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1CAIUS 32, 73--84 (1977)
Internal Structure and Properties of Mars
DAVID H. JOHNSTON AND M. NAFI TOKSOZ
Department of Earth and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Received August 4, 1976; revised January 3, 1977
Theoretical physical models of the Martian interior are presented in the light of new and revised data and constraints. These models include thermal evolution, densities, and seismic wave velocities. The interior of Mars appears to be Earth-like in many respects. Although thermal models indicate that Mars has passed its peak of evolution it may still have an astheno- sphere and may be moderately active tectonically. Mars has an Fe-FeS core with a radius of 1500-2000 kin. The mantle is enriched in FeO with an olivine composition of about FoTa. Theo- retically determined seismic wave velocities are relatively well constrained in the mantle with upper-mantle P , velocities ranging from 7.64 to 7.80 km/sec. However, there are wide varia- tions in Vp in the core dependent on composition. The shadow zone due to the core is larger than the Earth's.
hi this paper we present a set of physical models of the Martian interior based on available data. Some of the results pre- sented are extensions of work published in Johnston et al. (1974; hereafter referred to as Paper 1). However, improved theoretical techniques, revised constraints, and addi- tional data that have become available since 1974 warrant another study of the structure and properties of the interior of Mars.
Interest in the structure of Mars has a long and involved history. Early studies of the thermal evolution include Urey (1951, 1952), MacDonald (1962), Kopal (1962), Lee (1968), Anderson and Phinney (1967), Hanks and Anderson (1969), and Reynolds and Summers (1969). More recent papers (Binder, 1969; Binder and Davis, 1973; Anderson, 1972; Ringwood and Clark, 1971; Toks6z and Johnston, 1974, 1976; Johnston el al., 1974) have calculated density and compositional models including a metallic core. The debate over whether or not Mars has a core still continues, with
Strangway et al. (1976) postulating a planet with all undifferentiated deep interior.
In this paper, thermal models are briefly presented followed by density and seismic velocity models. The final section sun:- marizes the main features of the Martian structure.
DATA ON TtIE MARTIAN INTERIOR
Theoretical calculations of planetary interior models require constraints based on observed data to limit the problem to realistic models. Although Mars is not as strongly constrained as the Earth or Moon, data primarily from Mariner 9 have enabled us to revise and improve earlier thermal and density models. Many of these data are concerned with the interpre- tation of Mariner 9 photographs which yield evidence of surface evolution history, volcanism, and differentiation of the planet (Masursky, 1973; Soderblom et aI., 1974; Arvidson, 1974; Chapman, 1974; Jones, 1974; Malin, 1976; Murray et al., 1972; Mutch and Head, 1975). These types of
73
Copyright • 1977 by Academic Press, Inc. All rights of reproduction in any form reserved. ISSN 0019 1035
74 .I()ilNST()N ANI) T()KS(')Z
(l:)la art ' l)arti('ul'~rlN us('ful i11 (.,)nslr.dnin~ th(!rm:d hisi()ry in()d( ' I s . . \ l)()ssihh' (.v,)lu- li()u Ifist()ry l)r()p()s('d l)y M' i su rsky (1973) and ils r(dati()n 1(, (h(,rmal m()(l(,ls is dis(mss('d in Pat)(,r 1. I t a))l)(,ars tha t Mars, Ilk(' (h(' M()(m (1)r()l)ably the I,]arth, V('IIU~,
• In(l M(,r( 'ury also), suff(,r(,([ lhr()ugh a l)(,ri()d ()f int( ,ns( , l )ond)arthn( ' )~t aI)ottt 4 I).3. ;tg() (T1,ra and Wass(,rl)ur~, I!1761 sh()rtly al'l('r ()ri~iu. This implies thai :1 ('rusl had f ( )rme( l p r i o r t() t h i s t i n . ' , r('(luh'ing; r(,la- ( i v ( ' l y hi~;h in i t i 'd (1,ng)(,ratur(,s. Th( , la(('r sl:]~(,s ()[ ~ la r t i an ('v()luti()n sl1()w ('l)iS()(h's ()f l('(q()ni(' a n d v()h.ul i (" a( ' t iv i iy . Tluirsis v()h.anism pr()l):d)ly ()e(mrr(,d "tl)()u( a l)illi(m y( 'ars a~() (S()(h,rt)h)ln el aI., 1!)74) and is a nmj()r (.()nstrain( in th(' lh('rnutl (,v()luii()u :Ind t(q~Ii)('1'atllr(' m()(l(,ls ()f .~Ia)'s.
])(,rhal)s 11](' ii1()sl, iml)()rta)11 d:tta c()n- ('('rninV t im I)r(!s('nt s tru( ' tur( ' ()f Mars :Jr(' th(' mass, 31, :m(l m()m('ni-()[-h)('rl ia f't('l()r, ( ' /Ma "2. Th('s(' r()ughly (h't('t 'nfilw (h(' (l('n-
s i l y var ia t ion within (h(' l)lan('t and iu(U- ('~111' 1]I(! l)r('s('11('( ' ()f :i high-(h,11sily ('()r('. Whih, the ma~s ()f M a r s is well d('t(,rlniu('d, the n1()m(,nt-()f-in('rtia f'mt()r is n,)l. Th(, i))l('rl)r('talh)n ()I' lh(' s('('()nd z(m:11 harm()1fi(' ,)f lh(' gravi la l i ( )n 'd fMd (.I.,) in l(,)'ms ,)f lh(' hy(h'()st:~ti(~ 'rod n()nhydr()stali( ' ('()n- t ril)ut i(ms (h'l)('n(Is (wit i('ally ()n asSUml)( h)ns ,)f ( 'rusial struciur(~ (Bind(,r :in(l l)avi,-., I!)73 : W('ir. I(,)7. "): ]~.(,as(,nb(,r~, I(.)77) P.i)~([(,r and I)avi~ (I(,)73), a,..~umin~ a)) is<)stati('ally ('()mp(,nsal('d ('(luai()r]a] l)ulg;(.
TABIA;] I
] )AI¢ \M),YFF, IL'~ [ [S] ' ] I ) IN ~ I ~.l(s ~ [ ( ) ] ) E I , , ~
I)Itl'tt,[111'[ ('1' Vall l("
I~adius (kin) :i:)~!) Mean (]en~iiy (g/('m :~) :i.!)(i (',, M . 2 (1, : m.-).l flea) ()f fu,<i(m (manl l (~) (J /~) HI() ('p (nl:ulll(') ( . l 'g°(') 1 2 Sl lrf : | ( ' ( , l ( ,n l l ) tW:i l l lr ( , ( o ( , ) - - I ()
I : ('()ll('(')ll)';Ili())l (1)l)l)) I.')
Th 'I" ra(i,) I
K [ ~ )'a,(i() 5(),()()()
<d' ,~ kin, ('st]nmle U/:]/a ~ rauginV i'r~ml
al)oul 0.3?4 I() 0.370. .\ualy,~i~ ()t" 1he ~ rav i ty field and t(W)g-
r:tphy ~)|' Mars (Phill ips and. ~aunders , 1!}73) i~Mieales tha ; liar, surt 'aee m a y t)e divided in)() t xw) distinct grout)s : (dder erus( isosl,:itieally vonqwnsa led at a relatively' shallow d e p t h : "tnd lhe Th.trsis t)]a(eau, ( ' h ryse , and Amaz(mis h>wlands, whMt ar(' (rely I)arlially ~.m~pensated. "l'h(, Tharsi+ I)Iat('au is lhe m()st, 1)r, minent fea ture ass<)vialed xx il h :m ullc~)nll)elISaled Kravi ly :HI(HIIilIv. Tll( 'se (I:llii Sll~(,'sl :t desm'il)li(m ,,f Mars as :t sl)heroid m,'~rly in is~)stalic e(luil ibrium plus :m exlra m.~ss represented h,v Ih(' Thars is re~i(m, lh 'asenherg (I!)7'7) us(,,.< this m~)del 111 ealeu].tt(, i he i V ) l l h v d F i l -
stal iv ( .ml r i lmt i (m ~)i' ' l 'harsis 1,(, ,I._,. Thus , a s sumi ]~ t h a l t h p ri~zidily' s tq)port in~ Thars i s e~mhl be rela×ed, lh,as('nl)(,r~ find~ thai th(' b(,dx', m)w in hb'dr<,~lativ ('(lui- lil)rium, w(mhl hay(' :I n](m1('nt-(d-in(wlia Iat'(()r <d' 0.3(i,~4 N (1.001. This model is [ur(lwr jus(i[i(,d in l.hai lhe (q)th'al and dyn ' tmic f la t tening ( ' : th 'uhm'd :m' in much 1)(,tier :t~r(,oll/O111 l lmn (h()~e f(ir ~Uher In ( .Ms . Wp (hervt'()r(' adopt fiw this lmt)m • th(' value ,)I' ('r ,lit./2 (d)taim'd I) 3' Iteasen- I.,r,~. 'I'hi~ vahw is signifie:mily h)wer )hart the ().377 used hl P:q)er I. It :tllm's t}w (hqtsily m , . M s p r c s e m e d )he r . i . sm 'h :~ way ax t , )mnt )h ' l s ize an iner('ased densi ly e(mtrast t).tw('( 'n Ill(' sh:tllo~v I:ly('rs amt (h'(' I) int('ri+)r ,)f Mars, l)()ssil)ly imt)lyin~ a larlz('r c()r(, radius. ()th( 'r physi( , t l l):iranw- l(,rs fi)r Mars which are us('d in th(' th( ' rmal • 1111[ (h'ns]iy ('al('ul:tti()ns nr(' pr( 's( 'nt( 'd in Tal)le I. .\ (h ' taih 'd (liscussit)n ()I' lhes(' I):11'~It11('i('1's 111,:I 5" l)(' I'()t1111[ ill P t l l ) ( ' r I .
TI I Iq l IMAL M()I )I':I,~
The impl ied ( ,vo lmhm hist(wv and l)res- ('I)¢'(' ~d' a ('or(, discuss('d ill 11.' pr(w(,ding s('vti,)n llh1('(' S|I ' (111~ ( ' ( ) I I ~ ( r ~ t i l l i S ()II t ] Iv
ih(wm'd hist())'v ()f Mars. Tit(' pr('s('n('(, ()I" a weak ma¢n(,li<' IMd (l)()lgin()v cl (d., I!172) als() s(,('ms l() hnldy that l)r( 's( 'nt-(l 'u inl(,rlm] t(qnp('r~Itllr('s ~]l()U[(] l)r()(|tl('( ' :)
INTERNAL STRUCTURE OF MARS 7;5
IO00
E
2 0 0 0 E3
3000
. . . . . I i 1 . . . . ~ - -
_ _ ~ - - 1 5 0 0 ° C _ _ _ _ _ _
Partial Melt ~ - - --'~-'] . . . . . . . . . . . .
" -
\ \ x / \ t
\ / 2 0 0 0 ° C
,/ Liquid Fe-FeS Core
i
I I I I o I 2 5 4
Time, b.y.
FIG. I. T h e r m a l evolu t ion of the M a r t i a n inter ior as a func t ion of d e p t h ,~nd t ime based on the convee t ion t e m p e r a t u r e calcula t ions of Hsu i et al. (1976). Reg ions of m a n t l e par t ia l me l t ing and core fo rma t ion are shown. T h e shur t da shed line represen ts t h e top of h)eal par t ia l me l t t~ssoci'~ted wi th the convec t ive cur rents .
molten or partially m()lten core. Condensa- tion models of the solar nebula (Grossman and Larimer, 1974) suggest tha t the Mart ian core is enriched in FeS, and thus may contaiu small amounts of the heat- producing radioactive isotope 4°K (Lewis, 1971 ; Goettel, 1972).
Theoretical conduction thermal models consistent with the known constraints concerning the evolution of Mars and core formation are presented in Paper 1. Hsui et al. (1976) have calculated thermal models for Mars including the effect of solid-state convection by sinmltaneously solving the equation of m()tiou and the t ime-dependent energy equation in spherical geometry. Since the process of core formation is not well understood, its effect upon convective s tructure is difficult to determine. Thus, prior to core formation, the calculations are carried out in the mariner described in Paper 1, with similar initial conditions and physical parameters (Table I). After the separation of the core is completed, the core temperatures are assumed to follow an adiabatic gradient determined by the temp( 'rature at the core mantle boundary.
As in Paper 1, the presence ()f 4"K in the core is allowed.
The evolut ionary history of Mars from Hsui et al. is shown ill Fig. 1. I t is assumed tha t core formation takes place before 1.5 b.y. after origin. The planet continues to heat up slightly after core f()rmation but then starts to cool. Large tensile features of fractured plains (Carr, 1974) may have been associated with the heating-up period. A partially molten region in the upper mantle exists up to 1 b.y. ago. The thick lithosphere, however, resists lateral motions explaining the absence of plate t.e('tonics. The short dashed line shows tim top ()f local partial melt associated with t |w up- welling of convective currents. If' wat(,r is present near the Marti:tn surface, the solidus will be suppressed and partially molten regions may exist at a depth of 250 km at the present time. This could produce st)me present-day tectonic activity. There is a region of solid-state convection at the lower par t of the mantle. The c()r~ is completely molten.
The t)resent-day tenq)erature I)r()fih's from both the conduction and cunvection
76 J ( ) I t N S T O N A N I ) T( )KSOZ
2 0 0 0
O o
D - /
g ~ooo / r-- i
22~+--
il o L . . . . . . . . . . . . . . . . . . . . . . L z ___
0 1000 2 0 0 0 3 0 0 0 Depth, km
I.'m. 2. R.mge of the presenl-dny temper~thtres wilhin M'u's (shaded area), b.tmded by the uomhwl,i.n model of P:q)er I and lhe cotweelion model of ttstti +'t at. (1976). Also slmw'n are llm (h'y-m mile s.lidus t~,lld lhe Fe -li'e, '4 t.ul ecl b t Olllp('l ' ill Ill'ON.
~tt()~l(,ls at( , itm'rt)r(+ted t(~ }tt' I>,,utt(l.'~ (>n t i m t ~ ' m p ( ' r : t t t t r ( ' d i s t r ib t t t i (m w i t h i n Mars . q'lws(, ar( ' u sed in t he d , t t ' r t n i n a t i . t l t,f d e n s i t y nu>d('ls a n d a re sh(nvn in Vi~. 2. Also show n a re t he d r y - n m n t h ' s, d idus (~'xtrap<thtt('d pur idot i t~ ' ; (h 'u( 'n a n d l l i n g - wo(td, 1969) a n d :ttt ( 'xtrat)olat( '(1 I,'(, lg 'S m~t('clie m e l t i n g curv t ' <' tdculatt 'd I>y l ' ss ( ' l - n u t n (1975a ,b) . I n th ' t t v( )nvuct i ( , t nat>st l i k ( ' l y oc(~utr,s w i t h i n p h m e t a r y int.eri~.'s, w(' us( 'd l,]lt~ COllVt'(qive t,('lllp('l 'gttlll 'O tw(dih, ill t h e d ( ' t t w m i t m t i o n (if d t ' n .q ty a m l seismiu, w a w ' wqoeit i t ,s .
"I'ABIA': 11
UXll~Mt,Trl,Hts [~l , ; I ) IN I )ENblTY +\IIHH.J.S
Parameter Vahw,
Upper manile (l"oT;,I ]£o (Iniml') 1.255 dK/dT' (kl):u" °K ) I~. 17,1 , H T = 211°('1 (o(~ ~) 2.1 ~ I0 :'
l , .wt ' r tnanlle (spinel l"m:,) 1(0 (tnbar) I .sg:I
( !111'1! A o Ind~:ur) I . 2 . (7 ' = 20°(7) {o(, I) 7.:1 :< 111 :'
1 )I,:N~I't 'Y M( H ) E13,.4
"l'h~,,.'<"~h.al d<,ttsity m,)¢h,ls f . r ~[at 's can b(, t .onstrtuq~,d t tsin~ t tw m:tss :rod m, , tn~ 'n l - ~ff-int't'tia t'a<'t~w as (.<restraints if :t I.:tmwl- (,dff, e ~d" lh( ' I imnt l ( ' a n d core UOmlt~siti~ms is as,~ttnwtl. "l'ht's~' m<~<ltqs at'(' <,ah'ulal~'d I ' . r :t xsartn. ,,omprt,s~il>h,. l:tyt'r<,d plan<'1 f . l - h .wing th( ' t twhniqut* dt,sm'ib¢'d in Pap t ' r l aml in ,'4<d<ml,.t a m t Tul . : s6z ( l ! 173 ) . Sitter, t[t(, e<w(, u<mtp¢~si! ion is trot w4ql d¢,t(,rntitwd, we l)r( 'st 'nt a rang(' (,f tt(~ssil>h' <h' t ts i ty pr<,fih's.
T tu ' (h 'nsi t .v n . ,d ( ' l s :m, d<'r ive(I by ntmwriu~tl l . \" int~'~;t"tt ing t.h(' uqu: t t i (m (~f Itydr+~st.ati,~ ~ ,qu i l ib r i t tm wh('r~' t.h~' dm~sih',', p, is t'el:tt~'d t(, t im pr~,ssur(,, 1'. l<v a . ,,qtmti<~t~ (>1 ~ sl:tt.m assmn( 'd t~> tm t i t ( ' is(~t.h,rm:tl P;ireh . \ l u r n a g h a n uqu_aI i(tn (Hiruh, 193,'< 1952 : Mur tmffh : tn , 19:}7) :
] , = ~ K , ~ ( p , p , , ) 7 ~ (p "p,,)~,ruq. Ill)
K , ' rod p,, art ' t im isoth(wtnal t}ulk m¢,dtthm a n d d(qts i ty :tl / ' = 0 a n d at'u u(mtpt~l('d :tt. t i t ( ' l ( ' tnp( ' ra tur ( ' . 7', al dep ths f f iv( 'n t).\ Ih( ' th ( ' rm: t l m , ~ d ( ' l s s} .~vn in l,' iz. '2. 'l'h~' th ( , rnml ( ,x l )ansi(m (,~wlfi('i<,nt tn:ty It(' l ( ,n t -
iwrat t tr ( , d( ' lwnd<'nt "tnd is ]):ts~'d (>n <'xlr:tp-
I N T E R N A L S T R U C T U R E OF M A R S 7 7
olated data from experimental measure- ments for the appropriate material. Values for these parameters are listed in Table II.
Each model assumes a 50-km crust with a density of 3.0 g /cm a (Phillips et al., 1973) which amounts to about 3% of the total mass of Mars. The bulk modulus and thermal expansion used are typical of terrestrial crustal rocks (Clark, 1966, p. 94).
As a start ing model for the mantle, we assume a composition of Fo75. Values of Ko and d K / d T taken arc given by Chung (1971). The use of F()v5 as a mantle model was based on prel iminary density calcula- tions in order to roughly estimate the STP mantle density, and thus its equivalent olivine composition.
A phase change from olivine to spinel phase may occur where the temp(,rature profile cross(,s the P - T transit ion (Ander- son, 1967a), as shown in Fig. 3. For the conduction thermal model, this occurs at a depth of about 1500 km and for the c(m- vection model at a depth of 1200 kin. The s tandard tempera ture and pressure spinel- 1)hase density is constrained to be 1 0 ~ higher than the S T P olivine-phase density.
The elastic parameters for this layer arc again taken from Chung (1971) and are listed in Table II. Other possible mantle phase changes would have smaller effects and are not considered in this paper.
The core composition (and therefore density) is considered to be a free param(,t('r to be determhmd by the calculation. Core compositions consid(,r(,d range from F('ssS to FeS. An FeS composition has b(,en proposed by Lewis (1972) for the Mart ian core, and F(,ssS is similar to compositions proposed for the Ear th (Ussehnan, 1975b; King and Ahrens, 1973).
Usselman (1975a) has shown from ('xt)eri- mental determinat ions of the Fe FeS eutectic tempera ture tha t a solid solid phase t ransformation occurs in F('S at about 52 kbar. This is consistent with tim high-pressure phas(, (hpp) (wident from shock compr(,ssion studies of pyrrh(~tite reported by King and Ahr(ms (1973). Assuming no further transitions, this is t h(~ phase pr(,sent in the Mart ian core. l{(,c(,nt experim('ntal work suggests a valu(, of Ko for the' hpp of 1.2 mbar and a zero-pr('ssure density increase of 15(,:~ over th(' lmv-
2~o! , ~ 7 V
/ j : 200;
] / / 5 , 0o
ooo ........ 50[0 o ~o'oo Temperature, °C
Flu. 3. Present.-day temperat.ure profiles fron~ l he conduct.ion thermal model (solid line) and the ('onvection model (dashed lille) superimposed on the stabilil,y fields of olivine and spinel phase.
7~ ,1( )H NST( )N .,\N 1 ) T( )KSC')Z
1%1 °
0
Conduction Model Convection Model 0.58
/ / / /
0.57 .d// 1/
( / / ,/1, / ~/
0.36 ~7Y -5 / ,~ / , , 7
/ ~ l/z__ F
0.55
E 2 0 0 0
o 0 o 1500
I 0 0 0
+ /
/ /
' " / - '5 :
/ / . / -
/ -
/ - - P e 8 5 S . . . . . . . . . F e s o S
. . . . E u T - FeS
3.2 3_4 3.6 3.8 5.2 3.4 3.6 3.8 STP Mantle Density, g/cm 3
Fit ; . . I . Hlnnd:u 'd Ie tnp( ' ra t tu ' e :rod pr(,~m'(+ upptw-nt :u i lh! +.tensity +h~,v,'t~ :i,< it l 'tmut i<m of ni imt0nl (>f inertill, it+rid d e p t h t<+ lhi4 (!l)l'i!~ for v:i+ryin K core vt>nll)osiliims (hP,s;er ril4hi (!<)i'ili.!l') tutd for b o t h lelllperi+lttl 'O models. The hor izonl t t [ dashed l ine is l i ie nl<miont-ot'-in(,l ' l ia fac to r ttse(] in l i i is lmper.
prossuro ph:lso (Ahron.% 197t;: l'iuhul<> ¢'l a/ . , 1!)7li) .
"I 'h( 'rmal (+XflallS';i()ll i l l t l . u~nu is l(,lll- tl(,raturt~ (hqJ( 'nd(,nt a n d is I:ll.:cn 11~ I/c till
( ,xtral)()lnti tm o[ valu<,s r(' f l t)rted {+)l" T ir tm (Basinsl<i t'/ a/., 1955), :iv i l iscussi,d hy Siofffri¢,d and S d . n l . n (1974). It i.~ a,~sunl('d that, t, tl(' n w l t i n V of' i l l( ' ('<~ro m m . r i . l tins l i t t h ' offo('t tit ( ' h ' va tod t)rossul'os I)ll the physiual l la ramctcrs uscd in 1he dcns i ty c:/lcuh/I i~ ms.
l )ons i ty m,,d~,l,~ . re .ah 'u la tod t'<~r (.oru c tmi l l o s i l i ons tfl' li'(,.~,S, F(...+,N. cuto( ' l i ( ' , ; Ind F('S for bo th ('+m(hl(qiv(' and ('<mv('('tivu toml/or;:~turo i)r<4ilos and tix(,d m(,atl dt,nsily.' ~i + l i l t + l>htnct. In Fig. 4, m,~dds t , l ' v:lryi.¢ ( ' t in' ( . (m lpos i t i . n s :i+ro l)lott t ,d :is it fun ( ' t i on <,f ( ' i M a - ' , S T I > n m n t h ' (l(,n+ity, a n d uot'o ( h , l i t h l,'rtml th( 's( ' t)ll(' III+A 3" sch'( 't :t t h ' n s i l y mt~(h'l t t) : l l t)('st fits thc nl<mlunt-ol '-JHcrtia f -whw. Vu l id d.usi l . \ ' n l , ,dNs sal is t 'y in/1 ~th
( ' . l l a -> a n d I h . l nuan d t ' n s i l y a re t~l/Iainld/h' hi uV('l'y caso wi th Cl~l'O radi i v : i r y i n g fr lml 1500 to 2050 luu a n d b4TP n i a n t h ' dons i l ios run~;iug I'rtm~ :3.47 f<~ :3.5,~ g, unfL Tllt , M a r l h m i n a n l l c is tilter't, d(,iiso t h a n lho E : / r th ' s up twr n i a n t h ' , i n i p l y i n ~ till u n r M l - . . ' u t in l"u() :is p rcd ic t t ' d by ccmduil~at i tm lllt~(l('ls {~l' Iho s<~l:il" nohuh l (l.cxvis, 1 9 7 2 ) . l l o w ( ' v u r , S l lch n l i x h ' l s t h a t prt,di . t . I I l"( '~ u.ro in Mars a h m / w i th oxt r t ,nw onr ich- n . ' n I in Foi l ,fl' thu m a n t h , a l f lx 'a r I,~ t . ' int.t,nsi,,qt,nl w i th t h o d a t a . F ( , ( ) . ( l " ( , ( )
M / ( ) ) vahw.'~ t k l tMm'd t'rtmi the (h,n~ity nlo(iuls rlm~:l ~ t 'r t ,n 0.19 [or an fq'~ <.<~r(, t<~ 0.27 t~w :in Fo~,~ (.t,rt.. I,owis (1972), <,t, Iho ~Iiit 'r h: tnd, I)rt'tli('t, <~ u v : ih lo <,t' 0 .5 . l i i~ ulmt,si in.,~('.tmtflc tha t ~m/t, frt,(, ii'tm iv l)l'('s('llt in ttH' M a r l h m u~l'(,.
Fur |ho r v a r i a l h m s in d,,n,4ty : l i l t ] ( ' I H ' ( ~
r:t(liu,~ 111:13" I)(* tf lHain('d t'rom Fi~. -I t~.' tli lToront ;Lssunlc<l v:/I t . 's ot' ¢' M , / .
I N T E R N A L S T R U C T U R E OF MARS 79
Conduction M o d e l ~ ~ . ~ . ~ - - - i t
7..-_.-:_.-_-..-.. :7.--.- - - -
I
I 4 - I _.
3 ' l 0 l O00 2000 3000
Depth, km
Fro. 5. ])ensity profiles satisfying both the mean densii,y and moment of inertia for varying core compositions (see Fig. 4) using telnperatures from the conduction model.
Density profiles for valid models satisfy- ing C / M a ~ = 0.3654 are shown in Figs. 5 and 6 for the conduction and convection temperatures, respectively. Comparison of these figures shows the range of density variations due to extreme models of tem- perature and composition considered. Wc prefer models based on convective profiles (Fig. 6) since they represent more realistic thermal processes. Several features stand out. First, the change in core density is
reflected primarily in core radius, with rela- tively small changes in the STP mantle density. This is important because it allows us to set rather specific bounds oi1 the mantle c,)mposition and seismic velocities that will be discussed later. Second, close examination of these figures reveals that in the upper mantle, thermal expansion is dominant over compression resulting in a slight density inversion of about. 20~ at a depth of about 250-300 kin. This is tile
8 I
7,1-- I
I c.~ 6 ; -
^ >,
~ 5 ¸ -
Convection Model
r I
7_i F [ ' i J !
i t I : 1 i
I i l 4 . -
~ ) F . . . . . . . . . . . . T
o looo 2 o 0 6 Depth, km
I i
. . . . . . . . . . . . . . . . . . . . . . . . . . . •m
3000
FiG. 6. l)ensity profiles using temperature~ from the (.onvection model.
S0 ,I( )H NST()N AN 1) TOKSOZ
san to r(@()n wh(,r(, a s m a l l l)a)'ti:H l)I'pSstLr( ' ()f wa t ( ' r ( , )uhI indu( '( , local p a r t i a l m(,Iting:, as ( t is( 'uss( 'd ('arli(,r.
VI,:I,()(HTY ANI) TIIAVI+:I~ TIMI' : M()I)I,;I,N
S('islll i(! \VaV(' v('l()('il,V :IS :t l'tlll('|i()ll ~)f (h ' l ) th in the M a r t i a n m a n t h ' m a y h(, ( , s l i - m a t e d using: s(.ismi( ' ( , ( i tmli(ms ()I' s ta r ( ' ( 'mp i r i ( ' a l l y d( , t ( , rmin( ' ( l I'())' t(,l'l'(,sl r ial r,)('ks. M , ) s l ( ) f )h( , s ( ' hay( ' v(q,)(. iti( ,s (h'l)( 't ,h'))t ,)n lh(, m( ' an a t ( )mh ' we ig h t , ~;, a n d lh( '
(h ,z )s i lx , o. T h ( ' l l l ( ) S | ('1)1ll111()11 s(' i)Sll l i ( ' ( ' ( l / l l [ | i ( ) l l ()t'
sl t t l ( ' is I~irch 's law (P, i rch, 1!)6~i), M i l c h is ()f Ih( ' f ( ) l ' l l l
I " = aOD) + bp. (2)
Sim]n()ns (19(14) l)r()l)()s('d :~ V:('n(')':tliz('d t'()l'ltl ()f I l l( ' ( '(luati()n f()r / ~ wav('s lha l \vii] I)e us( 'd in t h i s l)al)('r:
I 'v = - -0 . ! )S + 0.7(21 - ~)
+ .l.(i()[7(~a() ~ + :2.769, (3)
)'('th'('l, in~: lh( ' fa('( l h:tl (~:t-ri( 'h r,)('ks have a h igh( ' r I" (hart ( ) t h o r ) ' . c k s wi th s i m i l a r fi~.
W a y ( ' v( 'h)( ' i t i( 's in )h( ' (.,)r(' a re (h't( ') '- m in ( ' d l'r()m l h(, ( 'ah 'uht t ( ' ( l 1)ulk m,) ( lu lus l)as( 'd ,)n ( '()ml),,sili()n a n d d ( ' n s i t y m(>(l('Is. Sin( '( ' th( ' c()r(' is m o l t e n ( lh( ' sh(,nr m()dul t ts .
= 0). 1",..,.,,, = ( K p)' :'. (1)
"17.,\1~1,1': 111
( ' tlI!;MI('\I, ANAI,YS]",5 I,'()1{ ,~] \g'l'hl'; .'~[()DI,iI~F, (WEI(IIIT PEItt'I';NT)
( )xi(le I)vr,)lit(, 3,1:tt's
F(%:, (t()l'(,
Hi()z 4 5 . t6 ;E).():I A 1 ..,( ):~ 3 . 5 4 :;. ()ll ICe( ) S;. 0 4 20 .5:1 .M~( ) 3 7 . 4 7 3 2 . :IS ( 'a( ) 3 .0, ' , 2 . (i(i K..,( ) 0 . 13 0. II l:('~()a 0 . 4 6 0. ~()
M e a n al()lni( ' w e i g h ( 22.(i, ';
]/(1~ (:i)Fp
.12.:12 3 .32
I : l . ,s2 37). If
2 .N9 (). 12 (). ,lg
2 2 . 1 2
"l 'h . m e a n a t m n i c we igh t ,)t' ( he m a n t l e m a y t)e found fr, m t a c (ms ido r ' l t i (m of it.,< ~)xido c (mq)os i l i (m as d i s c u s s e d in P a p e r 1. \V(' assure( , t h a t t h e m a n t h ' liltt3 1)(' m()d( 'h,d as a ierrost r ia l l )y r . l i t ( ' (l~inKw()()d, 1965) w i th an S T P dcn.'. i ly ~)t' :';.3S g: cm a w i l h ( ' . o u g h F ( ' ( ) a ( h l ( ' d as \vus t i t ( ' (p = .).745 ~: ('m a) l ( ) , ) h t a i n :t (hmsit.v ( , ( lu ivah 'n l l() lh( ' S T P Ul)l)('r-mantl(~ d(msi ly ~)t)tain(,(l l'r(ml lh(, lhe(m,l i ( 'a l (h,nsi iy in.dols. (',iv(,t, lh( ' r ( ' su l t in~ ( . , )mp(,si l i()n, th(. lll(,till a l (m l i c x~(.igh~" lllH.v lh ( 'n I). d ( ' l e r l ldn( ' ( t f,,r us(: i,~ (:;).
\V . will ( ' () input( ' s(,islniV v(,l()(.ily m , ) (Ms us ing the (.(mv(,('tiv(, t ,( 'mt)( 'r t t iur( ' l)r()tih' :m(l tw<) ( ' ( )mt)osi t i (ms 1)as(,(l ()n l:('.r,S a n d F( 'S (',)teN. Th(',~e r( ' l)r( 's(mt t x v , ) ( ' x t r ( ' m . s in ('~)r(' radius aml d( 'nsity. Tat)h ' I I I l ists the Ul)t)( , r -manth, ,)xi(Ic ( .~mqn)siti(ms a n d m e a n :~t()lni(' w('i~:hls l()r lh t , se models. T h . h)wer m : m l h ' is :t,'<sum('(t t(, h a v o :m rT~ (,(itml t(, l h a l ()1 l lw upt)( ' r m a n t h ' . Ftu ' th( , rm()r( ' , \vc i)r()t)(,,,<(' a lw.)-hLv('r(,d cru,,,I w i th :m Upl)('r I:ty(q' ,,f 20 ],:.n~ :IH([ l ' p = (i k m s e c . , . 1 a :{()-kin h m ( ' r lav(,r M l h / ' p - 7 k m s(,c. a l l h . u g h such an a s s u m t ) t i ( m is n<fl ne('( 's- >.ary l'~n' Ih( ' m( . l ( ' I s .
Sh('ar x~av(' v('h)('ili('s, I s , IH,:ly l)(' I',mm[ I)y ad. I ) l in~: a r(,:ts.)n:d)h' wdu( ' f(. ' P()iss(m's rally), a . / '( l 'v, I',,4), ()r l)v tlSillK Al~(h,r- s()n's (1!1(i71)) ('(luali~m ()1' ,~Ittt( ' I lS i l l g lh(', s(,ismi, t)tll'tlllllq(q' 0 ~ (2 lp ,~ )a . ( ' , iv('n I'1' an(t ¢, I ' s n l a y l h e n Ix' dctm'min( ' (1. l l~)~x.w'r, (he IIS(' ()1' | h i s ( ' l t l l t l t iO l l ()t" S( l l l ( ' (h. 's mH n(,c.s.'<aril.v ~:i,,,e imh, lwnd(ml re- suns t'()r Itl~. shear m()dulus (Amh'rs(m, 1!)7ti). Thus l 's is n,)l slr~mgly (..mstrain('(l.
Th(, rang;(, l(.r ( ' ( )mpr( 'ss i (mal a n d sho. tr wave v(qo('iti('s ( 'ah'u la lcd in the m a m . , r dvs(.ril)(,d al. ,v(, , I) ,mnd('d I)3 ('()r(. c,)mt)()si- l i .m~ (.1 l"('<.S and ICON, are sh()wn in l"iv:. 7. S(mw i m t . ¢ l a u t chara(,~.risti( 's ,d v( ,h. ' i ty m.. l ( ' ls at., r , 'adi ly at) lmr( 'ul, lCivst, lhc v:H'iqii~m ,,1 I)ossihl(' w,h)cil i ( 's in lhp M a ) ' l i a n m a m l ( ' is r ( ' l a t iv ( ' ly snmll l . ' ( ' aus ( ' ,)f lh( ' i n s v n s i t i v i l y .)f man ( l ( ' (h ,ns i ty t,> v:,)'.vi))~ ('(,)'(. (h 'nsil .v. W h i h ' m a m l ( ' (h,nsi- l i(,s at(' h)\~(q' f()r ili(' F('S ('()r(' ('()llll):Irc(| l()
I N T E R N A L S T R U C T U R E O F M A R S 8 1
0
i ! I 0 0 0 -
V e l o c i t y , k m / s e c 4 6 8
T
Vs
E
o
2000:-
3 0 0 0 , -
L ! 2 •
FIG. 7. Range of seismic wave velocities as a function of depth for both P and S waves (shaded areas), calculated using the densities shown in Fig. 6. The range is bounded by models with core compositions of FeS (dashed line) and FesaS (solid l ine .
the FessS cor(,, the mean atomic w(,ight is also lower and thus the velocities are higher. Second a large velocity contrast exists at the core-mantle boundary and this produc(,s a seismic shadow zone which is more prominent than that which exists in the Earth. Upper-nmntle (P,l) velocities range from 7.64 to 7.80 km/sec. A low-velocity zone associated with the density inversion
occurs at about 250 km. Velocity increases at the base of the mantle are due to the olivine-spinel phase change. In reality this boundary may be smeared out and less sharp than shown on the model.
Poisson's ratio generally varies from about 0.30 at the base of the crust to 0.35 near the core-mantle boundary. The high value reflects the enrichment of FeO in the Mart ian mantle.
To demonstrate the effects of these models on seismic wave propagation, travel times were calculated for the FeS core com- position. P - w a v e ray paths for a surface source (Marsquake or meteorite impact) shown in Fig. 8. Travel time versus distance for P waves is shown in the same figure. In the mantle, seismic ray propagation and the traw4-time curve are well behaved, except f,)r a reverse branch duc to the velocity increase at the bottom. There is no shadow zone from the upl)(,r-lnantle h)w-veloeity zone due t() the comp('nsating (,fleet of eurvature, i.e., r/V is m()notmd- tally decreasing with depth. Howev('r, r('la- tively h)wer amplitudes might t)e ('xl)e('t('d from 15 to 45 °. The most striking f("tture of these models, of course, is th(' shadow zone due to the core. For an F(,S core the rang(, is from 90 to 152 °, while for an F('ssS e()re this zone extends from 115 to 170 ° . Tim shadow zone for Mars ix larger than the
+ ; ; ! ! T -
1200 J( [ ; :
8ooi I~'0 ; J
I - i
: u I F
", 4QQ~ -i I J
i ~.- OL t _ . : ' Z : J ]
~ ~ / / 0 60 120 180 Delto , deg.
Fro. 8. B-wave ray paths and travel bime versus distance curves c-4culated from the FeS core veloeiW model shown in Fig. 7.
N2 , I ( ) I INST()N AN I) T( )KS( )Z
] ' ]al ' l t l 's ( h w (() a l~r(mt( 'r vd()eiiy ( , i n t r a s i t)(,tw(,(,n 1t1(' i n a n l h , tl.li(.| (,()r(,.
NI:XIXIAIIY A N I ) ( ! ( )N( ! I , l rSI ( )NN
\V(' hay( ' t)r( 's(ql(( '( l :t su i l ( ' ,)f t )h3s i ( 'a l l y r('alis(,i(, nl()(l(q,~ (if l h ( ' in t ( , r i ( ) r ()|' M:u 's i h l l l s a l i s f y t h e av . t i l a l )h , (,()l lst.rail i l .s. \ \ ' ha l has (!in(!rK(~d is a t)i('tur(' (If lh ( ' ~( : t r t ] : l i i h i l ( , r i l ) r ] ha l is s i m i l a r i~) t i i o t ' ]a r lh 's i l l l l l a l lV r(,sti( ,cls. ~() l l l ( , inl'(T('l l( '( 's t ha t Ct/ll ])(' i l ia( l ( , ()11 ( h i ' I )as is ()f l.tl('S(! m()d(,is : l r ( ' :
(1) T h ( , r n i a l h is t ( ) ry in()d(, ls in( l i ( !a i ( ' I l i a ( .~[al'S h a s ImSs( 'd i i s l ) ( ' ak ()f p v ( i l u l i ( ) n . [ [ ( ) w -
(,v('r, i l has i l l ] ast.h(,n()s])tl(,)'(' (a l l ( i l l ( 27)0
M n d( ' ( ' p ) a i l d , In( )s t l i k ( ' l y , (l ( ' ( ) .v ( ' ( ' i ing; h>w('r n m n t ] ( , . T h ( ' p h u l ( q m a y s i i l l I)(,
lll()(i( 'r:i(,( '[v a ( ' l i v ( ' l ( , ( ' l ( )n ic i l l ly .
(2) ~ l a i ' s h a s a ( 'or( ' xvi(ll ~i r a d i u s (if
: l t)()ul 1500 2 0 0 0 kn l ~.viih it ( ' ()nl l )()si l i ( )u ()li I l l ( ' l"(,-) ' i( 'h s h h , (if l h ( ' F(' I:(,~ z(,r()-
i ) r( 'ssur( ' ( 'ut( '( ' t i ( : ( '()nlt)()niti(Jn..~I~))'( ' s u l f u r - i ']('l i ('()l'('s (l() II()t S a t i s f y l.h(' ( ' ( ) l lSlr / t i l l l (ll" Ih( , l l l ( ) l l l l ' l l l (If i l w r l ia wh ih , s l l n t l h ~tl l ( ' l ) l lSl\ i ) l '~)v idhl~ a l l I?('( ) - r ich l i l a l i i [ ( ' . T I . , ])r('sl'ii( '( ' (d :l t i i ( )hol i (,()r(, is C() l isislcl i l w i i h all h i l ( , r n a l l y K('il( ' i ':tl( '(t in:. i~n(,l i( ' lind, h(M',-- ( 'w ' r , l t l ( ' l()\v (d)sorv( 'd f ie ld s l l 'Ol iTlh ni:ix" !)c ( iu(' i() oi l l l (q ' s l r a i i l i ( ' a l h ) l i w i l h h i l h c ( . ) r ( ' ()r less ( ,()ndu( ' l , iv( ' n l a i ( ' r m l ( lu( ' 1() ~i
h iK t i c r s u l f u r ( ' () l i I( ' l i t r('i~.Itiv(' I() 1 l i( ' Ea r l h 's ('()r('. Al t ( ' l ' l l a l ( ' lli()(l(qs ()I' I l i a~ l l c t i ( ' i i ( 'h l ~c i l ( ' ra l i()ll in f ( , r d i s i i n r l ]3' di f f ( ' i ' ( 'n! ] n i l , M s ( S l l ' , : i l l ~ W / I 3" ('1 (11., 1!)76).
(3 ) T h ( ' l i i ' t i l l l t ' ()f ~[a i 'S is ( ,n i ' i v lwd in 1:('() l ' e l a l i vc 1() ] ha { (d' Ih( ' ] ' ]a l ' lh : l l l l l ('()rr(','<l)()n(ls l() illl ( i l lv i l i ( ' ( . () l l i ])()sit i() i l (if' ; l l)()ul. l:()v;,. T l i v i i i a l i l h , is ( ,ssv i l l ia l l3 ]l(:l i l()~('l i( ', ')l lS w i t h ih ( ' <) l ivh l ( ' - i ( , -s l )h l ( ' l t it/as(' I I " l l lSJ l l ( i l l ()( '( ' t lrrJltg "/l ( | ( ' l ) ths r . i l l~ - i i l~ I 'r(dii 12()0 1<) 17)00 k in d( ' l ) ( 'ndc i i l ] ) r i i n . i r i l y ()ii l ho l ) rOsCl i l -d l i y l ( q n l ) c r a l u l e i))'()tih,. Th ( ' I l t)])( 'r I n : l l l l h ' has it ( l ( , i l s i l y i i lv ( , rs i ( ) l i (hi( ' i ( ) i l l ( ' ([()lll]li.:lli('(' ()[ i h ( ' r i l l a l (,xp.:tliSi()ll <)v('r ( '()lii])i '( 'ssi()li. This l l , i l i ] ) l ' l ' . t l -
l t l r ( ' i l i( 'r( 'as(' ( '()uht l)l'()(itl('(' :ill "lsl i i ( ' l i ( ) - st)ii( 'r( ' :ll :l d ( ' l ) lh (if a l ) ( ) t l l 27)0 k i l l . l.,)(':ll p . i r l i a ] i l i c l l i l i K ( ' ( I l l d i ) ( ' ( ' l l l " i l l lh is Z ( ) l i ( ' i [
snmll amoun(s (d' \valer (,xisi in the ul)por-
hI : l I l t ]c s3"s(cln. (4) Th( ' , ) l ' ( ' l i ( ' a l s ( ' i s ln i c w a v y w ' h . ' i t 3 "
l l l , ,( l( ' ls h a s ( ' d ,ill t h ( ' d ( ' n s i t y nl()(t( , ls ( , x h i h i t
m l r r ( ) w [ ) (m) lds (ill th ( . n r m t h ' v( . l ( ) r i i i ( , s ] m i
wid( , v a r i a t i ( , l l s i . t h ( ' ( ' ( ,re d ( ' p ( ' . ( h ' n i , ,n
( . ( , m t ) . s i ( i ( , n . Ts' l ) i ( , . / l U l ) l ) ( , r - u m l l i h , / ' . v( ,h , ( ' i ( i ( , s r a n ~ ( , f r ( ,n l 7.( i4 1() 7 .S0 k n l L~(,(..
, \ I l l , ' t l l I](! h ) w - v c h . ' i l V ZOlI( ' ([()pS It() |
pr ( )du ( ' ( ' a s l m d ( , \ x z()n(.. The' s h a t h m z - l i e
l~)r t} l ( ' ( '~)r( ' , I i~ ) \v ( ,v ( , r , o X l ( ' l l ( l s [ r ( ) l l l Ill)()[11
100 i,) 160 ° .
A'./¢' w/UeU / . i. 'oof, lu . r l (anic .mal3ses ,,f s ln fa re >ample~ from Vikin~ ~.itvs 1 :rod ;7 lmw' been re- p(.'led hy (~lark (l a/. (1976) and B'dr([ ¢'t el/. (197(i). The samples are character ized hy high i l ' .n, m(,der- :~l(, mngtleshun, ( 'ah'ium, and sulfur, nnd h.w aI:l- Illillllll: ttlilllldtl, llC(!s. , \ (.()ll:~):l,l'iS()l] i)f Ih0s(~ va, lll(~s with lh(' m:mI](' m()dels l)r()li()s(~(l in this t)al)(q' I'I'al)h. I l l ) sl.)x~s r(~as(m:d)](. :tgroein(,.l, est)e(.ia,lly l'.r lhe enr i rhed I"e. A si,nlde as(!en(ting (lifferenii;l,- t i , , . . f lhv in:mile ma, lerial will resull h, a s u b s ( a . - l i:ll dct)lelhm of .XI~() ( Ma(hg'azz% 1977: (:: . 'mi(,hael ,: . / . , 1!)74), ~ i v i . g . surl':..e . l iviu( ' C.ml).si l i (m (ff I I('H l'i?,' J~'ll I U0.
. \hhough sulfur is Ii.,i hwlu(h'd i)t our in:mile )..)del, lhe wh(de l)lanel is (mrivhed ill sulfur r(q~tliw, I . Earlh :tl)ulid:ul('es wh(.n lhe con. is in(eluded. l)(,n>ily ('(mshtoralhms preHude ~ 6 I()(< S():,, M})lllid/lll('('~ :('; ()}l~4(!l'V(!(I ili I}:( ~ ,>Ill'J'gl,('(' 5111ill)l(!N J'(ll'
IJl~, nmnI h'. Th(, r('l:l, iiv(,ly hilzh ('(m('(,tllr:Hi(m <,1' sulfur may
I)e (hie I(, :l i)r()vess t)r()l).)sed I)y lhig;ueldn (1976) in which sulfa((',~ :m(l (,ill(,r shits f()rnle(t hy l iho( . - H.mlh'aI wet~lheriug l)re('ilfiiai(' I t . in ~1 I)rine and :.'(' em'i('hed i . :~ lhin surf:w(, lay(.r.
,\( 'KN( )W I,I,H )( 151EN'I'S
\Ve w,,uld Ilk(, t(, (h:mk I)r. Alt)e)'i l lsui f(,r ihc Ihl ,r l l i t t l llllid(,],'- : l i l l l I ) r . .A . I I Io i l ] ) a i l I l y ]'(u' ('l)ll:- l i l i l iH~ Ihe Fay pa l i i s a i id l i':~vc]-I hno (' l lrv('. \ : : lhial) l t ! dis(,ilSSii)ns wet( , held w i l h M:u'( ' Mn,(b.!rll.zzo ll.nd I )rs. lh)t)erl [{ci~S(!lll)(q'g~ l{ot)eri [lllt4tl(~iiili> and .l()hn l~()l:7hi. V):(. ais() (h;mk ,Joan (h)nlberg f()r her c()nlri l)ulion i,) lhe (!()nll):ll:tlJ()iis. Tiffs r(!s(!arcli Wa,s s l lp l j i i l ' l ( 'd l iv X'.<\SA I l i idl !r ( ; i ' l l i i l N( IN-70Sl ali(I Sll i)(! i) i i lr: i( ' l (i(1437B i l i ld i ! r ( I ( )n l rac l N A ~ I - 97(1;I, l )a r i l y iu I)i'(,l)lt, i'al.i(m for il l(, ai::dy>i'. .)1' Vikil~g seisnlir (1:: :l.
I{ 1']1"1';I { EN C 1'>4
AiilXl.;NS> T. ,l. (197(i). Sh( . ' k way( ' (]:t l i i for l i l i t i l l lo nialeri~t ls (at)si I'IL(.I ]. 1~11.,4. 7 ' I ' I I I IN . . I /#ll'l'. (~t'IIIjII/],R. l ' . / . . 87, 32(L
INTERNAL STRUCTURE OF MARS 83
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