High-resolution Magellan images and altimetry of Venus reveal a wide range of styles and scales of surface deformation that cannot readily be explained within the classical terrestrial plate tectonic paradigm. The high correlation of long-wavelength topography and gravity and the large apparent depths of compensation suggest that Venus lacks an upper-mantle low-viscosity zone. A key difference between Earth and Venus may be the degree of coupling between the convecting mantle and the overlying lithosphere. Mantle flow should then have recognizable signatures in the relationships between surface topography, crustal deformation, and the observed gravity field

Hager, Bradford H.

Simons, Mark

Solomon, Sean C.

English

NASA Technical Reports Server

110 lntemational Colloquiumon Venus
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Figs. 1and 2. l-Large volcanic shield and gende slopes covered with ovedapping lays flows; 2--central domelike
part of some volcanic shields with many small volcanic hills and absence of expressed lava flows; 3--bright, smooth
lava plain; possesses numerous lava chatmels or lava flow fronts; 4-dark lava plain; smooth, or with sharp lava
channels; 5- hilly lava plain with clusters of small volcanic hills; 6--wrinlded plain with a net of gtabens; 7---areaof
ridge concentration (one or more interesting systems); g-ridge belt; 9-undivided tessera; 10--corona; I l-large
domelike uplift (beta); 12--volcano and lava flow; 13-.caldera; 14--arachnoid; 15--dome (central dark, and outer
bright areas are outlined); 16--impact crater and eject,,; 17--ridge; 18--graben rod/or fault; 19-scarp; 20--lava flow
direction; 21-lava flow boundary tad direction.
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N93-14376 'itS,c(3"1 
GEOID, TOPOGRAPHY, AND CONVECTION-DRIVEN
CRUSTAL DEFORMATION ON VENUS. Mark Simons,
Bradford H. Hager, and Scan C. Solomon, Department of Earth,
Atmospheric, and Planetary Sciences, Massachusetts Institute of
Technology, Cambridge MA 02139, USA.
Introduction: High-resolution Magellan images and altim-
etry of Venus reveal a wide range of styles and scales of surface
deform ation [1] that cannot readily be explained within the classical
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terrestrial plate tectonic paradigm. The high correlation of long-
wavelength topography and gravity and the large apparent depths of
compensation suggest that Venus lacks an upper-mantle low-
viscosity zone [2-5]. A key difference between Earth and Venus
may be the degree of coupling between the convecting mantle and
the overlying lithosphere. Mantle flow should then have recogniz-
able signatures in the relationships between surface topography,
crustal deformation, and the observed gravity field [6,7].
Model: We explore the effects of this coupling by means of a
f'mite element modeling technique. The crust and mantle in these
models are treated as viscous fluids. We solve both the equations of
motion and the heat equation at every time step using a modified
version of the two-dimensional Cartesian t'mite-element program
ConMan [8]. A passive marker chain tracks the crust-mantle inter-
face and permits vailation in the crustal buoyancy as well as specific
crustal and mantle rheologies. These rheologies depend on compo-
sition, temperature, and stress. In addition to the flow field, the
stress field in the lithosphere, the surface topography, and the
resulting geoid are readily calculated. The models presented here
use an irregular f'mite-element mesh that is 50 elements high and 160
elements wide. Our maximum resolution is in the 40-km-thick top
layer, where each element is 2 km high and 5 km wide. In all, the
mesh is 800 km in the horizontal dimension and 400 km in the
vertical dimension. We impose free-slip boundary conditions on the
top and side walls, with no flow through these walls. Flow at the
bottom boundary is constrained to be vertical with no horizontal
flow permitted. This last boundary condition gives a virtual 800
krn x 800 krn box. The surface topography is calculated from the
vertical stresses on the top wail of the box. Top and bottom
https://ntrs.nasa.gov/search.jsp?R=19930005188 2020-03-17T08:43:17+00:00Z
LPI Contribution No. 789 11 1
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400; 200' 400' 600' 8""00
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100
(b)
4000-- 200 400 600 800
Horizontal Distance, km
Fig. 1. Temperature contours at 130 m.y. for the (a) upwelling and
(b) downwelling models. Contour interval is IO0°C; the top of the box is at
500°C.
temperatures are fixed at 500°C and 1250<'(2 respectively. Initially,
we impose a linear temperature gradient across the lithosphere and
set the rest of the mantle to be isothermal. We investigate two
classes of models. Flow in the f'ast class is initiated with a sinusoidal
temperature perturbation throughout the box. This results in mantle
flow that is dominated by concentrated downwelling (Fig. lb). In
the second class of models, flow is driven by a hot patch at the side
of the box, thereby driving flow by concentrated upwelling (Fig. I a).
Results: In all our models, convection produces horizontal
eompressional stresses in lithosphere above downwelling mantle
and extensional stresses in lithosphere above upwelfing mantle. As
the convective vigor increases so does the magnitude of the stress.
In models with constant-viscosity mantle overlain by a constant-
viscosity crust, stress in the crust reaches values in excess of 100
MPa in less than 100 m.y. We find that the rate of increase in
compressive stress decreases with increasing crustal viscosity. This
is because the stronger the crust, the more the development of the
convective instability in the mantle driving the deformation is
impeded. We also fired that the magnitude of the peak compressive
smess achieved above the downwelling increases with higher vis-
c0sities and/or with thinner initial crustal layers, the stronger the
crustal lid, the more tractions from mantle convection are supported
in the crust. Since force balance on the crust requires that shear
traction integrated along the base be balanced by normal tractions
integrated through its thickness, the thinner the crust, the larger the
horizontal s_esses.
Both analytical models [9,10] and our numerical models of
convection-induced crustal flow indicate that the amplitude and
sign of the topography are highly time and rheology dependent. In
general, possible responses of the crust to mantle flow can be
divided into three categories. The fin'st involves little if any crustal
flow, and topography results mainly from the transmission of
normal tractions induced by density contrasts within the mantle.
The second possible regime involves substantial crustal flow, with
geologically rapid thickening over convective downwelling and
thinning over convective upwelling. In this regime the effects of
crustal thickness variations dominate the topography. A third pos-
sible regime lies between the fast two, with"in phase" deformation
on short timescales and crustal flow on longer timescales. A stxong
mantle lithosphere tends to shield the crust from convective shear
tractions, and topography results mainly from the transmission of
convective normal tractions. A relatively weak lower crust facili-
tates crustal deformation, and the isostatic effects of crustal thick-
ness variations dominate the topography.
Consideration of geoid to topography ratios (GTRs) can restrict
which regime of crustal response is appropriate for Venus. The
distribution of estimated GTRs for several highland regions on
Venus is bimodal with two clusters around 10 and 25 m/kin [5]. The
positive correlation of long-wavelength gravity and topography
impfies that there are no major regions that have negative GTRs. To
keep the GTRs positive, the geoid must follow the surface topogra-
phy in sign at all times. Although the regime of negligible crustal
flow can correctly predict both the sign and magnitude of the GTRs,
it does not allow for the crustal deformation (i.e., flow) inferred
from observations of tectonic features on Venus.
In contrast to the regime of negligible flow, that of time-
dependent crustal flow generates topography that changes sign.
Over a mantle downwelling, the topography is negative in the early
stages of deformation and positive in the later stages of deformation;
the converse holds over a mantle upwelling. During the transitional
period the topography goes through zero, the geoid does not go
through zero, and the GTR is unbounded; this singularity is not
observed on Venus. An example of the evolution of the GTR for a
model in the time-dependent regime is shown in Fig. 2. Note that
before 90 m.y. both topography and geoid are negative, but at 90
m.y. crustal thickening effects begin to dominate and the topogra-
phy switches sign, causing the GTRs to first become unbounded and
then negative.
In the absence of a mechanism by which the sign of the geoid
anomaly mimics that of the topography over a given upwelling or
downwelling, only the regime of rapid crustal flow is plausible. In
the case of mantle downwelling this would also require that the
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L3
100
5O
0
-50
-woo 20 40 60 80 100 120 140
Time, My
Fig. 2. Evolution of GTR with time. At each time step, the GTR shown is the
slope of the best fit line to the collection of geoid and topography values
upward continued to 250 km above the surface nodes in the model. The result
is for a downwelling model, with a crust of constant vi scosity 50 times that of
the mantle. In this model the sign of the topography is time-dependent, but that
of the geoid is not. The singularity at about 90 m.y. corresponds to the time
when topography crosses the zero datum. Note that the GTRs for this model
am neither always positive nor always bounded.
112 lnternationalColloquiumon Venus
lower mantle be more viscous than the upper mantle in order to
produce the required positive geold anomalies. This has already
been shown to be true for the Earth, where the observed geoid highs
over regions of mantle upwdling and regions of mantle down-
welling are best explained by the presence of a strong lower mantle
[11,12]. The large positive GTRs and the presence of large shield
volcanos in certain highland regions on Venus, such as Beta Regio
and Eistla Regio, are best explained as areas of mantle upwelling
[5,13,14]. The regime of rapid crustal flow predicts crustal thinning
over the upwelling. However, the extensive partial melt and ensuing
volcanism expected over such regions of mantle may outweigh the
effects of crustal thinning on the surface topography and thus also
yield postive GTRs [15].
References: [1] Solomon S. C. et al. (1991) Science,252,297.
[2] Kiefer W. S. et al. (1986)GRL, 13, 14. [3] Bills B. G. et al. (1987)
JGR, 92, 10. [4] Phillips R. J. et al. (1991) Science, 252, 651.
[5] Smrekar S. E. and Phillips R. J. (1991) EPSL, 107, 587.
[6] Phillips R. J. (1986) GRL, 13, 1141. [7 ] Phillips R. J. (1990) JGR,
95, 1301. [8] King S. D. et al. (1990)PEPI,59, 195. [91Bindschadler
D. L. and Parmentier E. M. (1990)JGR, 95, 21. [10] Schmeling H.
and Marquart G. (1990) GRL, 17, 2417. [11] Richards M. A. and
Hager B. H. (1984) JGR, 89, 5987. [12] Hager B. H. (1984) JGR,
89, 6003. [13] Grimm R. E. and Phillips R. J. (1991)JGR, 96, 8305.
[14] Grimm R. E. and Phillips R. J. (1991)JGR, in press.
[15] Phillips R. J. et al. (1991) Science, 25_, 65,1.
,,"N93-14377
VENUS GRAVITY: SUMMARY AND COMING EVENTS.
W. L. Sjogren, Jet Propulsion Laboratory, 4800 Oak Grove Drive.
Pasadena CA 91109, USA.
The first significant dataset to provide local measures of venu-
sian gravity field variations was that acquired from the Pioneer
Venus Orbiter (PVO) during the 1979-1981 period. These observa-
tions were S-band Doppler radio signals from the orbiting space-
craft received at Earth-based tracking stations. Early reductions of
these data were performed using two quite different techniques.
Estimates of the classical spherical harmonics were made to various
degrees and orders up to 10 [ 1,2,3]. At that time, solutions of much
higher degree and order were very difficult due to computer
limitations. These reductions, because of low degree and order,
revealed only the most prominent features with poor spatial resolu-
tion and very reduced peak amplitudes.
Another reduction technique was the line-of-sight acceleration
mapping that had been used successfully for the Moon and Mars.
This approach provided much more detail and revealed the high
correlation of gravity with topography [4,5,6]. However, this tech-
nique does not produce a global field as do the spherical harmonics.
It provided a mapping of features from approximately 50°N to 25°S
latitude for 360 ° of longitude. Other shortcomings were that the
accelerations were at spacecraft altitude rather than at the surface
and were not vertical accelerations; however, the reductions were
quick and cheaply accomplished. Other efforts to analyze these data
included local area reductions, where surface masses were esti-
mated [7,8,9].
The computer revolution over the past 10 years has allowed new
reductions with spherical harmonics. New fields up to degree and
order fifty (2600 parameters) have been made [10,11,12]. These
fields now provide the best representation for any serious geophysi-
cist doing quantitative modeling. There is now vertical gravity at the
surface from a global model that carries all the requirements of
dynamical consistency. There is one sizeable concern in that the
resolution over the entire planet is not uniform. This is due to the
Pioneer orbit, which had a high eccentricity, causing the high
latitude regions of Venus to be poorly resolved.
The Magellan (MGN) spacecraft, which went into orbit about
Venus in August 1990, has returned Doppler data for gravity field
reduction. However, because the high gain antenna was pointed at
Venus for SAR mapping, no gravity data were acquired until the
antenna was pointed back to Earth. This occmxed at spacecraft
altitudes higher than 2500 kin, greatly reducing local gravity
sensitivity. MGN has an eccentricity much smaller than PVO, so
there is new information in the polar regions. Present reductions
include two MGN circulations (486 days), which reduce uncertain-
ties and produce somewhat better resolution.
During March, April. and May 1992 new low-altitude data have
been acquired from both PVO and MGN. PVO periapsis latitude has
changed 27 °, from 16°N to 11°S. These data will provide better
def'mition in the southern hemisphere, particularly over Artemis.
The MGN mission now acquires periapsis gravity data for one orbit
out of eight (i.e., foregoes SAR mapping for one orbit/day), Since
MGN has an X-band radio signal, the data quality is a factor of 10
better than PVO. Only a small block of MGN data was acquired
before its periapsis went into occultation May 16. Solar conjunction
and periapsis occultation has also occurred for PVO.
In September of 1992 MGN periapsis will exit occultation and
its periapsis altitude will be lowered to approximately 170 kin.
Periapsis will be visible from Earth for a complete 360 ° longitude
coverage period (243 days). This should be an excellent dataset,
having low X-band data noise that in turn can be combined with the
PVO dataset.
In December 1992 PVO will exit periapsis occultation and low-
altitude data (-150 kin) in the southern hemisphere will be acquired
for about one month before PVO is lost due to the lack of fuel to
maneuver to safe altitudes.
In May 1993 there remains the possibility of aerobraking MGN
into a circular orbit, thus allowing global uniform resolution gravity
data to be acquired. One hopes that NASA has enough foresight to
keep Magellan alive so this is a reality. It is anticipated that if this
is done, harmonic solutions to degree and order 60-70 (5000
parameters) will be produced. One could then compare similar
features globally, resolve coronae and test many interior structure
models.
References: [1]AnandaM.P.etal. (1980)JGR,85,8303--8318.
[2] Williams B. G. et al. (1982) Icarus, 56,578-589. [3] Mottinger
N. A. et al. (1985) Proc. LPSC 15th, in JGR, 90° C739--C756.
[4] Phillips R. J. et al. (1979) Science, 205, 93-96. [5] Sjogren
W. L. et al. (1980) JGR, 85, 8295-8302. [6] Sjogren W. L. et al.
(1983) JGR, 88, 1119-1128. [7] Esposito P. B. et al. (1982) Icarus,
51,448-459. [8] Reasenberg R. D. et al. (1981) JGR, 86, 7173-7199.
[9] Sjogren W. L. et al. (1984) GRL, 11,489-491. [10] Nerem R. S.
(1991) Eos, 72,174-175. [11] McNamee J. B. et al. (1992)JGR, in
press. [ 12] Konopliv A. R. (1992) private communication of results
to be published (AGU presentation in Montreal, Canada).
N93-143781
DIFFERENT TYPES OF SMALL VOLCANOS ON VENUS.
E. N. Slyuta 1. I. V. Shalimov 2, and A. M. Nikishin 2, tVernadsky
Institute, Russian Academy of Science, 117975 Moscow, Russia,
2Moscow University, Moscow, Russia.
One of the studies of volcanic activity on Venus is the compari-
son of that with the analogous volcanic activity on Earth. The
preliminary report of such a comparison and description of a small


Geoid, topography, and convection-driven crustal deformation on Venus

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