Lithospheric rheology and flexure at Artemis Chasma, Venus

12 Pages·2007·1.48 MB·English

JOURNALO F GEOPHYSICALR ESEARCHV, OL. 101,N O. E5, PAGES1 2,697-12,70M8,A Y 25, 1996
Lithospheric rheology and flexure
at Artemis Chasma, Venus
C. David Brown and Robert E. Grimm
Departmenotf GeologyA, rizonaS tateU niversityT,e mpe
AbstracAt. rtemiCs hasmisaa na rcuat2e0, 00-km-diamzeotenreo fc onvergenacnedl i tho-
spheruicn derthrustoinnVg e nusIn. elastficle xurme odelinogft het opograpahtyA rtemis,
combinwedit ho bservatioofnt rse ncthe ctonicasll,o wu st od ocumelonct atle mperatgurraed ients
belo4w K k m-1 a nda nim mencsoem presins-ivpela fnoer caett hetr encLhi.t hosphrehreioc logy
onV enums ayb es trongtehra nw ouldb ep redictefrdo mc onventioenxatlr apolatioonfr so ck
mechaneicxsp erimenintp sa; rticultahre,b rittlseu rfacsetr engmthu srte acahf ewt enso fm ega-
pascatloss atisftyh eo bservleadc ko ff lexuralilnyd ucesdu rfacfaeu ltinEgl.a stipcl ateb ending
modeplsr ovidaen a dequaetset imaoteft heb endinmgo menattA rtemisb,u tt heyfa ilt oc on-
strain---eovre nre cognize--itnh-ep lanfoe rceT. hei nelastaicn alysiims plieasn i n-planfeo rceo f
theo rdeorf -1x 10T MN m-l;a p otentdiarli vinfgo rcies t hermtahli nninogfr egionatlhlyic k
lithosphienrt eh eh ighlantdost h en orthT.h elo wh eaftl uxa tA rtemiws,h icihs a comparatively
younsgt ructurisec , ompatibwleit ht hen otiotnh aVt enuhsa se xperiencae pdr olongpeder ioodf
coolinign t hel asst everhalu ndremdi llionye arsT.h ei nferencoefs uchex ceptionalollwyt hermal
gradienetsm bracethsr eee nd-membpeors sibilitie(1s):t hes urfacaeg eis > 600M a,( 2) thel itho-
sphertich ermaalg eis g reatethr anth es urfacaeg ea, nd/o(r3 )t heu ppemr antltee mperatuisr e
anomalouslylo w ((cid:127)-1550 K).
Introduction
striking conflict with the flexural interpretationi s the
completea bsenceo f trench-parallenl ormalf aulting on the
ArtemisC hasmais a 2000-km-diametearr cuatetr oughi n
outert renchw all (Figure1 , inset), a characteristipcr opertyo f
Aphrodite Terra, Venus, that is the manifestation of litho-
the convexu pwardb endingo f the lithospherea t subduction
sphericu nderthrustianngd i ntenses urfacdee formatio(nF igure
zones [e.g., Jones et al., 1979].
1). Oure xaminationo f the tectonicso f Artemis [Browna nd
ArtemisC hasmais an excellents ite for examiningf lexure
Grimm,1 995] hasr evealeda coherentp, late-likem otion of
on Venusb ecauseth e lithospherics trengtho f the underthrust
thec irculairn teriopr latformw hichp roducesdo utheavset rgent
plains shouldp rovide a senseo f how low the venusian heat
deformationo n the southeascth asmam argina kin to that at
flux mightb e.O therf lexures tudiehs aver eliedo n topography
terrestrials ubductionzo nesa ndp rominentl eft-lateral strike-
and gravity at coronaea nd volcanoes[ Sandwella nd Schubert,
slipd isp.l acementosn the eastm argin.T woi ndependenmt ea-
1992a; Johnsona nd Sandwell, 1994; Phillips, 1994; Mc-
surementso f strain agree that horizontal motions were limited
Governe t al., 1995], whicha rep roductosf mantleu pwelling
to no moret han -250 km. Artemisi s relativelyy oung,b oth
and magmatism.S ites of lithosphericu nderthrustingan d
with respectt o nearbyA phroditec hasmataa s well as in the
orogeny, on the other hand, are regions less contaminated
global stratigraphy,a nd its tectonicsa re not directly
by thermal anomalies,a nd they potentially provide more
attributableto mantlep lumep rocesses.
representativec onstraints on the geotherm of ancient litho-
SoutheaAstr temisC hasmias distinguishbedy its paired-l -
sphereS. uchi nformationis particularlyv aluablef or compari-
km-deeptr encha nd- 1-km-higho uterr ise,w hichS andwelal nd
son to interior thermal evolution models [Turcotte, 1993;
Schuber[t1 992a]i nterpretedto be analogousto the flexural
Arkani-Hamede t al., 1993; Parmentiera nd Hess, 1992] in-
trench-outer rise structures of subduction zones on Earth.
vokedt o explaint he apparentlyn ear-uniformsu rfacea ge of
Therea res everaol bservationins supporot f a flexuraol rigin
-400 Ma [Phillipse t al., 1992; Schabere t al., 1992]. Artemis
for this topography:( 1)the tectonic environmenti s one of
is unique for another reason: its flexural outer rise towers
lithospheriucn derthrustin[gB rowna ndG rimm,1 995], which
above thoseo f subductionz oneso n Earth, where outer rises are
is amenablteo flexurec ausedb y surfaces, ubsurfacaen, dh ori-
typically only a few hundredm eters high. Conventional
zontall oading;( 2) the outerr isei s smootha ndl argelyu nde-
flexure models may be inadequatefo r explaining such
formedi,n dicatinigt wasu pliftedn otb y foldingo r faultingb ut
topography.
by bendingo f thel ithospher(e3;) a gravityh igh northwesotf
thet renchc loselym atchetsh e regiono f geologicalliyn ferred
convergencies, indicativeo f the massa nomalye xpectedfr om Artemis ChasmaT opography
underthrusting[S chuberte t al., 1994], and is associatedw ith
the loading responsible for the flexure. One observation in A mapv iew of the topographya t the southeasmt argino f
Artemisi s providedi n Figure 1. The tectonicsa nd structural
geology of Artemis as a whole imply northwest-southeast-
directedc onvergencaet this boundarya, t an azimutho f-125 ø
Copyrigh1t 996b y theA mericanG eophysicUanl ion.
[Browna nd Grimm, 1995]. Sandwella nd Schubert[ 1992a]
Paper number9 6JE00834. performefdle xuralf its to topographyo n the southernm argin
0148-0227/96/96JE-00834509.00 where the trench and outer rise may also originate from
12,697
12,698 BROWN AND GRIMM: ARTEMIS CHASMA FLEXURE
dip to the southeast;t hey increasei n magnitude from south-
west to northeast( Figure 2a). The slope is subtractedf rom each
profile before measuringt he maximum outer rise amplitude,
full width at half-maximum (FWHM)of the outer rise, and
maximum trench depth. The amplitude varies from 1160 to
1570 km, generally decreasingfr om southwestt o northeast
38 øS (Figure2 b). The meana nds tandardd eviationo f the amplitude
are 1290 _+9 0 m. The width ranges from 130 to 255 km, and
also decreasesf rom southwestt o northeast (Figure 2c). The
39øS meanF WHM is 190 _+3 5 km. The trench depth shows no con-
sistent trend along strike (Figure 2d). It varies from 450 to
2030 m, with a mean value of 1180 _+4 20 m.
5.'
40:S
.''½(cid:127)- .......... '.''.' .'. .;.....:.:i..i : ..(cid:127)iL:i thospheric Rheology
41 'S We employ yield stress envelopes, which define the
ß strengtho f the lithospherea s a function of depth, in our flex-
. ure models [Goetze and Evans, 1979; Kohlstedt et al., 1995].
Yield envelopesr epresentt he maximum stress the lithosphere
.:.
can sustaina t a given depth, and they almost certainly overes-
.
timate the.net strength [Kirby, 1983; Kohlstedt et al., 1995].
In this sectionw e describeo ur two assumerdh eoiogicm odels
:: i...... ... :::':1 ...
for the venusian lithosphere. In the weak model we follow
138øE 140(cid:127)E 142(cid:127)E 144øE
conventional precepts in designing yield envelopes; these
Figure 1. Shadedr elief image of the southeastm argin of results are therefore most appropriate for comparison to the
Artemis Chasma.T he image, approximately6 50 km across, is findings of previous workers. With the strong model our
in equidistantc ylindrical projection. Topography is low-pass approachi s to maximize the yield stressest,h ereby placing an
filtered and contouredi n kilometers above mean planetary upper bound on the temperatureg radienti nferred from flexure
radius( 6051.85 km), whichi s markedb y the unlabeleds, triped modeling. General physical constantsa re definedi n Table 1;
contour.T he three profiles indicateda re shown in Figure 7. the weak and strong rheology model parametersa re listed in
The arrows point out wrinkle ridges. Profile 19 is marked in
Table 2.
25-km intervals; the dot on each profile denotest he origin.
The inset image (left-looking synthetic aperture radar)
Brittle Regime
illustratest he lack of trench-parallel deformation on the outer
rise. This image is an enlargemento f the boxed area and is 130 Yield envelopes usually describe the brittle, pressure-
km across. dependents trength of the lithosphere with the empirical
Byedee's rule for frictional sliding [Byerlee, 1978], in
Whichs trengthis a linearf unctiono f confiningp ressuraen d
vanishesa t the surface[ Bracea nd Kohlstedt,1 980] (Figure3 ).
bending, but the loading configuration is probably more
complex there.
We definet he deformationfr ont of the outer trenchs lope
-3.01(cid:127),,[ . ...] . ...] . ...[ . ..., ....[ . ......, . ..., . ...[ . ...[ . ...] . ... [,,,:tl.6
fold-and-thrusbt elt as the horizontal origin for our topo-
graphicp rofiles.T his nearlyl inear, ~300-km-longb oundary
c-(cid:127) 2.0
betweent he severely deformedt rench and the smooth, undis-
ruptedp lains trendsa t azimuth3 5ø; great circle topographic
profiles are extractedp erpendiculatro this feature.W e obtain
34 profiles,s paced~ 9 km apart( at the trench),b y bilinearly
interpolating elevations from the Global TopographyD ata '(cid:127) h,,I .... : .... [ .... I .... I .... I , , ,-I:,, , I .... [ .... : .... I .... I ....
Record( GTDR) [Ford and Pettengill, 1992]. We have examined '''1 .... I .... I .... I''''1 .... I''' {- '''1 .... I .... I''''1 .... I .... I''': .:
both the Altimeter-RadiometerC omposite Data Record
(ARCDR) footprintsa nd the altimeterp rofiles at the outer rise,
and are confidenot ur interpolatedp rofiles accuratelyr epresent
the topographyT. he GTDR errord atao ver this region indicate
:4øbC ....
that typical errors are ~50 m, with some orbits peaking at
120(cid:127) 00
about 100 m.
5 10 15 20 25 30 5 10 15 20 25 30
We characterizet he flexural topography at Artemis in two SW profilneu mber NE
ways.W e build an averagep rofile from the 34 original inter-
polated profiles; this step serves to eliminate some of the
Figure 2. Topographic trends along strike of Artemis
short-wavelengthn oise in the data that is not associatedw ith
Chasma.( a) Topographics lopeo f plainss outheasot f Artemis;
lithospheric flexure, and it providesu s with a representative
negative values indicate southeast dips. (b) Outer rise
cross section. Also, for each of the 34 profiles we determine amplitude(.c )Outer rise width at half-maximuma mplitude.( d)
the topographics lope of the plains, the outer rise amplitude Maximum trench depth. Horizontal lines signify the mean
and width, and the trenchd epth. Slopes are small (~0.01ø ) and values;o ne standardd eviationi s depictedb y shadedr egions.
BROWN AND GRIMM: ARTEMIS CHASMA FLEXURE 12,699
Table 1. Model Parameter Values differential stress / MPa
-4000 -2000 0 2000
Symbol Definition Value o
A flow law coefficient 104 '46M Pa- n s- 1
20
E Young'ms odulus 6.5x 10l øP a
g gravitya t surface 8.87m s- 2
n flow law stresse xponent 3.6 4o
R molarg asc onstant 8.314J mo1-K1- 1
Ts surfacet emperature 740 K
bx.,c strainra te 10-1 4S- 1 .= 60
tc thermadli ffusivity 10-- 6m 2 s- (cid:127)
Pc crusdt ensity 2900k gm - 3
8o
Pm mantldee nsity 3300k gm - 3
v Poisson's ratio 0.25
lOO
We incorporate Byerlee's rule in the weak rheology model.
12o
Applicationo f Byerlee's rule assumesth at preexistingf aults at
suitable orientations are present to accommodateb ending
Figure 3. Weak rheology (inner) and strong rheology (outer)
strains.I f faults of optimum orientation are not available, the yields trengthe nvelopesa t 4 K km- 1. Thes tressp rofilea t a
brittle strength will be greater, possibly reaching the ultimate bendingc urvaturoef +8 x 10- 7 m- 1 is indicatebdy the shaded
fracture strengtho f the rock [Sibson, 1985]. area. The base of the strong envelope is located at 153 km
The lithosphere being flexed at Artemis Chasma may not depth. The stress profile for a compressive in-plane force
(-6 x 1013N m- 1) withn ob ending(A 0.I)a ndf ollowingb end-
possessp reexisting faults which could accommodatef lexure:
ingt o a curvaturoef +5 x 10- 7 m- 1 (&0.II)a rea lsos hown(t he
the surfacei s smooth and largely undeformedo n the plains to
kink in A0.II reflects elastic unloading).
the southeasto f the trench (Figure 1, inset). Therefore, we are
unwilling to assumet hat Byerlee's rule provides a conserva-
tive bound on lithospheric strength. We instead describe the
brittle strength in the strong rheology model using a Mohr- comparisono f the Mohr-Coulomb failure strengtht o Byerlee's
Coulomb failure law, which has the form rule is depictedi n Figure 3.
r = r0 + (tan½)ho (1) Ductile Regime
Laboratory experiments show that rocks experience ductile
wherer and 0.na re the sheara nd normal stresses,r 0 represents creep at elevated temperatures.E mpirically, stressi s seen to be
the cohesion, and ½ is the angle of internal friction. We related to strain rate by a power law relationship:
convert( 1)into a form appropriate for constructingy ield en-
velopesb y deriving the differential stressA 0. = 0.1- 0'3 [e.g.,
A0=. expQ + V *Pi
Jaeger and Cook, 1969, pp. 87-91 ] for compression and n(cid:127)r (cid:127) (2)
tension, where 0.3 and 0.1, respectively, equal the confining
pressure( PrngZ).
We assumet hat tampi n (1) is equalt o the coefficiento f slid- where the coefficient A, stress exponent n, activation energy
ing friction; following Byerlee [1978], we assign tan(cid:127)p = 0.85 Q, and activation volume V* have values determinedb y labo-
for 0.n< 200 MPa and tamp= 0.60 for 0.n> 200 MPa. The com- ratory measurements.I n Figure 4 we have plotted (2) as a
pressive fracture strength has values of -150-400 MPa for functiono f temperaturefo r dry diabase[ Mackwelle t al., 1995]
common mafic rocks (basalt, diabase, gabbro, and dunite) and four different anhydrouso livine and duniref low laws. The
[Shimada et al., 1983; Goodman, 1989, p. 61]. Equivalent strengtho f naturalp olycrystallined unire[ Chopraa nd Pater-
cohesion values are-35-90 MPa. We let r0 = 50 MPa in the son, 1984], synthetico livine aggregates[K arato et al., 1986],
strong model. The Mohr-Coulomb model overestimates the and Goetze's [1978] high-temperaturoe livine are very similar.
strengtho f the upper lithosphereb ecausee xperimentsi ndicate Clearly, diabasei s weakera t all temperaturesA. n upperl imit
brittle fracture strength increasesn onlinearly with increasing on the strength of olivine is providedb y the strongests lip
confining pressure [e.g., Paterson, 1978, pp. 21-28]. A system,( 010)[001]; the constitutivee quation for this system,
determinedb y Bai et al. [1991], is alsop lottedi n Figure 4.
How certaina re we that these flow laws representt he maxi-
Table 2. Lithospheric Rheology Models mum yield stressest hat can be sustainedb y the venusian
lithosphere?M ackwell et al. [1995] demonstratedth e dramatic
Symbol Definition Weak Strong increasei n the strength of diabasep roducedb y ensuring sam-
ples were properly dehydratedC. hopraa nd Paterson [1984]
were even more thorough in drying their samples, and they
(cid:127):0 cohesionM, Pa 0 50
Q activatioenn ergyk,J m o-l(cid:127) 535 560 measuredth e water content using infrared spectroscopy,f ind-
V* activatiovno lumec, m3 mo-l(cid:127) 0 17 ing little change in strength below 0.01 weight percentH 20.
The agreementb etween the three anhydrousp olycrystalline
12,700 BROWN AND GRIMM: ARTEMIS CHASMA FLEXURE
differential stress / MPa In our flexure modeling we ignore the role of the crust in the
lithospherics trength.T he crust of the venusianp lains is -20-
0 500 1000 1500 2000
800 .... (cid:127) .... (cid:127) '' (cid:127) ' ' ' 20 50 km thick [Grimm and Hess, 1996], and the lower crust
might experienced uctile flow. However, at Artemis the crust
has not becomed ecoupledf rom the upper mantle lithosphere
MZKS95. ,
900 ...... (cid:127) G78 40 despitet he intenseu nderthrustingi,m plying that the crust and
.. (cid:127) KPF8.6.. ....... mantlea re mechanicallyw elded[ Browna nd Grimm, 1995]. By
neglectingt he crust we adheret o our principle of maximizing
60 the inferred thermal gradients.
000 (cid:127)
80 Elastic Plate Bending Analysis
100 To allow us to compareo ur resultst o those of Sandwella nd
Schubert[ 1992a], and to form a basis of comparison for our
IO0
inelastic flexure models which follow, we fit an analytic
'1(cid:127)00 elastic plate bending equation to the Artemis Chasma topo-
graphy. We consider a very general elastic solution for the
dT/dz = 4 K/km vertical displacement( w) as a functiono f distance( x) [Parsons
and Molnar, 1976]:
Figure 4. Differential stress as a function of temperaturefo r
several anhydrous rock flow laws; a depth scale is also [ 2P(St+w. tox
providedfo r 4 K km- 1. MZKS95:C olumbiad iabase(N i-NiO
buffer) [Mackwell et al., 1995]. G78: Goetze [1978] olivine
flow laws; the nearly linear segmenti s a low-temperatureD orn x exp - +mx + zo (3)
law. KPF86: Karato et al. [1986] synthetic olivine aggregate
powerl aw. CP84: Chopraa nd Paterson[ 1984] polycrystalline
dunite power law, the weak ductile rheologyu sed in this study. a=-(r1Nc/ - 1r/)2 (4a)
BMK91: (010)[001] slip system constitutive equationf or oli-
vine single crystals (opx buffer, IW oxygen fugacity [Myers
and Eugster, 1983]) [Bai et al., 1991]. The strong ductile P= +c rJ
rheologyu sed in this study is plotted with the bold, solid line.
Notet hatw is definedp ositivdeo wnN. cr- ' -4D(cid:127) 2 is thec om-
pressive buckling in-plane force, where the flexural wave-
dunite flow laws (Figure 4) is reassuring,a nd we doubt that length is defined as
laboratory experiments will find dunite to be significantly
stronger. [ 4D/1 /4
g=kApg] (5)
Also of possible concern is the need to extrapolate from
experimental temperatureso f -1500-1800 K to mechanical
lithospherec onditionso f <1100 K. Experimentalr esultss ug- and the flexural rigidity is a function of the elastic plate
gest that, to a very good approximation,t he activation energy thickness( he)
for dislocation creep is independento f temperatureo ver the
tested range. At lower temperatures( and higher stresses)t he
power law behavior of crystalc reep breaks down, and distinct,
D=1 2(v12- (cid:127)-(cid:127) (6)
weakerp rocessesd ominate [Kirby, 1983; Tsenn and Carter,
1987]. Evans and Goetze's [1979] olivine hardnesst ests over
a broad temperaturer ange (300-1800 K) revealeda sharp de- The mantle-surfaced ensityc ontrasti s Ap = Pm.W e initially let
creasei n strengtha t reducedt emperaturesT. hey suggestedt hat the in-plane force per unit length (N) be zero, and perform a
a Dom law, in which creep rate depends exponentially on nonlinearl east squaresf it [Presse t al., 1992, pp. 683-688] of
stress, applies at Act > 200 MPa [Goetze, 1978] (Figure 4). (3) to a -1500-km length of the averagep rofile with five free
Therefore, power laws overestimatel ithospherics trength. parameters:t he bending moment per unit length (M) applied at
In the weak rheology model we let the ductile strength of the trench, the trench depth (w0), the topographic slope (m),
the mantle be describedb y Chopra and Paterson's [1984] flow the verticalo ffset (z0), andt he flexuralw avelength( J,). Other
law (Figure4 ). For the strong rheology model we assumet hat parametersa nd their values are specifiedi n Table 1. The plate
Bai et al.'s [1991] (010)[001] slip system constitutive equa- curvaturise defineda s K = d2w/d2x, andt he elasticb ending
tion places an upper bound on the strength of the venusian moment is given by M =-DK.
mantle. For convenience, we retain Chopra and Paterson's The application of the elastic analysis to the averagep ro-
[1984] values of A and n, and simply raise the activation file yields he = 56 km, over 20% greatert han Sandwella nd
energyt o 560 kJ mo1-1( Figure4 ). We also includea n Schubert's [1992a] result for the southern chasma; the fit is
activation volume [Kirby, 1983]. In both rheology models, shown in Figure 5. We have not directly estimatedt he uncer-
ductiles tressesa re calculateda t a strain rate of 10- 14 s- 1, a tainty of he , but it realisticallyis at least 10 km [McQueena nd
reasonableu pperb oundf or a convergents etting, and the base Lambeck, 1989]. The maximumc urvaturea nd bendingm oment
of the mechanical lithosphere (z = hm) is definedb y a ductile (which are probably even more poorly determined) are
strength of 50 MPa. 7.8 x 10- 7 m- 1 and-7.9 x 1017N , respectively.
BROWN AND GRIMM: ARTEMIS CHASMA FLEXURE 12,701
1.5 wherez n is the neutral surfaced epth, which is iteratively de-
terminedb y the requirementt hat the horizontals tressr esultant
1.0 NW elasti SE
C _ equal the in-plane force:
E
0.5 inelastic ,
N-(cid:127):-m A O(z)dz (9)
._o)0 .0
--0.5
Having determinedt he full stress profile, we can proceed to
calculate the bending moment:
-' 00 0 100 200 300 400 500 600
distance / km M--mfA: o'ii(fzo)Ahzmd(cid:127)i(Zz )-z dz( 10)
Figure 5. Averaget opographicp rofile, vertically exagger-
atedb y a factoro f 145. Elasticp lateb endingm odelf it (dashed)
and inelastic flexure model fit (dotted) are plotted. The Here the bending moment is representedb y the difference in
inelasticp rofilew asc reateadt the4 K km- 1 geothermc alcu- moment of the net stressd istribution of the in-plane force and
lated by matching the first zero crossing moment-curvature bending (Arrii(z) Ao'(z) of (9)) and the in-plane stress
pair of the elastic solution to identical valuesf or an inelastic
distribution at zero curvature( Arri(z)) (Figure 3). Our model
rheologyth; e appliedb endingm omenits -6.8 x 1017N , and
assumest hat the in-plane force is applied prior to bending, and
the trench depth boundaryc ondition is 1.1 km. No in-plane
it accounts for the effects of elastic unloading following
force is included.
plastic failure [McAdoo et al., 1978; Mueller et al., 1996].
By reducing( 7) to four first-order differential equationsa nd
To estimate the mechanical plate thickness (hm) and linear
employing the moment-curvature relationship, we solve the
temperatureg radient( dT/dz) that relatet o the elasticm odel, we
flexure equationa s a two-pointb oundaryv aluep roblemu singa
apply the moment-curvaturem atching technique of McNutt finite difference routine [Phillips, 1990; Mueller and Phillips,
and Menard [1982]. We assumet he moment and curvature of
1995]. We specify the displacement and applied moment on
the elasticm odel at the first zero crossing equal the M-K pair
the left (trench) end of the profile; the boundary conditions on
for an inelastic lithospherei n which stressesa re limited by the
the right end are zero displacementa nd curvature.W e initially
yield envelope. We iteratively calculatet he inelastic moment
neglectr rxza nd assumeN is constanwt ith distance.
at the elastic curvaturea s a function of thermal gradient (with
the weak rheology), and find agreement with the elastic Evaluation of Elastic Model Results
momenatt dT/dz= 4.0K km- ], whichc orrespondtos hm = 99
km. This geotherm is similar to that determinedb y Sandwell Figure 5 includes an inelastic flexure curve for the same
and Schubert [1992a]. temperatureg radient implied by the elastic modeling: 4 K
km- ] (weakr heology)C. learly,t hiss olutionfa ils,a s the outer
rise amplitudei s just half the observedh eight. Perhaps this
Inelastic Flexure Modeling
shortcoming can be explained by a failure of the first zero
crossingm oment-curvaturem atching technique[ McNutt and
Model Theory and Solution
Menard, 1982]. Mueller and Phillips [1995] showedt hat this
The solution to the inelastic bending of the lithosphere method systematicallyu nderestimateshm but using the maxi-
musts atisfyt he force balancef or the large deflectiona nd finite mum moment-curvature values instead results in a far more
deformationo f a plate [Fung, 1965, pp. 463-470; Liu, 1980; accurate determination. In this case, the latter method yields
Mueller and Phillips, 1995]: dT/dz= 3.6K km- 1 (hm = 111 km), only a minorc hangea, nd
yet there is no improvementt o the modeledf it.
d(cid:127) 2M=[[-d( dxNx)+ (r xrx) z]d(cid:127)((;x )- N' hd(mx(2;))+w) A pg(w7)( xFro)m the inelastic modeling perspective a given geotherm
dx and strength envelope will limit the maximum bending
moment (and outer rise height) allowed. For instance, the
wherer rxz(x,hmis) a basal sheart raction.E quation( 3) is an saturationm omenta t 3.6 K km- 1 is-8.8 x 10(cid:127)7 N, so very
analytics olutiont o (7) for a purelye lasticp late (with (cid:127)xz equal little additional amplitude can be attained in the inelastic
to zero), but for our inelastic modeling we require numerical model by increasing the applied moment. A higher geotherm
solutions. A condition of (7) is that the horizontal strain and would further limit the maximum attainable flexural amplitude,
bending slope (dw/dx)are small comparedt o unity. Both whereasa lower geotherm would producea n inappropriately
parametersa re <5% at Artemis based on the slopes and long flexural wavelength. Therefore, unlike elastic plates, an
curvatures in the elastic fit. arbitrarily large outer rise height cannot be generatedb y an
To reduce( 7) to a single independentv ariable (w), we must inelastic lithosphere for all flexural wavelengths. Recogniz-
construct a relationship between curvature and bending ing this additional constraint, is it possible to explain the
moment [Mueller and Phillips, 1995]. For each curvaturew e Artemis outer rise in the context of an inelastic, finite-
determinea stressp rofile subjectt o the plastic strength limits strength lithosphere?
of the yield envelope, assuming a Tresca yield criterion. The inclusion of an in-plane force introducesa n additional
Elastic core stressesa re related to the curvatureb y modeling parameter. It, too, is limited by the net strength of
the lithosphere( i.e., (9) with Ao'(z) equal to the compressional
zXo=r zlZ) -Zn)
or tensionaly ield strength),b ut it modulatesb oth the flexural
- (8)
amplitude and wavelength. The latter property can be seen in
12,702 BROWN AND GRIMM: ARTEMIS CHASMA FLEXURE
(3) and (4) for the elasticp late:t he sinusoidawl avelength( fl(cid:127)) moment that an elastic-plastic lithosphere can sustain, and it
is decreasedb y a compressivei n-plane force, and the damping is reacheda s curvaturein creases.B endingo n the outert rench
wavelength (ot(cid:127))is increased.S imilar behavior occursw ith walls of convergentz onesi s characterizebdy positive curva-
inelastic plate flexure. This insight suggestst hat an in-plane tures,a ndw e do not pursues olutions with negative curvatures
force may play a crucial role in the Artemis Chasma topo- at this boundaryL. arge positivea ppliedm omentsw ouldr esult
graphy, and it might explain the failure of the inelastic model in an upturni n the deflectionp rofile at the intendedt rench.
depictedi n Figure 5. Within the diagram( Figure 6) we have contouredt he F'WHM
We have attempted to obtain least squaresf its of equation of the modeledo uterr ise as a function of in-plane force and
(3) to the Artemis trench-outer rise with N as a sixth free bending moment at the trench. The outer rise width is a maxi-
parameter.H owever, the in-plane force is completely undeter- mum at N = 0, and it decreases with both tensional and com-
minedv: aryingN by up to 10T MN m- 1 in both compression pressionailn -plane forces.T his behavior parallels that of the
and tension fails to improve the rms error at any value. This elastic plate (equation (3)), but it can also be viewed as a
finding verifies the more complete analysis of Mueller and consequencoe f the thinning elastic core when an in-plane
Phillips [1995]. In all fits the valueso f he are similar to the N force is applied (Figure 3). Figure 6 and corresponding
- 0 results. We therefore proceed with our fully inelastic diagramsf or other geothermsd emonstratet hat the FWHM is
modeling. primarily a function of the in-plane force and the mechanical
plate thickness;t herefore, the observed outer rise width alone
Inelastic Model Results shouldp rovide constraints on the allowed combinations of N
and dT/dz.
Our approachi s to explore the three-dimensionalp arameter
The oblique shadedb and in Figure 6 marks the inelastic
space of temperature gradient, in-plane force, and applied
flexure model solutions that satisfy both the mean amplitude
bending moment (with an additional degree of freedom pro-
and FWHM of the Artemis outer rise to within two standard de-
vided by the rheological models) by forward modeling with
viations. The amplitude is dependento n both the in-plane
inelastic flexure solutions. Our goal is to match the observed
force and appliedm oment,a s we would expect from the elastic
outer rise height and F'WHM of Artemis. The results are not
solution (equation( 3)). These results imply that the in-plane
sensitivet o the trench depth boundary condition,w hich we set
force must be compressionaal nd quite large--no zero in-plane
to 1 km (Figure 2d). An example of the output of our model is
force solutions are capable of reproducingt he ~l.3-km outer
depictedi n Figure 6. This interaction diagram delineates the
rise height. Inferred applied bending moments, too, are very
saturationm oment (for positive curvatures)a s a function of in-
large. The resultss howni n Figure 6 are not unique,a nd they do
planefo rcef or a thermagl radienot f 5 K km- 1 andt he strong
not explain the entire observedr ange of the FWHM (Figure
rheology. The saturation moment is the maximum bending
2c). We must invoke higher and lower thermal gradients to
producen arrower and wider outer rises, respectively, for this
rheology. However, the along-strike variation in the FWHM
' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I could also be explainedb y a constant geotherm but a nonuni-
dT/dz - 5 K/km form rheology (e.g., a changing crustal thickness). Similar
diagramsb uilt at other geothermsa nd using the weak rheology
260
mirror the patterns seen in Figure 6; in particular, a compres-
280
sional in-plane force is always required.
E
Figure 6 illustrates our ability to satisfy the amplitude and
width of the Artemis outer rise with the inelastic flexure model,
240 but convincing solutions must also match the slopes of the
outer rise flanks. In Figure 7 we demonstratet hat complete
inelastic model solutions provide good fits to typical
topographicp rofiles of the southeastc hasmaf or the parameter
200 values indicated by plots such as Figure 6. In some casest here
are disparitieso n the outer trench wall, but we emphasize that
theses olutionasr en otu niqueo; therc ombinationosf d T/dzN, ,
180 .......
and M can provide equivalento r better fits. Typical rms misfits
strong are ~ 100-150 m.
To determinei f a basal shear traction might affect the mag-
-15 nitude of the loads, we have also solved (7) for nonzero, con-
-12 -10 -8 -6 -4 -2 0
stantC rx(zi n whicht he in-planef orcei s a linear functiono f x).
bendingm oment/104N? Becauseo f the x dependenceo f N, we must create a moment-
curvature-in-planef orce surfacet o solve (7); we bilinearly in-
Figure 6. In-plane force-bending moment interaction
terpolateo ver this surfacet o determinet he curvaturea t a given
diagramfo r the strongr heologya t 5 K km- 1. The sinuous
N and M. We find that these inelastic profiles are essentially
envelopec orrespondsto the saturationm omenta s a function
indistinguishablefr om those with constantN and zero Crxz
of in-plane force. Outerr ise width from inelastic model solu-
tions is contoured in kilometers. The diagonal shadedb and when the distance over which N varies is long (~1000 km).
marks agreementw ith both the observedo uterr ise amplitude The outer rise shape is slightly altered by the decreasei n N
and width to within two standardd eviations. The stippled area with distancef rom the trench, but the basal shear stressa ppar-
at right indicates conditions at which no surface failure ently doesn ot modify the flexural signatureb ecausei t is of the
occurred.C ircle correspondsto Figure 7a. order of 10 times less than the bending stresses.
BROWN AND GRIMM: ARTEMIS CHASMA FLEXURE 12,703
I ' ' ' I ' ' ' I ' ' ' differential stress / MPa
1 - 800 - 400 0 4OO
0
' ' ' I ' ' '(cid:127)(cid:127),,,(cid:127)- I ' /'! '
o
-1
nou nload,i ng
E,,, 1 / / b 19
10
E
ß
elastic
I ' ' ' I ' ' ' I ' ' '
20 . /,,/,,u' nloading
0
-1
-200 200 400 600 800
distance / km 30 , . , I ! i
Figure 7. Inelasticm odelf its to threet opographicp rofiles Figure 8. Comparison of lithospheric stressd istributions
indicatedin Figure 1, verticallye xaggeratedb y a factor of 7 3. with (solid) and without (dashed)e lastic unloading; brittle
(a) Strongr heology,d T/dz= 5 K km- 1, N = -8.5 x 1013 N strengthe nvelope is marked by bold lines. In the former case,
m- 1, M =-7.2 x 1017N . (b) Thisp rofileis similairn shape the in-plane force was completely applied prior to any bend-
to the averagep rofile (Figure 5). Weak rheology,d T/dz = 3.6 K ing; depths initially in compressivep lastic failure yield in
km- 1, N = -1.0 x 10T MN m- 1, M = -3.5 x 1017 N. The tensiona t even moderateb endingc urvaturesI.f the application
arrows mark a ridge that may be unrelated to the flexural of the in-plane force and the occurrenceo f bending are
topography, and which therefore exaggeratest he outer rise synchronous, near-surface failure is precluded because the
width. (c) Strong rheology, dT/dz = 7.3 K km- 1, N = lithospheren ever fails in compression(n o unloading).
-4.1 x 1013N m- 1, M =-3.6 x 1017N .
Absence of Surface Faulting
A possible means to avert unloading is for the in-plane
Another feature of Figure 6 is the domain in which no sur- force magnitude to track the bending curvature such that the
face failure occurs,m arkedb y the stippleda rea. Surfacen ormal surfaces tressn ever intersectst he yield envelope on the outer
faulting is inducedw hen bending curvaturesa re large enough rise. With time, a given point on the surfacec oulde xperience
for the stressp rofile to intersect the Mohr-Coulomb envelope both a gradually increasing compressionali n-plane force and
in tension (Figure 3); thus, the zone of no failure is confined to bending such that the surfaces tress remains approximately
relatively small moments. The surfacei s always at failure in zero. Becauset he curvaturei ncreases almost linearly from the
the weak rheology model becauset he surface strength is as- back flank of the outer rise to the trench, surfacef aulting would
sumedt o be zero. There is an enormous discrepancy between be precludedi f the in-plane force increasesin a similar manner
the inferredi n-plane force and appliedm oment( constrainedb y toward the trench.
the outer rise amplitude and FWHM) and the conditions of no The spatial arrangemento f wrinkle ridges on the plains
surfacef ailure (Figure 6). The bendingc urvaturesa t Artemis are southeasto f Artemis is suggestive of the variation in surface
so large( -7-10 x 107 m- 1) thati t appeartso be impossible stress( Figure 1). The wrinkle ridges, which reflect shortening,
to avoid surface failure, a situation that persists at other trend roughly parallel to the chasma,a nd they extend for thou-
thermal gradients. sandso f kilometers acrosst he plains. However, the wrinkle
A very simplew ay in which to prevents urfacef aulting is to ridges are conspicuouslya bsent on the outer trench wall and
assumea higherb rittle strength;h owever, for most parameter outer rise peak--thus, there is neither extensionaln or contrac-
combinationsa cohesiono f at least 200 MPa is necessaryT. he tional deformation in this zone. The position where the
widespreadd eformationo n Venus indicatest hat the strengtho f wrinkle ridges end on the back side of the outer rise is near
surfacem aterialsi s probablyn ot this large; such a cohesion is where the flexural modelsp redict a changei n sign of the curva-
also contrary to most laboratory measurementso f the fracture ture. Therefore, the wrinkle ridges are another manifestation of
strengtho f rocks [Schultz, 1993]. the compressivei n-plane force, and their formation has been
So far we have assumeda very simple loading sequencea: n inhibited on the outer rise becauseb ending stresses canceled
in-plane force is applied first, perhaps associatedw ith a re- the in-plane stresses.
gional stressi n the downgoing lithosphere, and bending fol- We can simulate the proposed relationship between in-
lows as the lithospherei s distorteda t the outer rise. Therefore, plane force and bending in our models by leaving out elastic
at shallow depths, the lithosphere first fails in compression unloading when constructingt he stressp rofiles (Figure 8); we
becauseo f the in-plane force; with bending, elastic unloading thereby assumen o initial compressionalf ailure has occurred.
occursu ntil the tensionaly ield strength is reached[ Mueller et With this modification we discover that we can now find con-
al., 1996] (Figure 8). This is the causeo f the dominant surface ditions that satisfy all three key observablesa t Artemis: the
failure in the flexure models: elastic unloading does not outer rise width and height and the lack of surfaced eformation
progress far before tensional failure is reached despite the (Figure 9). This model is an approximation becausew e have
compressionali n-plane force. not includedt he postulatedl ateral in-plane force variation in
12,704 BROWN AND GRIMM: ARTEMIS CHASMA FLEXURE
Phillips, 1995]. For Artemis the agreement between the
temperatureg radiente stimateso f the elastic and inelastic solu-
tions is attributedt o the range of permissibleg eothermsw ith
the in-plane force as a free parameteri n the inelastic model.
For instance, the moment-matching technique predicts a
240.g(cid:127) eothermo f 3.3 K km- l for the maximumc urvaturoe f an
elastic fit to profile 1 (Figure 7a). Inelastic model solutions
from3 to 4 K km- l, a rangeo f 25% in thermagl radient,
provide good fits undert he weak rheology with variable in-
plane force and applied moment.
To place an upper bound on the temperatureg radient, we
consider the highest geotherm that includes the maximum
FWHM within the range of acceptable solutions. However,
forward-modeledfi ts (Figure 7)indicate that the widest outer
rise can be satisfactorily fit by somewhatn arrower synthetic
-20 strong profiles. In addition, some of the topography on the
. southeast-facingo uter rise slope may not be flexural (arrows,
, , , I .... I .... I .... I .... I
Figure 7b), exaggerating the measuredF WHM. We have cali-
-20 -15 -10 - 5 0
brated this uncertaintyb y comparing synthetic profiles to the
bendingm omen/t 1017N
widest portions of the outer rise, and accept 210 km as the
maximum FWHM for limiting the geotherm. Taking this
Figure 9. Interaction diagram for inelastic flexure in which adjustmenitn to account,t he upperb oundsi mplied by the weak
the in-plane force and bending are applied concurrently.
ands trongr heologym odelsa re3 .4 and5 .1 K km- 1, respec-
Strongrh eologiys illustrateadt 4 K km- 1. Noticeth ats urface
tively. When the conditiono f no surfacefa ulting is incorpo-
failure can be averteda t the large bending moments requiredt o
ratedin to the strongm odelt, he upperb oundis 3.8 K kin-l;
reproducet he Artemis Chasma outer rise amplitude and width
this value is somewhatl ess preciseb ecauseo ur solutions do
(compareF igure 6).
not include the spatially variable in-plane force. Narrower
segmentso f the outer rise can be explained by higher thermal
gradientso r by locally weaker rheology.
the flexural solutions. For a typical profile (Figure 7a) the
A broad range of geotherms, in-plane forces, and applied
constantin -plane force model indicatesa needf or a factor of 2
momentsi s allowed becauseo f the nonuniquenesso f the solu-
or 3 change in N acrosst he outer rise to avoid surfacef ailure
tions (Table 3), but these three parametersa re strongly inter-
with the implied change in curvature.O ur model that allows a
dependenwt hen constrainedb y the outer rise width and height
laterally variable in-plane force indicates that such a change
(Figures6 and 9). Our inelasticm odel is relatively sensitive to
over only 100-200 km will appreciablyd ecreaset he outer rise
the ~90-m variations in the amplitude (Figure 2b), which are
height, implying that still larger forces and moments are
explainedb y small changesi n the applied loads. The ~35-km
required.
variations in the width (Figure 2c) imply changes in some
combination of temperatureg radient, lithospheric rheology,
Discussion and in-plane force. Suchc hangesm ust occur over the trench
length of ~300 km coveredb y our profiles (Figure 1).
Our inelastic flexural modeling indicates that the elastic
solution coupled with the moment-curvaturem atching tech-
Sources of Loads
nique succeedsi n estimating the approximate geotherm at
Artemis, but it fails to distinguish the presenceo f a large, In-plane force. A typical compressive in-plane force
compressivei n-plane force. To understandt he seeming con- requirebdy the flexurafli ts to Artemisis -1 x 1014 N m- 1,
tradictionb etweent heset wo results,w e have run accuracyt ests althoughi t may be locally lower (Table 3). The observationo f
for the elastic flexure methods using an approach similar to a lack of surfacef aulting near the chasma implies that this
that of Mueller and Phillips [ 1995]. The elastic plate equation
is fit to a series of synthetic inelastic flexure profiles which
Table 3. Inelastic Flexure Model Results
are generated for different values of in-plane force (N is
assumedto be zero in the elastic fits). For each fit we perform
the moment-curvature matching calculation for both the first Parameter Weak Rheology* StrongR heology'(cid:127)
zero crossing and maximum curvatures. We find that the
mechanical lithosphere thickness estimatedv ia the elastic fit Full Outer Rise WidthR anges
can be in error by up to ~30% for compressionali n-plane dT/dzK, km- 1 3.4-5.4 3.8-6.4
forces, dependingo n such factors as the thermal gradient, Mean Outer Rise Width
trench depth, and applied moment. The errors can be even
dT/dzK, krn- 1 2.8-4.0 3.8-4.4
larger for in-plane tension.
N, N m- 1 -(3.0-15)x 1013 -(9.3-14)x 1013
These findingsi ntimate that flexure modelingo f terrestrial
M, N -(3.5-15)x 1017 -(4.9-10)x 1017
subductionz ones, where stressesr anging from tension to
compressionc an arise from interplate coupling and the trans-
* Two constraintso: uterr ise heighta nd width.
mittal of slab-pull forces [e.g., Spence,1 987], might be inac- ? Three constraintso: uterr ise heighta nd width and no surfacef ailure.
curateb ecauseo f the neglect of in-plane forces [Mueller and (cid:127) Upper boundst o geothermo ver rangeo f outerr ise widths.
BROWN AND GRIMM: ARTEMIS CHASMA FLEXURE 12,705
force decreases from the trench across the outer rise, but it more than -250 km long [Brown and Grimm, 1995]? Terres-
persistsf or thousandso f kilometers into NsomekaP lanitia. trial subductionz ones, with much longer slabs, rarely exhibit
The region southo f Artemis lacks any candidatef eaturest hat bendingm omentsg reatetrh an- 3 x 1017 N [e.g., Levitta nd
might provide the requisite driving stresseso r the strains Sandwell, 1995]. The large gravity anomaly at Artemis
accommodatingt he convergencea t Artemis [Brown and [Schuberte t al., 1994] implies a negatively buoyant slab, and
Grimm, 1995]. The chasmataa nd highlands to the north are it must contribute to the moment applied at the trench.
morep lausibles ourcer egionsW. e infer that the in-plane force However, it is unclear how the buoyancy of a slab on Venus
is transmitted from the overriding plate to the downgoing would compare to one of similar dimensions on Earth: while
lithosphereb y congestedm otion at Artemis.T he absenceo f the venusianl ithospherem ay be older than that subductingo n
pore fluids on Venus,h encel argef rictionals tressesis, a likely Earth, the crustc ould also be thicker. We might ask whether
explanation for highly coupled underthrustingc omparedt o there is any correlation between such slab characteristicsa s
terrestrial subduction zones. age, length, and dip and the flexurally derived bending
A possible cause of the in-plane driving force is mantle moments for terrestrial subduction zones.
flow tractionsa ppliedt o the base of the lithosphere, aidedb y To answer this question, we have calculated the moments
the probablel ack of a low-viscosity zone on Venus [Phillips, (torques)i nduceda t the trench by the negative buoyancy of
1986, 1990]. Phillips [1990] derived relationships between subducteds labs, using the thermal model of McKenzie [1969]
in-plane stressa nd long-wavelength gravity for a thin elastic and the parameterso f Jarrard [ 1986], and we comparedt hem to
lithosphere overlying an isoviscous mantle. We have exam- the flexural first zero crossing bending moments reportedf or
ined the long-wavelength geoid in the Artemis region up to 15 subduction zones [McNutt and Menard, 1982; McNutt,
degree 10 (wavelengths -4000 km and greater) using the 1984; Levitt and Sandwell, 1995]. We find no meaningful
spherical harmonic gravity model (MGNP90LSAAP [Sjogren correlation between the slab-pull moment and the flexural
et al., 1996]). The theory shouldb e valid at these wavelengths moment, a result that might be explained by the scatter in
assumingt he depth of the densitya nomaly driving the flow is reportedf lexural moments,w hich can exceeda n order of mag-
shallowert han -400 km [Phillips, 1990]. The maximum geoid nitude for a given trench. However, there is also no correlation
height is -70 m over southeastT hetis Regio, correspondingt o between the slab moment and maximum flexural moment. This
a predicteidn -planef orceo f-1 x 1013 N m- 1, considerably finding can be interpreteda s evidence that other factors domi-
less than the flexurally derived values.H owever, partial crustal nate the relationship between slab thermal buoyancy and
compensation of Thetis [Grimm, 1994] might obscure the flexure at the trench, such as phase changes within the slab,
presenceo f a stronger mantle anomaly. interplate friction, stress transmittal through the mantle
Differential topographyi s a related mechanismf or generat- wedge, viscousr esistanceo f the mantle, and inhibited penetra-
ing stressesi n the lithosphere (e.g., ridge push in oceanic tion of the lower mantle [Davies, 1980, 1981]. It is notable,
lithosphere). The in-plane force producedb y topography is though, that Jarrard [1986] (using the same thermal model)
given by the moment of the anomalous density [Dahlen, found a correlation between the predicted slab-pull force and
1981]. For a very simple configurationo f thermally thinned trench depth, another flexural property.
lithosphere the in-plane force is approximately N =-pmghL, A force not acting at terrestrial subduction zones may
where h is the topographic relief and L is the ambient thick- contribute to the loading at Artemis. Sandwell and Schubert
nesso f thet hermalli thospherFeo. ra 4 K km- 1 geothermL, -- [1992b] suggestedt hat perhapst opography northwest of the
500 km for a half-spacec ooling model. There is roughly 3 km trench loads the underthrustp late. This inner ridge (Figure 1)
of relief between southeast Artemis and the rifts south of might be a consequenceo f the convergence at Artemis, as
Thetis;t hus,N ---4 x 1013N m- 1. Phillips[ 1990] pointed uplift of the overriding plate has been measuredf or terrestrial
out that the geoid expressiono f topographics tresses[ Dahlen, subductionz ones. On Earth such topographyi s rapidly eroded,
1981] is identical to his result for flow coupling. and it may not play a significantr ole in the slab force balance.
The requiredd riving force per unit length might be less if Becauseo ur models do not include this region, any vertical
the area over which it is applied is larger than the -800-kin- loading northwest of the trench is implicitly accountedf or in
long southeastc hasmaw here stressesa re presumably focused. the applied bending moments.
The maximum length over which the force could be applied is Summary. The fact that the requisite in-plane driving
the diameter of Artemis (2000 km). Therefore, the driving forces are not evident in the gravity field means that the
force could be, at most, a factor of 2.5 smaller than the flexu- proposed mechanisms are incorrect, the force is not fully
rally derivedfo rce;t hati s, it mustb e at least- 4 x 1023 N expressedi n the geoid, or the flexural rise is a relict feature,
m- 1, andi t is probablys ubstantialllayr gerS. uche nhancementf rozen in by the cooling lithosphere. The dominant sourceo f
of the driving force makes the mechanismss uggesteda bove the applied bending moment is the negatively buoyant slab.
marginally acceptable. The lack of correlation between slab properties and flexural
The postulatedd ecreasei n the in-plane force from the trench moments at subduction zones affirms that the short Artemis
to the outer rise connotes that a regional stress has not been slab is not discrepant with the large moment, as long as the
continuously applied to the downgoing lithosphere. A slab-pull torque exceedst he flexural moment. For Artemis the
regional in-plane force would have produced contractional slab must have a shallow dip and a large density anomaly to
deformation on the trench slope, either before flexure com- supply the inferred moment. Paradoxically, given the
mencedo r before that section of the crust passedt hrough the missing in-plane driving force, Artemis should be active or
outer rise. Therefore, the in-plane force and flexure may have very young, as the slab has not yet thermally assimilated.
grown with time, maintainingt he surfaces tressesn ear zero.
Implications for Venus Thermal Evolution
Bending moment. The largea ppliedb endingm oments
(typically-7 x 1027N )thatw eh avein ferreadl sop resenat Artemis Chasma, and possibly Latona Corona [Sandwell
dilemma: what is their source if the slab beneath Artemis is no and Schubert, 1992a], standa lone with exceptionallyl ow heat
12,706 BROWNA ND GRIMM: ARTEMIS CHASMAF LEXURE
flow estimatesc omparedt o other featureso n Venus [Phillips et Conclusions
al., 1996]. Our resultsi mply a thermalg radientn o greatert han
4 K km- 1 to explaint he maximumou terr isew idthu nderth e This study of flexure at Artemis Chasmap rovides insights
into the fallibility of elastic flexure models, the rheology of
strong rheology with the adjunct condition of no surface
the lithosphere, the forces responsible for Artemis, and the
faulting. Studies of several coronae indicate geotherms of
approximate6l yto 24 K km- 1 [Sandwealln dS chuber1t,9 92a; recent thermal state of Venus.
1. The elastic plate bending model, coupled with the
Johnson and Sandwell, 1994]. The gravity anomalies over
large volcanoesim ply thermalg radientso f 5-7 K km- 1 moment-curvaturem atching technique,i s generally not accu-
rate when an in-plane force is present. Because in-plane
[McGovern et al., 1995]; Phillips [1994] estimateda 7-10 K
km- 1 geothermat Atla Regio. stressesm ight play an important role in tectonicsa nd flexure
both elsewhereo n Venus and in subductions ettings on Earth,
Comparisono f the deformation styles and geodynamically
their omission from flexure models may introduces ignificant
inferred heat flows of featuresp n Venus provides insight on
errors into estimateso f lithospherict hermal structure[ Mueller
the thermal evolution of the planet. Coronae and volcanoes
and Phillips, 1995]. A simple, though incomplete, test of the
may exhibit higher heat flows becauset he lithosphere in
validity of the moment-curvaturem atching technique is to
which they formed was youngera t the time of loading than the
comparea n inelastic synthetic flexural profile (generateda t
lithosphere at Artemis, and/or these structuresw ere responsi-
the geotherm inferred via the elastic fit) to the observed
ble for thermal rejuvenation of the lithosphere. Coronae are
inferred to be relatively older than large volcanoes; both topography( Figure 5). The agreementb etweent he temperature
gradientsf ound from the elastic and fully inelastic models is
featuret ypes are about one-fourtht o one-half the mean surface
attributed to the range of in-plane force-geotherm combina-
ageo n average[ Price and Suppe, 1994; Namiki and Solomon,
tions capableo f reproducinga given flexural profile. If the in-
1994]. The unique style of the Artemis underthrustingc om-
plane force was somehow independently known, the true
pared to other, older contractional structureso n the planet
inelasticg eothermc ouldb e quite differentf rom the one derived
[Brown and Grimm, 1995] and the possible age-heat flux
from the moment-curvature matching technique.
correlation suggested here are concordant signs that, on
2. For a lithosphericr heologyb ased on standarde xtrapola-
average, the venusian lithosphere has monotonically cooled
tions of rock mechanics experiments, the inelastic flexure
in the last several hundred million years [Turcotte, 1993;
model indicates that thermal gradients for at least some parts
Arkani-Hamed et al., 1993].
of southeaAstr temism ustb e lesst han3 .4 K km- 1 (Table3 ).
If we poset he surfacet emperatureg radienta s a function of
Applying the strongest rheology we judge plausible, the
age (t) for a semi-infinite half-spacec ooling model, we obtain
geothermm usbt e lesst han4 K km- 1 for the widesot uterr ise
[Turcotte and Schubert, 1982, pp. 158-167]
cross sections. Narrower portions of the outer rise could be
consistenwt ith eitherh igherg eotherm(s< 6.4 K km- (cid:127)) or
(11) locally weaker lithosphere.
3. The flexural bending moment is of the order of
-7 x 1017 N. Bendingm omentsa ren ot directlyc onvertible
where Tmi s the zero-age,o r mantle, temperatureI.f the age of from the slab densitya nomaly, which is also compensatedb y
the lithosphere at the time of loading was 400 Ma (the mean other mechanismsT. he negativelyb uoyant underthrusst lab at
surfacaeg e)(,1 1)p redictdsT /dz= 5.1K km-1 fora nominaTl m Artemis is the primary sourceo f the flexural moment.
of 1750 K. Becauselo cal geothermsb elow 4 K km- 1 are 4. A sizable, compressivei n-plane force of the order of
inferred even for the strong rheology (Table 3), we must -1 x 10T MN m- 1 is requirebdy botht hef lexuraml odelinagn d
modify our assumptions. thel acko f outetrr enchsl opefa ultingi;t is alsoe xpressbeyd
We considert hree end-membero ptions. (1) The last global the pervasive wrinkle ridgeso n the southeastp lains. Mantle
resurfacinge vent completely reassimilatedt he preexisting flow coupling and lithospheric thinning might supply
lithosphere, after which the present lithosphere began to adequated riving forces. Surfacef aulting on the outer trench
form; thus, t should correspondt o the age of this event. We wall is precludedo nly if the in-plane force increasesa cross
would then infer that t > 400 Ma to satisfy the lowest this zone and if near-surfaces trength is at least a few tens of
geotherm.T he upper bound on the surfacea ge derivedf rom megapascals.
crater statisticsi s -800 Ma [Phillips et al., 1992], for which 5. As a zone of underthrusting, Artemis should enforce
we calculatdeT /dz= 3.6 K km- 1. (2) Ther esurfacinegv entm ay upperb oundso n heat flow at the time of loading. The low
have reduced, but not completely reset, the lithospheric temperatureg radients--comparablet o those of the Moon--
thermala ge. For example,l imited extensionapl rocessesc ould attestt o the exceptionalc ooling that has occurredin the last
have induceds ufficient magmatism without forming entirely few hundredm illion years of venusiant hermal evolution. Our
new lithosphere [Grimm and Hess, 1996]. In this case, the results favor a thick (>300-km) thermal lithosphere
observeds urfacea ge only furnishesa lower limit on the effec- [Kucinskasa nd Turcotte, 1994]. The low heat flux complies
tive thermala ge. (3) The mantle may have becomea bnormally with the half-spacec ooling model if the thermal age of the
cool by the time the lithosphereb egant o form [Arkani-Hamed lithosphereis over 600 Ma and/ort he mantlet emperatureis as
et al., 1993].T o achievea 4 K km- 1 geothermat 400 Ma, we low as 1550 K.
wouldr equireT m = 1550 K. In summary,a ny of these three, 6. The uniform, plate-like motions observeda t Artemis
simple, end-members cenariost aken alone can explain a 4 K Chasma reflect a spatially coherent tectonic style that is
km- 1 temperaturger adienitn the contexto f the half-space unusualo n Venus [Brown and Grimm, 1995]. Deformation
cooling model. Our flexural results admit, but do not require, involves throughgoingf ailure and modestt ranslation( <250
lower heat flows; some combination of the above schemes km) of a rigid lithosphere,d istinct from the distributed,c rust-
wouldb er equireidf t heg eotherwma sa sl owa s3 K km-1 . dominatedt ectonicss eene lsewhereo n the planet. The thermal