of a given water content do not differ significantly; that of
mud is 2 per cent higher, but the difference is barely significant and has been
ignored.
T h e conductivity at the temperature and pressure of the ocean floor is not the
same as that measured in the laboratory at a temperature of about 25 degC and a
pressure of one atmosphere. T h e temperature coefficient of the thermal conductivity of ocean sediments has been determined by Butler (Von Herzen & Maxwell
1959, Ratcliffe 1960); he finds that the conductivity decreases by 6 per cent
between 25 and 4deg C. Pressure is believed to increase the conductivity by about
I per cent for every I ooofm of depth. At the depths of our stations a uniform
correction of 4 per cent is adequate and the resistivity has been taken as
R
=
168+678w
(1)
T h e resistivities for the five stations measured in 1952have been recalculated from
E. C. Bullard and A. Day
286
this relation. The results for these stations given in Figure 3 therefore differ
slightly from those given previously (Bullard 1954).
The conductivity required in a heat flow measurement is not the arithmetic
mean over the length of the temperature probe, but the reciprocal of the mean
resistance; since the relation (I) is linear the mean resistance can be found directly
from the mean water content of a core. This has been found by averaging the
water contents obtained on 6-inch lengths of core.
Unfortunately in 1954 and 1956 we were unable to obtain cores covering the
full 4.6m length of the probe. It is necessary therefore to consider the error
incurred if the conductivity is deduced from a core that is shorter than the probe.
The individual 6-inch samples taken at the heat flow stations have water contents varying from 23 to 64 per cent, but this variability is considerably reduced
when the water content is averaged down a core. Ten cores with lengths exceeding
2-4m gave an average water content of 43 per cent and all lay between 40 and 48
per cent. The variation of the mean water content with depth is shown in Figure 2.
C
6
1
I
I
I
I
I
0
1
2
3
4
5
Depth
FIG.2.-Variation
(m)
of water content 0 and conductivity x with depth,
mean of 10cores.
Here all 6-inch samples from the 10 cores lying in ~ f depth
t
ranges have been
averaged. The corresponding conductivities are also shown.
If the conductivity for the long set of junctions is estimated from the mean
water content between depths of 0.3 and 2*4m, it will on the average be underestimated by 1.3 per cent; that of the short set in the bottom half of the probe will
be underestimated by 2-2per cent. There will also be a random error in estimating
the conductivity of the missing lower half of a core; this will be less than the
standard deviation of the conductivity of the 10 cores from this mean which is 4
per cent. No correction has been made for these errors which are negligible. The
smallness of the variability in the mean water contents of the cores is probably due
to the uniformity of the sediments. The probe would not penetrate the sandy sediments of the abyssal plains and our stations are all in situations where softer sediments could be found; in the Atlantic they are mixtures of globigerina ooze and
clay and at the single station in the Mediterranean a soft black mud. The above
average water contents could not be expected to apply to other types of sediment.
The flow of heat through the floor of the Atlantic Ocean
287
4. The measurements
In 1954 the temperatures were recorded for 22 minutes, this gave an undesirably large correction for lack of equilibrium (mean 29 per cent). The interval during
which measurements were taken was therefore increased to between 40 and 50
minutes in 1956 and 1958, this reduced the mean corrections for these years to 19
and 15 per cent. The correction was determined by fitting the theoretical relation
between temperature and time (equation 7 of Bullard 1954) to the observations by
least squares. With one exception the fit was satisfactory, the standard deviation
of a measured temperature being 0'0044 deg C. This is several times larger than in
the measurements made in 1952, the increase is due primarily to a deterioration
in the galvanometer mirrors. If the measurements were independent the standard
error of the extrapolated equilibrium gradient would be about 2 per cent, but this
is probably an underestimate since the errors at successive measured points on a
record tend to be correlated (as can be seen in Figure 3 of Bullard & others 1956).
The record at station 17 did not give a satisfactory record from the Iong set of
junctions. The uppermost junctions were suddenly heated by about 0.1 deg C
after the probe had been 16 minutes in the sediment; presumably the ship pulled on
the probe and bent it somewhere below the top junction causing frictional heating
near the top, but no disturbance lower down. The heat flow at this station has
been calculated from the results from the short set of junctions.
On several occasions the probe did not penetrate completely. There is then
some doubt as to what proportion of it was in the sediment, though an estimate
can be made from the mud sticking to it and from the position of the sharp bend
which is usually produced on pulling out. I n 1954 there was only one such station
(number 6); the heat flow at it has been deduced from the long junction assuming
158 cm of the probe to have been sticking out of the sediment. The results from the
short junctions, which were in the upper half of the probe, have not been used at
this station. In 1956 and 1958 the short junctions were in the lower part of the
tube and were unaffected by incomplete penetration. The heat flow adopted for
such stations is that obtained from the short junctions. For stations with complete penetration the mean of the results from the short and long junctions was
adopted. The results for the long and short sets of junctions at 9 stations with
complete penetration show a systematic difference. At every station the temperature gradient is less for the long set of junctions than for the short set. The difference varies from 0.3 to 18 per cent and averages 8.8 per cent. A small difference
in the opposite direction might have been expected in the measurements made in
1956 and 1958, since the water content, on the average, decreases with depth and
the conductivity increases; this should cause the short set of junctions to give a
gradient 0.9 per cent smaller than the long set. In 1954, when the short junctions
were in the upper half, the observed differences were in the same direction as
1956 and 1958, but were only 0.3 and 2-4 per cent and not significant. The observed differences are also in the opposite direction from those that would be
produced by chemical or bacterial heating near the surface. The cause of the
discrepancy has not been established, the most likely explanation seems to be
that there is some movement of water in the top metre or two of sediment and that
this transports a small part of the heat and reduces the gradient near the surface.
There are 5 stations with incomplete penetration at which results were obtained
from both sets of junctions. Four of these give a larger gradient over the whole
probe than over the bottom half, this is the reverse of the behaviour found at the
stations with complete penetration. One of these stations (number 12 in Table 2)
*
13
Incomplete penetration.
tDisturbed.
20
21
I8
19
16
I7
15
'
4
40 59
42 18
41 27
43 42
5 47
04
22 58
27 I8
45 28
46 32
46 30
46 37
36 20
35 36
35 34
36 39
44 55
9
19 02
18 56
17 21
1 0 45
21 00
13
13'
9 59
4 34
I0
11
I2
12'
W
N
39O 36'
35 59
35 58
Longitude
Latitude
6
7
8
Station
number
4592
4413
4084
4109
4844
5375
5380
5 146
4844
125 I
4534
3020
Depth
m
1.32,
22.8
0.72
1.15
52*8*
I '20"
t
50'5
21.5
t
1.19
8.61"
I .08
I *40*
0.90"
I '09
0*98
0.71
1'21
I .06*
0.87
1958 June-July
22 4
33'0
21 '7
21.6
61.6*
2 1 '3
20.5
20.5
21'2
51.0
#'O*
68.3*
51.2
1956July-August
31'5
22.6
45 '7
21.6
53 '5
22'2
415.8*
20.7
1954November
45'9*
23.0
37'4
23.1
56.6
21'3
Thermal
Temp.
cond.
Heat flow
gradient cal/cms"C pcal/cmZ s
"C/km
XIO-4
Long Junction
h
Short junctions
-.
50.7
55 '2
49 '0
38.8
23 '0
21.8
I '17
1'21
I '14
0.85
23 '2
2 1 '9
21.8
0.93
1.18
1'39
1 '34
I '20
6.52
20.7
21 '2
20'1
20'1
21 '3
I '40
I '20
0.78
22.8
22.6
21.8
1'24
2 1 '3
34'5
55 ' 0
61 '4
3 '4'9
56.7
66.6
36.4
55 '5
63.6
0.87
23.1
37'5
58.0
-
Thermal
Temp.
cond.
Heat flow
gradient cal/cms"C pcallcmzs
XIO-4
"C/km
/-
-
2
Measurements of heat $ow
Table
1'21
I .16
I '14
0.78
0.75
1.09
I '29
6.52
1'14
1'34
0'93
I '14
1'39
1'22
1.06
0.87
Adopted
heat flow
p cal/cmZ s
Y
p
?
B
a
L!
=
?
m
h)
03
00
The flow of heat through the floor of the Atlantic Ocean
289
is exceptional in having a very high heat flow and a large difference between the
two gradients. The mean discrepancy for the other 4 is 4.1per cent, this is probably due to an underestimate of the penetration, it is quite possible that the sharp
bend in the probe on pulling out usually occurs somewhat below the surface and
also that the topmost unconsolidated sediment is washed off the probe on the way
up to the sea surface. An underestimate of penetration by 30 cm would produce
overestimate of the gradient by 7 per cent.
5. Discussion
The results are given in Table 2 and Figure 3. The figure also shows the
revised results at the five stations from Bullard (1954) and therefore contains all
FIG.3.-Heat
flow in pcal/cm2s, contours in metres.
the measurements made from Discovery 11. Preliminary results for stations 6, 7
and 8 were given by Bullard, Maxwell & Revelle (1956), these are superseded by
those of Table 2. All heat flows in this paper are in pcallcmzs, this unit has not been
repeated after each value referred to in the text.
The value of 6.5pcallcm2s found at station 12 is 4-7 times the largest
value found at any other station and is clearly exceptional. This value was found
from the short set of junctions. The long set is believed not to have penetrated
completely and to have projected 84cm above the sediment; if this is correct the
heat flow derived from it is 8-6, whilst if it did penetrate completely it would be
T
E. C. Bullard and A. Day
290
7.0. T h e reality of the high heat flow is therefore confirmed by the long set of
junctions.
The station is in the central valley of the Mid-Atlantic Ridge (Heezen & others
1959, Hill 1960). It is most desirable that further measurements should be made
both in the valley and on lines crossing the ridge. This will not be easy since the
area is rocky and it is a matter of chance whether the probe hits a pocket of sediment or a rock. Two galvanometers were broken and a coring tube bent in efforts
to repeat the measurement at station 12. Similar high heat flows (up to 8.1) have
been found by expeditions from the Scripps Institution on the crest of the East
Pacific Rise (Bullard, Maxwell & Revelle 1956, von Herzen 1959). A histogram
of these values is shown in the upper section of Figure 4. It seems probable that
very high values of the heat flow are characteristic of the crests of mid-ocean ridges.
10
-
CI
Pacific
10
-
5 -
-
Atlantic
I
I
I
I
I
I
1
I
I
The observed temperature gradient of 3 15 deg Cfkm will only continue to the
bottom of the sediments. I n the lavas that almost certainly underlie the sediments, it will be reduced to about 14odegC/km if the conductivity is 0.005 cal/cm
secdegC. These values suggest that molten rock is present at depths of a few
kilometres below the ocean floor. T h e origin of the Mid-Atlantic Ridge has been
discussed by Hess (1954) and by Heezen, Ewing & Tharp (1959). It forms part
of a worldwide system of connected ocean ridges, one branch of which runs into
the Red Sea. Since the Red Sea has a central valley which is believed to be a tensional crack and to be floored by a dyke (Girdler 1958), it is natural to suggest that
the central valleys of other parts of the system, and in particular the central valley
in which our station 12 lies, are similar features. Such a world encircling tensional feature might be due to convection currents in the mantle rising under the
ridges, spreading out sideways and sinking again. T h e horizontal limbs of the
currents would produce the forces that open the tensional crack and the rising
current would bring hot material near the surface and produce vulcanism and a
high heat flow.
The flow of heat through the floor of the Atlantic Ocean
291
Such a scheme is speculative, but it is worth considering what other observable
phenomena it might produce. A positive gravity anomaly might be expected over
the valley due to the intrusion of dense rock into the opening crack (as in the Red
Sea) but this should be superposed on a regional low associated with the rising
current. The orders of magnitude of the quantities involved have been considered
by Bullard & others (1956) who conclude that if the temperature in the rising
current is one or two hundred degrees above the normal value an anomaly of - 10
to - 30 mgal would be expected. No gravity measurement appears to have been
made over the central valley of any ridge. The values on the ridge are very
scattered but do not show any consistent tendency to be below the values in the
neighbouring areas.
If the rising current under the ridge turned down again on each side, a low
heat flow would be expected over the descending limbs. The stations in Figure 3
do not show strips of low heat flow, but are so sparsely distributed that if they exist
they could easily have been missed. There are values of 0.54and 0.55 about 700 km
to the east of the crest. Von Herzen has found values as low as 0-14in the basin
I 6ookm to the west of the crest of the East Pacific Rise and a value of 0-23
I oookm to the east. He suggests that the pattern he has found is due to convection in the mantle. Clearly much remains to be done to elucidate the meaning of
these high and low heat flows which were entirely unexpected.
The remaining 20 observations give a symmetrical histogram with a single
peak. Their mean is I so6 & 0.055 and their standard deviation 0.26. The Pacific
results, with the values along the crest of the East Pacific Rise excluded, give
I -0g& 0.094 with a standard deviation of 0.65. If all values within z ooo km on
each side of the rise are excluded (which excludes the very low values in the neighbouring basins but not the low values in the Chile trench) the mean is I -17& 0.1I
and the standard deviation 0.60. There thus appears to be no significant difference between the mean of our small sample of heat flows in the eastern basin
of the north Atlantic and that of the larger sample drawn from a wide area in the
Pacific. This suggests that the mean of both sets
has some real significance as a mean for the oceans away from ridges. The spread
of the Pacific results is greater, probably because they are drawn from a wider
variety of environment including an ocean trench.
The results away from the ridge do not show any obvious trends. It is possible
that their variation from 0.54 to I -39pcal/cm~sis controlled by local factors such
as irregularities in the buried rock surface beneath the sediment and that the
station spacing is too wide to reveal the real pattern. The large difference between
stations 14and 15 which are only 7 km apart and give heat flows of I '39 and 0.93
is curious and unexplained.
Acknowledgments
We are indebted to the Director of the National Institute of Oceanography for
allowing us to use Discovery 11 for these measurements and to the Captain, officers
and crew of the ship and to the staff of the Institute for much assistance in the
troublesome operation of the equipment. We have also had much help from the
292
E. C. Bullard and A. Day
staff and students of this Department, especially from Dr M. N. Hill, Mr M. Keen
and Dr T. Allen. We are also indebted to Mr D. W. Butler and Mr E. H. Ratcliffe of the National Physical Laboratory for their measurements on the thermal
conductivity of our specimens.
Department of Geodesy and Geophysics,
Cambridge :
1960May.
References
Bullard, E. C., 1954. Proc. Roy. SOC.A., 222,408-429.
Bullard, E. C.,Maxwell, A. E. & Revelle, R., 1956. Adw. Geophys., 3, 153-181.
Girdler, R. W.,1958. Quart. J. Geol. SOC.
Lond., 114, 79-105.
Heezen, B. C.,Tharp, M. & Ewing, M., 1959. The Floors of the Oceans, I. The
North Atlantic, Geol. SOC.
Amer. Sp. Pap. 65:
Hess, H. H., 1954. Proc. Roy. SOC.
A., 222, 341-348.
Hill, M. N.,1960. Deep-sea Res., 6, 193-205.
Ratcliffe, E. H.,1960. J. Geophys. Res., 65, 1535-1541.
Von Herzen, R., 1959. Nature (Lond.), 183,882-883.
Von Herzen, R. & Maxwell, A. E., 1959.J. Geophys. Res., 64,1557-1563.