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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

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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.

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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.

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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.

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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.

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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

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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 2C to 12C, 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 10C. 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 0C water until a pressure of over 1 kbar is reached (water depth greater than 10 km). Water at 25C 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 10C 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

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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

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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

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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

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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 15C 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 130C 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

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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

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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

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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~ , , ~ ~ OCR for page 141
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

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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. 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