Hot spot heat transfer: Its application to Venus and implications to Venus and Earth

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 88, NO. BI0, PAGES 8305-8317, OCTOBER 10, 1983

Hot Spot Heat Transfer' Its Application to Venus and Implications to Venus and Earth

PAUL MORGAN AND ROGER J. PHILLIPS •

Lunar and Planetary Institute, Houston, Texas 77058

Gross similarities between earth and Venus suggest that both planets might be expected to lose heat by the same mechanism. Available data do not resolve plate tectonics on Venus, however, and other heat loss mechanisms, such as hot spot heat loss, have been suggested. Using a model which gives a relationship among surface elevation, lithospheric thickness, and heat flux, we test the hot spot heat loss mechanism for Venus and determine that it can easily explain the predicted heat loss of the planet with a modest number of hot spots (of the order of 35). Approximately 93% of the mapped topography of Venus can be explained solely on the basis of lithospheric thickness variations. Additional compensation is required for topography above a radius of 6053 km, and this can be effected by incorporating a variable thickness crust into the model. If crust is assumed to be generated on the crests of the hot spots, probably by processes associated with volcanism, the model is consistent with almost 99% of the mapped Venus topography. The model is also basically consistent with available gravity data and interpretations which indicate compensated topography and great depths of compensation (100-1000 km) for the mid-latitudes of the planet. The remaining approximately 1% of the topography not explained by hot spot crustal generation is thought to be compensated at a shallower depth primarily by variations in crustal thickness which are not directly related to hot spot volcanism. The models, relating surface elevation to lithospheric thickness and heat flow, are grossly consistent with either a plate tectonic or hot spot heat loss mechanism for Venus. The range of lithospheric thicknesses implied by the range of elevations on Venus implies that if plate tectonics is the dominant heat loss mechanism on Venus, the mean plate velocities are slower than on earth. Slow spreading ridges should be resolvable by the available Venus topographic data but are not apparent. Comparison and anal?i• t•f the hyp•t•rnetric curves for earth and Venus suggest basic differences between the curves, the skewed terrestrial ocean floor curve being consistent with plate tectonics, but the relatively symmetrical venusian curve indicates that either plate tectonics differs on Venus from the terrestrial analogue or that plate tectonics does not dominate the topographic expression of Venus tectonism. The venusian curve is consistent with a hot spot heat loss mechanism. A hot spot crustal genesis mechanism is proposed which would probably result in crust very similar to the granite-greenstone terranes of many terrestrial Archaean cratons. We speculate that hot spot heat loss may have preceded plate tectonics as the dominant terrestrial heat loss mechanism.

INTRODUCTION

Venus is the most earthlike planet in the solar system, having a mean radius of 6051.5 km, approximately 95% of the earth's 6371.0 km mean radius. The mean density of Venus is 5.245 Mg m -3, 5% less than that of the earth, but most of this contrast appears to result from the difference in self-compres- sion of the two planets [ Goettet et at., 1981 ]. Recent models of the thermal evolution of Venus predict interior temperatures very similar to those indicated for the regions of the Earth's mantle subject to solid state convection [ Turcotte et at., 1979; Phillips and Matin, 1983]. It might therefore be expected that the thermally driven tectonic processes on the earth, dominated by plate tectonics, would prevail on Venus. Unfortunately, the presently available topographic data for Venus [e.g., Masursky et at., 1980; Pettengitt et at., 1980] do not unequivocally resolve features on the surface of the planet that might be diagnostic of seafloor spreading. Arvidson and Davies [1981] claim that terrestrial style trench, transform, and ridge systems should be resolved by the available data from Venus, but Brass and Harri- son [1982] suggest that if significant sedimentation occurs on

•Also at the Department of Geological Sciences, Southern Methodist University, Dallas, Texas 75275.

Paper number 3B0748 0148-0227/83/003 B-0748505.00

Venus, these tectonic features would be completely unrecogniz- able topographically.

The most important known physical differences between the earth and Venus are the high atmospheric pressure and surface temperature of Venus (approximately 9.6 MPa and 470øC, respectively, at the median elevation; [Seiff et at. 1980]), and the very low abundance of water in the atmosphere of Venus [Hoffman et al., 1980]. From the high surface temperature on Venus it has been inferred that the venusJan litho-

sphere would be more buoyant than that of the earth, and therefore less likely to subduct [Anderson, 1981; Phillips et at., 1981]. Negative buoyancy may not be the dominating factor for subduction on the Earth, however, as consumption of terrestrial oceanic crust is approximately uniformly distributed with age [Parsons, 1982]; presumably most of the oceanic litho- phere is negatively buoyant if it represents the cooling product of the asthenosphere. Thus the relatively more buoyant lithosphere on Venus does not conclusively preclude venusian plate tectonics. There is, however, sufficient uncertainty in the applicability of plate tectonics to Venus to warrant the investi- gation of other heat loss mechanisms for the planet.

Another important physical difference between Venus and earth is the relationship between long-wavelength topography and gravity on the two planets. On earth these parameters are poorly correlated, but on Venus there is a strong correlation between gravity and topography for all resolvable wavelengths [Phillips and Lambeck, 1980; Reasenberg et at., 1981]. Anal- yses of these data indicate that the isostatic depth of compensation for most Venus topography is deep, 100-1000 km [Phillips

8306 MORGAN AND PHILLIPS: VENUS HOT SPOT HEAT TRANSFER

et al., 1981; Phillips and Malin, 1983]. This result, plus consid- Hawaiian example it is predicted to be subordinate to conduc- erations of the effects of the high surface temperature of Venus tive heat loss. However, apparent volcanic morphology of some upon lithospheric strength, suggest that the topography of highland regions of Venus [e.g., Saunders and Malin, 1977; Venus may be dynamically supported by the internal processes Campbell and Burns, 1980] indicates that volcanism may be of (heat transfer?) in its upper mantle [ Phillips et al., 1981; Phillips local significance to elevation on Venus, and we have examined and Malin, 1983]. the effects on topography of a crustal component generated

Two alternative heat loss mechanisms to seafloor spread- primarily by volcanic processes in the system. ing have been proposed for Venus, conduction and 'hot spot tectonics' [e.g., Phillips and Malin, 1983; Solomon and Head, 1982]. Although these two mechanisms are generally treated separately, they are intrinsically linked. Phillips and Malin [1983] and Solomon and Head [1982] consider the consequences of uniform conductive heat loss over the planet and calculate a uniform lithospheric thickness of less than 50 km, a very thin lithosphere to support the observed topography unless all the topography is geologically young. However, the uniform heat flow hypothesis must be discarded because solid state convection must dominate the heat transfer in the interior of the

planet [Turcotte et al., 1979; Phillips and Malin, 1983], and therefore heat transfer into the base of the lithosphere must be spatially variable. Thinner lithosphere and higher heat flow is expected over the rising limbs of the venusian mantle convection system, grading to lower heat flow and thicker lithosphere over the descending convective flow. A limiting case of the variable heat flow conductive mechanism is extreme thinning over the mantle upwellings until the convective system is capable of penetrating the lithosphere by magmatic activity, and volcanic heat loss can supplement the conductive heat loss in a system of hot spot tectonics. Hot spot tectonics is thus considered to represent a heat loss mechanism that is composed of both anomalous conductive heat loss across a thinned lithospheric thermal boundary layer and convective heat loss through volcanic activity.

Published calculations of hot spot heat loss for Venus concentrate on the volcanic component of the heat loss [e.g., Solomon and Head, 1982]. Using Hawaii as a model, Solomon and Head demonstrate that an unreasonably large number of hot spot volcanoes (10 4 ) equivalent to the Hawaiian volcano system would be required to account for the total predicted heat loss of Venus. As acknowledged by Solomon and Head, however, enhanced conducted heat flow may accompany heat loss. The Hawaiian hot spot is manifested by a broad swell with elevated conductive heat flow in addition to the volcanic heat

loss [Detrick et al., 1981]. Using the estimate of the Hawaii volcanic flux of 2 X 10 -2 km 3 yr -• given by Solomon and Head and assuming heat to be lost by solidifying basaltic magma cooling from 1000 ø C to 0 ø C, a volcanic heat loss of 2.5 X 109 W is calculated. Detrick et al. report an anomalous heat flux of 7-12 mW m -2 for the Hawaiian swell, which over the area of the swell (approximately 1000 km X 2700 km) results in an anomalous 19-32 X 10 9 W conductive heat loss over the swell. Thus anomalous conductive heat loss is an order of magnitude greater than volcanic heat loss for the Hawaii system. This heat loss is in addition to normal conductive heat loss appropriate for the age of the oceanic floor of the Hawaiian swell.

As conductive heat loss appears to dominate in terrestrial hot spots if Hawaii can be taken as a representative example, we have developed a model to test the hypothesis that conductive hot spot heat loss is an efficient heat loss mechanism for Venus and that most of the topography of Venus results from spatially varying thermal expansion in response to spatially varying heat flow. Volcanic heat loss is not included in the model, as from the

HOT SPOT/TOPOGRAPHY MODELS

Zero-Thickness Crust Model

A simple model has been developed for Venus to relate elevation to surface heat flow and lithospheric thickness. The model is somewhat similar to the models used to explain the variation in ocean floor elevation and heat flow as a function of

age of ocean floor [e.g., Sclater et al., 1980], except that the system is further simplified by assuming steady state conditions. We assume that the mantle of Venus is capped by a single lithospheric plate of global extent, at rest with respect to a mantle convection system reference frame. Lithospheric strength is assumed to be insignificant, and as a first approximation it is assumed that there is no chemical differentiation in the litho-

sphere (i.e., no crust), no heat sources in the lithosphere, and that the lithosphere represents a conductive cooling layer on convecting, isothermal (at least in its upper part) asthenosphere. The surface temperature and lithosphere thermal conductivity are assumed to remain constant, and therefore lithospheric thickness is inversely proportional to its thermal gradient and surface heat flow. If vertical buoyancy is assumed to be the primary parameter controlling elevation, the difference in surface elevation of two columns of lithosphere will be the result of differences in the mean density of the two columns down to the depth of compensation (isostasy). These density differences are thermally induced (thermal isostasy), a higher heat flow column having a lower mean density and higher surface elevation than a lower heat flow column.

Three hypothetical lithosphere/asthenosphere columns are shown in Figure 1, for which the condition of isostasy requires that

where OA is the asthenosphere density, OL is the mean lithosphere density, and A, and L, are the asthenosphere and lithosphere thicknesses, respectively, in the nth column. Assuming the coefficient of volume expansion, a, to be constant, from the conditions defined above, the thermal gradient in the lithosphere is uniform in each column, and the mean lithosphere density is given by

OL = OA[ 1 + a(TA-Ts)/2] (2)

where TA and Ts are the temperatures of the asthenosphere and surface, respectively, and P L is therefore constant under the present assumptions. Surface heat flow, Q,, is given by

Q,, - K( TA- Ts) / Ln (3)

where K is thermal conductivity. A reference set of lithosphere thickness-elevation-heat

flow conditions is required to solve (1) to determine the varia-

MORGAN AND PHILLIPS: VENUS HOT SPOT HEAT TRANSFER 8307

A• •

_ __ p_E_P_T_H_ _0 COMPENSATION

TEMPERATURE

DENSITY

Fig. 1. (Left) Three hypothetical lithosphere/asthenosphere columns with no crust. Column 1' thick lithosphere. Column 2: thinner lithosphere. Column 3: no lithosphere. (Center and Right) Temperature and density profiles in the three columns. Symbols are explained in the text.

tion in lithospheric thickness and surface heat flow as functions spheric thickness and the density contrast between the litho- of surface elevation. To test the hypothesis that the hot spot sphere and the asthenosphere. Since the mean radius of Venus is model represents the dominant form of topographic control for 6051.5 km, the radius of the surface elevation of the unbounded Venus, we assume that its mean elevation is the expression of a Venus asthenosphere is therefore 6053.0 km. These calculations mean lithospheric column for the planet. From a parameterized for Venus follow similar published calculations for the relation- convection approach, Phillips and Malin [1983] have calcu- ship between topography and lithospheric thickness for the lated, based on an assumption of chondritic heat sources and no terrestrial oceanic lithosphere, with an additional factor in the core heat flux, a mean lithospheric thickness and heat flow for terrestrial calculations due to loading by the oceans [Crough, Venus of the order of 100 km and 50 mW m -2, respectively. 1975; Oldenberg, 1975; and others]. Venus has a well-defined mean elevation, equivalent to a radius Lithospheric thickness and heat flow can be calculated for of 6051.5 km. Kaula and Phillips [ 1981], assuming equivalent any Venus elevation less than 6053 km (there is a singularity in heat sources between Venus and Earth, calculated with steady the heat flow calculation at an elevation of 6053 km), using (3) state boundary layer theory a temperature drop across the and (4)with the calculated unbounded asthenosphere elevation venusJan lithosphere of about 1000 ø C, in substantial agreement (6053.0 km). We have made these calculations at 0.5-km incre- with the thermal history calculations of Phillips and Malin merits from 6049.25 km to 6052.75 km, the results of which are [1983]. This temperature drop indicates a lithosphere thermal listed in Table 1. Using data on surface area as a function of conductivity of 5 W m -1 K -1, a value higher than that typically elevation from Masursky et al. [1980], we have also calculated assumed for the earth [e.g., Sclater et al., 1980], but not unreal- total heat loss from each elevation increment, and total heat loss istic if the Venus lithosphere is approximately 500øC hotter for the area of Venus for which elevation data are available than the earth's lithosphere, as radiative heat transfer is expected to become effective at temperatures above 1000øC [e.g., Basaltic Volcanism Study Project, 1981, pp. 1151-1155].

We can rewrite (1,) in terms of the difference & between the surface elevation of the nth lithosphere/asthenosphere column and the surface elevation of the unbounded asthenosphere column (column 3 in Figure 1):

d,, = L,,(Pz:/PA- 1) (4)

where d, is positive downwards. By assuming an asthenosphere density pA of 3.2 gcm -3 (based on peridotite composition at

(approximately 93% of the planet). This total heat loss exceeded the total heat loss predicted from the heat flow from the parameterized convection calculations by over 25%. This discrepancy results from the inverse proportionality of heat flow to lithospheric thickness, most of the heat being lost through thin lithosphere at high elevations, and is very sensitive to the minimum lithospheric thickness used. Corrected heat flow values in Table 1 are scaled by a factor of 0.79 from the values originally calculated to be consistent with the input assumption of a mean surface heat flow of Venus of 50 mW m -2. This scaling is equivalent to reducing the mean lithospheric thermal conductivity K from 5.0 to 3.95 W m -• K -•, a value closer to values commonly

1500 øC), a volume coefficient of thermal expansion, a, of used for the terrestrial lithosphere conductivity [e.g., Sctater et 3 X 10 -SøC -• (typical of olivine and other mafic minerals up to at., 1980]. If elevations above 6053 km are included in the 1000øC [Roy et at., 1981], and a 1000øC temperature drop analysis, a further reduction in thermal conductivityis required across the lithosphere, a mean lithosphere density p,• of 3.248 to match the mean surface heat flow of Venus, but we have not Mg m -3 was calculated for the Venus model from (2). Thus, by made this additional reduction at the present due to uncertain- assuming a mean lithospheric thickness of 100 km [Phillips and ties in the heat loss from these areas of higher elevation (see Matin, 1983] to be expressed by the mean surface elevation of Table 1). Venus, the mean elevation of the unbounded asthenosphere It should be emphasized that the minimum lithospheric with respect to this reference column, d,, is calculated to be 1.5 thickness resulting from our analysis (16.7 km) is purely a result km, the result being directly proportional to the mean litho- of the elevation increments that we chose to analyze, which were

TABLE 1. Parameters for Lithosphere Calculated From (3) and (4) for No-Crust Lithosphere Model for 0.5-km Increments of Planetary Radius From 6049.25 to 6052.75

Mean Radius, d, L, Q, Qcorr, Area, Total Q, km km km mW m -2 mW m -2 % X 10 8 W

6052.75 .25 16.7 300 237 5.376 54,534

6052.25 .75 50.0 100 79 8.982 30,271

6051.75 1.25 83.3 60 47 17.376 35,135

6051.25 1.75 117. 43 34 33.664 48,785

6050.75 2.25 150. 33 26 20.533 22,836

6050.25 2.75 183. 27 21 6.091 5,542 6049.75 3.25 217. 23 18 0.607 471

6049.25 3.75 250. 20 16 0.008 5

>6053.0 • -ve 16.7 300 237 7.363 74,444 >6053.02 -ve 250. 20 16 7.363 4,963

The d refers to depression of surface from unbounded asthenosphere elevation of 6053.0 km. L is lithospheric thickness, Q is heat flow calculated on the basis of the initial mean lithosphere assumptions, Q½orr is heat flow corrected by decreasing thermal conductivity to make total Venus heat flux match a mean heat flux of 50 mW m -2. Area data for each elevation increment taken from Masursky et al. [1980, Table 1], and Total Q is calculated using Q½orr' Lowest portion of table indicates heat flux lost from areas of Venus with elevations above 6053.0 km, assuming (1) that these areas are represented by the thinnest lithosphere and (2) that these areas are represented by the thickest lithosphere.

in turn dictated by the published topographic data for Venus. The topography is not particularly sensitive to this choice, but heat flow increases rapidly as the lithospheric thickness approaches zero, and is poorly constrained. While quantitatively our results are dependent on a number of assumptions, particularly regard- ing the reference conditions, our aim is to show qualitatively that the variations in the topography of Venus, interpreted in terms of variations in lithospheric thickness, can adequately accommodate the heat loss of the planet.

The typical spacing of centers of elevated topography in the equatorial region of Venus is on the order of 5000 km. The Venus topography, calculated lithospheric thickness, heat flow, and inferred convection system are shown in Figure 2, scaled to a horizontal wavelength of 5000 km. The relationships between heat flow and lithospheric thickness and between area and total heat flow for each elevation increment are shown in Figure 3 as a function of planetary radius.

With the parameters that we have assumed in the calculation of the elevation of the unbounded asthenosphere, the zero- thickness crust can be used for all Venus elevations up to 6053 km. Although it may be argued that the mean lithospheric thickness and/or the temperature drop across the venusian lithosphere may be less than assumed in our calculation, thus reducing the unbounded lithosphere elevation, the high surface temperature of Venus suggests that these parameters are unlikely to be significantly larger than assumed. Thus it is improbable that higher elevations can be explained by this model. We therefore extend the model to include the effects of a

variable thickness crust.

Variable Thickness Crust Model

It can easily be shown that the addition of a uniform thickness crust with a uniform density contrast to the underlying lithosphere and identical thermal properties to the underlying lithospheric upper mantle modifies only slightly the results of the no crust analysis presented above. The only modification is derived from minor changes in the mean crustal and underlying lit.hospheric densities as the thermal gradient in the litho-

sphere changes with lithospheric thickness. The inverse relationship between elevation and lithospheric thickness is preserved. Significant departures from the no-crust model are introduced, however, if a variable thickness crust is considered.

Our simple model of the lithosphere incorporating variable thickness crust is illustrated in Figure 4. We assume that the crust has the same thermal properties as the underlying lithospheric mantle, i.e., same thermal conductivity and expansion coefficients, and no upward enrichment of radiogenic heat producing elements, U, Th, and K. (The validity and implications of these assumptions are discussed below.) At the Moho, a uniform density contrast between the crust and mantle of 0.43 Mg m -3 is assumed based on the density contrast at the terrestrial Moho [Drake et al., 1959]. At any depth, the crust and mantle lithosphere densities are assumed to be a function of temperature and the volume coefficient of expansion, the mantle lithosphere density becoming equal to the underlying uniform asthenosphere density at the base of the lithosphere. A similar analysis of lithospheric thickness and topography has been presented with slightly different assumptions for the terrestrial continental lithosphere by Crough and Thompson [1976].

For the three lithosphere/athenosphere columns shown in Figure 4, the condition of isostasy gives

•c•C• + •L• + •oaA • = •c2C2 + •L2L2 + •o,4A2 -- •o,4A3 (5)

where •Cn and •z• are the mean crustal and mantle lithosphere densities in the nth columns, respectively, Pa is the asthenosphere density, and Cn, Ln, and A, are the crustal, mantle lithosphere, and asthenosphere thicknesses in the nth column, respectively. As shown in Figure 4, •cn and •z• are different for different columns, as the Moho temperature TMn and hence the temperature drops across the crustal and mantle portions of the lithosphere are dependent on the ratio of crust to mantle lithosphere thickness. From the geometry illustrated in the temperature and density profiles shown in Figure 4, it is easily shown that

APPROXIMATE HORIZONTAL SCALE, Km

-500 0 500 1000 1500 2000 2500 3000

6054 4 I I I I I I

E 6052 t'= """-'-'•''- 6050 Radius: topography ' •'•'•-- 6048 J without variable thickness crust

0 I _1_ i i I I I

100 t •--•.•.•_____•.__ •'"' 200 Lithospheric thickness 300

Inferred convection system (diagrammatic)

50- -8

-150 100

6049 6050 6051 6052 6053 >6053

RADIUS, Km

Fig. 3. (Upper) Percentage of area of Venus represented by each elevation increment, and calculated total heat loss from each elevation increment, plotted as a function of plantary radius. (Lower) Litho- spheric thickness and heat flow calculated for each elevation increment as a function of planetary radius. The dashed lines and points on the right of both plots show the range in uncertainties in parameters assuming that the topography above 6053 km has lithosphere ranging between

Fig. 2. Relationship among topography, lithospheric thickness, the thickest and thinnest predicted lithospheres for the topography heat flow, and inferred convection system from the simple hot spot below 6053 km. topography model. The horizontal scale is based on a topographic wavelength of 5000 km, the length of each elevation increment is scaled according to the square root of the total area represented by each elevation increment, and the scale has an arbitrary zero. Horizontal To calculate the difference in height dn between the surface lines represent actual model data and results; smooth curves show elevation of any lithosphere/asthenosphere column and the inferred relationships. surface elevation of the unbounded asthenosphere column, (5)

reduces to

•Ln -- PAl 1 + a(TA-Ts)[L,,/(2(C,, + L,,))]] (6) d n -- Cn(•cn/•o A - 1) + Ln(•Ln/PA - 1) (8)

•c,, = [PA[ 1 + a( TA- Ts)(L,,/(C. + L.))]-Ap] (7) ß [ 1 + a( T A- Ts)[ C,,/(2(C,+ L,))]] where d,is positive downwards.

As analyses of gravity data indicate that isostatic compcn- where a is the volume coefficient of expansion, TA - Ts is the sation for topography on Venus occurs primarily at relatively temperature drop across the lithosphere, and Ap is the Moho great depths ()100 km) and crustal compensation of topo- density contrast. graphy at these depths is unlikely from mechanical considcra-

1 2 3 TEMPERATURE DENSITY

d, L F

.... DEPTH OF COMPENSATION

Ts T.• p• I I I

ß X T•2

•c2 I

/ Pc•

L_ 2 PL2

-i i _

Fig. 4. (Left) Three hypothetical lithosphere/asthenosphere columns with variable thickness crust. Column 1: thick lithosphere, thin crust. Column 2: thick lithosphere, thick crust. Column 3: no lithosphere. (Center and right) Temperature and density profiles in the three columns. Symbols are explained in the text.

tions [Phillips et al., 1981; Phillips and Malin, 1983], we examine the effects of a variable thickness crust only as a local augmentation of the zero-thickness crust model. We seek to apply this augmentation only over the areas of Venus with elevations greater than 6053 km (in total less than 7.5% of the mapped surface of Venus) and thus use again the elevation of the unbounded asthenosphere calculated in the zero-thickness crust model (6053.0 km) as the base level for the variable thickness crust topographic variations defined by (8). The bounding cases for this augmentation are Cn = 0, for the zero- thickness crust model, and Cn = Ln, where the lithosphere is totally occupied by the crust. The elevations possible using C n = L n are tabulated in Table 2 as a function of lithospheric thickness, and the range of the possible variable thickness crust augmentation over the zero-thickness topography is shown in Figure 5.

We emphasize that only the lower curve of Figure 5 represents a model consistent with analyses of available Venus gravity data, and elevations between the two curves represent possible local augmentation of the zero-thickness crust model by variable thickness crust effects. With the possible exception of Ishtar Terra, as discussed later, elevation augmentation by crustal thickening must occur in areas of thin lithosphere to be consistent with the gravity analyses.

It is possible, even probable, that there is a nonzero thickness crust over all the venusJan lithosphere. This crust may be

•6068

0 I I 510 I I I 500 1000 1 0 2000 2500 3000

APPROXIMATE HORIZONTAL SCALE, Km

Fig. 5. Range of elevations locally possible with variable thickness crust in the framework of the zero-thickness crust model. Lower

bound shows elevations predicted by zero-thickness crust model (from Figure 2). Upper bound is maximum elevation possible if crust locally increases from zero to full thickness of lithosphere. Horizontal scale as for Figure 2. Horizontal lines represent calculated elevations, dashed lines are smoothed curves. See text for possible relationship between variable thickness and zero-thickness crust models.

Variations in Lithosphere Thermal Parameters

For both the zero-thickness and variable thickness crust

models, it has been assumed that the lithosphere has constant considered as equivalent to a variable thickness crust superim- thermal properties, conductivity and expansion coefficient, and posed on a uniform thickness crust defined by the minimum zero heat production throughout its thickness. Varying thermal crustal thickness. In this case, the elevation of the unbounded properties will modify the magnitude response of topography to asthenosphere must be recomputed using (8) with the mean lithospheric thickness' equations for a two-layer lithospheric lithospheric parameters for the effect of the uniform thickness conductivity and upward concentration of heat producing ele- crust. For example, with the same. assumptions as before, the ments are given by Crough and Thompson [ 1976]. If conductiv- inclusion of a 17 km uniform thickness crust into the model ityvariations increase the Moho temperature with respect to the reduces the elevation of the unbounded asthenosphere from constant conductivity model, both crustal and mantle mean 6053 to 6051 km. With the restriction that the lithosphere densities willdecreaseandtheelevationwillincrease. Similarly, cannot be thinner than the uniform thickness crust, however, a conductivity induced decrease in Moho temperature results in application of (8) with Cn = const for different lithospheric an elevation decrease. For constant crust and lithosphere thick- thicknesses gives elevations insignificantly different from those predicted by the zero-thickness crust model. Similarly, the results of the variable thickness crust model are not significantly changed by the inclusion of a uniform thickness crust base, although the total range of elevations predicted is reduced as the range of possible variation in crustal thickness is reduced. Thus as the inclusion of a uniform thickness crust layer into the models does not significantly alter the results of our models and as we have no data from which to estimate a thickness for this

layer, we do not consider it further.

TABLE 2. Maximum Elevation Augmentation for Variable Thickness Crust Model

L (km) dL (km)

16.7 2.02 50.0 6.07 83.3 10.1

117.0 14.2 150.0 18.2 183.0 22.3 217.0 26.3 250.0 30.4

nesses, these changes will also result in an increase or decrease in surface heat flow for an increase or decrease in Moho temperature, respectively.

Upward concentration of radiogenic heat producing elements has the effect of increasing the Moho temperature, and for a constant lithosphere thickness will result in a higher elevation. For a laterally uniform upward concentration of heat- producing elements, this effect would be undetectable in the topographic variations, which would only reflect mantle heat flow and resulting lithospheric thickness variations. Lateral variations in upward concentration of heat producing elements would most probably be linked to variations in crustal thickness and would cause a minor amplification of the crustal thickness elevation effect. Vertical variations in the expansion coefficient would be reflected in their effect in the mean volume expansion coefficient for the lithosphere. An increase in the mean coefficient would increase the topographic relief predicted by the zero-thickness crust model but have the reverse effect for the variable thickness crust model. A decrease in the mean coeffi-

cient would have the opposite effect. For a reasonable range in all these thermal parameters, however, their effects on surface elevation are secondary to the basic effects of the lithospheric

Upper elevation bound dL above the elevation of the top of the and crustal thickness variations predicted by the above models. unbounded asthenosphere, as a function of lithospheric thickness, L, for variable thickness crust model. Upper elevation bound calculated As there is no control on these parameters for Venus, their assuming maximum crustal component on lithosphere, i.e., Cn = Ln, variations are not included in the present analysis, and it is with zero-thickness crust as the reference background. assumed that the net effects of these variations are insignificant.

APPLICATION OF MODELS TO VENUS

The hot spot/topography models were developed to test rather than prove the hypothesis that hot spot tectonics could be the dominant heat loss/tectonic process on Venus. Without constraints on many of the parameters that we have assumed or taken from other calculations for our models and without data

constraining the internal structure of Venus, the hypothesis cannot be proved, and our arguments are really to examine plausibility. Thus if it is accepted that our models, the parameters defining them, and our results are reasonable, we can state whether or not the hypothesis is reasonable. We examine the application of our models to Venus first on a global scale, then on a more local scale.

From the elevation data analysis presented by Masursky et al. [ 1980, Table 1 ], almost 93% of Venus' topography is below a radius of 6053.0 km and can therefore be explained by a zero- thickness crust (or uniform thickness crust) model (Figure 2). Our model calculations give a depth of compensation for the topography of the order of 250 km (the depth of the deepest lateral density contrast defined by the maximum lithospheric thickness in the models), which is consistent with the analyses of orbital gravity data [Phillips et al., 1981' Phillips and Malin, 1983]. Our model is based upon simple isostatic balance calculations, but the assumption that density variations in the lithosphere / asthenosphere columns are thermal in origin, maintained by asthenospheric convection, implies that topographic support is a dynamic rather than a static process. The results of the simple hot spot/topography model therefore support the hot spot tectonics hypothesis.

Elevations above 6053 km can be explained bythe variable thickness crust model (Figure 5), but to be consistent with the large depths of compensation indicated by the gravity analyses, crustal thickness variations must augment topography primarily supported by lithospheric thickness variations. High topography with deep compensation occurs where the lithosphere thins, and to augment this topography by crustal thickness variations, the crust must thicken over the thin lithosphere. The magnitude of this augmentation is defined by the.crustal thickening, which is limited by the condition that the crustal thickness cannot exceed the lithospheric thickness. A suggested mechanism for the localization of 'thick' crust in areas of thin

lithosphere is that crustal generation is related to volcanic activity localized in the high heat flow/thin lithosphere areas. The minimum Venus lithospheric thickness is essentially uncon- strained, but assuming that it is of the order of 20 km, the results presented in Table 2 indicate that with an increase in crustal thickness of the order of 20 km in the thin lithosphere areas, elevations up to 6055 km can be explained by variable thickness crust augmentation Of the zero-thickness crust model. Almost 99% of Venus topography is below a radius of 6055 km, and thus it is demonstrated that the hypothesis that hot spot tectonics is the dominant heat loss/tectonic process of Venus is basically consistent with the topography and geophysical data currently available for the planet.

Further support on a more local scale for the scenario of crustal thickening by volcanic activity is provided by the radar identification of shield volcanoes on Beta Regio [Saunders and Malin, 1977], one of the areas of Venus primarily in the elevation range 6053-6055 km, and by the suggestion of a basaltic surface composition near Beta Regio from Venera geochemical results [Surkov et al., 1983]. Some topography may be due to volcanic construction, but the gravity analyses indicate primar-

ily isostatic compensation for the high elevations, although this result is nonunique. Beta Regio and possibly also Alta Regio, a similar feature at the eastern extremity of Aphrodite Terra, have compensation depths of the order of 1000 km [Phillips and Malin, 1983], too deep to be explained by the lithospheric thickness models alone in their present form. If these areas of high topography overlie vigorous ascending mantle plumes, however, density variations within the plumes could explain the large compensation depths.

Ishtar Terra is the only region in the mapped area of Venus with regional topography in excess of 6055 km, and thus is inconsistent with the simple hot spot/topography model with variable thickness crust elevation augmentation on the hot spots. The maximum elevation of Ishtar Terra, 6062.1 km, if completely isostatically supported, would require a crustal thickness increase of approximately 60 km in our models. High resolution gravity data are not available for the latitude of Ishtar Terra, and although early calculations indicated a shallow (<100 km) compensation for this feature [Phillips et al., 1981], W. L. Sjogren [ personal communication, 1983] has now calculated a depth of compensation of approximately 170 km under portions of Ishtar. More gravity data are required to determine whether Ishtar is isostatically supported by crustal thickening in an area of low heat flow, or is a very young feature.

We use variations in crustal thickness to explain the highest 7% of the Venus topography. The only supporting evidence for the extent of the application of the variable thickness crust model to Venus comes from estimates of the amount of crustal

differentiation on Venus. Assuming equivalent potassium con- centrations on Venus and earth and similar transport and release processes for 4øAr in the two planets, Venus atmospheric 4øAr data [Hoffman et al., 1980] suggest that approximately 30% as much magma has differentiated from the mantle on Venus as on the earth. If it is assumed that magmatic activity is directly related to crustal generation and that the mean crustal thickness is similar for the two planets, crust should cover approximately 10% of the surface of Venus. Thus from the meager evidence available, the use of variable thickness crust to explain the topography of 7% of the surface of Venus is not unreasonable. Our basic models for the relationship among topography, lithospheric and crustal thicknesses, and hot spot heat loss as applied to Venus are illustrated diagrammatically in Figure 6.

HOT SPOTS VERSUS PLATE TECTONICS ON VENUS

The one-dimensional models presented above, explaining Venus topography primarily as a function of lithospheric thickness, are equally applicable to hot spot or seafloor spreading mechanisms for the heat loss from the planet if transient heat flow is introduced into the models. Cooling boundary layer models have been successfully used to explain the elevation of the ocean floor as a function of lithospheric thickness on earth [e.g., Oldenburg, 1975; $clater et al., 1980]. However, if the Venus topography is analogous to the topography of the earth's ocean floor, it would be expected that the relationship between elevation and lithospheric thickness would be subdued on Venus as there is no ocean on Venus to cause additional subsi-

dence of the lower elevation areas by surface loading and the ambient surface temperature of Venus is higher [Arvidson and Davies, 1981; Headetal., 1981; Phillips and Malin, 1983]. The range in elevations for the bulk of the area of Venus (the 93% of the area below 6053 km) is, however, almost as great as the range

BETA REGIO '-•='"• GENTLE ROLLING ' 0 R /:"'" ":" '='•'• :..-•, ,. :-•.... :•:'% i:'), U P LAIN D S, e.g.

[•• TERRA .

Ii j{ Plu-- j{11 Asthenosphere Isostatic Compensation I i t I I ' Gentle I I • I Do•,n•o• I I u:,•o• I I • I I I I I • I I I I I • I I I I I I I I I i . I

(Scai•

Change)

! i • ! ! ! ! i ! -! ! ! i

0 1000 2000 3000 4000 5000 6000

APPROXIMATE HORIZONTAL SCALE, KM

Fig. 6. Diagrammatic representation of topographic compensation on Venus deduced from the simple hot spot and variable thickness crust models.

in topography for the portions of the earth's oceans which slower than on Earth by a factor of two or three. Slow spreading appear to be the result of a cooling boundary layer (not includ- ridges should be resolvable by the available Venus topographic ing trench systems which would be unresolvable in the Venus data [Phillips and Malin, 1983], and the Equatorial Highlands data), as shown in Figure 7. may be in this class [Kaula and Phillips, 1981]. Kaula and

The range in earth ocean topography is explained bya cooling Phillips calculated, however, that these ridges would not be layer with a maximum age of 180m.y.[Parsons, 1982]. Allother sufficient to account for all the venusian heat loss, and thus we factors being equal, if the Venus lithosphere is assumed to be suggest that if present, plate cooling heat loss is subordinate to analogous to the earth's oceanic lithosphere, a cooling age can hot spot heat loss on Venus. be estimated for each elevation increment on Venus based on the Further evidence with which to examine the applicability lithosphere thickness required to support the topography (see of plate tectonics or hot spots on Venus is contained in the Table 1). Using the asymptotic relationship between litho- shapes of the hypsometric curves for the planets. The Venus spheric thickness and age derived by Oldenberg [ 1975, equation hypsometric curve has commonly been compared to the terres- (l 8)] and assuming the thermal parameters of the venusian and trial curve [e.g., Masursky et al., 1980] with the comments that terrestrial lithospheres to be equivalent, the thick lithosphere, there are some fundamental differences and basic similarities up to 250 km, required by the low elevation areas of Venus between the curves. The fundamental difference is in the strong would require cooling times on the order of 700 m.y., and a bimodal distribution of elevation on the earth, a reflection of significant area of Venus, over 25%, has a predicted age older the difference in thickness of the oceanic and continental crusts, than 200 m.y. The mean predicted cooling age calculated for the in contrast to the dominantly unimodal elevation distribution Venus lithosphere is 150 m.y., almost three times the mean for Venus. The development of the contrasting continental and cooling age for the earth's oceanic lithosphere of 58 m.y. (calcu- oceanic crusts on the earth is a consequence of plate tectonics, lated from the data presented by Sclater et al. [1980, Table All). but the small areas of high elevation on the Venus hypsometric If the effects of sedimentation blanketing topography are consi- curve also suggests that there may be some continental type dered [e.g., Brass and Harrison, 1982], an even greater mean crust on Venus and that the curve could reflect a plate tectonic cooling age for the Venus lithosphere is indicated. regime with much less crustal differentiation. The main (lower)

Instability convection processes at the base of the litho- peaks of the two hypsometric curves are generally similar and sphere [Parsons and McKenzie, 1978] or reheating of the plate reasonably symmetric in published comparisons [e.g., Masursky bypassageoverahotspot[DetrickandCrough, 1978;Heestand etal., 1980; McGill, 1982]. However, recentlypublishedbathy- and Crough, 1981; S. T. Crough, personal communication, metric data for the terrestrial oceans [Gates and Nelson, 1975] 1982] may prevent the development of verythick lithosphere by indicate that the terrestrial hypsometric curves used in these cooling in a plate tectonic system. In a static hot spot-fixed plate comparisons are incorrect and that the main (oceanic) peak of system, thicker lithosphere may develop because there is no the terrestrial curve is significantly skewed and somewhat reheating of the plate by passage over hot spots, but instability irregular. convection processes could still be significant. However, the Consistent with the seafloor spreading concepts, much of thicker lithosphere required by the Venus topography cannot the ocean floor has a depth dependent on time since formation, exclude plate tectonics as the main heat loss mechanism on and which can be predicted from boundary layer theory. A basic Venus, but the older mean age of the lithosphere required by the proportionality between depth and the square root of age has thicker lithosphere suggests that if seafloor spreading exists, it is been derived theoretically [e.g., Oldenburg, 1975], and observa-

30 •

6053 6052

• Earth Ocean Floor

! r i i i I

4 5 6 7

DEPTH, KM

• Venus

6051 6050 6(•49

RADIUS, KM

Fig. 7. Hypsometric histograms (upper) for the earth's ocean floor below 2.5 km depth, excluding trenches, and (lower) Venus below a radius of 6053 km. Arrows indicate means for the data shown. Terres-

trial data from Gates and Nelson [ 1975]; Venus data from Masursky et a/.[1980].

tionally confirmed [e.g., Lister, 1977; Parsons and Sclater, 1977]. This relationship predicts a short residence time for the ocean floor at shallow depths and a longer residence time at greater depths. This suggests that the hypsometric curve for the terrestrial oceans should be skewed towards greater depths. In an extreme example, if only the oldest ocean floor (180 m.y.?) was subducted, the curve would be strongly skewed towards the depth of the oldest ocean floor (approximately 6.2 km from the predictive equations of Parsons and Sclater [ 1977]) and drop off very steeply below this depth.

If, as is more realistic, any age of plate can be subducted, the skewed hypsometric curve will be modified according to any bias towards subduction at particular ages (depths). Should, for example, the probability of subduction increase in a nonlinear manner with increasing age, an approximately symmetric hypsometric curve could be produced. Subduction appears to be related to the geometry of the plates, however, rather than age of subducted crust, and Parsons [ 1982] has shown that subduction is approximately uniformly distributed with age and that this observation preserves the predicted skew in the hypsometric curve [Parsons, 1982 (equation (8) and Figure 6)].

Recent depth-area data from the oceans [ Gates and Nelson, 1975] define a skewed hypsometric curve for the terrestrial oceans, as shown in Figure 7. The data do not quite match the predictions of Parsons [1982] in that the curve is bimodal and the main peak in the curve is 500-900 m shallower than predicted. Parsons explains these differences as being in part due to sedimentation on the ocean floor and possibly in part due to constructive volcanism on the oceanic floor [e.g., Watts et al., 1980] and/or due to oceanic swells [e.g., Crough, 1978]. We have reanalyzed the area-age data for the ocean floor given by Sclater et al. [1980], however, and suggest that the smaller, shallower depth peak in the hypsometric curve is due to varia-

tions from the linear relationship between area per unit age and age derived by Parsons [1982]. In view of our conclusions on Venus, below, we believe that the main peak of the curve is probably shallower than predicted due to reheating of the oceanic lithosphere during its passage over sublithospheric hot spots, as most recently proposed by Heestand and Crough [ 1981 ]. The rapid dropoff in per cent area at depths greater than 5.5 km expresses that the ocean floor effectively reaches a thermally mature baselevel and that relatively little area is occupied by ocean floor at greater depths.

The main portion of the hypsometric curve for Venus is significantly different from the terrestrial ocean hypsometric curve, as is shown in Figure 7. The main peak of the Venus curve is relatively symmetrical, and this is demonstrated even more in smooth, as opposed to histogram, representations of the curve [e.g., Masursky et al., 1980]. The mean and mode are closer for the Venus curve (--- 0.2 kin; see Figure 7 and Masursky et al. [ 1980]) than for the terrestrial ocean curve (> 0.4 km; Figure 7), indicating greater symmetry in the Venus curve. Slight asymme- try in the Venus curve towards higher elevations can be explained by the hot spot/topography models as the result of crustal augmentation of topography at higher elevations, super- imposed on an essentially symmetric distribution of topography due to variations in lithospheric thickness. Error bars for both the terrestrial and venusian curves are very small (see caption, Figure 8), and thus the differences between the curves cannot be explained as experimental error but must be due to differences in geologic processes. For example, the symmetry in the Venus hypsogram may imply that a thermally mature baselevel is not a strong feature of venusJan tectonics.

A further illustration of the difference between the Venus

and terrestrial ocean hypsometric curves and the relationship of these curves to terrestrial style plate tectonics is obtained by considering the relationships among cumulative area, predicted plate age, and depth. As Parsons [1982] demonstrates, with a uniform rate of plate production and uniformly distributed subduction with plate age, the cumulative area of the plate is directly proportional to plate age, and this linear relationship is approximately valid for terrestrial oceans up to the maximum age of the plates. It follows that any isochron on an oceanic plate is proportional to the area of the plate younger than the isochron. On a global scale, therefore, it should be possible to use cumulative area in place of plate age and reproduce the linear depth to square root of age relationship with a linear depth to square root of cumulative area relationship. Curves for this latter relationship are plotted for terrestrial oceans and Venus below 6053 km in Figure 8.

The observational and theoretical curves for the depth of the terrestrial ocean floor as a function of the square root of cumulative area are both approximately linear up to a cumulative area of 90% or more, where the curves drop off rapidly as the maximum age of the ocean floor is approached. The depth versus square root of age relationship, and hence plate tectonics, are therefore expressed in the area-depth data. Minor departures from the linear relationship appear to be due to minor departures from a uniform rate of plate production and unevenly distributed rates of subduction with age. The rapid dropoff in the cumulative curve for depths greater than 5.5 km is an expression of the rapid dropoff in the hypsometric curve at this depth, as discussed above. The corresponding observational curve for Venus is also approximately linear for radii greater than 6051 kin. Given the large number of samples in any data point in Figure 8, the departure from linearity is probably

_ EARTH OCEAN FLOOR

I I I I I I I I I I

0 2 4 6 8 10 V' CUMULATIVE AREA %

6053 -

6051 -

6050 -

6049 , , , , , , • , 0 2 • 6 8 1'0

X/CUMULATIVE AREA %

Fig. 8. Plots of depth as a function of the square root of cumulative area (Left) for the earth's ocean floor. Upper curve, observed depths from Gates and Nelson [ 1975]. Lower curve, predicted depths from Parsons[ 1982]. (Right) Observed plot for Venus, data from Masursky et al.[ 1980]. Statistical error bars for the terrestrial data have not been calculated as individual data errors are variable, but are expected to be small on such a large data set. From the data spacing for the Venus data (approximately a 75x 100 km grid; Masursky et al[ 1980]) it has been calculated that over 55,000 data are represented by the above curve, and as each data has a random measurement error in the range ñ200 m, the errors in the means used to derive the above curve are too small to plot.

beyond the one standard deviation errors of the individual points. We will not comment specifically on the significance of these departures but only state that the curves for both planets are roughly in agreement with the linear relationship expected for seafloor spreading with uniform plate velocities and uniform plate consumption with age. Departures from linearity might be due to variations in plate velocity with time, plate consumption with age, or other geologic processes unrelated to seafloor spreading.

The striking difference between the two depth/square root of cumulative area curves (Figure 8) is the length of the quasi- linear portions of the curves. If a seafloor spreading hypothesis is accepted as the source of the linear portion of the Venus curve, then this portion is expected to be shorter than the corresponding portion on the terrestrial curve, as is in fact observed, based upon simple boundary layer theory arguments [e.g., Phillips and Malin, 1983]. What is significantly different about the curves for the two planets is the shape of the curves at lower elevations or greater depths. Acceptance of a seafloor spreading hypothesis as the source of the linear portion of the Venus cumulative curve implies that the venusJan seafloor does not reach a thermally mature baselevel comparable to the terrestrial ocean basins. That is, the venusian seafloor spreading must operate in the presence of significant topographic depressions within the boundary layer.

Alternatively, the entire width of the venusJan hypsogram

IMPLICATIONS OF HOT SPOT HEAT LOSS ON VENUS

Crustal Genesis

In a plate tectonic system it is commonly hypothesized that continental type crust is differentiated from the mantle in a two stage process: (1) the generation of basaltic crust at mid-ocean ridges and (2) further differentiation of this crust to yield calc- alkaline magmas erupted in magmatic arc systems from remelting of oceanic crust after subduction [e.g., Hess, 1962; Ring- wood, 1969]. In a pure hot spot system, no subduction occurs; therefore it may only be expected that the first stage of differentiation, or basaltic volcanism, would be produced at the hot spot. However, the thick lithosphere predicted for the low topography of Venus indicates that the hypothesized hot spots have been spatially stable for a great time, of the order of a minimum of 700 m.y., and over such a time interval even very low rates of volcanism (25 X 10 -9 km 3 yr -• per km 2 of hot spot area) would result in volcanic piles of the same thickness as the thin lithosphere over the hot spots (of the order of 17 km). An indication that this occurs is given by the Venus topography between 6053 km and 6055 km (see above). Any higher rate of volcanism would result in remelting of the base of the volcanic pile and possible further differentiation and reeruption of more highly evolved crustal material.

Additionally, it has been proposed that erosion and sedi- can be assumed to represent a seafloor spreading process, with mentation on Venus could produce sedimentary sections suffi- the deficiency in area at greater depths caused by preferential ciently thick for their bases to be melted by the regional consumption of older seafloor. This hypothesis requires, how- geothermal gradient[ Warner, 1983]. This process would supple- ever, an finplausibly thick lithosphere, as argued above. ment the volcanic crustal recycling or even dominate if erosion

rates are so rapid that large volcanic piles rarely develop. The volcanics remain an integral part of the system, however, as the sediment source. Crustal genesis could occur at slower rates and under lower geothermal gradients on the flanks of the hot spots, where sedimentation and minor volcanism might be expected. Thus crustal genesis is a possible, even probable consequence of hot spot heat loss.

We can only speculate on the efficiency of basaltic and more evolved crustal genesis in a hot spot system relative to a plate tectonics system. This efficiency depends on the ratio of volcanic to conductive heat loss on the hot spots. In plate tectonics, most of the heat is released during the generation and cooling of new oceanic lithosphere, and all oceanic crust is eventually recycled and available for further differentiation. In the hot spot system, only a small part of the heat may be released in the generation of new crust if the Hawaiian swell is a representative hot spot system (see above), and it is only if sufficient subsequent volcanism occurs that the crust will be recycled. Thus a hot spot would be expected to have a lower efficiency of crustal genesis than a plate tectonic system, which is compatible with the low volume of evolved crust indicated for Venus by the 4øAr data.

What would hot spot crust look like? Presumably it would be a complex mixture of hot spot volcanism, intruding and intruded hy more evolved magmatic products. Episodes of hot spot volcanism are likely to be associated with periods of maximum strength of the upwelling convection system, and with associated uplift, continental rift-like volcanic systems are likely to develop. McGill et al. [1981] have remarked on the morphologic similarities between Beta Regio, one of the areas thought to have contemporary volcanism on Venus, and the East African rift system. The base of the volcanic pile will probably be further differentiated by partial remelting as it is heated during burial [e.g., Arth and Hanson, 1972], and its magmatic products will be more viscous than the primary basal-

strengths and areas of the hot spots on both planets, •the Hawaiian system probably representing the most robust terrestrial hot spot, but there appear to be gross similarities between the terrestrial and the proposed venusian hot spot systems.

It has been suggested that a system of hot spot tectonics was active on the earth during all or part of the Archaean [e.g., Hargraves, 1981]. The hot spot model presented above can be tested for applicability to the earth's Archaean by evaluating its efficiency as a heat loss mechanism. The present mean heat flux of the earth is estimated to be 82 mW m -2 from the global heat loss estimate given by Sclater et al. [ 1980]. Heat flow was much higher during the Archaean due to higher abundances of radiogenic elements early in the earth's history, and estimates of this higher heat flux range from 110 to 180 mW m -2 at 2500 m.y., and 160 to 280 mW m -2 at 3500 m.y. [e.g., Wasserburg et al., 1964; McKenzie and Weiss, 1975]. If the simple Venus hot spot heat loss model (Table 1) is adapted to reflect probable terrestrial lithosphere conditions, the mean global heat flux predicted by the Venus lithospheric thickness remains approximately constant, the lower terrestrial lithosphere thermal conductivity being compensated by the higher temperature drop across the earth's lithosphere. The model will predict higher heat flux if any of the following modifications are made: (1) increase the number of hot spots; (2)increase the mean diameter of each hot spot; (3) thin the lithosphere and hence increase the heat flux from each hot spot; and (4) decrease the maximum thickness of the lithosphere, as would be expected for a planet with higher heat flux and less time for a thick lithosphere to develop. Com- binations of these modifications can be made which are compatible with high heat loss in the Archaean and thus the concepts of hot spot tectonics are consistent with probable Archaean thermal conditions.

CONCLUSIONS

tic magma and are likely to be predominantly volumetrically A simple model relating surface elevation to lithospheric represented by plutonic activity. Hence the resulting crust thickness and heat flow clearly demonstrates that the heat loss would possibly comprise of large intermediate to acidic plutons from Venus can be explained in terms of conductive hot spot intruding and dissected by rift controlled (linear sections) basal- heat flow. Approximately 93% of the topography of the mapped tic volcanism. This description is closely matched by the tona- surface area of Venus can be explained in terms of simple litic plutons interspersed with greenstone belts of many terrestrial thermal compensation, the surface elevation being linearly Archaean cratons. related to lithospheric thickness which in turn is inversely pro-

Comparison Between Terrestrial and VenusJan Hot Spots

Are the terrestrial and postulated venusian hot spot sys-

portional to surface heat flow. Thin lithosphere is thought to be related to rising convection plumes in the venusian mantle, and this interpretation is consistent with the Venus gravity data. Most of the compensation would appear to take place at depth (up to 250 km) by the density contrast between the lithosphere

tems comparable? The type example of a terrestrial hot spot is and asthenosphere. For two highland areas which appear to the Hawaiian swell, approximately 1000 km in diameter, or exhibit active volcanism, Beta Regio and eastern Aphrodite 0.15% of the earth's surface area if it is assumed to be a circular feature in a fixed plate-hot spot reference frame. This last assumption certainly understates the strength of the Hawaiian hot spot but probably represents it as a more typical, weaker hot spot on the earth. How many Hawaiian swells would be required to explain the predicted hot spot areas of Venus, a little over 5% of the total surface area (the high heat loss elevation increment, 6052.5-6053.0 km, Table 1)? Assuming all the hot spots to have a similar aerial extent, approximately 35 Hawaiian

Terra, greater compensation depths (up to 1000 km) can be explained by density contrasts within underlying, relatively vigorous, mantle plumes.

For the approximately 7% of the topography above a radius of 6053 km, we have proposed that the topography is partially isostatically compensated by a variable thickness buoyant crust. Gravity data from middle and low latitudes of the planet indicate great depths of compensation for the topography (greater than 100 km), so at these latitudes the crustal

type hot spots would be required, very similar to the number of buoyancy must only augment the lithosphere/asthenosphere predicted hot spots for the earth [e.g., Heestand and Crough, buoyancy. By this mechanism, all topography up to an elevation 1981]. If significant portions ofthe area of Venus above 6053 km of 6055 km, almost 99% of the mapped area of the planet, can be also represent hot spots, the number of Venus hot spots could explained. Higher elevations must be explained by thicker crust possibly be as many as 70. There is undoubtedly a range in than can be accommodated by thethinnestlithosphereand there-

8316 MORGAN AND PmLLWS: VENUS HOT SPOT HEAT TRANSFER

fore must occur in areas off the crests of the hot spots. Only one mapped area, Ishtar Terra, definitely requires thicker crust (up to 60 km). This area has been previously postulated to be the only true continent on Venus [Phillips et al., 1981], but more gravity data are required to resolve the depth and mode of compensation for this feature.

The basic surface elevation-lithospheric thickness-heat flow model is compatible with both hot spot and plate tectonic modes of heat loss for Venus. However, the thick lithosphere (up to 250 km) required to explain the low elevations of Venus requires a very long cooling time (of the order of 700 m.y.) to develop from thin newly formed or thinned lithosphere. The elevation distribution and calculated lithospheric thicknesses indicate that if plate tectonics is occurring on Venus, it is a factor of two or three slower than on the earth. Features identified as

possible slow spreading ridges on Venus cannot account for the total heat loss, and are probably subordinate to hot spot heat loss. The skew in the hypsometric curve towards greater depths for terrestrial oceans is predicted by relatively rapid sinking of young ocean floor during its early stages of cooling and the apparent flattening of the depth-age relationship for sea floor older than approximately 80 m.y.

The main peak of the Venus hypsometric curve shows little skew, indicating that if seafloor spreading is operative on Venus there is a different age/depth/area relationship for lithospheric plates on Venus than in the terrestrial oceanic lithosphere. The width of the curve is consistent with hot spot/topography models we have developed for the planet, because in our models thick lithosphere can develop over the fixed locations of the descending limbs of the asthenospheric convection system and the curve's symmetry presumably reflects gross symmetry about a mean in the heat output of the convection system. The width of the hypsogram interpreted in terms of seafloor spreading implies a lithosphere up to 250 km in thickness, which we consider unlikely to develop in a plate tectonics system in the presence of chondritic levels of heat production in the planet. We therefore favor the hypothesis that Venus loses heat by a system of dominantly conductive hot spots, probably directly related to a major mantle convection system, and possibly sup- plemented by hot spot volcanic heat loss.

We have proposed a model of hot spot crustal genesis for Venus, where basaltic hot spot volcanics are recycled and further differentiated by burial and remelting. If the venusian lithosphere is assumed to be fixed with respect to the mantle convection system, this model predicts thicker crust on the hot spots than elsewhere, a prediction consistent with the observed topography and gravity. Sedimentary recycling may augment

that an analogous terrestrial hot spot system would be capable of the higher rates of heat loss predicted for the Archaean.

Acknowledgments. Our understandings of terrestrial hot spots and crustal genesis have benefited from discussions with S. T. Crough and L. D. Ashwal, respectively. We thank J. L. Warner for providing us with a preprint of his paper on sedimentary processes on Venus [ Warner, 1983] and S.C. Solomon for providing a critical review of a draft of this manuscript. This study was performed at the Lunar and Planetary Institute, which is operated by the Universities Space Research Association under contract NASW-3389 from the National

Aeronautics and Space Administration. This is LPI contribution number 502.

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Hot spot heat transfer: Its application to Venus and implications to Venus and Earth

Documents

Absolute plate motions constrained by shear wave splitting orientations with implications for hot spot motions and mantle flow

Optical properties of the Venus upper clouds from the data obtained by Venus Monitoring Camera on-board the Venus Express

Venus orbiter: Ishtar

Venus in Two Acts | MoMA

Topographic comparisons of uplift features on Venus and Earth: Implications for Venus tectonics

Magnetic lineations within Shatsky Rise, northwest Pacific Ocean: Implications for hot spot-triple junction interaction and oceanic plateau formation

Upper mantle seismic structure beneath the Ethiopian hot spot: Rifting at the edge of the African low-velocity anomaly

An Alternate View of Venus

Building of the Amsterdam-Saint Paul plateau: A 10 Myr history of a ridge-hot spot interaction and variations in the strength of the hot spot source

Interaction between the Mid-Atlantic Ridge and the Azores hot spot during the last 85 Myr: Emplacement and rifting of the hot spot-derived plateaus

Visualisation of hot spot development in bulk coal

La máscara de Venus

Analytical Modeling of TCP Clients in Wi-Fi Hot Spot Networks

The Birth of Venus? (2015)

Deforestation in Lacandonia (southeast Mexico): evidence for the declaration of the northernmost tropical hot-spot

Magmatic effects of the Cobb hot spot on the Juan de Fuca Ridge

Hf isotope constraints on mantle sources and shallow-level contaminants during Kerguelen hot spot activity since ∼120 Ma

spatial analysis of crime hot-spot in the northeast penang

Post-Glacial Spatial Dynamics in a Rainforest Biodiversity Hot Spot

On the uncertainties in hot spot reconstructions and the significance of moving hot spot reference frames