Joumalofvokanolog
andgeothermalresearch
Journal of Volcanology and Geothermal
Research 64 ( 1995) 53-60
Effects of planetary thermal structure on the ascent and cooling of
magma on Venus
Susan E.H. Salcimoto*, Maria T. Zuber’
Department of Earth and Planetary Sciences, The Johns Hopkins University,Baltimore, MD 21218, USA
Received 16 June 1993; revised version accepted 23 June 1994
Abstract
Magellan radar images of the surface of Venus show a spatially broad distribution of volcanic features. Models
of magmatic ascent processes to planetary surfaces indicate that the thermal structure of the interior significantly
influences the rate of magmatic cooling and thus the amount of magma that can be transported to the surface
before solidification. In order to understand which aspects of planetary thermal structure have the greatest influence on the cooling of buoyantly ascending magma, we have constructed magma cooling profiles for a plutonic
ascent mechanism, and evaluated the profiles for variations in the surface and mantle temperature, surface temperature gradient, and thermal gradient curvature. Results show that, for a wide variety of thermal conditions,
smaller and slower magma bodies are capable of reaching the surface on Venus compared to Earth, primarily due
to the higher surface temperature of Venus. Little to no effect on the cooling and transport of magma are found to
result from elevated mantle temperatures, elevation-dependent surface temperature variations, or details of the
thermal gradient curvature. The enhanced tendency of magma to reach the surface on Venus may provide at least
a partial explanation for the extensive spatial distribution of observed volcanism on the surface.
1.Introduction
The Magellan images of Venus have revealed
a broad spatial distribution of volcanic landforms (Head et al., 199 1, 1992). Previous work
in modeling the ascent of magma on both Venus
and Earth (Marsh, 1978,1982; Marsh and Kantha, 1978; Sakimoto et al., 1992) has indicated
that the planetary thermal structure significantly
influences magmatic cooling rates and thus the
amount of magma that can be transported to the
surface before solidification. Since thermal
structure may play a prominent role in controlling the distribution and magnitude of planetary
volcanism, and given that the thermal structure
of Venus is likely to be different from that of
Earth (Kaula and Phillips, 198 1; Phillips, 198 1;
Kaula, 1983), it is worthwhile to investigate the
effects of different aspects of planetary thermal
structure on magma ascent in more detail. In order to understand which aspects of the thermal
structure have the greatest influence on the cooling of ascending magma, we have constructed
magma cooling profiles for a plutonic buoyant
ascent mechanism, and evaluated the profiles for
variations in the surface temperature, surface and
mantle temperature gradient, and thermal gradient curvature with depth. The cooling curves
were then compared to constrain magma ascent
velocities, source depths, and body sizes for Venus relative to Earth.
0377-0273/95/$09.50
0 1995 Elsevier Science B.V. All rights reserved
SSDIO377-0273(94)00044-l
S.E.H. Sakimoto, M. T. Zuber /Journal of‘ Volcanologyand Geothermal Research 64 (1995) 53-60
54
2. Planetary thermal structure
Because of the wide variety of possible thermal structure parameters-and
thus variations-it
is desirable that the expression for the thermal
structure be flexible as well as mathematically
convenient. Here, the planetary thermal structure is modeled as:
(1)
which gives dimensionless
temperature
as a
function of dimensionless depth where is T the
temperature, To is the source depth temperature,
z is the depth, z. is the source depth, and n is a
constant controlling thermal gradient curvature
with depth. A dimensionless surface temperature adjustment is accomplished with:
r=&
(2)
TO
where T, is the surface temperature. Equation
( 1) is used both for its mathematical simplicity
as well as its tit to the thermal gradients predicted by cooling half-space models (e.g., Sclater
et al., 1980) that describe, to first order, the
Temperature (T/To)
1
0
^o
s
r
‘i
8
1
Fig. 1.Thermal structures for Earth and Venus calculated from
Eq. ( 1 ), plotted as dimensionless temperature vs. dimensionless depth. Earth curve is a typical oceanic geotherm. Venus curve A has the same surface thermal gradient and curvature shape as Earth (n = 2) but a shallower source depth.
Venus curve B has a similar surface thermal gradient and
source depth as Earth but a higher curvature (n = 3 ). Venus
curve C has the same source depth and curvature shape as
Earth (n = 2) but a smaller surface thermal gradient.
cooling with age of the terrestrial oceanic lithosphere. Figure 1 shows several curves produced
from Eq. ( 1) by varying one or more of the following: surface temperature,
mantle temperature, magma source depth, and thermal gradient
curvature. The surface temperature gradient for
any particular thermal structure is found by calculating dT/dz as z approaches zero. For otherwise similar thermal structures, the high surface
temperature of Venus allows - but does not require - a shallower minimum magma source
depth than on Earth.
3. Composition
The morphological resemblance of the venusian plains, volcanic features and structures to
basaltic plains, features and structures on Earth
(Campbell et al., 1989; Head et al., 1992), and
the Soviet Venera and Vega lander bulk density
and elemental abundance data (Surkov et al.,
1983, 1984, 1987) imply a basaltic composition
for the majority of the surface of Venus. Accordingly, a basaltic (olivine tholeiite) magmatic
composition is used here. For ease of comparison, the magmatic compositions and thus the solidus and liquidus of the ascending magma are
assumed to be the same on both Venus and Earth.
Also, because of a probable dry Venus lithosphere (Kaula, 1990; Donahue and Hodges,
1992 ), a dry olivine tholeiite (quartz eclogite at
high pressures) solidus and liquidus from the experimental data of Lambert and Wyllie ( 1972)
is assumed for a magmatic composition when
comparing magmatic cooling curves for Earth
and Venus.
4. Plutonic ascent
The pluton ascent model is described in detail
in previous publications (Marsh, 1978, 1982;
Marsh and Kantha, 1978), and is essentially a
low Reynolds number, high Peclet number problem of heat transfer through a thin thermal
boundary layer around a sphere. The model is
constructed for maximum possible heat transfer,
S.E.H. Sakimoto, M.T. Zuber / Journal of Volcanologyand Geothermal Research 64 (1995) 53-60
0.4
0.5
0.6
0.7
0.6
0.9
1
Trr,
1.1
0.4
0.5
0.6
0.7
0.8
0.9
55
1
T/r,
Fig. 2. Basaltic cooling curves for pluton ascent on Earth and Venus contoured in the dimensionless parameter Jfo and plotted as
dimensionless temperature vs. dimensionless depth. The terrestrial thermal structure is the same as in Fig. 1, and the venusian
thermal structure has the same surface thermal gradient and shape but a source depth 60% that of Earth. In order for the magma
to reach the surface unsolidified, the cooling curve must not cross the solidus. For these thermal structures, JtOfor Earth is 1.2
and Jt, for Venus is 1.4.
and so yields an upper bound on magmatic cooling and thus a lower bound on magma ascent velocity. The thermal effects of crystallization during ascent are discussed in Marsh ( 1978), and
are generally small compared to the thermal
structure effects in this analysis and thus are not
treated here. The model assumes constant velocity buoyant ascent, body-averaged magma temperatures and properties, and an initially crystalfree magma. The resulting plutonic cooling
curves, which are dominated by the convective
cooling terms and strongly influenced by the planetary thermal structure, are expressed mathematically by:
+(g-)([ J+;)t,l”)[e-‘J+~“(
- 1w(
i
(-l)“n![(J+y)ll”-p
p=O
(n-r))!
1
(3)
where J=3 Nu
y=cxgV/C,, is
to is
total ascent time, Nu=O.8 Pe112,Pe= Va/lc,Peis
the Peclet number, V is the velocity of magmatic
ascent, a is the body radius, u ( = 1 x 10T6
m2 s-’ ) is the thermal diffusivity, Q!( = 6 x low5
K- ’ ) is the coefficient of thermal expansion, g is
the gravitational acceleration, and C, ( = 1250
J kg- ‘K- I ) is specific heat capacity. The parameter T is the mean magma temperature, Tois the
magma temperature in the source region, and 12
is a constant that defines the shape of the planetary thermal gradient (Eq. 1). Equation (3) reduces to the expression for the thermal gradient
(Eq. 1) for an infinitely slow ascent (dimensionless ascent time Jfo=~), and to the adiabatic curve T/T,, = eMy’for an infinitely fast ascent (Jto= 0). Typical plots of the resulting
cooling curves for terrestrial and Venus conditions, contoured in Jto values, are illustrated in
Fig. 2. In order for the magma to reach the surface unsolidified, the cooling curve must not
cross the solidus before it reaches the surface. The
allowable Jto values obtained from the cooling
56
S. E. H. Sakimoto, M. T Zuher /Journal of Cblcanologyand Geothermal Research 64 (I 995) 53-60
curve plots for Venus and Earth can be directly
compared with:
Ascent velocity and pluton radius vs. thermal gradient
I
I
I
I
(4)
Pluton Ascent
n=2
to obtain relative minimum magma ascent velocities, source depths, and body sizes where Vis
the minimum magma ascent velocity, a is the
minimum magma body radius, z0 is the minimum magma source depth, &, is the dimensionless ascent parameter determined from the cooling curves, and the subscripts ‘E’and ‘V’ indicate
Earth and Venus values, respectively.
ZRO
amir
..................
--5
-31
Vhl
I
--
I
I
I
I
I
I
I
I
I
I
5. Results
Cooling curves for the plutonic ascent mechanism model were calculated for a variety of Venus surface temperature gradients, thermal gradient curvatures, and the variation of surface
temperature with elevation on Venus.
In general, for the pluton ascent mechanism
model presented here, the influence of the planetary surface temperature dominates the effects
of variations in surface temperature gradient,
thermal gradient curvature, and mantle temperature. The higher surface temperature of Venus,
for otherwise similar planetary thermal structures, allows considerably smaller minimum
possible magma body sizes and slower ascent velocities than would be possible on Earth for a
reasonable range of source depths and venusian
surface thermal gradients ( 1O-25 K/km; Zuber,
1987; Grimm and Solomon, 1988; Zuber and
Parmentier, 1990). The results for the pluton ascent model for variations in surface temperature
gradient and two different thermal gradient curvatures are shown in Fig. 3. For example, for the
same gradient curvature (n= 2) and surface
thermal gradient as on Earth, a pluton on Venus
could have a minimum source depth of about
two-thirds of Earth’s, an ascent velocity of about
one-third of Earth’s, and a body radius about twothirds of Earth’s, and still reach the surface unsolidified. The results shown are for a dry basaltic (olivine tholeiite ) composition (Lambert and
I
Pluton Ascent
n=3
amin . ..-...............................
=\
I
._
__
“3
Vrnln
-
-
-
---
I
I
I
I
1
1.2
1.4
1.6
3
Thermal Gradient (dWd2)
Fig. 3. Earth-normalized results for basalt on Venus. (a) Dimensionless minimum ascent velocity and minimum pluton
radius vs. surface thermal gradient for n=2, and (b) n=3
gradient shapes for plutonic ascent.
Wyllie, 1972 ). The surface temperature effect is
greater for more primitive magma compositions,
but may be smaller for magmas of higher crystallinity. For example, for the case above of the same
venusian gradient curvature (n = 2 ) and surface
thermal gradient as on Earth, a venusian peridotitic pluton, with solidus and liquidus taken
from Takahashi and Kushiro ( 1983 ), could have
an ascent velocity of about one-fourth (instead
of one-third) of Earth’s, and a body radius about
three-fifths (instead of two-thirds) of Earth’s,
and still reach the surface unsolidified. Normally, peridotite plutons would not be buoyant,
S.E. H. Sakimoto, M. T. Zuber /Journal of Volcanologyand Geothermal Research 64 (I 992;)S3-60
57
Ascent velocity and pluton radius vs. thermal gradient
2
-
I
I
1
I
I
I
Pluton Ascent
n=2
I
I
I
I
I
I
Pluton Ascent
a=3
Vmln
1-__1_
0.6
0.8
1
_I
1.6
1.6
Fig. 4. Earth-normalized results for the effects of elevation-dependent surface temperature variations on basaltic magma transport on Venus. Solid curves are for surface temperature of 660°K (highlands) and dashed lines are for surface temperature of
740°K (lowlands). (a) Dimensionless minimum ascent velocity and minimum pluton radius vs. surface thermal gradient for
n= 2, and (b ) n = 3 gradient shapes for plutonic ascent.
but the example serves as a compositional end
member of the enhanced venusian magma transport possibilities.
The thermal and mechanical effects of crystallization have been neglected in this model and
eruption may occur as long as the magma reaches
the surface unsolidified. A rough estimate of the
enhanced venusian magma transport effect of
crystallization on eruption probability may be
obtained by noting that, for eruptions of basaltic
magma below the 55% crystal content “eruptability limit” (Marsh, 198 1) , the effect is reduced
by 5-lo%, and for eruptions near the liquidus,
1O-2096.
A higher venusian surface thermal gradient
(relative to Earth) also enhances magma transport possibilities, but to a much lesser degree than
the surface temperature effect. Similarly, for
higher values of thermal gradient curvature with
depth (n > 2 in Eq. 1) , the minimum possible as-
58
S. E. H. Sakimoto, M. T. Zuber /Journal of Volcanologyand Geothermal Research 64 (I 99s) 53-60
cent velocities and body sizes are also considerably less than those of Earth for plutonic ascent.
The effects of small variations in surface or
mantle temperatures are not significant. For the
thermal structures investigated, the effect on the
model of a postulated 100 K hotter Venus mantle (Phillips and Malin, 1983; Stevenson et al.,
1983; Sotin and Parmentier, 1989) is simply to
decrease the minimum possible source depth on
Venus by approximately 10% (on average) of the
total. The variation of surface temperature with
elevation on Venus is approximately 8 K km-’
and decreases with increasing elevation (740660 K, Seiff, 1983). Figure 4 shows the effect of
these temperature variations on magma ascent.
The solutions are nearly identical to those for
higher mantle temperatures; and slightly greater
than the effect of elevated venusian surface thermal gradients.
6. Discussion
For all of the thermal structures considered for
plutonic magma ascent in this model, the minimum magmatic ascent velocity, the minimum
body size, and the minimum source depth are
significantly smaller on Venus than on Earth.
This enhanced range of conditions
favoring
magma transport to the surface is due primarily
to the high surface temperature on Venus; elevation-dependent
surface temperatures,
higher
mantle temperatures,
and/or higher gradient
curvatures have little additional significant effect. Due to the larger difference between the solidus and liquidus temperatures, more primitive
magma compositions than the basaltic olivine
tholeiite that we assumed in this analysis experience more favorable transport conditions than
the silicic compositions. The same ‘AT’ type of
argument indicates that, according to this analysis, more crystalline magmas should reach the
surface more easily on Venus than on Earth. This
result neglects the (possibly significant ) considerations of latent heat of crystallization and considerable viscosity increases due to the addition
of crystals in the end stages of cooling. However,
considering only the thermal aspects of magma
cooling and transport, we might expect more
magmas on Venus capable of erupting or reaching the near-surface close to the crystallinity
eruption limit (approximately
55% crystals;
Marsh, 198 1) than is found on Earth. The abovementioned neglect of most of the thermal effects
of crystallization, as well as the initial assumption of a constant velocity of ascent, may make
this analysis more useful for considering the
transport of magma from the base of the thermal
lithosphere to a high-level magma chamber than
it is for near-surface (the last lo-20% of the ascent distance) analyses (Marsh and Kantha,
1978). However, as long as the assumptions of
constant velocity buoyant ascent and low crystal
content are valid, this model also applies to magmatic ascent from the relatively near-surface
proposed magma reservoirs in neutral buoyancy
zones and/or shallow magma chambers on Venus (Head and Wilson, 1986, 1992). The additional effects of an extensional stress field on
magmatic ascent are not considered in this analysis; however, an extensional tectonic regime
such as those seen in Beta or Atla Regio (Schaber, 1982; Campbell et al., 1984; Head et al.,
1992) would further facilitate magma reaching
the surface.
For all venusian thermal structures considered, the ascent of plutons through the venusian
lithosphere is significantly facilitated primarily
due to the high surface temperature compared to
Earth. Thus, our model results would suggest a
wider range of sizes of intrusive and/or extrusive volcanic events over a wider spatial distribution of locations. This increased ease of volcanic activity in our model is independent of
time. Therefore, our model neither lends support to catastrophic (Schaber et al., 1992) or episodic (Turcotte, 1992) resurfacing mechanisms
that have been invoked to explain the nearly spatially random distribution
of impact craters
(Phillips et al., 1992) on the Venus surface, nor
helps distinguish between these models and
equilibrium resurfacing models (Phillips et al.,
1992 ). However, our model is consistent with the
broad spatial distribution of surface volcanism
on Venus.
S.E.H. Sakimoto, M.T. Zuber /Journal of Volcanologyand Geothermal Research 64 (1995) 53-60
7. Conclusions
For a wide variety of possible venusian thermal structures, smaller and slower magma bodies are capable of reaching the surface on Venus
compared to Earth. This result is a consequence
primarily of Venus’ high surface temperature.
Elevated mantle temperatures, elevation-dependent surface temperatures, and details of the curvature of the near-surface thermal gradient contribute relatively little - if any - significant
additional thermal effects on magma cooling and
transport. The enhanced ability of magmas to
reach the surface may be at least a partial explanation for the broad spatial distribution of surface volcanism on Venus.
Acknowledgments
We thank Bruce Marsh for many helpful discussions. This work was supported by NASA
grant NGT-50587 to S.E.H. Sakimoto and B.D.
Marsh, and a NASA Planetary Geology and
Geophysics Program grant to M.T. Zuber.
References
Campbell, D.B., Head, J.W., Harmon, J.K. and Hine, A.A.,
1984. Venus: Volcanism and rift formation in Beta Regio.
Science, 226: 167-l 70.
Campbell, D.B., Head, J.W., Hine, A.A., Harmon, J.K.,
Senske, D.A. and Fisher, PC., 1989. Styles of volcanism
on Venus: New Arecibo high resolution radar data. Science, 246: 373-377.
Donahue, T.M. and Hodges Jr., R.R., 1992. Past and present
water budget of Venus. J. Geophys. Res., 97: 6083-6091.
Grimm, R.E. and Solomon, SC., 1988. Viscous relaxation of
impact crater relief on Venus: Constraints on crustal
thickness and thermal gradient. J. Geophys. Res., 93:
11,911-11,929.
Head, J.W. and Wilson, L., 1986. Volcanic processes and
landforms on Venus: Theory, predictions, and observations. J. Geophys. Res., 91: 9407-9446.
Head, J.W. and Wilson, L., 1992. Magma reservoirs and neutral buoyancy zones on Venus: Implications for the formation and evolution of volcanic landforms. J. Geophys.
Res., 97: 3877-3903.
Head, J.W., Campbell, D.B., Elachi, C., Guest, J.E., McKenzie, D.P., Saunders, R.S., Schaber, G.G. and Schub-
59
ert, G., 199 1. Venus Volcanism: Initial analysis from Magellan data. Science, 252: 276-288.
Head, J.W., Crumpler, L.S., Aubele, J.C., Guest, J.E. and
Saunders, R.S., 1992. Venus volcanism: Classification of
volcanic features and structures, associations, and global
distribution from Magellan data. J. Geophys. Res., 97:
13,153-13,197.
Kaula, W.K., 1983. Minimal upper mantle temperature variations consistent with observed heat flow and plate velocities. J. Geophys. Res., 88, 10,323-10,332.
Kaula, W.M., 1990. Venus: A contrast in evolution to Earth.
Science, 247: 1191-l 196.
Kaula, W.M. and Phillips, R.J., 1981. Quantitative tests for
plate tectonics on Venus. Geophys. Res. Lett., 8: 11871190.
Lambert, LB. and Wyllie, P.J., 1972. Melting of gabbro
(quartz eclogite) with excess water to 35 kilobars, with
geological applications. J. Geol., 80: 693-708.
Marsh, B.D., 1978. On the cooling of ascending andesitic
magma. Philos. Trans. R. Sot. London., 288: 61 l-625.
Marsh, B.D., 198 1. On the crystallinity, probability of occurrence, and rheology of lava and magma. Contrib. Mineral. Petrol., 78: 85-98.
Marsh, B.D., 1982. On the mechanics of igneous diapirism,
stoping, and zone melting. Am. J. Sci., 282: 808-855.
Marsh, B.D. and Kantha, L.H., 1978. On the heat and mass
transfer from an ascending magma. Earth Planet. Sci. Lett.,
39: 435-443.
Phillips, R.J. and Malin, M.C., 1983. The interior of Venus
and tectonic implications. In: D.M. Hunten, L. Colin, T.M.
Donahue and V.I. Moroz (Editors), Venus. University of
Arizona Press, Tucson, AZ, pp. 159-2 14.
Phillips, R.J., Kaula, W.M., McGill, G.E. and Malin, M.C.,
198 1, Tectonics and evolution of Venus. Science, 2 12:
879-887.
Phillips, R.J., Raubertas, R.F., Arvidson, R.E., Sarkar, I.C.,
Herrick, R.R., Izenberg, N. and Grimm, R.E., 1992. Impact craters and Venus resurfacing history. J. Geophys.
Res., 97: 15,923-l 5,948.
Sakimoto, S.E.H., Zuber, M.T. and Marsh, B.D., 1992. Cooling of ascending magma on Venus and Earth. 23rd Lunar
and Planetary Science Conference, pp. 1203-l 204.
Schaber, G.G., 1982. Venus: Limited extension and volcanism along zones of lithospheric weakness. Geophys. Res.
Lett., 9: 499-502.
Schaber, G.G., Strom, R.G., Moore, H.J., Soderblom, L.A.,
Kirk, R.L., Chadwick, D.J., Dawson, D.D., Gaddis, L.R.,
Boyce, J.M. and Russell, J., 1992. Geology and distribution of impact craters on Venus: What are they telling us?
J. Geophys. Res., 97: 13,257-13,301.
Sclater, J.G., Jaupart, C. and Galson, D., 1980. The heat flow
through oceanic and continental crust and the heat loss of
the earth. Rev. Geophys. Space Phys., 18: 269-312.
Seiff, A., 1983. Thermal structure of the atmosphere of Venus. In: D.M. Hunten, L. Colin, T.M. Donahue and V.I.
Moroz (Editors), Venus. University of Arizona Press,
Tucson, AZ, pp. 2 15-279.
60
S.E.H. Sakimoto, M. T. Zuber /Journal of Volcanologyand Geothermal Research 64 (I 995) 53-60
Sotin, C. and Parmentier, E.M., 1989. Dynamical consequences of compositional and thermal density stratification beneath spreading centers. Geophys. Res. Lett., 16:
835-838.
Stevenson, D.J., Spohn, T. and Schubert, G., 1983. Magnetism and thermal evolution of the terrestrial planets. lcarus, 54: 466-489.
Surkov, Y.A., Moskalyeva, L.P., Shcheglov, O.P., Kharyukova, V.P., Manvelyan, O.S., Kirichenko, V.S. and Dudin., D.A., 1983. Determination of the elemental composition of rocks on Venus by Venera 13 and Venera 14
(preliminary results). J. Geophys. Res., 88: A481-A493.
Surkov, Y.A., Barsukov, L.P., Moskalyeva, L.P., Kharyukova, V.P. and Kemurdzhian, A.L., 1984. New data on
the composition, structure, and properties of Venus rock
obtained by Venera 13 and Venera 14. J. Geophys. Rex.
89: B393-B402.
Surkov, Y.A., Kimozov, F.F., Glazov, V.N., Dunchenko, A.G.
and Tatsy, L.P., 1987. Uranium, thorium, and potassium
in the venusian rocks at the landing sites of Vega 1 and 2.
J. Geophys. Res., 92: E537-E540.
Takahashi, E. and Kushiro, I., 1983. Melting of a dry peridotite at high pressures and basalt magma genesis. Am.
Mineral., 68: 859-879.
Turcotte, D.L., 1992. Episodic plate tectonics on Venus. In:
International Colloquium on Venus, Aug. 10-12, Pasadena, CA, LPI Contrib. No. 789, pp. 127-128.
Zuber, M.T., 1987. Constraints on the lithospheric structure
of Venus from mechanical models and tectonic surface
features. J. Geophys. Res., 92: E541 -E55 1.
Zuber, M.T. and Parmentier, E.M., 1990. On the relationship between isostatic elevation and the wavelengths of
tectonic surface features on Venus. Icarus, 85: 290-308.