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OCR for page 141
8
Long-Term Eustasy and
Epeirogeny in Continents
C. G. A. HARRISON
University of Miami
INTRODUCTION
It is well known that over time intervals of hundreds of
millions of years, sea level has fluctuated by several hun
dreds of meters. The main evidence for this is the chang- the two.
ing area of marine sediment deposited on the continents
through time, indicating that at certain periods continents
have been flooded by sea water much more than they are
today, whereas at other periods there appears to have been
relatively little flooding. Part of this change is the result
of the variable amount of water locked up in continental
ice sheets. The waxing and waning of continental ice
sheets during the Pleistocene happens on a time scale
shorter than those discussed in this chapter, being gener
ally less than 100,000 years. However, there is a long
period time signal in this, in that today, during an intergla
cial period, there is a significant amount of water locked
up in continental ice sheets, and so if we go back to a time
when there was no continental glaciation there would be a
significant increase in sea level at that time compared with
today.
It appears that the most likely cause of large-scale
changes in sea level is the variable volume of ridge mate
rial, which can produce a signal of several hundred meters.
If seafloor spreading increases, then the volume of the
ridge crest starts to increase, displacing water and causing
additional flooding of the continental areas. The critical
141
quantity is the area of seafloor produced per unit time.
This can be changed either by an increase in spreading rate
over a ridge crest of constant length, or by an increase in
the length of the ridge crest, or by some combination of
When individual continental flooding curves are stud-
ied, it is found that different amounts of sea-level change
are required to cause the desired amount of flooding. It is
thought that this is because the continents themselves can
undergo vertical motion. If this is accompanied by little or
no relative horizontal motion or tectonism, the change is
termed epeirogeny. Some geologists believe that there is
no such thing as epeirogeny, but the evidence, both from
the ocean basins (Menard, 1973; Crough, 1979) and from
continental areas, is overwhelming. Any area of the Earth
can undergo slow vertical motion up to several hundred
meters, unaccompanied by any evidence of folding or
tecton~sm.
Many other possibilities exist for changing sea level by
tens to hundreds of meters. For instance, a change of the
pattern of subduction can cause the ocean basins to be-
come on average younger or older and so produce a sea-
level change that is in principle caused by a similar effect
to that caused by varying the amount of seafloor produced
per unit time interval. If the area of the ocean basin changes
because of continental growth or continental destruction,
this will also cause a sea-level change. Sedimentation
OCR for page 142
142
rates have fluctuated through time, and if the ocean basins
have more or less sediment in them, this can also cause
significant sea-level changes. There are undoubtedly other
factors that have not been considered that have the capa-
bility of causing significant sea-level changes. In this
chapter, I discuss the effects mentioned above, as well as
some other effects, in order to arrive at a pattern of sea-
level change during the past 200 million years (m.y.~.
VERY LONG TIME CHANGES OF FLOODING
Over time scales of hundreds of millions of years, the
average amount of continental flooding is expected to
remain approximately constant. This is because erosion is
effective at reducing continental elevations above sea level,
but inefficient at eroding the continental shelves. The rate
of chemical erosion is almost independent of continental
elevation above sea level and is calculated to be about 8.1
m/m.y. (Holland, 1981~. Therefore in several hundred
million years even the relatively low lying continental
elevations will be eroded to sea level. It is presumed that
chemical erosion below sea level is fairly small, except for
the minor effect of submarine springs debauching on the
continental shelf or slope. Mechanical erosion is more
effective at removing the elevations of the high areas of
the continents since ~ is highly correlated with elevation.
Mechanical denudation rates given by Holland (1981) lie
between 56 and 67 m/m.y. These may be considerably too
high for a long-term average due to the influence of man
on present-day erosion rates. But even if they are a factor
of 2 too high, a time period of only a few hundred million
years is necessary to erode much of the high continental
areas down to elevations close to sea level, even allowing
for isostatic uplift due to the offloading produced by denu-
dation. These time constants appear to be considerably
shorter than those derived by Stephenson (1984) for ero-
sion models of the continental lithosphere in which flexure
is taken into account. He obtains time constants of 200
m.y. to 400 m.y. for erosion to reduce topographic undula-
tions to 1/e of their amplitude. It is more in agreement
with the rough estimates of erosion time constants by
England and Richardson (1980) of 50 m.y. to 200 m.y.
Aeolian erosion is small in comparison with mechani-
cal erosion or chemical erosion by rivers but could be
important as a means of erosion for Africa, which is being
eroded by rivers at a much slower rate than the other
continents, because of its aridity (Hay and Southam, 1977;
Pro spero, 1981~.
If relative sea level remains perfectly constant for an
individual continent, the processes of erosion will serve to
plane down areas above sea level, the resulting sediment
supply filling up the volume between shelves and the sea
C. G. A. HARRISON
surface, such that only a gradual slope between the highest
elevations and the edge of the continental shelf is pro-
duced. Fluctuations in relative sea level could cause a
pumping action whereby some of the sediment deposited
on the slope during high stands is eroded away during low
stands and deposited on the continental slope or rise, or
into the deep ocean basins by the mechanism of turbidity
currents.
These arguments suggest that long-term flooding val-
ues should not change drastically, even if the area of the
continental crust has changed appreciably or if the volume
of ocean has grown with time. This conclusion was also
reached by Wise (1974), who argued that there were no
long-term changes in the amount of continental flooding.
Others have argued that there is a secular decrease of
flooding during the Phanerozoic that could be explained
either by a thickening of the continental crust by about 1
m/m.y. (Hallam, 1971) or, much less likely, by expansion
of the Earth (Egyed, 1956) the expansion occurring in
the oceanic regions. Other arguments have been presented
(Abbott and Hoffman, 1984) that suggest that both conti-
nental area and continental volume have not changed
substantially for the past 2 billion years (b.y.~. If this is the
case, then the larger volume of ridge material that had to
exist 2 b.y. ago to allow the Earth to lose the larger amount
of radiogenic heat being produced at that time would have
caused submergence of much of the continental crust, thus
reducing erosion and negating one of the assumptions
made in Abbott and Hoffman's model. Since recent data
on continental flooding suggest a flooding not much greater
than the present day at the beginning of the Phanerozoic,
we prefer the model that calls for approximately constant
freeboard when averaged over very long time intervals.
So the discussion in the rest of this chapter shall be limited
to sea-level change over time scales greater than a few
hundred thousand years and less than a few hundred mil-
lion years.
Possible long-term trends in the volume of oceanic
water have been summarized by Southam and Hay (19811.
Rubey (1951) originally proposed that the volume of oce-
anic water had grown uniformly with time since the crea-
tion of the Earth. Since the average depth of the water in
the oceans in meters is approximately the same as the age
of the Earth in millions of years, the effect would be to
cause a deepening of the oceans at a rate of 1 m/m.y.
(0.001 mm/yr). There is also the possibility that the sub-
duction of wet sediments could cause a long-term change
in the volume of the ocean water if the rate at which this
water is recycled to the oceans is not constant. This is
difficult to quantify. Southam and Hay arrived at a figure
of about 0.01-mm/yr reduction in ocean depth if none of
the water were to be recycled.
OCR for page 143
LONG-TERM EUSTASY AND EPEIROGENY IN CONTINENTS
METHODS
In this section we derive an expression for the change
in freeboard produced by a change in volume of the ridge
system. The change may then be used to estimate the
change in the area of continent flooded by marine waters if
the shape of the hypsographic curve is known.
The first effect that has to be taken into account is that
if the ocean floor is loaded by extra water, it will respond
isostatically, and so the effect of sea-level change seen by
a continent is diminished. This is illustrated in Figure
8.1 a. The change in sea level (or more correctly sea depth)
is s = h + d. The change in freeboard is given by -h.
For a water density of 1.02 g/cm3 and an asthenosphere
density of 3.4 g/cm3 the relationship between s and h is
given by h = 0.7s.
(a)
T
w
1
1
d
if
was
Id 1
( b) 1 - ~ IN e Seo
o
. _
-
o
I1J
:
id
AGAIN ht (42-Al)
dI~
a;
Al A
FIGURE 8.1 (a) Method of calculating the isostatic response of
an ocean basin to an increased depth of ocean water, s (equal to
h + d). (b) Method of relating a volume change to a sea-surface
height change. Al, A2, and t are taken from the continental
hypsographic curve. The change in depth of the oceans is given
by h + d: d represents the isostatic response of the ocean basins
to the extra load of the water; the change in freeboard, h, is less
than the change in ocean depth. This model is slightly different
from that used by Hays and Pitman (1973), Pitman (1978), and
Kominz (1984), who assumed that the continents above present-
day sea level did not respond isostatically to the extra load of the
water. The volume of extra water or extra ridge crest is shown by
the shaded region. The elevation difference between the two
cumulative areas Al and A2 is given by t.
143
Since much of this work involves the calculation of
volumes, it is necessary to translate these volumes into
sea-level changes. Figure 8.1b shows the principle on
which this is done. The shape of the continental area as a
function of elevation is given by the continental hypsogra-
phic curve (Harrison et al., 1983~. A change in the posi-
tion of the ocean surface of an amount h is caused by a
volume change of V, which is shown by the shaded area in
Figure 8.1b.
V=(h+ d jAi + ~ (A2-Ai) t (8~1)
The modern continental hypsographic curves were used to
plot the variation of V with h that is shown in Figure 8.2.
A power curve
h = 19.694~' 9679 (V > fold my (8.2)
where h is measured in meters and V in 10~6 m3, fits the
calculated points with an rms error of 1.6 m. A straight
line constrained to pass through the origin, and shown in
Figure 8.2, fits the data with an rms error of 3.6 m and has
a slope of 17.95 x 10-~6 m-2. In converting volume V to
freeboard-in, we shall use the power curve. If the volume
is small or negative, the power curve cannot be used, and
as an approximation, the expression h = l9.1V is used to
·0 200
150
o
D 100
a)
UL
50
or
Oc 4; ~6 8 10 12
Volume. 1016 m3
16 18
FIGURE 8.2 Relationship between freeboard change (in m) and
volume change (in 10'6 m3) using modern hypsographic data.
The power law curve h = 19.694 V09679 fits the data points to
within the size of the small dots. The straight line shown on the
graph is the straight line constrained to go through the origin that
minimizes the sums of the squared deviations of h. The lower
curve and the right-hand ordinate show the deviation between the
calculation of Hays and Pitman (1973) (hp) and the one pre-
sented in this paper (hH). Hays and Pitman (1973) used hyp-
sographic data from Sverdrup et al. (1942) and also did not allow
for the fact that the newly flooded areas will subside isostatically
as sea level increases.
OCR for page 144
144
extrapolate to small or negative values of volume. Since
negative values of volume are small, this approximation
does not introduce any significant inaccuracy.
VOLUME OF MID-OCEAN RIDGES
The most recent estimate of the volume of mid-ocean
ridges has been made by Kominz (19841. She analyzed
very carefully all the data pertaining to the position of
ancient ridge crests and their spreading rates. She investi-
gated the errors produced by inaccurate estimates of spread-
ing rates caused by errors in the time scale of reversals,
inaccurate estimates of ridge lengths, the effect of uncer-
tainties in her calculations of variation in areas of oceanic
crust, which would be older than 150 m.y. ago (Ma),
subducted ridges for which only remanent triple junctions
remain, and completely subducted ridge crests.. It should
be emphasized that any attempt to calculate ridge volumes
for times as long ago as 80 m.y. is fraught with difficulty.
Of the oceanic crust that existed then, only 31.2 percent is
left, so that large extrapolations need to be made to deter-
mine the age-area relationship for crust aged up to 70 Ma.
Nevertheless, the work of Kominz is by far the best esti-
mate of mid-ocean ridge volumes.
TABLE 8;1 Volume Changes (10~6 ma)
C. G. A. HARRISON
Her conclusion was that ridge-crest volume changes
since 80 Ma have produced an increase in freeboard of 180
m. The analysis of possible errors indicated that the
maximum possible sea-level fall could have been 317 m
and the smallest could have been -3 m. Table 8.1 presents
data on ridge-crest volume calculated from Kominz (1984~.
The rise in freeboard calculated for the volume of crust 80
Ma is 175.0 m, about 5 m less than Kominz calculated
using older hypsographic information.
It has been postulated that the added volume of ridge-
crest material produced by increased spreading rates should
be counteracted by the effect of increased subduction rates.
Hager (1980) suggested that the increased subduction rates
should cause the marginal basins in the western Pacific to
subside, having an effect opposite to that of the ridge-crest
volume. While this may occur to some extent, it is unlikely
to cause the ridge-crest volume effect to be entirely oblit-
erated. The area of the marginal basins today is 26.9 x
10~2 m2 (Sclater et al., 19801. In order to counteract the
volume of ridge-crest material, these basins would have to
subside on average 3.45 km. In addition, there should
today be a strong correlation between marginal basin depth
and subduction rate, which does not exist in the magnitude
necessary to remove the ridge-crest volume effect. Since
Sedimentation
of Average
~. . . ~. . . _' . . .
Time, Seafloor Ice Pacific
Ma Spreading Volumea Volcanism Deposition Sediments Crystal Age
CaCO3 Recent
Continental Ocean
Collision Cooling Total
Free-
board (m)
O O O O O O O O O O O
5 -0.713 0.315 0.129 -0.129 -0.381 -0.052 0.133 0.036 -0.662 -12.6
10 -1.331 0.630 0.269 -0.258 -0.381 -0.103 0.265 0.071 -0.838 -16.0
15 -0.816 0.945 0.420 -0.386 -0.381 -0.155 0.398 0.107 0.132 2.8
20 -0.513 1.260 0.585 -0.515 -0.381 -0.206 0.530 0.142 0.902 17.8
25 0.026 1.575 0.763 -0.644 -0.381 -0.258 0.663 0.178 1.922 37.1
30 0.345 1.890 0.955 -0.773 -0.381 -0.309 0.795 0.214 2.736 52.2
35 0.463 2.205 1.164 -0.902 -0.381 -0.361 0.928 0.249 3.365 63.7
40 1.312 2.520 1.390 -1.030 -0.381 -0.413 1.060 0.285 5.103 95.4
45 2.039 2.520 1.634 -1.115 -0.381 -0.464 1.193 0.320 5.746 107.0
50 3.736 2.520 1.899 -1.288 -0.381 -0.516 1.193 0.356 7.519 138.8
55 4.343 2.520 2.186 -1.~17 -0.381 -0.567 1.193 0.356 8.233 151.5
60 5.765 2.520 2.497 -1.546 -0.381 -0.619 1.193 0.356 9.785 179.1
65 5.872 2.520 2.833 -~.674 -0.381 -0.671 1.193 0.356 10.048 183.8
70 6.867 2.520 3.197 -1.8Q ~-0.381 -0.722 1.193 0.356 11.227 204.6
75 8.311 2.520 2.697 -1.932 -0.381 -0.774 1.193 0.356 11.990 218.0
80 9.554 2.520 2.197 -2.061 -0.381 -0.825 1.193 0.356 12.553 227.9
100 -2.576
80 9.554 2.520 2.197 0 - 0.381 - 0.825 1.193 0.356 14.614 264.1
aCorrected for density of continental ice.
b80 Ma result omitting the CaCO3 contribution.
OCR for page 145
LONG-TERM EUSTASY AND EPEIROGENY IN CONTINENTS
TABLE 8.2 Uplift and Subsidence (Bond, 1979)
Time Interval
Continent
Movement
Miocene-Present
Eocene-Miocene
Campanian/
Maastrichtian-Eocene
Turonian/Coniacian
Campanian/
Maastrichtian
Albian-Turonian/
Coniacian
Africa
Africa
N. American
Australia
None
Australia
Europe
Uplift, ~90 m
Uplift, ~135 m
Uplift, ~1 10 m
Subsidence, ~1 10 m
Uplift, ~ 1 10 m?
Uplift, ~ 1 10 m?
there is no firm estimate of the magnitude of this effect, it
has not been considered further.
ICE-VOLUME EFFECT
A certain amount of water is today locked up in conti-
nental ice sheets. In earlier times, when the Earth was
warmer than today, the amount so locked up would be
minimal, and so an allowance has to be made for this
added volume of ocean water in the past. Opinions differ
as to the amount of water in today's continental ice sheets.
Kennett (1982) estimated a figure of 3 x 10~6 m3, whereas
Holmes (1978) estimated afigure of 2.5 x 10~6 m3. Since
the density of continental ice is 0.9 g/cm3, Holmes' figure
gives a freeboard change of 43.2 m, whereas Kennett's
figure produces a change of 51.5 m.
We use a compromise between these two figures, choos-
ing a volume of 2.8 x 10~6 m3 of continental ice today. The
rate of buildup of the ice through time is obviously some-
thing that needs to be specified. Kominz (1984) assumed
that buildup started 15 Ma. It is generally believed that
there was a significant buildup of continental ice starting
at the end of the Eocene (Kennett, 1982~. We shall there-
fore assume that the present ice volume commenced accu-
mulating at 40 Ma and has built up since that time uni-
formly. It should be emphasized that this chapter is not
dealing with time scales as short as the Pleistocene glacia-
tion variations. This choice of 40 Ma as the start of signifi-
cant buildup of continental ice is a compromise. Matthews
(1984) suggested a buildup that started 100 Ma and ended
35 Ma. A new curve of freeboard change could be made
by reformulating Tables 8.1 and 8.2 to obtain revised
volume estimates through time and then using Eq. (8.2) to
calculate revised freeboard values. One effect of this
would be to make the low stand of sea level calculated to
occur 10 Ma even lower (-25 m).
145
VOLCANIC ACTIVITY
Schlanger et al. ( 1981) and Watts et al. ( 1980) have
suggested that a large area in the equatorial Pacific Ocean
underwent a thermally induced uplift accompanied by large
amounts of extrusive volcanic activity. Using a number of
lines of different evidence, they came to the conclusion
that the thermally induced uplift produced an excess vol-
ume of 2 x 10~6 m3 between 110 and 70 Ma. We have
assumed a uniform buildup during this 40-m.y. time inter-
val and then an exponential decay with a time constant of
62.8 m.y. with an amplitude of 3200 m (Parsons and Sclater,
1977), which are the same parameters as those for the
oceanic crust. Other parameters for the decay of ridge-
crest topography have been calculated (e.g., Schroeder,
1984), but we prefer to use the generally accepted values
given above.
The depth 70 Ma was 3590 m, and the depth today is
5190 m, giving a total subsidence during this time interval
of 1600 m. This allows us to write down two equations for
depth at these two time intervals, with two unknowns,
being a, the depth to which the Nauru basin will subside
after an infinite time, and t, the age from which subsidence
is assumed to start in order to obtain the right value for
subsidence between 70 Ma and today:
3590 = a - 3200 exp(-t/62.8' (8.3)
and
5190 = a - 3200 expL-(t + 70~/62.83. (8.4)
The values of the unknowns are, a = 5970 m, and t =
18.6 m.y. Since the youngest age that we need to consider
is close to 20 m.y., we can use the exponential form for
subsidence rather than the form in which subsidence is
dependent on the square root of time, which is the correct
expression when the age is less than 20 m.y. Since we are
interested in volume changes that differ from the present
value, we must offset the volumes so calculated by the
present volume.
Schlanger et al. ( 198 1 J suggested that this large volume
of uplift was matched by a similar volume of material on
the Farallon plate, all of which material has since been
subducted. The islands formed during this period of vol-
canism on the Farallon plate acted as stepping stones for
reefal foraminifera whose distribution without such step-
ping stones would otherwise be difficult to explain.
Schlanger et al. (1981) also added to this volume the effect
of other volcanic activity in the ocean basins. Since the
additional data that they use are somewhat more specula-
tive as to the size of the effect, they have not been included
in our calculation.
OCR for page 146
146
This information on volume changes is presented in
Table 8.1, along with volume changes produced by spread-
ing activity (Kominz, 1984) and ice volume changes. The
total volume change for the effects of seafloor spreading,
ice volume, and Pacific volcanism during the past 80 m.y.
is 14.271 X 10~6 m3, which is equivalent to sea-level fall
during this time of 258 m. This is somewhat more than
that calculated by Kominz because of the added effect of
Pacific volcanism. This is offset somewhat (8 m) by the
slightly less steep plot of freeboard versus volume (used in
this chapter) than that obtained by the equation used by
Kominz (see Figure 8.21.
OCEAN SEDIMENT VOLUMES
Harrison et al. (1981) discussed the possibility that
changes in the amount of sediment in the ocean basins
could have a significant effect on sea level. Planktonic
foraminifera did not evolve into volumetrically important
sources of deep-sea sediments until the later Cretaceous.
The average thickness of carbonates in the ocean basins
today is 300 m (calculated for a carbonate density of 2.7
g/cm31. It has been estimated that 90 percent of this is
composed of the tests of pelagic foraminifera. We there-
fore assume that deep-water carbonate sediments built up
uniformly starting 100 Ma such that today there is an
additional thickness of 270 m over the ocean basins. The
isostatic response to sediments is considerably greater than
that for water, since the sediments have a higher density.
In order to achieve the same effect on sea level, we can
replace the sediments with a water layer, which is (Pa - Ps)/
(Pa - Pw) times as thick as the sediment, or 79.4 m, where
Pa is the density of the asthenosphere, ps is the density of
the carbonate, and Pw is the density of the water. We
assume that the sediment layer covers an area equivalent
to all oceanic areas below a depth of 1 km, which gives a
total volume of 2.576 x 10~6 m3. Since this addition of
sediment serves to decrease the freeboard as we go back in
time, the equivalent volumes are negative. They are tabu-
lated in Table 8.1.
There is a small additional effect due to ocean sediment
volumes. It has been shown that sedimentation rates dur-
ing the past 5 m.y. have been considerably greater than
during the earlier Tertiary and Mesozoic (Southam and
Hay, 1981~. The additional thickness of sediment pro-
duced is equivalent to a layer 40 m thick over the ocean
floor (Harrison et al., 1981), which gives a volume change
of 0.381 x 10~6 m3. This has been taken into account in
Table 8.1.
A third effect of sediment volume has to do with the
change in average age of the ocean basins. The average
age has increased by about 20 m.y. during the past 80 m.y.
(Harrison et al., 1981~. We assume that the noncarbonate
C. G. A. HARRISON
deposition has occurred uniformly through time (except
for the recent past, which has already been taken care of).
Therefore there is more sediment in the ocean basins today
than there was 80 Ma because the ocean basins are on
average older today than they were. The average noncar-
bonate sedimentation rate is 11.65 kg/m2 per 1000 yr (Sloan,
19851. For an average age change of 20 m.y. over the
whole area of the ocean basins deeper than 1 km, this
translates to an equivalent water volume of 0.825 x 10~6
m3 (see Table 8.1~. This effect is in the opposite direction
to that of the ridge-crest volume effect, since the sedimen-
tation on the ocean floor tends to decrease the r~dge-crest
topographic effect somewhat.
REDUCTION IN CONTINENTAL AREA
Mountain building, by increasing the thickness of the
continental crust, serves to decrease its area, and hence
increases the area of the ocean basins. This will then
cause a lowering of ocean depth and an increase in free-
board. We have attempted to allow for this phenomenon
(Harrison et al., 1981, 1985~. Most of the effect is caused
by the collision of India with the rest of Asia. Additional
amounts are contributed by the collision of Arabia with
Asia and the collision of the continents on either side of
the Alps. The revised reduction in continental area is 3.2
x 10~2 m2. When the area is multiplied by an average
oceanic depth of 3729 m (Menard and Smith, 1966), a
volume increase of 1.193 x 10~6 m3 is reached. This is
apportioned uniformly from 45 Ma to the present and is
shown in Table 8.1.
The reduction in continental area was calculated using
elevations greater than 500 m in Asia, Europe, India, and
Arabia and assuming that these were caused by crustal
shortening using an isostatically balanced model to obtain
the increase in thickness (Harrison et al., 1985~. Allow-
ance was made for elevations above 500 m in these conti-
nental areas that were not caused by collision on either
side of the Tethys as it closed. The reduction in area is
considerably less than that which would be calculated
from the timing and speed of collision and the length over
which collision occurred (Le Pichon et al., 1986) or from
the present rates of consumption, projecting them back
into the past (Parsons, 19811. One possibility is that the
elevated areas produced by collision have been eroded
away, and indeed, the present erosion rates appear to be
removing as much continental crust as is being piled up by
collision. But a calculation of the sediment deposited in
the Bengal fan reveals that this is only one fortieth of that
necessary to explain the discrepancy (Harrison et al., 19851.
We conclude that the present erosion rates are considera-
bly higher than average erosion rates over the past 40 m.y.,
possibly because of anthropogenic effects, and that the
OCR for page 147
LONG-TERM EUSTASY AND EPEIROGENY IN CONTINENTS
collision rate of continental crust has been on average
much less than that which pertains today, possibly because
much oceanic crust existed in the region of collision.
OCEAN COOLING
A small effect should be present because of the cooling
of oceanic water since the Cretaceous. Southam and Hay
(1981) quote Fairbridge (1961) as giving a 2-m rise of sea
level for each 1 °C rise in temperature. We shall follow the
practice of this paper and calculate the volume change on
warming the oceanic waters. One difficulty is that the
volume coefficient of expansion of water increases rapidly
with rises in temperature and pressure. We have analyzed
the effect of a temperature increase, compared with today,
of oceanic water going from 2°C to 12°C, this 10° increase
being roughly what oxygen isotopic data from Inoceramus
indicate (Saltzman and Barron, 1982~. Only the water
below a depth of 200 m was assumed to increase in tem-
perature. Volume coefficients of expansion were taken
from Sverdrup et al. (1942~. The average coefficient of
expansion was determined at a depth by assuming that the
coefficient of expansion at any depth may be written:
V dZ =a+ bT. (8.5)
It is easy to show that the average coefficient of expan-
sion between temperatures To and T2 is given by:
1 dV b(T + T ~
V ~ = a+ 2 (8.6)
The values of a and b are calculated from data pre-
sented in Table 9 of Sverdrup et al. (1942) for a salinity of
3.5 percent. These average coefficients of expansion were
used to determine the depth variation, which was assumed
to be of the form:
V <~ =P+qx+rx, (8.7)
where x is the depth. (l/V)(dV/dl) was evaluated at depths
of 0, 2, and 4 km in order to determine the coefficients p,
q, and r in Eq. (8.7~. The average coefficient of expansion
over a depth range from 0.2 km to y km is therefore
Y SEA LEVEL MEASURED FROM CONTINENTAL
~ ~FLOODING
J(D + qx+ rx ~ dx
0.2
147
below 200 m to warm up by 10°C. The answer is 0.249 x
l6 m3
Since thermal expansion of the water increases the water
depth without increasing the loading of the deep ocean
basins, it is not appropriate to use this volume in the same
way as the other volumes are used. The formal calculation
of how much freeboard is affected by this effect is compli-
cated. An approximation is to increase the volume by a
factor of 1/0.7 and to add up the other volumes given in
Table 8.1. The change in freeboard produced by this
increase in temperature is then found to be 7.2 m for the
ocean surface at its present elevation. This is more than a
factor of 2 smaller than the figure given by Fairbridge
(1961~. In order to obtain such an increase in ocean depth
(2 m/K), it would be necessary to have an average coeffi-
cient of thermal expansion in a 6-km-deep ocean of 333 x
10-6 K-~. Examination of the table given by Millero (1982)
shows that such coefficients of thermal expansion are not
achieved for 0°C water until a pressure of over 1 kbar is
reached (water depth greater than 10 km). Water at 25°C
has such an expansion coefficient at a pressure of 0.5 kbar.
It is clear that it is impossible to achieve an average ther-
mal expansion of the amount given by Fairbridge (1961)
for a 10°C warming of the present ocean.
The volume change was assumed to begin at 50 Ma,
which is about the time that benthic foraminifera oxygen-
isotopic data suggest that the bottom water started to cool.
Although there have been significant events in this bottom
water cooling, it is permissible in this study to apply a
uniform rate to the cooling, since the effect is so much
smaller than some of the other effects discussed. The
effect has been included in Table 8.1.
SU*IMARY OF VOLUME EFFECTS
Table 8.1 also shows the total change in freeboard after
allowing for all eight factors summarized in Table 8.1.
Total change in freeboard during the past 80 m.y. has been
228 m. If the absence of deep-water carbonates during the
Cretaceous is made up by the presence of the equivalent
volume of shallow-water carbonates, then the change in
freeboard will be 264 m. The various volume changes are
illustrated in Figure 8.3.
y - 0.2 (8.8)
This allows us to use the data from Menard and Smith
(1966) on area as a function of depth in the ocean basins to
calculate the total volume change on allowing the water
So far, we have used only continental hypsometry to
determine the additional area of the oceans as freeboard is
decreased, so that we could calculate what the freeboard
change is for a change in volume of the ocean basins or the
water in them. But a far more significant use can be made
of hypsographic curves to determine directly the change in
OCR for page 148
148
4
o
2
o o
0 10
,4
RIDGE C R E ST
/ VOLUME
-~ CONTINENTAL ICE
PACIFIC VOLCANISM
CONTINENTAL
20 30 40 50 60 70 80
AGE, MYBP
FIGURE 8.3 Volume estimates for six phenomena. A decrease
in volume as time progresses produces a sea-level fall (or free-
board increase). Although volume changes are not linearly re-
lated to changes in freeboard because of the increase in area of
the water as sea-level rises, the straight line in Figure 8.2 can
then be used as an approximate linear relationship. Slopes of
lines in this figure may then be roughly equated with rates of
freeboard change, as shown in the top left-hand corner.
freeboard, using additional data consisting of the amount
of continent flooded. This is determined by measuring the
area of continent covered by marine sediments through
time. This method has formed the basis for a number of
measurements of eustatic sea-level change through time
(Egyed, 1956; Hallam, 1971~. A modern set of paleogeo-
graphic maps (Barron et al., 1981) allows us to calculate a
FIGURE 8.4 Freeboard change measured
from amount of continental flooding dur-
ing the past 180 m.y. The crosses repre-
sent mean values from results from six
individual continents, and the horizontal
bars show the limits of the standard error
of this mean value. The open circles show
the value calculated from the total amount
of flooding and the world hypsographic
curve.
C. G. A. HARRISON
better estimate of the amount of continental flooding and
hence eustatic sea-level rise during the Mesozoic and
Cenozoic (Harrison et al., 19851. Sea-level rises (i.e.,
changes in freeboard) calculated in this way are shown on
Figure 8.4. Modern hypsographic data (Harrison et al.,
1983) for all major continental areas excluding Antarctica
and Greenland were used to determine the freeboard re-
duction necessary to produce the desired amount of flood-
ing. There are several things to note about this curve.
First, the amplitude of the change since the Cretaceous (80
Ma) is 153 m. Second, there appears to be a pronounced
regression and transgression during the Neogene. A
comparison with the data on volume changes (Table 8.1)
reveals that the amplitude of the change calculated from
flooding is considerably less than that estimated from
volume changes, being only 67 percent of the latter. In
addition, the volume change data do not show any evi-
dence for the relatively large freeboard at 60 Ma, in com-
parison with the data on either side.
Wise (1974) showed that if the time slices used to make
the paleogeographic maps are lengthened, the area of flood-
ing goes up. This is because all marine deposits occurring
within the time slice are included when preparing the
paleogeographic map, and small changes in vertical mo-
tion between various parts of the continent will be trans-
formed into flooding estimates that are too large for any
one instant of time. For this reason, the maps in Barron et
al. (1981) were made from the closest individual maps in
the primary references, with no attempt being made to
combine different primary maps if their ages did not agree
with the uniformly spaced 20-m.y. ages in the maps in
280 _
240
200
160
a)
In
._
- 120_
>
~0
40
O
X
X
o
o
X
0 ~
_ 1 1
0 2C 40 60
80 100 120 140 160 180
Age, M Y BP
OCR for page 149
LONG-TERM EUSTASY AND EPEIROGENY IN CONTINENTS
Barron et al. (1981~. Nevertheless, it is probable that areas
of flooding have still been somewhat overestimated, and
so the data shown in Figure 8.4 are probably maximum
estimates. This means that the discrepancy between Fig-
ure 8.4 and Table 8.1 is even larger than it appears at first
sight, especially if the absence of deep-water carbonates in
the Mesozoic is counteracted by the presence of equiva-
lent volumes of shallow-water carbonates.
The presence of the Paleocene regression presents fur-
ther problems. Bond (1985) suggested that, in some cases,
the evidence for the presence of Paleocene marine sedi-
ments has been removed by erosion and that the value
measured from paleogeographic maps is probably too low.
But we then have to ask why erosion removed the Paleo-
cene sediments in preference to sediments of other ages. It
seems likely that erosion could cause removal of young
sediments if sea level were suddenly to drop so that these
sediments became exposed to aeolian and hydrologic ero-
sion. Thus, even if the record has been obliterated by
erosion, the presence of this erosion suggests, in and of
itself, that there was some amount of regression during
this time. There may, however, be a slight displacement in
time of the age of the maximum regression.
It is possible that the Paleocene regression is caused by
an amplification of the ridge-crest volume effect, as dis-
cussed by Pitman (1978~. The position of the shoreline on
a subsiding continental margin is highly dependent upon
the relative rates of margin subsidence and freeboard in-
crease. Subtle changes in the rate of change of ridge-crest
volume can result in large changes in the amount of con-
tinental shelf flooded and so possibly cause an effect similar
to Paleocene regression. It can be seen in Figure 8.3 that
there are some small changes in the rate at which ridge-
crest volume is being reduced that might produce the desired
effect.
The Paleocene regression has been seen many times
before in data of the same sort. Flooding data from Russia,
analyzed by Hallam (1977) show a regression of about the
same magnitude at the beginning of the Tertiary. How-
ever, this pronounced regression is not nearly so obvious
on Hallam's (1984) eustatic sea-level diagram.
EPEIROGENY OF THE CONTINENTS
An alternative way of estimating the average change in
freeboard is to measure the amount of flooding for indi-
vidual continents and to use the hypsographic curve for
each continent to determine a freeboard change for each
continent in turn. Then these estimates may be averaged
to produce a mean freeboard curve, which is assumed to be
a eustatic curve. This has been done, and the results are
shown in Figure 8.4, along with the standard error esti-
mates about each mean value. It can be seen that the result
149
so estimated is very close to that determined by using the
global flooding estimates and the global hypsographic
curve. The difference between the two values is never
greater than 20 m and is usually much less. The two
methods differ because they weight the data from individ-
ual continents differently. The global data set weights a
continent according to its area, whereas the other method
weights each continent equally. But there are obviously
major differences between individual continents, as can be
seen by the rather large standard error estimates. Bond
(1978a,b, 1979) suggested that the differences between
individual continents were due to the fact that the average
elevations of continents can rise and fall in response to
forces beneath them. The deviation of sea level from the
mean for each continent is shown in Figure 8.5. This
figure illustrates the type of mean vertical motion that
each continent must have undergone in order to bring its
own "sea-level" curve into agreement with the average. It
is not necessary to assume, or likely, that each continent
suffers the same vertical motion over its whole area. Rather,
the figure shows what the average motion must have been
to reach agreement with the mean curve.
Bond (1979) interpreted similar data in a slightly differ-
ent way. He produced an estimate of the error involved in
determining sea-level change for individual continents.
The highest sea-level rise was calculated on the basis that
the whole of the continental shelves was flooded (the
assumption made in this chapter), whereas the lowest sea-
level rise was calculated assuming that the present-day
shelf only had 50 percent of its area flooded in the past.
Bond then made the assumption that the groupings of
elevations shown in this figure was not by chance, but
reflected real events in sea-level history. Thus, the group-
ing of elevations between -30 m and 80 m for four of his
continents during the Miocene represented the sea level at
that time. This enabled him to postulate that since the
Miocene, Africa has risen epeirogenically by about 90 m.
This correction is then applied to all earlier data from
Africa. It is then also observed that the African data, even
with this correction, do not agree with the data from the
other continents during the Eocene, and so a second cor-
rection, of 135 m, is also applied to the African data.
Corrections are also applied to Australia, North America,
and Europe at various times in order to allow complete
agreement between the various curves. A summary of the
epeirogenic changes suggested by Bond is shown in Table
8.2. It can be seen that most of the epeirogenic motions
suggested by Bond have been uplifts.
Since these motions are corrected before eustatic sea
level is calculated, the eustatic sea-level changes suggested
by Bond during this time interval will be somewhat less
than if the same data had been used with the method of
Harrison et al. (1983~. Bond (1979) attempted a measure
OCR for page 150
150
FIGURE 8.5 Sea-level calculations for
each of six continents. The mean sea level
has been subtracted from each continental
value for each time interval, and the re-
sults for each continent have been
smoothed by taking 0.8 of the central value
and 0.1 of the values on either side. Curves
that fall going forward in time indicate
that the continent, or a large portion of it,
has undergone subsidence during the time
interval. The North American results were
calculated using the North American hyp-
sographic curve excluding Greenland. The
curve for Africa has been calculated using
the new flooding data for 60 Ma produced
by Bond (19851. See Hamson et al. (1985~.
ment of the error of his sea-level estimations by making
two calculations, one in which all of the shelf areas are
presumed to be flooded, and another in which only 50
percent of the shelf areas are presumed to be flooded,
which will give a lower estimate of sea level. Bond argued
that since the real percentage of flooded shelf was likely to
be greater than 50 percent, this second figure would give a
minimum estimate of sea level. Bond's results show that
at 70 Ma, the maximum estimate of sea-level rise is 141 m,
and the minimum estimate of sea-level rise is 80 m. These
figures bracket an interpolated value for this time interval
taken from Figure 8.4 (see also Figure 8.8~. The actual
values of flooded area measured by Bond must be some-
what larger than those measured by Harrison et al., other-
wise there would have been more of a discrepancy be-
tween the two results.
We prefer the unbiased calculation that supposes that
the modern hypsographic curves are in general like those
of previous eras apart from a coherent change discussed in
the next section, and that the best estimate of eustatic sea-
level change is obtained by the calculation that assumes
this, i.e., the one done in Figure 8.4. The epeirogenic
movements suggested by Bond (1979) are also seen in the
curves (Figure 8.5) except for the European uplift during
the Cretaceous.
If the possibility exists that portions of continents can
undergo slow epeirogenic movements of amplitude up to
several hundred meters, then observations of sea level
taken at any one point in a continent are not necessarily of
eustatic sea-level change. In order to obtain eustatic sea-
level change it is necessary to average over a large number
of individual places on a continent or preferably on a
series of continents. Measurement of long-term eustatic
sea-level changes is thus as fraught with difficulty as the
C. G. A. HARRISON
+~n
.__ _
+1 00 _
~ +50
111
O
in ~
_50
-100
+ AFRICA
x ASIA °
o N. AMERICA / \
-a S. AMERICA / \ - °
-tUROPELIA'° - - -I ~
\\ ~ ~' -__ _
-150 . ~ , . , , . . 1
0 20 40 60 80 100 120 140 160 18C
MYBP
establishment of the glacio-eustatic signal, where data from
different areas often give significantly different results,
presumably due to tectonic or epeirogenic changes that
have taken place at some or all of the observation points.
Sea-level changes measured in one place have been
used to infer eustatic changes. For instance, Sleep (1976)
estimated a eustatic sea-level fall of 325 m since the late
Turonian-early Coniacian based on the presence of shal-
low-water marine sediments onlapping onto the continen-
tal craton in Minnesota. The present elevation of the
. .
craton is 375 m, which was corrected by 50 m to allow for
regional uplift due to erosion. Hancock and Kauffman
(1979) calculated a sea-level fall of over 600 m since the
Campanian. It seems much more likely that this figure is
a combination of eustatic effects, plus an epeirogenic ele-
vation of the appropriate land areas since the Campanian.
Other people have attempted to calculate eustatic changes
from evidence found in Grillings on the continental mar-
gins. This is done by finding the present day depth of
sediments of a certain age in the continental margins. This
has then to be corrected for continental margin subsi-
dence, produced by the slow cooling of the lithosphere
following the thermal event that marked the original breakup
of the continent. Isostatic adjustments have to be made for
the added load of the sediment, and this can be done by
using either local isostatic compensation or regional com-
pensation and flexure of the lithosphere. Finally, the depth
of the water during the time of deposition has to be esti-
mated from the sedimentology or from benthic fossils
found in the sediment. An example of this is shown by-
Watts and Steckler (1979), who arrived at a freeboard fall
of 114 m during the past 75 m.y. This was from a number
of wells drilled into the eastern margin of North America,
including the Cost B-2 well and four wells off the coast of
OCR for page 151
LONG-TERM EUSTASY AND EPEIROGENY IN CONTINENTS
Nova Scotia. A more recent analysis gives a fall of 140 m
since 83 Ma (Watts and Thorne, 1984~. This number is
considerably less than that arrived at by a consideration of
volumes (Table 8.1~. The discrepancy may be removed if
it is imagined that this borderland of North America has
suffered, in addition to the normal thermal subsidence, an
additional long-term epeirogenic subsidence as well.
Hallam (1984) pointed out that in some cases evidence for
significant differences in the thicknesses of sediments exists
from one area of a craton to another. For instance, there is
little correlation between the thicknesses of sediments
deposited in Dorset and northeast Yorkshire during the
Jurassic. This he attributed to taphrogenic influences.
The presence of depocenters on continental margins that
migrate through time seems to imply a variability in the
rate of subsidence, which probably cannot be allowed for
in any thermal cooling model, and which therefore may
make any estimates of eustatic sea-level change from these
margins inaccurate.
Morner (1976) introduced another complication into
our ideas of relative and absolute sea-level changes. He
coined the term "geoidal eustasy," by which he means
changes of relative sea level produced by changes in the
Earth's geoid with time. The present-day geoid departs
from the best-fitting ablate spheroid by an amplitude of
about +110 m. The GEM 10B model (torch et al., 1979)
shows a high of 100 m centered on New Guinea and a low
of-120 m in Antarctica. Morner suggested that the geoid
is constantly changing its shape through time. The ocean
surface adjusts to the instantaneous position of the geoid,
whereas the continental areas take a finite time to respond
to the geoid changes. The result is that freeboard changes
occur that are not uniform over the surface of the Earth.
However, before this mechanism of relative sea-level
change can be accepted, it is important to know how fast
the geoid can change. Current opinion seems to be that the
geoid represents events on the Earth that happened a very
long time ago (Crough and Jurdy, 1980; Anderson, 1982;
Chase and McNutt, 1982), and so we must expect that
changes in the geoid happen very slowly.
COMPARISON OF VOLUME AND FLOODING
ESTIMATES
We have seen that the estimates of sea-level change
since the Cretaceous calculated from volume estimates of
ridge crest, marine sediment, continental ice, thermal
bulges, cooling, and ocean-basin area change (242 m) and
that from continental flooding (153 m) are different. A1-
though the errors in either of these estimates are large
enough to permit this difference, it might be worthwhile to
consider what the difference could be caused by, suppos-
ing it to be real. The numbers can be made to agree if it is
151
supposed that the continental hypsographic curves were
steeper in the past than they are today. In this case, to
flood a certain area would require a larger decrease in
freeboard than would be calculated by using the present-
day hypsographic curve.
Southam and Hay (1981) suggested that the continental
hypsographic curve was steeper in the early Mesozoic
than it is today because of all the sediment since eroded
and deposited onto the passive-margin continental slopes
and rises. They produced a hypsographic curve for the
early Mesozoic accounting for this effect. A rough esti-
mate of freeboard change from the present day to produce
the desired amount of flooding in the Cretaceous is 700 m.
If their hypsographic curve is correct, then the amount of
erosion that had taken place between the early Mesozoic
and the Cretaceous was considerably greater than that
which has occurred since. Alternatively, since they did not
produce any details of how the hypsographic curve was
established except to give one with the required average
continental elevation, it is possible that other hypsogra-
phic curves could be developed that require a smaller
freeboard increase but that still satisfy the requirement of
average elevation outlined by Southam and Hay (1981~.
An alternative possibility is that the continents have
thermally contracted since the splitting up of Pangea. The
central regions of Pangea were presumably isolated from
major mantle convection currents, allowing the mantle
beneath the continental areas to become slightly warmer
than the average. When Pangea split apart in response to
a new pattern of convection, the mantle would have be-
come ventilated, allowing it to cool and so contract, caus-
ing the desired effect (Anderson, 1982~. If the contraction
of about 100 m occurred in the lithosphere immediately
beneath the continents, of thickness about 200 km, then
the average temperature drop would be on the order of
15°C to produce the desired effect. A simple model can be
used (Carslaw and Jaeger, 1959) in which the base of the
lithosphere is suddenly cooled at the time of breakup (180
Ma). In order to obtain a subsidence of 100 m between
100 Ma and today, the cooling at the base of the litho-
sphere has to be on the order of 130°C to achieve the right
magnitude of subsidence.
DISCUSSION OF EPEIROGENIC MOVEMENTS
We have shown that continents have probably moved
independently vertically over distances of several hundred
meters, with time constants of tens to hundreds of millions
of years. It is probable that these movements are caused
by convection currents within the mantle or possibly by
thermal effects beneath the continental lithosphere. An
interesting calculation has been done by Hager et al. ( 1985~.
They took three-dimensional seismic velocity anomalies
OCR for page 152
152
within the mantle and converted them to density anoma-
lies. These density anomalies were inverted to obtain the
flow field within the mantle. This flow field was in turn
used to calculate deviations of the upper and lower sur-
faces of the mantle. Depending on the viscosity model
used in the analysis, the upper surface can be deflected up
to several hundred meters with a wavelength of about
10,000 km. This is not a deflection of the geoid, but of the
upper surface of the Earth. The deflection of the geoid is
considerably less, being in general only a few tens of
meters. If this pattern of highs and lows changes as a
result of a long-term change in the pattern of convection
within the Earth, then we would expect the continents to
experience up to several hundred meters of vertical mo-
tion, reflected in the amount of flooding that occurs through
time. Alternatively, the pattern of convection may remain
constant, but the continents may move laterally over the
highs and lows, causing the same effect. Interestingly
enough, one of the models produced (B. Hager, Massachu-
setts Institute of Technology, personal communication)
shows that Africa is currently situated on a surface high of
about 600-m amplitude. This is rather larger than what we
would predict from the flooding difference between Africa
and the rest of the continents during the past 40 m.y.
(Figure 8.5, 150 m) or from the position of the modal
elevation in Africa, compared with that from other conti-
nents, but it is of the correct order of magnitude. What is
necessary to check out this hypothesis is to be able to
determine how the convection pattern within the Earth
changes with time, and to predict how Africa moved across
this convection pattern during the past 100 m.y.
It is interesting to note that Stefanick and Jurdy (1984)
calculated that Africa has a much greater density of hot
spots than any other portion of the Earth of comparable
size. This is true for the 42 hot-spot catalogue of Crough
and Jurdy (1980), and for the 117 hot-spot catalogue of
Burke and Wilson (1976~. This confirms earlier estimates
that Africa is a region of intense hot-spot density. For the
117 hot-spot catalogue, most of Africa has a hot-spot
density of more than twice the global average. Maybe the
relative uplift of Africa with respect to the rest of the
continents during the past 40 m.y. is in some way con-
nected with this large density of hot spots.
CHANGING THE AGE DISTRIBUTION OF THE
OCEAN BASINS
Changes in the rate of seafloor spreading, as measured
by the area of oceanic crust produced per unit time inter-
val, can produce significant changes in the average depth
of the basins and thus change sea level, as discussed ear-
lier. The reason is that the age distribution of the oceanic
C. G. A. HARRISON
crust is changed by changes in the rate of seafloor spread-
ing. Higher rates of spreading usually mean that there is
more young crust present, whereas slow spreading rates
usually imply that the crust as a whole is older. Changes
in the age distribution can also be affected by the converse
process to seafloor spreading, namely subduction. If the
subduction process changes the amount of young versus
old crust that is subducted per unit time interval, then the
pattern of oceanic crustal age will be altered, thus affect-
ing the average depth and the freeboard.
We shall show that this is a potentially powerful method
of affecting sea level over time periods of tens of millions
of years. The effect of changing the pattern of subduction
in the past has been taken into account by the cataloguing
of Kominz (1984~. What we wish to show is that even
with constant spreading rates, the effect of the age of the
ocean basins being subducted could have a profound influ-
ence on sea level in the future. The pattern of the distribu-
tion of the area of oceanic crust as a function of age is one
in which there is a monotonically decreasing area as the
age is increased (Berger and Winterer, 1974; Harrison,
1980; Sclater et al., 1980~. This pattern is most easily
produced if there is a constant rate of production of oce-
anic crust and if subduction occurs uniformly for crust of
all ages. The following equations are easy to derive. The
area of crust produced per unit time is A km2/(m.y.~; B
km2/(m.y.~2 is the area of crust subducted per unit time for
each unit time age interval; TmaX is the maximum age of
the crust; and TaV is the average age of the oceanic crust.
A = BT (8.9)
max
T = T /3 (8.10)
av max
a=A-Bt, (8.11)
where a is the areal distribution of oceanic crust as a
function of age t. The total area of the ocean basins is
ATmaX/2. Now, obviously, if B is not a constant, but rather
depends on the age of the oceanic crust, then the situation
of having a uniformly decreasing area as a function of age
will not remain. The oceanic crust will change its age
distribution pattern to reflect the rate at which oceanic
crust of different age is being subducted.
Parsons (1982) calculated the rate at which oceanic
crust is being subducted as a function of the age of the
oceanic crust. Details of this are given in Table 8.3. This
table presents the same data as are in Figure 3 of Parsons
(1982~. The numbers in the second column should all be
equal, for a steady-state situation to apply, and it is obvi-
ous that this is not remotely the case. There are some
problems with the interpretation of these figures. They do
not produce the same consumption rate (2.506 km2/yr) as
the creation rate (global sum of 3 km2/yr). Most of the
discrepancy is caused by the fact that the oceanic crustal
OCR for page 153
LONG-TERM EUSTASY AND EPEIROGENY IN CONTINENTS
TABLE 8.3 Subduction Rates
Age Interval
(Ma)
Area of Crust Subducted
per Unit Age Interval,
10-1° km2/yr
Oto4 40
4to9 182
9 to 20 338
20to35 291
35 to 52 336
52to65 153
Average O to 65: 223 + 49 (standard error)
65 to 80 45
80 to 95 34
95 to 110 243
110 to 125 25
125tol40 159
140 to 160 14
160 to 180 22
Average 65 to 180: 77 + 33 (standard error)
Note: The first mean is significantly greater
than the second mean with a confidence of 97.5
percent.
area is growing at the expense of the continental area, a
fact that has been discussed above, and that produces a
rate of sea-level fall that can be calculated in the following
way. The total generation of seafloor is equal to the total
consumption rate of continental and oceanic crust (Par-
sons, 1981~. But part of this consumption, notably that
between Arabia and India on the one hand and Asia on the
other, causes an increase in the area of oceanic crust, by an
amount of 0.229 km2/yr, which will cause a eustatic free-
b o ard incre as e of 1 . 8 m/m . y . ~ 0 .00 1 8 mm/yr) .
In order to calculate the effect of a consumption rate
that is not uniform, we have made a calculation in which
we start with an oceanic crust that has a uniformly de-
creasing area versus age plot, and have the total consump-
tion of crust of all ages equal to the production of new
crust. The consumption of crust is assumed to vary with
age in the same way as the figures in Table 8.3 indicate.
The maximum age of crust is assumed to be 180 Ma. The
average elevation of the crust is calculated from the nor-
mal equations relating elevation to age (Parsons and Sclater,
1977~. Then the age distribution after a time lapse of 1
m.y. is calculated by the following procedure: al is the
area of crust in the ith million year age group, where i runs
from 1 to 180; ci is the rate of consumption per million
years for the ith million year age group; bi is the age
distribution after a time lapse of l m.y.
153
bi ~ =ai -C
i = ~
(8. 12)
(8.13)
The average elevation for the area depth distribution
given by b' (i=l, 181) may now be calculated. The
change in freeboard produced by the ci's given in Table
8.3 is equal to 2.93 m allowing for a ratio of ocean surface
area to oceanic crust area of 0.837 (Menard and Smith,
19661. Thus, if this consumption pattern continues for
several tens of millions of years, it could cause a signifi-
cant change in the freeboard. Over 10 m.y., the system is
approximately linear with time. But over longer time
periods the effect will average out to less than 2.93 m/m.y.
(0.0029 mm/yr).
CRETACEOUS FLUCTUATIONS
The Cretaceous Interior Seaway of North America is a
notable feature of the major transgression that occurred
worldwide during this time. Evidence exists from sedi-
mentary deposits that there were major fluctuations during
the Cretaceous of the depth of the Interior Seaway, which
at times stretched from the Gulf of Mexico to the Arctic
Ocean. This evidence consists of sets of sedimentary beds
that exhibit transgressive-regressive cycles. The trans-
gressive portion of a cycle exhibits upward-fining se-
quences, from near-shore sands to deeper water pelagic
carbonates with relatively little terrigenous sediment. The
pattern is repeated in reverse order during the regressive
portion of the cycle. It is thought that the maximum depth
of water after the major transgressive cycles was several
hundred meters. Eicher ( 1969) calculated a maximum depth
of 500 m for the Bridge Creek Limestone member of the
Greenhorn Formation (lower Turonian) and the Fairport
member of the Carlile Shale (middle Turonian). This was
done on the basis of the percent of pelagic foraminifera
compared to total foraminifera in these members. An even
larger estimate was obtained by estimates of the paleo-
slope of river drainage basins. Although changes as large
as 500 m are probably overestimates of the real situation,
it seems unlikely that the sedimentological signal could be
produced by a change of less than 100 m. These cycles
have been tied into worldwide changes of sea level with a
time precision of about 0.3 m.y. (Kauffman, 19771.
What we seek to determine is the range of change in
freeboard that might occur if seafloor spreading rates change
with a periodicity of about 10 m.y. There are in fact 10
transgressive-regressive cycles recorded during the whole
of the Cretaceous, giving a periodicity of 7 m.y., but the
OCR for page 154
OCR for page 156
OCR for page 157
OCR for page 158
Representative terms from entire chapter:
oceanic crust
154 c. G. A. HARRISON
Time - 0 MY Time = 5 MYaverage depth is calculated using the usual age-depth rela
t~,, i, tionships (Parsons and Sclater, 1977). From this, the change
| Am, A :, infreeboard may tee calculated. Spreadingis then reduced
j Am,, ~Am, to its old value for 5 m.y., and the average depth is again
Am, calculated. This process is repeated a number of times, in
, , ~ it, I ~order to determine the magnitude of freeboard change that
0 5C 100 ~50 05 ~5 45 95 ~45
Age, MY occurs after each 5-m.y. period of enhanced or reduced
Time - ~0 MY Time = ~5 Sty spreading rate. This model is illustrated in Figure 8.6.
is, Calculation of average depth of the oceanic crust al
\ ~ Am, lows us to determine the change in depth of the inland sea.
\ ~ ~Due to the isostatic response of the continental crust by
~\ ~ ~5, loading of an added water depth, the water depth is in
,l~ , , ~ ~
LONG-TERM EUSTASY AND EPEIROGENY IN CONTINENTS
about 60 m around a depth that is on average about 300 m
greater than it was when the process started.
Now it appears extremely unlikely that the world's
spreading centers could all undergo a factor-of-2 change
in spreading rate at 5-m.y. intervals, exactly synchronized
with each other, or that an additional portion of ridge crest
could turn on and off to produce the extra amount of
young crust necessary to give the effect discussed above.
Even if this strange phenomenon happened, it would not
give the magnitude of effect seen in the paleodepths of the
Western Interior Seaway. A more likely possibility is that
only one portion of the ridge crest is involved in changing
its spreading rate roughly every 5 m.y. If this portion of
the world ridge-crest system is, say, 20 percent of the total
ridge system, then the eustatic effect would be about 15 m.
This is the sort of magnitude of the third-order cycles of
Vail et al. (1977) with which the transgressive-regressive
cycles in the Western Interior Seaway have been corre-
lated, so that a worldwide correlation could be possible. If
the changes in spreading occurred in the Pacific, then they
would be matched by changes in subduction rates of the
Pacific Ocean basin, and in particular in subduction rates
at the western margin of North America. It is possible that
during increased rates of subduction to the west of the
Western Interior Seaway, the shallow basin could be caused
to subside tectonically, whereas during times of reduced
subduction rate, uplift of the basin could occur. In this
way, the tectonic effects could amplify the eustatic sea-
level effects of changing ridge-crest volume, to give the
large changes in depth inferred from the transgressive-
regressive cycles of sedimentation. Unfortunately, since
much of the Cretaceous is in the magnetic quiet zone, it
would be difficult, if not impossible, to determine whether
changes in spreading rate of this sort had occurred. Fur-
ther information about models of flooding of the Western
Interior Seaway can be found in Harrison (1985~.
CONCLUSIONS
Various phenomena that can affect sea level over a time
scale of tens to hundreds of millions of years have been
discussed. During the Neozoic, the most important of
these has been the effect of changing ridge-crest volume,
which has altered continental freeboard by a volume change
of 9.55 x 10~6 m3 over the past 80 m.y. The buildup of
continental ice has caused an additional effect of 2.52 x
10~6 m3, but over a shorter time scale of about 40 m.y. An
additional effect of 3.20 x 10~6 m3 is provided by the
thermal bulge that is thought to have occurred during a
time of enhanced volcanism in the Pacific, this being over
a time scale of about 70 m.y. Smaller effects are produced
by the reduction in continental area during the collision of
155
-280
-24
-20
- 160
C)
Cal
0-12
m
I3J
-80
-4
o
o
X o
o
(a Q
. . . . . . . .
o
o
o
o
.
x
.
x
0 20
40 60 80
AGE, MYBP
FIGURE 8.8 Changes in freeboard produced by volume effects.
The small dots allow for the deep-water carbonate volume. The
open dots show freeboard without this effect. The crosses show
freeboard changes predicted from amounts of continental flood-
ing, taken from Figure 8.3.
the continents on either side of Tethys (1.19 X 10~6 ma over
a time scale of 45 m.y. and in the same direction as the
other three effects) and possibly an effect in the opposite
direction of 2.58 x 10'6 m3 produced by deposition of
calcium carbonate in the deep ocean starting 100 Ma. The
curve of freeboard, calculated from these figures (and
other small effects) and using a modern hypsographic curve
to obtain the volume of water flooding onto the continents
(a small correction) is shown in Figure 8.8. The total
freeboard change is 228 m. If the carbonate deposition is
not a factor (i.e., if the deep-water carbonates just replaced
shallow-water carbonates), then the increase in freeboard
is 264 m. These calculations have large errors associated
with them, such as those discussed by Kominz (1984~.
The area of present land flooded 80 Ma was about 51.5
x 106 km2. Using the present-day hypsographic curve, a
freeboard decrease of 150 m is necessary to flood this
area, which is considerably less than that calculated from
volume estimates. This suggests that the continental
hypsographic curves were somewhat steeper in the past
than they are today, requiring larger freeboard decreases
to cause the same amount of flooding. It is possible that
this decrease in the elevation of the hypsographic curves
with time is caused by a cooling of the continents follow-
ing breakup of Pangea about 200 Ma.
Variations in the amount of freeboard change to flood
156
different continents by the observed amounts indicates
that the continents themselves have suffered vertical mo-
tions. These epeirogenic motions have amplitudes of up to
hundreds of meters, and occur on time scales of tens of
millions of years. Because of these vertical motions, esti-
mates of freeboard change measured at one place may not
indicate true eustatic sea-level changes.
Sea-level changes necessary to produce the large ef-
fects of water depth seen in the Western Interior Seaway
of North America are likely to be caused by an amplifica-
tion of a eustatic change. Since the transgressive-regres-
sive cycles can be correlated with worldwide sea-level
changes, there must be a eustatic signal present. Amplifi-
cation by tectonic subsidence and uplift, produced by
varying speeds of subduction, may be the mechanism
whereby tens of meters of eustatic sea-level change can
produce hundreds of meters of water depth change within
the Western Interior Seaway.
NOTE ADDED IN PROOF
Further discussion about sea-level changes on time scales
appropriate to this chapter may be found in Heller and
Angevine (1985), Sahagian (1987, 1988), and Harrison
(19881.
ACKNOWLEDGMENTS
I have benefitted from discussions with Garry Brass,
Bill Hay, Eric Saltzman, and Kim Miskell-Gerhardt.
Reviews by Michelle Kominz and Tony Hallam materially
improved this paper. Some of this research was supported
by grants from the National Science Foundation. Contri-
bution from the University of Miami, Rosenstiel School of
Marine and Atmospheric Science.
REFERENCES
Abbott, D. H., and S. E. Hoffman (1984J. Archean plate tecton-
ics revisited. 1. Heat flow, spreading rate, and the age of
subducting oceanic lithosphere and their effects on the origin
and evolution of the continents, Tectonics 3, 429~48.
Anderson, D. L. (19821. Hotspots, polar wander, Mesozoic
convection and the geoid, Nature 297, 391-393.
Barron, E. J., C. G. A. Harrison, J. L. Sloan II, and W. W. Hay
(1981~. Paleogeography 180 million years ago to the present,
Eclogae Geol. Helv. 74, 443-470.
Berger, W. H., and E. L. Winterer (19741. Plate stratigraphy and
the fluctuating carbonate line, in Pelagic Sediments on Land
and under the Sea, K. J. Hsu and H. Jenkyns, eds., Spec. Publ.
Int. Assoc. Sedimentol. 1, pp. 1 1-48.
C. G. A. HARRISON
Bond, G. C. (1978a). Evidence for late Tertiary uplift of Africa
relative to North America, South America, Australia, and
Europe, J. Geol. 86, 47-65.
Bond, G. C. (1978b). Speculations on real sea level changes and
vertical motions of continents at selected times in the Creta-
ceous and Tertiary periods, Geology 6, 247-250.
Bond, G. C. (1979~. Evidence for some uplifts of large magni-
tude in continental platforms, Tectonophysics 61, 285-305.
Bond, G. C. (1985~. Comment on "Continental Hypsography"
by C. G. A. Harrison et al., Tectonics 4, 251-255.
Burke, K., and J. T. Wilson (19761. Hot spots on the Earth's
surface, Sci. Am. 235, 46-57.
Carslaw, H. S., and J. C. Jaeger (19591. Conduction of Heat in
Solids, second edition, Clarendon Press, Oxford, 510 pp.
Chase, C. G.,. and M. K. McNutt (1982~. The geoid: Effect of
compensated topography and uncompensated oceanic trenches,
Geophys. Res. Lett. 9, 29-32.
Crough, T. (1979). Hotspot epeirogeny, Tectonophysics 61,
321-333.
Crough, S. T., and D. M. Jurdy (1980~. Subducted lithosphere,
hotspots, and the geoid, Earth Planet. Sci. Lett. 48, 15-22.
Egyed, L. (1956). Change of Earth dimension as determined
from paleogeographic data, Geophysica Pura e Applicata 33,
42~8.
Eicher, D. L. (1969). Paleobathymetry of Cretaceous Greenhorn
Sea in eastern Colorado, Am. Assoc. Petrol. Geol. Bull. 53,
1075-1090.
England, P. C., and S. W. Richardson (19801. Erosion and the
age dependence of continental heat flow, Geophys. J. R. As-
tron. Soc. 62, 421~37.
Fairbridge, R. W. (1961~. Eustatic changes in sea level, in
Physics and Chemistry of the Earth, vol. 4, L. H. Ahrens, F.
Press, K. Rankama, and S. K. Runcorn, eds., Pergamon, New
York, pp. 99-185.
Hager, B. (1980~. Eustatic sea level and spreading rate are not
simply related, EOS 61, 374.
Hager, B., R. W. Clayton, M. A. Richards, R. P. Comer, and A.
M. Dziewonski, (1985~. Lower mantle heterogeneity, dynamic
topography and the geoid, Nature 313, 541-545.
Hallam, A. (1971~. Re-evaluation of the paleogeographic argu-
ment for an expanding Earth, Nature 232, 180-182.
Hallam, A. (19771. Secular change in marine inundation of
USSR and North America through the Phanerozoic, Nature
269, 769-772.
Hallam, A. (1984~. Pre-Quaternary sea-level changes, Ann. Rev.
Earth Planet. Sci. 12, 205-243.
Hancock, J. M., and E. G. Kauffman (1979). The great trans-
gressions of the late Cretaceous, J. Geol. Soc. London 136,
175-186.
Harrison, C. G. A. (19801. Spreading rates and heat flow, Geo-
phys. Res. Lett. 7, 1041-1044.
Harrison, C. G. A. (1985). Modelling fluctuations in water depth
during the Cretaceous, in Fine-Grained Deposits and Biofa-
cies of the Cretaceous Western Interior Seaway: Evidence for
Cyclic Sedimentary Processes, E. Kauffman, F. Zelt, and L.
Pratt, eds., Soc. Econ. Paleontol. Mineral., Tulsa, Okla., pp.
11-15.
LONG-TERM EUSTASY AND EPEIROGENY IN CONTINENTS
Harrison, C. G. A. (1988~. Eustasy and epeirogeny of continents
on time scales between about 1 and 100 m.y., Paleoceanogra-
phy 3, 671-684.
Harrison, C. G. A., G. W. Brass, E. Saltzman, J. Sloan II, J.
Southam, and J. Whitman (19811. Sea level variations, global
sedimentation rates and the hypsographic curve, Earth Planet.
Sci. Lett. 54, 1-16.
Harrison, C. G. A., G. W. Brass, K. Miskell-Gerhardt, and E.
Saltzman (1985). Reply to 'Comment on "Continental Hyp-
sography" by Harrison et al. (1983)' by G.C. Bond, Tectonics
4, 257-262.
Hay, W. W., and J. R. Southam (1977). Modulation of marine
sedimentation by the continental shelves, in The Role of Fossil
Fuel CO2 in the Oceans, N. R. Andersen and A. Malahoff,
eds., Plenum Press, New York, pp. 569-605.
Hays, J. D., and W. C. Pitman III (19731. Lithospheric plate
motion, sea level changes and climatic and ecological
consequences, Nature 246, 18-22.
Helter, P. L., and C. L. Angevine (19851. Sea-level cycles during
growth of Atlantic-type oceans, Earth Planet. Sci. Lett. 75,
417-426.
Holland, H. D. (1981). River transport to the oceans, in The Sea,
Vol. 7, C. Emiliani, ea., Wiley, New York, pp. 763-800.
Holmes, A. (19781. Principles of Physical Geology, third edi-
tion, Wiley, New York, 730 pp.
Kauffman, E. G. (1977~. Geological and biological overview:
Western interior Cretaceous basin, in Cretaceous Facies,
Faunas and Paleoenvironments across the Western Interior
Basin, E. G. Kauffman, ea., The Mountain Geologist, vol. 14,
pp. 75-99.
Kennett, J. P. (1982). Marine Geology, Prentice-Hall, Engle-
wood Cliffs, N.J., 813 pp.
Kominz, M. ~ 1984 J. Oceanic ridge volumes and sea-level
change an error analysis, in Interregional Unconformities
and Hydrocarbon Accumulation, J. S. Schlee, ea., Am. Assoc.
Pet. Geol. Mem. 36, pp. 109-127.
Le Pichon, X., P. Huchon, and E. Barrier (1986). Pangea, geoid
and the evolution of the western margin of the Pacific Ocean,
in Formation of Ocean Margins, N. Nasu, ea., Terra Scientific
Publication Co., Tokyo.
Lerch, F. J., S. M. Klosko, R. E. Laubscher, and C. A. Wagner
(19791. Gravity model improvement using GEOS-3 (GEM 9
and 10), J. Geophys. Res. 84, 3897-3916.
Matthews, R. K. (19841. Oxygen isotope record of ice volume
history: 100 million years of glacio-eustatic sea-level fluctua-
tion, in Interregional Unconformities and Hydrocarbon Accu-
mulation, J. S. Schlee, ea., Am. Assoc. Pet. Geol. Mem. 36,
pp. 97-107.
Menard, H. W. (1973~. Epeirogeny and plate tectonics, EOS 54,
1244-1255.
Menard, H. W., and S. M. Smith (1966~. Hypsometry of ocean
basin provinces, J. Geophys. Res. 71, 4305-4325.
Millero, F. J. (1982~. The thermodynamics of seawater, Part I.
The PVT properties, Ocean Sci. Eng. 7, 403-460.
Morner, N.-A. (1976). Eustasy and geoid changes, J. Geol. 84,
123-151.
Parsons, B. (1981). The rates of plate creation and consumption,
Geophys. J. R. Astron. Soc. 67, 437-448.
157
Parsons, B. (19824. Causes and consequences of the relation
between area and age of the ocean floor, J. Geophys. Res. 87,
289-302.
Parsons, B., and J. G. Sclater (1977). An analysis of the vari-
ation of ocean floor bathymetry and heat flow with age, J.
Geophys. Res. 82, 803-827.
Pitman, W. C., III (1978~. Relationship between eustasy and
stratigraphic sequences of passive margins, Geol. Soc. Am.
Bull. 89, 1389-1403.
Prospero, J. M. (1981~. Eolian transport to the world ocean, in
The Sea, Vol. 7, C. Emiliani, ea., Wiley, New York, pp.
801-874.
Rubey, W. W. ~ 1951). Geological history of sea water, Geol.
Soc. Am. Bull. 62, 1111-1147.
Sahagian, D. (1987~. Epeirogeny and eustatic sea level changes
as inferred from Cretaceous shoreline deposits: Applications
to the central and western United States, J. Geophys. Res. 92,
4895-4904.
Sahagian, D. (19881. Ocean temperature-induced change in
lithospheric thermal structure: A mechanism for long-term
eustatic sea level change, J. Geol. 96, 254-261.
Saltzman, E. S., and E. J. Barron (1982~. Deep circulation in the
late Cretaceous: Oxygen isotope paleotemperatures from Ino-
ceramus remains in DSDP cores, Paleogeogr. Paleoclim.
Paleoecol. 40, 167-181.
Schlanger, S. O., H. C. Jenkyns, and I. Premoli-Silva (19811.
Volcanism and vertical tectonics in the Pacific basin related to
global Cretaceous transgressions, Earth Planet. Sci. Lett. 52,
435-449.
Schroeder, W. (19841. The empirical age-depth relation and
depth anomalies in the Pacific ocean basin, J. Geophys. Res.
89, 9873-9883.
Sclater, J. G., C. Jaupart, and D. Galson (19801. The heat flow
through oceanic and continental crust and the heat loss of the
Earth, Rev. Geophys. Space Phys. 18, 269-311.
Sleep, N. H. (19761. Platform subsidence mechanisms and
"eustatic" sea-level changes, Tectonophysics 36, 45-56.
Sloan, J. L., II (1985) Cenozoic Organic Carbon Deposition in
the Deep Sea, M.S. thesis, University of Miami, Fla.
Southam, I. R., and W. W. Hay (19811. Global sedimentary
mass balance and sea level changes, in The Sea, Vol. 7, C.
Emiliani, ea., Wiley, New York, pp. 1617-1684.
Stefanick, M., and D. M. Jurdy (19841. The distribution of hot
spots, J. Geophys. Res. 89, 9919-9925.
Stephenson, R. (19841. Flexural models of continental litho-
sphere based on the long-term erosional decay of topography,
Geophys. J. R. Astron. Soc. 77, 385-413.
Sverdrup, H. U., M. W. Johnson, and R. H. Fleming (1942). The
Oceans, Prentice-Hall, Englewood Cliffs, N.J.
Vail, P. R., R. M. Mitchum, and S. Thompson III (19781. Rela-
tive changes of sea level from coastal onlap, Am. Assoc. Pet-
rol. Geol. Bull. 63, 1-63.
Watts, A., and M. S. Steckler (1979~. Subsidence and eustasy at
the continental margin of Eastern North America, in Deep
Drilling Results in the Atlantic Ocean: Continental Margins
and Paleoenvironment, M. Talwani, W. W. Hay, and W. B. F.
Ryan, eds., Maurice Ewing Series 3, American Geophysical
Union, Washington, D.C., pp. 218-234.
158
Watts, A. B., and J. Thorne (19841. Tectonics, global changes in
sea level and their relationship to stratigraphical sequences at
the US Atlantic continental margin, Mar. Petrol. Geol. 1,
3 19-339.
Watts, A. B., J. H. Bodine, and N. M. Ribe (1980~. Observations
C. G. A. HARRISON
of flexure and the geological evolution of the Pacific ocean
basin, Nature 283, 532-537.
Wise, D. U. (1974~. Continental margins, freeboard and the
volumes of continents and oceans through time, in The Geol-
ogy of Continental Margins, C. A. Burk and C. L. Drake, eds.,
Springer-Verlag, New York, pp. 45-58.
