Gravity, bathymetry and convection in the earth

EARTH AND PLANETARY SCIENCE LETTERS 18 (1973) 3 9 1 - 4 0 7 . NORTH-HOLLAND PUBLISHING COMPANY

[]

GRAVITY, BATHYMETRY AND CONVECTION IN THE EARTH *

Roger N. A N D E R S O N * *

University of California, San Diego, Marine Physical Laboratory of the Scripps Institution of Oceanography, La Jolla, California 92037, USA Dan M c K E N Z I E **

Department of Geodesy and Geophysics, Cambridge University, Madingley Rise, Madingley Road, Cambridge CB3 OEZ, England and J o h n G. S C L A T E R * *

Department of Earth and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Received 27 November 1972 Revised version received 21 February 1973

All active midocean ridges show a uniform relationship between depth and age of the oceanic crust. Recently, it has been shown by numerical methods that convective flow in a Newtonian fluid will have a positive gravity anomaly and an upward surface deformation associated with an ascending limb. If there is thermal convection in the upper mantle, these calculations predict that there may be a correlation between free air gravity anomalies and differences from the uniform relationship between oceanic depth and age. To investigate such a correlation, we considered the crestal elevation and free air gravity anomaly over the crest of the midocean ridges. It has been suggested that the differences from the depth versus age relationship are related to spreading rate. Thus, we also considered a correlation between crestal elevation and changes in rate along the ridge axis. We found a positive correlation between free air gravity and differences in crestal depth of the midocean ridge system. We found no correlation between spreading rate and gravity and no uniform relationship which holds in all the oceans between spreading rate and observed crestal depths. The long wavelength gravity anomalies which are correlated with the differences in crestal depttt cannot be supported by an 80 km thick lithosphere. Thus, they are considered evidence of flow within the aesthenosphere. Further, the correlation between gravity anomaly and differences in crestal depth has the same sign and gradient as predicted by the investigations of convection in a Newtonian fluid.

1. I n t r o d u c t i o n T h e striking success o f plate t e c t o n i c s as a desc r i p t i o n o f t h e e a r t h ' s surface m o t i o n s has b e e n possible o n l y because the k i n e m a t i c p r o b l e m was sepa* Contribution of the Scripps Institution of Oceanography, new series. ** Authors have been listed alphabetically.

r a t e d f r o m the p r o b l e m o f the driving m e c h a n i s m . R a p i d advances in o u r u n d e r s t a n d i n g o f the n a t u r e o f ridges, t r e n c h e s , a n d t r a n s f o r m faults were possible because these s t r u c t u r e s are d i r e c t l y a n d simply related to the k i n e m a t i c plate m o t i o n s a n d are n o t the surface e x p r e s s i o n s o f m a n t l e m o t i o n s . R e c e n t l y , D u f f i e l d [ 1 ] h a s s h o w n the r e m a r k a b l e similarity b e t w e e n the g e o m e t r y o f cool plates o f lava in a lava

392

R.N. Anderson et al., Gravity, bathymetry and convection in the earth

lake in Hawaii and the topography of the sea floor, and Oldenburg and Brune [2] have demonstrated how candle wax can form ridges offset by transform faults when the cool skin on a molten pool of wax is stretched. These two examples demonstrate in a particularly clear manner that the detailed shape of the plate boundaries is unrelated to motions in the mantle beneath the lithosphere. Furthermore, there exist few surface geophysical observations which need be explained by the motions beneath the plates, and it is for this reason that plate tectonics has been so useful. McKenzie [3] attempted to distinguish between (a) those surface observations which were little affected by the existence of plates, and (b) those which were dominated by their strength, thermal behaviour, and motions. Of the observations examined, the plate motions themselves, the heat flow through the floors of the deep ocean basins, and the long wavelength gravity anomalies observed by satellites are still believed to be little affected by the plates. Deep earthquakes are now known to be the result of faulting within plates as they sink through the mantle beneath island arcs. They, therefore, mark the position of the sinking boundary layer, or plate, after it has separated from the earth's surface. The extent of the region which sinks with the descending boundary layers is not known. The other observation which McKenzie [3] believed reflected the motions below the plates was the mean oceanic depth. This view must now be modified since Sclater et al. [4] have clearly demonstrated that the major influence on the depth of an oceanic plate is its age, with no influence from below needed to account for this correlation. They did, however, find regional differences from the empirical model which best fits the mean depth as a function of age. These differences were, in general, not obviously related to any features of the ocean floor, and it appeared probable that they were the surface expressions of motions beneath the lithosphere. McKenzie et al. [5] have recently investigated convection in a Newtonian fluid heated from within or below by numerical methods. They required the mean heat flux through the upper surface of the convection region to agree with the mean heat flow through the deep ocean basins, and used the best

available estimates of the various physical parameters in the governing equations. They found that the resulting horizontal velocities, surface deformation and gravity anomalies all lay within the range observed on the earth. In particular, the gravity anomaly was positive over a region where the fluid was rising and negative over a sinking region. This relationship was, therefore, the same as that for low Rayleigh number convection, and the sign of the correlation does not change with increasing Rayleigh number as McKenzie [3] supposed. These results suggested a simple test of whether the long wavelength gravity field and surface deformation are both the result of vertical motions below the plates. If they are, then they should be correlated and the slope of this correlation should agree in value and sign with that obtained from the numerical calculations. The tests below show that this is indeed the case. The correlation is most easily demonstrated by comparing the depth of the ridge axis below the sea surface with the gravity anomaly at the same place. Ridge depths are used for this purpose because the empirical relationship between oceanic depth and age mentioned earlier [5] predicts a uniform crestal elevation everywhere along the midocean ridge system, since the age is the same. Thus, no corrections need be applied. The depth of the other parts of the sea floor depend on their age, and, therefore, two-dimensional comparisons of depth and gravity anomaly require tedious corrections for the cooling of the plate. Our analysis shows a clear dependence between gravity and deviations in the crestal depth of the midocean ridges, and independence between these deviations and spreading rate. Because of their long wavelength, the gravity anomalies cannot be supported by the strength of the plates. Thus, they, and the differences in elevation, must result from flow beneath the lithosphere.

2. Method and data

The crestal elevations were taken from charts, compilation sheets, and profiles. Wherever possible, they were averaged for each one degree along strike and plotted against either latitude or longitude along the world-wide midocean ridge system. The

R.N. Anderson et al., Gravity, bathymetry and convection in the earth

Mid-Atlantic ridge points were taken from the charts of Uchupi [6], Zhivago [7], and Simpson (personal communication). The North Pacific data came from the charts of Chase et al. [8]. The South Pacific data were taken from profiles presented by Anderson and Sclater [9], Herron [10], Hayes et al. [11], and Scripps, unpublished data. The charts of Chase et al. [8], Van Andel et al. [12], and Sclater and Klitgord [13] were used to determine the averages for the Galapagos spreading center. The points for the Southwest Indian ridge were taken from the charts of Simpson (personal communication) and Fischer et al. [14]. For the rest of the Indian Ocean the charts of Fischer et al. [15], Fischer et al. [14], Fischer [16], two profiles, Conrad 11 and Conrad 8, from the submarine topography department of the Lamont-Doherty Geological Observation, and the chart of Hayes and Connolly [17] were used to determine the one degree average. The chart of Hayes and Connolly [17], together with Eltanin 27 profiles [ 11], and the Russian chart of the Pacific [18], were examined in the determination of the one degree averages for the Pacific-Antarctic ridge. In the Arctic, the chart of Vogt et al. [19], a Russian tectonic chart [20] and the profiles of Johnson and Heezen [21] were used to compute the depths. The average depths from the charts were checked against detailed surveys in the North Atlantic at 60°N [22], 45°N [23], and at 22°N [24]. On the southwest branch the depths were checked against surveys at 38°E [25] and 62°E [26]. The five degree averages for the free air gravity anomalies with respect to the best fitting ellipsoid f = 1/298.255 [27] were calculated from the spherical harmonic coefficients of the gravitational field of degree 2 through 16 of Gaposchkin and Lambeck [28] (fig. 1). They were plotted against either latitude or longitude along strike of the ridges. Observed spreading rates were taken from Pitman and Talwani [29] and Dickson et al. [30] in the Atlantic, from Larson et al. [31], and Sclater et al. [4] in the North Pacific, from Anderson and Sclater [9], Herron [10], Herron and Hayes [32], and Hayes et al. [11] for the South Pacific, form Hey et al. [33], Raft [34], Grim [35] for the Galapagos spreading center. For the Indian Ocean, the data are from Bergh [25], McKenzie and Sclater [36], and Weissel and Hayes

393

[37]. For the Pacific-Antarctic ridge, the observed spreading rates were taken from Weissel and Hayes [37], and Hayes et al. [11]. The spreading rates for the Arctic were taken from Vogt et al. [19]. Large sections of the Atlantic, Pacific, and Southwest branch have no published spreading rates. We computed theoretical spreading rates for these areas. For the Atlantic between 20°N and 20 ° S, we used the pole of Pitman and Talwani [29] at 70°N, 33°W, for the North Pacific between 10°N and the equator, the pole of Chase [38] at 36°N, 108°W, and the Southwest branch, the pole of McKenzie and Sclater [36] at 16° S, 38°W. The spreading rate data were plotted against either latitude or longitude and were superimposed over similar plots of the gravity and elevation (figs. 2a, b, and c). We examined 48,100 km, or 91%, of the 52,000 km of the world-wide ridge system. We left out only the Juan de Fuca ridge, Gulf of California, Chile ridge and the Red Sea and Gulf of Aden. The mean depth of the crest of the total system is 2 5 0 3 ± 442 m (table 1). The Pacific and Indian Ocean ridges have greater mean depths than either the Atlantic or the Southwest Indian ridges. However, if we exclude the North Atlantic from 40 ° to 70 ° N, the Madagascar plateau intersection with the Southwest Indian ridge, and the junction of the Pacific-Antarctic ridge and the Macquarie ridge (leaving some 80% of the world-wide system), the mean depth is 2631 ± 279 m, which is almost exactly the same as given by Sclater et al. [4]. These areas represent the most obvious positive correlations and have been suggested by Morgan [39] and others to be hot spot locations. The mean gravity is slightly positive 4.6 ± 13.6 as has been suggested by Kaula [40] and Lambeck [41] and is unaffected by the removal of the areas mentioned above. The individual ridges have a large variation but are all slightly positive except the PacificAntarctic which has a large negative free air anomaly [40]. The mean spreading half rate is 2.80 ± 2.04 cm/yr. Unlike the gravity, the mean spreading rate varies greatly between individual ridges but, except the Pacific, very little within the ridges. The removal of the three elevated regions mentioned above slightly increases the mean half rate to 3.06 -+ 2.11 cm/yr.

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R.N. Anderson et al., Gravity, bathymetry and convection in the earth

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R.N. Anderson et al., Gravity, bathyrnetry and convection in the earth

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Table 1 Length, m e a n depth free air gravity anomaly and spreading rate of the world-wide midocean ridge system Ridges

Length km

No. of 500 k m points

Depth ± S.D.

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R.N. Anderson et al., Gravity, bathymetry and convection in the earth

398

3. Correlations

inated by the area around the intersection of the Madagascar plateau with the ridge axis. The rest of the Indian Ocean shows a similar correlation except for either side of the Amsterdam and St. Paul Islands where deep depths are associated witil a large positive free air gravity anomaly. Over the Pacific-Antarctic ridge, the correlation between gravity and elevation breaks down. In the Arctic, the depth data over the Nansen ridge are too sparse for a good correlation based upon only seven points (fig. 2c). To examine possible correlations, we determined 500 km average points for the three parameters. We

The Mid-Atlantic ridge shows a clear correlation between crestal elevation and gravity: where the gravity is positive, such as over the Azores triple junction, the elevation is high and where the gravity is negative, such as the Atlantic at 10°N, the elevation is below the average (fig. 2a). The Pacific ridge crest is deep, the spreading rate is high, and the gravity anomaly shows little variability about the mean. There is a positive correlation in the Southwest Indian ridge (fig. 2b) which appears to be doraGRAVITY

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R.N. Anderson et al., Gravity, bathymetry and convection in the earth

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R.N. Anderson et al., Gravity, bathymetry and convection in the earth

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Fig. 5. Plots of 500 km averages of gravity versus spreading rate for each ocean and the total population. then plotted the gravity versus depth (fig. 3), spreading rate versus depth (fig. 4), and gravity versus spreading rate (fig. 5). Plots were constructed for each ocean individually and for the whole world-wide system. Regression lines with gravity as the independent variable ( A g mgals = 41.5 -- 1.47 × 10 - 2 Az m) and depth as the independent variable (Az m = 256.8 -- 14.8 A g regals) were fitted to the total population (fig. 3). These lines were superimposed on the individual oceans. The Atlantic, Southwest branch, and perhaps the Indian Ocean fit these lines. The

Pacific has too little variability to show any correlation, and the Pacific-Antarctic/Arctic shows no correlation. It is possible that the observed correlation is entirely due to isolated top•graphic highs such as the North Atlantic from 40 ° to 70 ° N, the Southwest Indian ridge/Madagascar plateau intersection, and the junction of the Macquarie ridge and the Pacific-Antarctic ridge. These elevated regions were removed and new regression lines fit to the total population (zSg = + 43.61 - 1.47 X 10 - 2 Az and Az =

401

R.N. Anderson et al., Gravity, bathymetry and convection in the earth

relation between gravity and elevation on all of the ridges, with the exception of the Pacific Ocean, and for the total population (table 2). Examination of fig. 3 indicates this is due to there only being a small variation about the mean. Only the Indian Ocean and the Arctic show a statistical dependence between elevation and spreading rate. To investigate the possible dominance of the three elevated regions mentioned previously, we performed the same test excluding these areas. Again elevation correlates with gravity, but not spreading rate. However, the removal of the ridge axis-Madagascar plateau intersection makes the elevation independent of gravity on the Southwest Indian ridge. This statistical analysis presents numerical support for our qualitative statements based on figs. 3 and 4 that there is a correlation between gravity and elevation but none between spreading rate and elevation.

2694 - 13.77 Ag mgals). The slopes are the same, only the mean elevation has changed. This clearly demonstrates that the correlation between gravity and elevation is independent of these features. Each ocean shows a different relationship between spreading rate and crestal depth (fig. 4). The total population clearly shows that fast spreading ridges (i.e., the East Pacific Rise) are consistently deeper than 2600 m. All the variability of the crestal elevation occurs on slow spreading ridge. For example, the Nansen ridge, with a spreading rate of 1 cm/yr, has a depth of 3100 m whereas the Reykjanes ridge, with the same spreading rate, has a mean depth of 1600 m. Furthermore, the mean depth of the slow spreading ridges is shallower than the fast spreading ridge (table 1). The free air gravity anomaly appears to be totally independent of spreading rate (fig. 5). The best fit regression line through the total population is close to horizontal. The only striking observation is that the scatter on the one fast ridge, the East Pacific Rise, is much less than that over the slower spreading ridges. The independence of gravity and spreading rate permits a multiple regression analysis of variance of the dependent variable crestal elevation against the two independent variables. Our null hypothesis is that the depth is dependent upon gravity and spreading rate. We find a positive cor-

4. Negative gravity anomalies in ocean basins Kaula [40] has pointed out that eleven of the deep, major midocean basins have large negative gravity anomalies. We have examined all of these basins with mean ages greater than 40 mybp. We have tabulated the mean depth corrected for sediment thickness [4], the mean free air gravity anomaly,

Table 2 F test from multiple regression with the dependent variable elevation and the independent variables gravity and spreading rate Ridges Atlantic Pacific Ocean Southwest Indian Ridge Indian Ocean Pacific-Antarctic Arctic All Atlantic south of 40° N Southwest Indian Ridge Madagascar Plateau Total: (Atlantic north of 40° N) Madagascar Plateau, Macquarie T.J.) * Correlates bit with opposite slope

No. of values

Elevation/Gravity

Elevation/Spreading Rate

F

F95

F

F9s

26 23 13 23 7 7 99 20

61.9 16.05 * 27.7 7.0 7.04 25.35 21.65 18.5

4.28 4.35 4.84 4.35 7.71 7.71 4.0 4.45

0.22 0.21 3.2 15.4 7.76 20.0 0.36 0.89

4.28 4.35 4.84 4.35 7.71 7.71 4.0 4.45

9

3.26

5.99

2.97

5.99

84

10.77

4.00

0.85

4.0

4

9

Brazil Basin

Argentine Basin

4

4

Wharton Basin

South Australia Basin

110-145

38-51

100-120

70-90

100

90-110

45-60

80 135

Age range

5.9

5.5

6.1

4.75

4.8

5.5

5.6

5.8

Depth km

0.2

1.0

0.2

2.0

2.0

1.5

0.2

0.2

Mean sed. thickn, km

6.0

6.1

6.2

5.95

6.0

6.4

5.7

5.9

Correct. depth

6.0

4.9

5.9

5.6

6.0

5.9

5.2

5.9

-17

34

20

-53

-28

- 16

-19

-22

Theoretical* Mean depth free air** gravity

Larson, Chase 157]

McKenzie and Sclater [36] McKenzie and Sclater [36] JOIDES Sci. Staff [55] Weissel, Hayes [37]

Pitman (pers. comm)

Pitman (pers. comm)

Pitman and Talwani [29]

Age

[59]

[531

Ewing et al. [54]

Ewing et al. [54]

Francis et al.

Ewing et a1.[52]

Ewing et al. [52]

Ewing et al. [52]

Sed. Thickn.

Chase et al. [81

Ewing et al. [58]

Hayes, Connolly Houtz, Markel [17] [56]

Anon [59]

Anon [591

Anon

Uchupi [6]

Uchupi 161

Uchupi [61

Depth

References

* From Sclater and Detrick [4]. ** From Kaula [39]. The negatives in the northeast Pacific and either side of the East Pacific Rise in the South Pacific have not been considered because the mean crustal ages are either too young or not well enough known.

Northwest Pacific

7

6

Central Indian Basin

Pacific

4

Somali Basin

Indian Ocean

6

Area in 5×5 ° squares

Nares Abyssal Plain

A tlan tic

Feature

Table 3 Oceanic basins with large negative free air gravity anomalies

o~

?

t,3

4~

R.N. Anderson et al., Gravity, bathymetry and convection in the earth

and the depth predicted by the extended empirical depth versus age curve for the North Pacific [42] (table 3). All these basins have deeper mean corrected depths than that predicted by the empirical curve. Further, the empirical curve is below the average for the oceans because it is based upon subsidence in the northeast Pacific where the crestal elevation is deep (2780 m) and the regional gravity anomaly is negative. We found two regions with a positive free air gravity anomaly in the Pacific. One is centered just south of Hawaii [40] and the other, which is less obvious, is located east of the Tuamotu Islands and west of the East Pacific Rise at 15°S - 20°S, 110°W - 120°W. Both areas have elevations significantly shallower than those predicted from their respective ages. These areas of positive free air gravity and the negatives in the older basins are evidence that one-dimensional correlation between crestal depth and gravity over the midocean ridges may extend to two dimensions in the deep basins. Menard [43] found similar correlation in the northeastern Pacific after correcting depth for subsidence of the oceanic crust with age.

5. Conclusions We have found no correlation between spreading rate and gravity. Further, there is no uniform relationship which holds in all the oceans between spreading rate and observed crestal depth. The independence of these two parameters rules out models invoking differences in spreading rate as the causal mechanism for the observed differences in crestal elevation. We have observed a dependence between free air gravity anomalies and the crestal depth of the entire midocean ridge system. Depths shallower than the norm have a positive anomaly while those deeper than the norm have a negative anomaly. We have further shown that the old ocean basins deeper than the norm also have a negative gravity anomaly. It should be pointed out that our analysis deals only with long wavelength variations along the strike of the midocean ridges. We cannot distinguish relative anomalies at right angles to the ridge crest. Lambeck [41] has argued that ridges should show a positive gravity anomaly of limited lateral extent, whose magnitude decreases with increasing spreading rate.

403

We examined the data for such a correlation but failed to find any such effect. This result suggests that if such a gravity anomaly exists, it does not contribute appreciably to the long wavelength components of the earth's gravity field. The gravity anomalies can easily be accounted for by the observed elevation deviations from the norm of the crests of the midocean ridges [44]. The addition of 1 km of crust produces a gravity anomaly of 75 mgals for a horizontal slab of otherwise infinite dimensions (from the simple Bouguer correction). However, the question is not whether the topography can produce the observed gravity anomalies, but whether the lithosphere has sufficient strength to support the mass excess required to produce the observed gravity field. McKenzie [45] has modeled the crust of the earth as an elastic plate floating on an inviscid fluid. His analysis was two dimensional. Lambeck [41] has extended this analysis to three dimensions. Lambeck [41] and McKenzie [45] based on analyses of the stress release in large earthquakes by Brune and Allen [46] and Wyss [47], have estimated a range of 200 to 1000 bars for the maximum shear stress that the lithosphere can support without failure. Our calculations, based upon the above models, show that the long wavelength gravity anomalies over the North Atlantic, the Southwest Indian ridge and the Amsterdam-St. Paul region. cannot be supported by the lithospheric plate (table 4) even when its thickness is taken as 80 km. Hence they must result from aesthenospheric flow. The uniform decrease of elevation with increasing age of the oceanic crust from a mean depth of close to 2500 m at the crest to approximately 6000 m in the very old basins is controlled by processes within the lithosphere. Direct evidence for this comes from the excellent match between the empirical curve for the uniform increase of depth with age in the North Pacific and similar curves for all other ocean ridges. Two theoretical models of the lithospheric plate, one by McKenzie [45] expanded by Sclater and Francheteau [48] and the other by Parker and Oldenburg [49], have been proposed which can adequately account for the empirical correlation. The first model accounts for the elevation decrease by the thermal contraction of the oceanic plate as it cools and spreads from oceanic ridges. This model assumes a

404

R.N. Anderson et al., Gravity, bathymetry and convection in the earth

Table 4 Maximum shear stress in an 80 km thick lithosphere required to support positive gravity anomalies with the given wavelength (h) o

Ridge crests with positive anomalies

h km

Ag, gals × 10-3

North Atlantic between 30° N and Iceland Southwest Indian Ridge Amsterdam St. Paul Hawaiian Anomaly

7000 3000 3000 1000

70 40 30 20

k' -

max

k'

Lambeck [40]

McKenzie[43]

0.04 0.08 0.08 0.25

13,150 1,750 1,315 89

17,500 2,810 2,110 278

21r (lithospheric thickness/2)

coefficient of thermal expansion and predicts a density contrast between the lithosphere and aesthenosphere. The second model assumes a density contrast and predicts a coefficient of thermal expansion. The important point is that both adequately demonstrate that the correlation between crustal depth and age may be controlled wholly by lithospheric processes. Further support is presented by the empirical curve's ability to account for the sharp topography ramp observed in the eastern Pacific where major reorganization of the plate boundaries has resulted in a jump of the ridge axis [4], [9], [50]. We have shown in this paper that superimposed upon the 3500 m decrease in elevation with age due to the cooling plate are long wavelength (-+ 500 m) deviations in elevation for crust of a given age. These deviations are correlated with equally long wavelength gravity anomalies which must be supported by flow in the aesthenosphere.

6. Thermal convection Though the surface motions of the earth are now known in considerable detail, very little is yet understood about the three-dimensional flow in the earth and about the forces which maintain the motions. The motions at depth are difficult to study because they produce few surface effects. For instance, there is now no reason to believe that ridges are the surface evidence for rising convection currents at depth. Only the plate motions themselves and the gravity

field observed by satellites must be consequences of three-dimensional flow beneath the plates. Other observations, such as the high heat flow near ridges or deep earthquakes beneath trenches, now appear to be explained by the production and destruction of plates. Various attempts have been in the past to relate the satellite gravity field to mass flow within the earth. Any such attempt depends on some theory of convection at depth, and at present, no such theory is generally accepted. In geophysics, convection currents are often drawn as closed circular cells, but they need not have such a shape. Indeed the only existing evidence for convection in the mantle is the occurrence of earthquakes beneath island arcs, and here the detached boundary layer is planar, not cylindrical. It is therefore important to study convection under conditions which resemble those in the mantle. In particular a considerable fraction of the heat carried to the surface by the flow is generated within the fluid by radioactive decay. Flow driven by such internal heating is very different from flow driven by heating from below. Also the variation of viscosity with temperature must be included since otherwise the cold surface boundary layer, or plate, does not have mechanical strength. The other important effects which should be included are the shear stress heating and the nonlinear dependence of strain rate on stress. Both are likely to produce marked changes in the form of the flow, and though the first is easy to include, the second is not. The equations governing convection in a fluid

R.N. Anderson et.al., Gravity, bathymetry and convection in the earth

with these properties are exceedingly complicated and possess dominant nonlinear terms. No analytic solutions have been obtained and it is unlikely that any will be. Therefore numerical methods must be used to study the form of the convection and to calculate the gravity field produced by the flow. Though it is likely that experiments on convection in suitable liquids will provide checks on these calculations, it is of importance to discover if the results of the calculations resemble the behaviour of the mantle. The most direct test presently possible is the relation between the external gravity field and the deviations from the norm of the elevation of oceanic crust. Wilson [51] and Morgan [39] have suggested that oceanic volcanic islands such as Hawaii mark the sites of rising regions within the mantle, or hot spots. Whether or not this view is correct, the relation between volcanism and convection is less direct than that between the flow, the mass distribution, and the surface deformation. Recently McKenzie et al. [5] have studied the surface deformation and gravity field resulting from convection at high Rayleigh numbers. Their numerical experiments were carried out on a Newtonian fluid with constant properties and confined within a rectangular box 700 km deep with stress-free boundaries. Only two-dimensional flow was permitted. The experiments were designed to study the changes in the flow which occurred as the Rayleigh number was increased and the differences between convection driven by internal heating and heating from below. The result of most geophysical interest (and that which caused the present investigation) was the discovery that the gravity anomaly over a rising region was always positive. This result was independent of whether the flow was driven by internal heating or heating from below (or a mixture), of the Rayleigh number, of the aspect ratio of the box in which the experiment was carried out, and of whether the flow was steady. At high Rayleigh number both the surface deformation and the gravity anomaly are controlled by the behaviour of a shallow surface boundary layer, and the positive correlation is approximately 1 mgal for every 30 m of surface deformation. This relationship has been superimposed upon the observed data in fig. 3, and agrees with that data both in sign and order of magnitude. This is evidence that the observed positive gravity anomaly and excess ridge ele-

405

vation can be caused by flow in the aesthenosphere. This further suggests that positive gravity anomalies and increases in depth above the norm indicate areas of upwelling, and negative anomalies and depths deeper than the norm are indicative of areas of downgoing mantle material. If further work in other parts of the ocean shows the same correlation between gravity and elevation, then the free-air satellite gravity field of the earth might represent a map of aesthenospheric flow. The pattern of the flow beneath the plates appears to provide a major part of the energy required to move the plates, and, therefore, the correlation between gravity and elevation described above may lead towards an understanding of the driving mechanism.

Acknowledgements We would like to thank Robert L. Fisher, H.W. Menard, Peter Molnar, Robert L. Parker, and Tom Hanks for fruitful discussions. We thank Bill Kaula for a copy of his gravity map that was used for fig. 1 and Kurt Lambeck for a preprint of his paper. This research was supported by the Office of Naval Research and the National Science Foundation.

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