The thermal evolution of Mars is governed by subsolidus mantle convection beneath a thick lithosphere. Models of the interior evolution are developed by parameterizing mantle convective heat transport in terms of mantle viscosity, the superadiabatic temperature rise across the mantle and mantle heat production. Geological, geophysical, and geochemical observations of the composition and structure of the interior and of the timing of major events in Martian evolution, such as global differentiation, atmospheric outgassing and the formation of the hemispherical dichotomy and Tharsis, are used to constrain the model computations. Isotope systematics of SNC meteorites suggest core formation essentially contemporaneously with the completion of accretion. Other aspects of this investigation are discussed

Drake, M. J.

Schubert, G.

Sleep, N. H.

Solomon, Sean C.

Turcotte, D. L.

English

NASA Technical Reports Server

N94- 31109
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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.
Introduction. High-resolution Magellan images and altimetry of Venus reveal a wide
range of styles and scales of surface deformation [1] 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 [2-5]. A key difference between Earth and Venus
may b¢ the degree of coupling between the convecting mande and the overlying lithosphere.
Mantle flow should then have recognizable 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 finite element modelling
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 2-D Cartesian finite-element program ConMan [8]. A passive marker chain
tracks the crust-mantle interface and permits variation in the crustal buoyancy as well as
specific crustal and mantle theologies. These rheologies depend on composition, 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 finite-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 km by 800 km box. The surface
topography is calculated from the vertical stresses on the top wall of the box. Top and bottom
temperatures axe fixed at 500°C and 1250°C, 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 first class is initiated with a sinusoidal
temperature perturbation throughout the box. This results in mantle flow that is dominated
by concentrated downwelling (Figure Ib). 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 (Figure la).
o 0110o 100
3OO
2OO 400 600 800
Horizontal Distance, km
2OO 4O0 600 800
HorizontalDistance,km
Figure I. Temperature contours at 130 My for the (a) upwelling and (b) downwelling models.
Contour interval is 100 °C; the top of the box is at 500 °C.
CRUSTAL DEFORMATION ON VENUS: SimonsM. et al.
Results. In all our models, convection produces horizontal compressional stresses in
lithosphere above downwelling mantle and extensional stresses in lithosphere above
upwelling 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 My. 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 find that the magnitude of the peak compressive
stress achieved above the downwelling increases with higher viscosities and/or with thinner
initial crustal layers; the stronger the crustal lid, the more are tractions from mantle
convection 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 stresses.
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 first 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 possible
regime lies between the first two, with "in phase" deformation on short time scales and
crustal flow on longer time scales. A strong 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 facilitates crustal deformation, and the
isostatie effects of crustal thickness variations dominate the topography.
Consideration of geoid to topography ratios (GTRs) can restrict which regime of crustal
response is appropriate for Venus. The distibuti0n of estimated GTRs for several highland
regions on Venus is bimodal with two clusters around 10 and 25 m/km [5]. The positive
correlation of long-wavelength gravity and topography implies that there are no major regions
that have negative GTRs. To keep the GTRs positive, the geoid must follow the surface
topogaphy 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 Figure 2. Note that before 90 My both topography and geoid are negative, but at
90 My crustal thickening effects begin to dominate and the topography 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
L .
t
CRUSTAL DEFORMATION ON VENUS: Simons M. et al.
plausible. In the case of mantle downwelling this would also require that the 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 upwelling and regions of mantle downwelling are best explained by the
presence of a strong lower mantle [11,12]. The large positive GTRs and the presence of
large shield volcanoes in certain highland regions on Venus, such as Beta Regio and Eisfla
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].
100
50
i0
-50
'loo(i .....2O 4O 60 8O 140
Time, My
S
100 120
Figure 2. Evolution of GTR with time. At each time step, the GTR shown is the slope of the
best fit Hne 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 downweIling model , with a crust of
constant viscosity 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 My corresponds to
the time when topography crosses the zero datum. Note that the GTRs for this model are
neither always positive nor always bounded.
LI
_L=_
References: [1] S. C. Solomon et al., Science, 252,297, 1991; [2] W. S. Kiefer et al.,
Geophys. Res. Lett., 13, 14, 1986; [3] B. G. Bills et al., J. Geophys. Res., 92, 10, 1987; [4] R.
J. Phillips et al., Science, 252, 651, 1991; [5] S. E. Smrekar and R. J. Phillips, Earth Planet.
Sci. Lett., 107, 587, 1991; [6] R. J. Phillips, Geophys. Res. Lett., 13, 1141, 1986; [7] R. J.
Phillips, J. Geophys. Res., 95, 1301, 1990; [8] S. D. King et al., Phys. Earth Planet. Inter., 59,
195, 1990; [9] D. L. Bindschadler and E. M. Parmentier, J. Geophys. Res, 95, 21, 1990; [10]
H. Schmeling and G. Marquart, Geophys. Res. Lett, 17, 2417, 1990; [11] M. A. Richards and
B. H. Hager, J. Geophys. Res , 89, 5987, 1984; [12] B. H. Hager, J. Geophys. Res , 89, 6003,
1984; [13] R. E. Grimm and R. J. Phillips, J. Geophys. Res., 96, 8305, 1991; [14] R. E. Grimm
and R. J. Phillips, J. Geophys. Res, in press, 1991; [15] R. J. Phillips et al,, Science, 252, 651,
1991.
Geoid, Topography, and Convection-Driven Crustal Deformation on Venus;
Simousl BradfordI-LHager1,andScanC. Solomon2,1Departmentof Earth,Atmospheric,
ianetary Sciences, Massachusetts Institute of Technolo_v, Cambridge, MA 02139,
5.a_nent of Terrestrial Magnetism, Carnegie Institution _t_Washington, Washington, DC
Introduct/on. High-resolution Magellan images and altimetry of Venus reveal a wide range of
styles._d .sca..lesof surface deformation [1] that cannot readily be explained within the classical
1e.r_. m.ai plate tectomcP .a_ig_n. The high correlation of long-wavelength topography and gravity
_o me large apparent aepms oI 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 me convecting mantle and the overlying lithosphere. Mantle flow should then have
recogniza.ble signature_ in the relationships between the observed surface topography, crustal
deformation, and the gra.vity field [6,7]. Therefore, comparison of model results with
onservafional oata can help to constrain such parameters as crustal and thermal boundary layer
thicknesses as well ks the character of mantle flow below different Venusian features. We explore
in this paper the effects of this coupling by means of a finite element modelling technique.
Mode/. The crust and mantle in the models are treated as viscous fluids'. We solve both the
equations of motion and the heat equation at each time step using a modified version of the two-
dimens!on_, _ian finite-qlement .program ComMon [8]. Our formulation assigns material
pml_rti _ u_,ea.cnelemen.t ann explicitly .trac_ the flee surface topography and the crust-mantle
mter_, ce ny. lettm_ _e grid deform with time m a semi-Lagrangian fashion. This procedure
l]erml_ vanauon re.the crustal buoyancy as well as specific crustal and mantle rheologies that can
oepeno on composmon, 1emperature and stress. In addition to the flow field, the stress field in the
lithosphere, the surface topography, and the resultintz _eoid are readily calculated. The model
domain is a square box. We impose free-slip bounda_r_ conditions on'the bottom and side walls,
with no flow through these walls. The top of the box is a true free surface, so there is no need to
derive surface topography from vertical stresses on the top of the box. We investigate two classes
of models. In the first class flow is dominated by concentrated upwelling (Figure la), and in the
second class flow Is dominated by concentrated downwelling (Figure lb). We vary the initial .
crustal and thermal boundary layer thicknesses as well as the effect of crustal and mantle vtscos_ties
that are either constant, temperature-dependent, or fully non-Newtonian.
Resu/ts. In all of our models, convection produces horizontal compressional stresses in
lithosphere above downwelling mantle and extensional stresses in lithosphere above upwelling
mantle. As the convective vigor increases so does the magnitude of the stress. In models with
constant-viscosity mantle overlain by a constant-vlscosity crust, stress in the crust reaches values
of.! than100M.y.We that r toof m om.r ivo
,_ with increasing crustal vtscoslty. This is because the stronger the crust, _e more the
Üevetopment of the convective instability in the mantle driving the deformation is impeded. We
f'md that the magn!tude.0 f the peak compressive stress achieved above the downwelling
_ with hlgh_vlscoslties anger with thinner initial crustal layers; the stronger the ¢mastal
.o, me more .are u'act_ons _'om mantle convection supported in the crust. Since force balance on
crust re_imres,th.atshe_. tractions !ntegrat_l along the base be balanced by normal tractions
mlegra!.en mr.ougn its m_ckness, the thinner me crust, the larger the horizontal stresses.
tram analytical models [9,10] and our numerical models of convection-induced ca'ustal flow
indicate that the amplitude and sign of the topography axe time- and theology-dependent. In
8eneral, possible responses of the crust to mantle flow can be divided into three catego.ries.. The
first in.volv_ little, if an.y, cn?.stal, flow, and topography results mainly from the transmmsion of
normal tracuons mouceo t_y 0ens_ty contrasts within the mantle. The second possible regime
mvo!v.es substantial crusta! flow, with geologically rapid thickening over convective downwelling
ann mmmng over convective upwelhng. In this regime the effects of crustal thickness variations
dominate the topography. A third possible regime lies between the first two, with "in phase"
deformation on short time scales and crustal flow on longer time scales. A strong mantle
lithosphere tends to shield the crust fi-om convective shear tractions, and topography results mainly
f.f
F
t
CRUSTAL DEFORMATION ON VENUS: Simons M. et aL
from the transmission of convective normal tractions. A relatively weak lower crust facilitates
crustal deformation, and the isostatic effects of crustal thickness variations dominate the
topograp.by.. - - ,-,to.to--,,_,,h,,ratios(GTR__)can restricth_e_.gime.ofc.ms_tal_nr_Svl_cn_
t_usideradon ox geom- .u_...t_', _.','T" ____,..._,,.a GTRs for several higmano regions o
o,,,,-,,rl te for Venus. The msmouuon o,._-..%,__ ,#, ,,,_..,_.;,,_,_ lation ot tong-
•_im_al with two clusters around 10 and _ m/g_n__t_-_...,, ot_ --_ions that have negative
- " to h implies mat mc_ a_ _., ,_oj .... e,- " si at allwavelen vtty and pograp y . ee to h m gn
 gth. e mustfollowthesuff.a
_JTRs. l-og_pu1o_rtt_ F'__'"'"-' th..c._-- . ,_ ..... _i_ nr_llC[OOUllJle_t_:[_m_-_
--- - " i "bLc crustal Bow tam _._,-,.-.,-_ r • •times. Although the regtmeof neg! gl ..... ,_._..... ..m., ¢_,- the crustal deformaUon (i.e.,
• " t account su'81 ttO|wmut 3 .v. ,
magmtude of the G.T_, ,t O.ocs no --'- r,_o_,g"___nnd narticularlv areas of cxtensrvcly
flow) inferred from ouservauons of tectom_ ,,..,,,.--.---, - ,- .
deformed terrain, on Venus. . ...... L_, ^¢,,.,,e.de,_ndent crustal flow j_enerates
In contrast to the regime of neghg_me now, Lu__._- _:j: _j_,_oranhv is negatTve in the early
• _ver a mantle oow,w_m-s, ,_v r-=--r _ atoooc,raph¥ thatchanges mgn. ........ *-_-¢.-.-,.-ation"he converse hoJds over
.,_._ _'fdeformationand positiveinme !aversta..gesv.L___.. _._ throu,,hzero,the eoid does.
o_'e,_ -- • " " "0¢1trio 93 uy ,o,..,,-.,.-_ _ g
mantle upwelling, _Dunng. thet_ns..,tton.al pen_. ,,.:...mPOg_a_t,_ _ not observed on Venus.
not o throu h zero,_and me u.rK _s un._.unoc_, ._m.=,_p_,.o_,a 9n a v mimics that of the
Ignc the _gs_nce of a mechamsm by which thv s_gn o, .,,, _.---- anom I_
• " or downwelling, only the regime of rapid crustal flow is
to h over'a given upwelhng .-- • ire that the lower mantleb.e, morepo .gra.p y oownwellm this would also requ.. . . .
plausible. In the case of mantle -- . _ngj .... .!-,. ,,-,,uired nosmve geo_d anomahes., This .
:- ..... ,he, the ,nner mantle in oroer to prt_u_._ m,.. ,,._. ._ K--.,_ _ ,-,_..,I....t,.,.,. the observeo
vt_.u-._ ,_- ....... Kr- . to 1301¢1zor me r._t m, _.u ....
la ering of viscostty structure h_ already,..b_nshow_,,_ of mantle downwe, ing are best.
Y anUe U W{_lllli aiiu till ....id hi over regions of m p 8 ar e rove GTRs and _e
gee . ghs wet mantle[all,12]. The I g pos .explained by the p_nce of a sty_ .ng/ow(:_ _'i-_'la re_,ions on Venus, such as Beta Reg_.o and
resence of largeslueio voican.o_ in ____._r_,, .......  Tiin- r5 13 14] The regime oz rapm
• 1 " as areas ox i:IIa|lttU u w_.,at _ t ' ' J" • " "
_stla Reg_o, P . • " However, the areal g• are best ex am_ melUn and ensuing
w r icts crustal thmnmg over the upwe.l[_t_g.• - ]P ..... _ ^,-. ^f crustal
crustal.flo p_i .... , -_..,..,,;_,- exacted over such reglons may outwe_gn me _l,_.m v
vo_camsm _.o c_, _,:_.:._,vran _ thus also yield positive _rt_s [x:,J.
thinning on me sunacc _t,ur_-.v,,_
References. [1] S. C. Solomon et el., Science, 252, 297, 1991; [2] W. S. Kiefer et al., Geophys. Res. Lett.,
I_, 14, 1986; [3] B. G. Bills et aL, J. Geophys. Res., 92, 10, 1987; [4] 11. J. Phillips et al., Science, 252, 651,
1991;[5]s. J. E 587,1991;[61 J a o ,hys.
Res. Left., 13, 1141, 1986; [7] It. J. t,mtttps, J. ucoF,,.w ..... , ,1301, 1990; [8] S. D. King et al., Phys. Earth
Planet. Inter., 59, 195, 1990; [9] D. L. Bindschadler and E. M. Parmentier, J. Geophys. Res, 95, 21, 1990; [10] H.
Res. Let[, 17, 2417, 199_, [11] IV[.A. Richardsand B. I-L Hager, J.
elin and G. Marquart, Geophys. 6003 1984; 13] R. E. Grimm and R. J.Schm g h . Res , 89, , [
Geophys. Res , 89, 5987, 1984; [12] B. H. Hager, J. Geop ys Geophys. Res., 97, 16035,
Phillips, J. Geophys. Res., 96, 8305, 1991; [14] 11. E. Grimm and R. J. Phillips, J.
1992; [15] R. J. Phillips et al., Scienc_ 252, 651, 1991.
• "¢" 0
0
100 _ 100
3oo
4% 2oo 4oo 6oo 4% 200 400 600 8_
Horizontal Distance,km Horizontal Distance, km
ntours for the (a) upwelling and (b) downwel!_g models. The box is
Fi re 1. Temperature _ .... . " 1 To and bottom temperatures aregu . . " em_on and 400 km m the vemca, l_km m the honzonta_ mm . .
_30e_ -at 500 °C and 1250 °C, respectively. Contour interval _s 100 C.


Origin and thermal evolution of Mars

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