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 asthenosphere and may be moderately active tectonically. Mars has an F e - F e S core with a radius of
1500-2000 kin. The mantle is enriched in FeO with an olivine composition of about FoTa. Theoretically 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 variations in Vp in the core dependent on composition. The shadow zone due to the core is larger
than the Earth's.
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.
hi this paper we present a set of physical
models of the Martian interior based on
available data. Some of the results presented are extensions of work published in
Johnston et al. (1974; hereafter referred to
as Paper 1). However, improved theoretical
techniques, revised constraints, and additional 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
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 interpretation 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 AcademicPress, 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('Is..\ l)()ssihh' (.v,)luli()u Ifist()ry l)r()p()s('d l)y M ' i s u r s k y (1973)
a n d ils r(dati()n 1(, (h(,rmal m()(l(,ls is
dis(mss('d in Pat)(,r 1. I t a))l)(,ars that 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 tin.',
r('(luh'ing; r(,la( i v ( ' l y hi~;h initi'd (1,ng)(,ratur(,s. Th(, la(('r
sl:]~(,s ()[ ~ l a r t i a n ('v()luti()n sl1()w ('l)iS()(h's
()f l('(q()ni(' a n d v()h.uli(" a('tiviiy. 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 tim I)r(!s('nt stru('tur(' ()f Mars :Jr('
th(' mass, 31, :m(l m()m('ni-()[-h)('rl ia f't('l()r,
( ' / M a "2. Th('s(' r()ughly (h't('t'nfilw (h(' (l('ns i l y variation 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(' gravilali()n'd fMd (.I.,) in l(,)'ms ,)f
lh(' hy(h'()st:~ti(~ 'rod n()nhydr()stali(' ('()nt 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'
I~adius (kin)
Mean (]en~iiy (g/('m :~)
(',, M . 2
flea) ()f fu,<i(m (manll(~)(J/~)
('p (nl:ulll(') (.l'g°(')
Sllrf:|('(, l(,nll)tW:illlr(, ( o ( , )
I : ('()ll('(')ll)';Ili())l (1)l)l))
Th 'I" ra(i,)
K [ ~ )'a,(i()
Valll("
:i:)~!)
:i.!)(i
(1, :m.-).l
HI()
1 2
- -I()
I.')
I
5(),()()()
<d' ,~ kin, ('st]nmle U/:]/a ~ rauginV i'r~ml
al)oul 0.3?4 I() 0.370.
.\ualy,~i~ ()t" 1he ~ r a v i t y field and t(W)gr:tphy ~)|' Mars (Phillips 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 v o n q w n s a l e d at a relatively'
shallow d e p t h : "tnd lhe Th.trsis t)]a(eau,
( ' h r y s e , 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 feature
ass<)vialed xxil h :m ullc~)nll)elISaled Kravily
:HI(HIIilIv. Tll('se (I:llii Sll~(,'sl :t desm'il)li(m
,,f M a r s as :t sl)heroid m,'~rly in is~)stalic
e(luilibrium plus :m exlra m.~ss represented
h,v Ih(' Tharsis 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 staliv ( . m l r i l m t i ( m ~)i' 'l'harsis 1,(, ,I._,. Thus,
a s s u m i ] ~ t h a l t h p ri~zidily' stq)portin~
Tharsis e~mhl be rela×ed, lh,as('nl)(,r~ find~
thai th(' b(,dx', m)w in hb'dr<,~lativ ('(luilil)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
d y n ' t m i c flattening (':th'uhm'd :m' in much
1)(,tier :t~r(,oll/O111 llmn (h()~e f(ir ~Uher
I n ( . M s . Wp (hervt'()r(' adopt fiw this lmt)m •
th(' value ,)I'('r ,lit./2(d)taim'd I)3' IteasenI.,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 ) h e r . i. sm'h :~
way ax t,)mnt)h'lsize an iner('ased densily
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(,tl l):iranwl(,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,:I5" l)(' I'()t1111[ ill Ptll)('r I.
TIIIqlIMAL M()I )I':I,~
T h e implied (,volmhm 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('( ' :)
I N T E R N A L STRUCTURE OF MARS
. . . . .
I
i
1
_ _ ~
Melt
Partial
. . . .
7;5
~ - -
--1500°C______
~ - - --'~-'] . . . . . . . . . . . .
IO00 " E
\\x
/
\
/
\
2000
t
2000°C
,/
E3
Liquid Fe-FeS Core
3000
i
o
I
I
I
I
2
5
I
4
Time, b.y.
FIG. I. T h e r m a l e v o l u t i o n of t h e M a r t i a n interior as a f u n c t i o n of d e p t h ,~nd t i m e b a s e d on t h e
c o n v e e t i o n t e m p e r a t u r e calculations of H s u i et al. (1976). R e g i o n s of m a n t l e partial m e l t i n g a n d
core f o r m a t i o n are s h o w n . T h e s h u r t d a s h e d line r e p r e s e n t s the top of h)eal partial m e l t t~ssoci'~ted
with the convective currents.
molten or partially m()lten core. Condensation models of the solar nebula (Grossman
and Larimer, 1974) suggest t h a t the
Martian core is enriched in FeS, and thus
m a y contaiu small amounts of the heatproducing 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 time-dependent
energy equation in spherical geometry.
Since the process of core formation is not
well understood, its effect upon convective
structure 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 evolutionary history of Mars from
Hsui et al. is shown ill Fig. 1. It is assumed
t h a 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) m a y 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 upwelling of convective currents. If' wat(,r is
present near the Marti:tn surface, the
solidus will be suppressed and partially
molten regions m a y exist at a depth of
2 5 0 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 part 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()ItNSTON
A N I ) T()KSOZ
22~+-2000
O
o
D
-
g
/
~ooo/
r--
i
il
oL ......................
0
L
1000
2000
Depth, km
z
___
3000
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~'mp('r:ttttr('
distribttti(m
within
Mars.
q'lws(, ar(' u s e d in t h e 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 r e s h ( n v n in Vi~. 2.
Also s h o w n a r e t h e d r y - n m n t h ' s, d i d u s
(~'xtrap<thtt('d p u r i d o t 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 c u r v t ' <'tdculatt'd I>y l'ss('ln u t n ( 1 9 7 5 a , b ) . I n t h ' t t v()nvucti(,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 t y a m l seismiu,
w a w ' wqoeitit,s.
"I'ABIA': 11
UXll~Mt,Trl,Hts [~l,;I) IN I ) E N b l T Y +\IIHH.J.S
Parameter
Vahw,
Upper manile (l"oT;,I
]£o (Iniml')
dK/dT' (kl):u" °K )
, H T = 211°('1 (o(~
1.255
"l'h~,,.'<"~h.al d<,ttsity m,)¢h,ls f . r ~[at's can
b(, t.onstrtuq~,d ttsin~ ttw m:tss :rod m,,tn~'nl~ff-int't'tia t'a<'t~w as (.<restraints if :t I.:tmwl(,dff,e ~d" lh(' Iimntl(' 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 . w i n g th(' ttwhniqut* dt,sm'ib¢'d in P a p t ' r l
a m l 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'ttsity
pr<,fih's.
T t u ' (h'nsit.v n.,d('ls :m, d<'rive(I b y
ntmwriu~tll.\" int~'~;t"tting t.h(' uqu:tti(m (~f
Itydr+~st.ati,~ ~,quilibrittm wh('r~' t.h~' dm~sih',',
p, is t'el:tt~'d t(, t i m pr~,ssur(,, 1'. l<v a .
,,qtmti<~t~ (>1~ sl:tt.m assmn('d t~> tm tit('
is(~t.h,rm:tl
P;ireh . \ l u r n a g h a n
uqu_aI i(tn
(Hiruh, 193,'< 1952 : M u r t m f f h : t n , 19:}7) :
], =
~K,~(p,p,,)7
~
(p "p,,)~,ruq.
Ill)
I~. 17,1
~)
l,.wt'r tnanlle (spinel l"m:,)
1(0 (tnbar)
(
1)I,:N~I't'Y M( H ) E13,.4
2.1 ~ I0 :'
I .sg:I
!111'1!
A o Ind~:ur)
.(7' = 20°(7) {o(, I)
I .2
7.:1 :< 111 :'
K , 'rod p,, art' tim isoth(wtnal t}ulk m¢,dtthm
a n d d(qtsity :tl / ' = 0 a n d at'u u(mtpt~l('d :tt.
tit(' l('tnp('ratur('. 7', al d e p t h s ffiv('n t).\ Ih('
th('rm:tl m , ~ d ( ' l s s } . ~ v n in l,'iz. '2. 'l'h~'
th(,rnml (,xl)ansi(m (,~wlfi('i<,nt tn:ty It(' l ( , n t iwratttr( , d('lwnd<'nt "tnd is ]):ts~'d (>n <'xlr:tp-
INTERNAL
STRUCTURE
olated data from experimental measurements 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 / c m 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 starting model for the mantle, we
assume a composition of Fo75. Values of Ko
and d K / d T taken arc given b y Chung
(1971). The use of F()v5 as a mantle model
was based on preliminary density calculations in order to roughly estimate the S T P
mantle density, and thus its equivalent
olivine composition.
A phase change from olivine to spinel
phase m a y occur where the temp(,rature
profile cross(,s the P - T transition (Anderson, 1967a), as shown in Fig. 3. For the
conduction thermal model, this occurs at a
depth of about 1500 km and for the c(mvection model at a depth of 1200 kin. The
standard temperature and pressure spinel1)hase density is constrained to be 1 0 ~
higher than the S T P olivine-phase density.
2~o!
,
OF M A R S
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 b y the calculation. Core
compositions consid(,r(,d range from F('ssS
to FeS. An FeS composition has b(,en
proposed b y Lewis (1972) for the Martian
core, and F(,ssS is similar to compositions
proposed for the E a r t h (Ussehnan, 1975b;
King and Ahrens, 1973).
Usselman (1975a) has shown from ('xt)erimental determinations of the Fe FeS
eutectic t e m p e r a t u r e that a solid solid
phase transformation 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 Martian 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-
~
200;
]
7
o
V
/j:
//
........ 50[0
77
5 , 0o
~o'oo
ooo
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
Conduction Model
Convection Model
0.58
////
0.57
1/
1%1°
( //
/
.d//
,/1,
~/
0
0.36
~7Y
-5/,~
/ ,, 7
F
/
~
l/z__
0.55
/
E2000
/
'"
o
0
o 1500
/
+
/
/-
/-'5:
/.
//
I000
3.2
3_4
-.........
....
Pe85S
FesoS
EuT
-
FeS
3.6
3.8 5.2
3.4
3.6
STP Mantle Density, g/cm 3
3.8
Fit;..I. Hlnnd:u'd Ietnp('rattu'e :rod pr(,~m'(+ upptw-nt:uilh! +.tensity +h~,v,'t~ :i,< it l'tmut i<m of niimt0nl
(>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. T h e horizonltt[ dashed line is liie nl<miont-ot'-in(,l'lia f a c t o r ttse(] in liiis 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(,llltl(,raturt~ (hqJ('nd(,nt a n d is I:ll.:cn 11~ I/c till
(,xtral)()lntitm o[ valu<,s r('flt)rted {+)l" T irtm
(Basinsl<i t'/ a/., 1955), :iv iliscussi,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' ill(' ('<~ro m m . r i . l tins
l i t t h ' offo('t tit ( ' h ' v a t o d t)rossul'os I)ll the
physiual llaramctcrs uscd in 1he dcnsity
c:/lcuh/I i~ms.
l)onsity m,,d~,l,~ . r e .ah'ulatod t'<~r (.oru
c t m i l l o s i l i o n s tfl' li'(,.~,S, F(...+,N. cuto('li(', ;Ind
F('S for b o t h ('+m(hl(qiv(' and ('<mv('('tivu
toml/or;:~turo i)r<4ilos and tix(,d m(,atl dt,nsily.'
~i + lilt + l>htnct. In Fig. 4, m,~dds t,l' v:lryi.¢
( ' . l l a ->a n d I h . l n u a n d t ' n s i l y a r e t~l/Iainld/h'
hi uV('l'y caso w i t h Cl~l'O radii v : i r y i n g frlml
1500 to 2050 luu a n d b4TP n i a n t h ' d o n s i l i o s
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 l h o
E : / r t h ' s u p t w r 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 r c d i c t t ' d b y ccmduil~atitm
lllt~(l('ls {~l' Iho s<~l:il" n o h u h l (l.cxvis, 1 9 7 2 ) .
llow('vur,
Sllch n l i x h ' l s
u.ro in M a r s a h m /
n.'nI
t h a t prt,di.t . I I l"('~
w i t h oxtrt,nw onrich-
in F o i l ,fl' t h u m a n t h , alflx'ar I,~ t . '
int.t,nsi,,qt,nl
with t h o d a t a .
F(,(). (l"(,()
M / ( ) ) vahw.'~ t k l t M m ' d t'rtmi the (h,n~ity
nlo(iuls rlm~:l ~ t'rt,n 0.19 [or an fq'~ <.<~r(, t<~
0.27 t~w :in Fo~,~ (.t,rt.. I,owis (1972), <,t, Iho
('tin' ( . ( m l p o s i t i . n s :i+ro l)lottt,d :is it f u n ( ' t i o n
<,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+A3" sch'('t :t t h ' n s i l y
~Iiit'r h:tnd, I)rt'tli('t, <~ u v:ihlo <,t' 0.5. li i~
ulmt,si in.,~('.tmtflc that ~m/t, frt,(, ii'tm iv
l)l'('s('llt in ttH' M a r l h m u~l'(,.
F u r | h o r v a r i a l h m s in d,,n,4ty : l i l t ] ( ' I H ' ( ~
mt~(h'l tt):ll t)('st fits thc nl<mlunt-ol'-JHcrtia
f-whw. Vulid d.usil.\' nl,,dNs salist'yin/1 ~th
r:t(liu,~ 111:13" I)(* tflHain('d t'rom Fi~. -I t~.'
tlilToront ;Lssunlc<l v:/It.'s ot' ¢' M , / .
79
I N T E R N A L S T R U C T U R E OF MARS
Conduction M o d e l
~~.~.~---it
:7.--.-
7..-_.-:_.-_-..-..
- - -
I
I
4 -
I
3
'
lO00
0
_.
2000
Depth, km
l
3000
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 satisfying 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 temperature 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
8
reflected primarily in core radius, with relatively 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
I
Convection Model
I
i
7,1--
r
I
I
I
F[
7_i'
iJ
!
¸-
it
:1
I
i
I
il
c.~ 6;
-
^
>,
~5
4.~)F
o
............
................
...........
•m
T
looo
2o06
3000
Depth, km
FiG. 6. l)ensity profiles using temperature~ from the (.onvection model.
S0
,I( )H NST()N AN 1) TOKSOZ
s a n t o r(@()n wh(,r(, a s m a l l l)a)'ti:H l)I'pSstLr( '
()f w a t ( ' r (,)uhI indu('(, local p a r t i a l m(,Iting:,
as (tis('uss('d ('arli(,r.
VI,:I,()(HTY ANI) TIIAVI+:I~ TIMI': M()I)I,;I,N
S('isllli(! \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(, (,slimated
using: s(.ismi(' (,(itmli(ms ()I' s t a r ( '
( ' m p i r i ( ' a l l y d(,t(,rmin('(l I'())' t(,l'l'(,sl rial r,)('ks.
M , ) s l ()f)h(,s(' hay(' v(q,)(.iti(,s (h'l)('t,h'))t ,)n
lh(, m ( ' a n a t ( ) m h ' w e i g h t , ~;, a n d lh('
(h,z)silx, o.
Th('
lll()S|
('1)1ll111()11
s('i)Sllli('
('(l/ll[|i()ll
()t'
slttl(' is I~irch's law (P, irch, 1!)6~i), M i l c h is
()f Ih(' f()l'lll
I"
=
aOD) + bp.
(2)
Sim]n()ns (19(14) l)r()l)()s('d :~ V:('n(')':tliz('d
t'()l'ltl ()f Ill(' ('(luati()n f()r / ~ wav('s lhal \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 high('r I" (hart ( ) t h o r ) ' . c k s w i t h s i m i l a r fi~.
W a y ( ' v('h)('iti('s in )h(' (.,)r(' are (h't(')'m i n ( ' d l'r()m l h(, ('ah'uhtt('(l 1)ulk m,)(lulus
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()dultts.
= 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
A 1..,( ):~
ICe( )
.M~( )
( 'a( )
K..,( )
l:('~()a
4 5 . t6
3.54
S;. 04
37.47
3.0,',
0. 13
0.46
M e a n al()lni(' w e i g h (
]/(1~ (:i)Fp
;E).():I
:;. ()ll
20.5:1
32. :IS
2. (i(i
0. II
0. ~()
.12.:12
22.(i,';
22.12
3.32
I:l.,s2
37). If
2 .N9
(). 12
(). ,lg
"l'h. m e a n a t m n i c w e i g h t ,)t' ( h e m a n t l e
m a y t)e f o u n d fr, m t a c ( m s i d o r ' l t i ( m of it.,<
~)xido c ( m q ) o s 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 ierrostrial l)yr.lit(' (l~inKw()()d, 1965)
with an S T P dcn.'.ily ~)t' :';.3S g: cm a w i l h
( ' . o u g h F ( ' ( ) a ( h l ( ' d as \vustit(' (p = .).745
~: ('m a) l ( ) , ) h t a i n :t (hmsit.v (,(luivah'nl l()
lh(' S T P Ul)l)('r-mantl(~ d(msily ~)t)tain(,(l
l'r(ml lh(, lhe(m,li('al (h,nsiiy in.dols. (',iv(,t,
lh(' r('sultin~ (.,)mp(,sili()n, th(. lll(,till a l ( m l i c
x~(.igh~" lllH.v lh('n I). d('lerlldn('(t f,,r us(:
i,~ (:;).
\V. will ('()input(' s(,islniV v(,l()(.ily m , ) ( M s
u s i n g t h e (.(mv(,('tiv(, t,('mt)('rttiur(' l)r()tih'
:m(l tw<) ('()mt)ositi(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 lists the
Ul)t)(,r-manth, ,)xi(Ic (.~mqn)siti(ms a n d m e a n
:~t()lni(' w('i~:hls l()r lht,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 t h :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 s u c h an a s s u m t ) t i ( m is n<fl ne('('s>.ary l'~n' Ih(' m(.l('Is.
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,rs()n's (1!1(i71)) ('(luali~m ()1' ,~Ittt(' IlSillg lh(',
s(,ismi, t)tll'tlllllq(q' 0 ~ (2lp ,~)a. (',iv('n
I'1' an(t ¢, I's n l a y l h e n Ix' dctm'min('(1.
ll~)~x.w'r, (he IIS(' ()1' | h i s ('ltlltltiOll ()t" S(lll('
(h.'s mH n(,c.s.'<aril.v ~:i,,,e imh,lwnd(ml resuns t'()r Itl~. shear m()dulus (Amh'rs(m,
1!)7ti). T h u s l's is n,)l slr~mgly (..mstrain('(l.
Th(, rang;(, l(.r ('()mpr('ssi(mal a n d sho.tr
wave v(qo('iti('s ('ah'ulalcd in the m a m . , r
dvs(.ril)(,d al.,v(,, I),mnd('d I)3 ('()r(. c,)mt)()sili.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.'ity
m..l('ls at., r,'adily at)lmr('ul, lCivst, lhc
v:H'iqii~m ,,1 I)ossihl(' w,h)cili('s
in lhp
M a ) ' l i a n m a m l ( ' is r('lativ('ly snmll l . ' ( ' a u s ( '
,)f lh(' i n s v n s i t i v i l y .)f m a n ( l ( ' (h,nsity t,>
v:,)'.vi))~ ('(,)'(. (h'nsil.v. W h i h ' m a m l ( ' (h,nsil i(,s at(' h)\~(q' f()r ili(' F('S ('()r(' ('()llll):Irc(| l()
INTERNAL
Velocity,
4
0
STRUCTURE
8
T
Vs
!
i
I000
-
E
o
2000:-
3000,
-
L
!
2
81
occurs at about 250 km. Velocity increases
at the base of the mantle are due to the
olivine-spinel phase change. I n reality this
b o u n d a r y m a y be smeared out and less
sharp t h a n 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
M a r t i a n mantle.
To demonstrate the effects of these
models on seismic wave propagation, travel
times were calculated for the FeS core composition. 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. I n
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()notmdtally decreasing with depth. Howev('r, r('latively 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
km/sec
6
OF MARS
•
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
line.
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 b o u n d a r y 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
+
1200
;
;
J(
!
!
T
-
[;:
8ooi
I~'0
;
J
I
:
-
i
u
I
F
",
4QQ~
-i
I
J
i
~.~
~
/
/
OL
0
t
_ .
:
60
'
Z
:
120
J
]
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()IINST()N
]']al'ltl'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,lrSI()NN
\V(' hay(' t)r('s(ql(('(l :t suil(' ,)f t)h3si('ally
r('alis(,i(, nl()(l(q,~ (if lh(' int(,ri()r ()|' M:u's i h l l l
s a l i s f y t h e av.tilal)h, (,()llst.railil.s. \ \ ' h a 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
] h a l is s i m i l a r i~) t i i o t']arlh's ill l l l a l l V
r(,sti(,cls. ~()lll(, inl'(T('ll('('s t h a t Ct/ll ])(' ilia(l(,
()11 ( h i ' I)asis ()f l.tl('S(! m()d(,is :lr(' :
(1) T h ( , r n i a l h i s t ( ) r y in()d(,ls in(li(!ai(' 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 ill] ast.h(,n()s])tl(,)'(' (all(ill( 27)0
M n d('('p) a i l d , In()st l i k ( ' l y , (l ('().v('('iing;
h>w('r n m n t ] ( , . T h ( ' p h u l ( q m a y siill I)(,
lll()(i('r:i(,('[v a ( ' l i v ( ' l ( , ( ' l ( ) n i c i l l l y .
(2) ~ l a i ' s h a s a ('or(' xvi(ll ~i r a d i u s (if
:lt)()ul 1500 2 0 0 0 k n l ~.viih it ('()nll)()sili()u ()li
Ill(' l"(,-)'i('h s h h , (if l h ( ' F(' I:(,~ z(,r()-
i)r('ssur(' ('ut('('ti(: ('()nlt)()niti(Jn..~I~))'(' s u l f u r i']('li ('()l'('s (l() II()t S a t i s f y l.h(' ('()llSlr/tilll (ll"
Ih(, l l l ( ) l l l l ' l l l (If i l w r l ia w h i h , s l l n t l h ~tll('l)llSl\
i)l'~)vidhl~ all I?('( )-rich lilalii[('. TI., ])r('sl'ii('('
(d :l tii()holi (,()r(, is C()lisislclil
wiih all
hil(,rnally
K('il('i':tl('(t in:.i~n(,li(' lind, h(M',-('w'r, ltl(' l()\v (d)sorv('d field sll'OliTlh ni:ix"
!)c (iu(' i() oilll(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 i K t i c r s u l f u r ('()liI('lit r('i~.Itiv(' I() 1 li(' E a r l h's
('()r('. A l t ( ' l ' l l a l ( ' lli()(l(qs ()I' I l i a ~ l l c t i ( ' ii('hl
~cil('ral i()ll inf(,r d i s i i n r l ]3' diff('i'('n! ] n i l , M s
(Sll',:ill~W/I 3" ('1 (11., 1!)76).
(3) Th(' l i i ' t i l l l t ' ()f ~[ai'S is (,ni'ivlwd in
1:('() l ' e l a l i v c 1() ] h a { (d' Ih(' ]']al'lh :lllll
('()rr(','<l)()n(ls l() illl (illvili(' (.()lli])()siti()il (if'
;ll)()ul. l:()v;,. T l i v i i i a l i l h , is (,ssvilliall3
]l(:lil()~('li(',')llS w i t h
ih(' <)livhl('-i(,-sl)hl('l
tit/as(' II"lllSJll(ill ()('('tlrrJltg "/l (|('l)ths r.ill~iil~ I'r(dii 12()0 1<) 17)00 k i n d('l)('ndciil
] ) r i i n . i r i l y ()ii l h o l)rOsClil-dliy l ( q n l ) c r a l u l e
i))'()tih,. T h ( ' Ilt)])('r I n : l l l l h ' has it (l(,ilsily
iilv(,rsi()li (hi(' i()ill(' ([()lll]li.:lli('(' ()[ i h ( ' r i l l a l
(,xp.:tliSi()ll <)v('r ('()lii])i'('ssi()li. This l l,ili])l'l'.tlltlr(' ili('r('as(' ('()uht l)l'()(itl('(' :ill "lslii('li()st)ii('r(' :ll :l d('l)lh (if al)()tll 27)0 kill. l.,)(':ll
p.irlia] iliclliliK
('(Ill d i)('('lll" ill lhis Z()li('
i[
AN I) T ( ) K S ( ) Z
snmll a m o u n ( s (d' \valer (,xisi in the ul)porhI:lIlt ]c s3"s(cln.
(4) T h ( ' , ) l ' ( ' l i ( ' a l s ( ' i s l n i c w a v y w ' h . ' i t 3 "
lll,,(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 ) l d s (ill th(. n r m t h ' v(.l()riii(,s ] m i
wid(, v a r i a t i ( , l l s i . t h ( ' ('(,re d ( ' p ( ' . ( h ' n i ,,n
(.(,mt).si(i(,n.
Ts'l)i(,./l
Ul)l)(,r-umllih,
/'.
v(,h,('i(i(,s r a n ~ ( , fr(,nl 7.(i4 1() 7.S0 k n l L~(,(..
,\
Ill,'tllI](!
h ) w - v c h . ' i l V ZOlI(' ([()pS
It()|
p r ( ) d u ( ' ( ' a s l m d ( , \ x z()n(.. The' s h a t h m z - l i e
l~)r t}l(' ('~)r(', Ii~)\v(,v(,r,
oXl('ll(ls
[r()lll
Ill)()[11
100 i,) 1 6 0 ° .
A'./¢' w/UeU / . i.'oof, lu.rl(anic .mal3ses ,,f slnfare
>ample~ from Vikin~ ~.itvs 1 :rod ;7 lmw' been rep(.'led hy (~lark (l a/. (1976) and B'dr([ ¢'t el/. (197(i).
T h e samples are characterized hy high il'.n, m(,der:~l(, mngtleshun, ('ah'ium, and sulfur, nnd h.w aI:lIllillllll: 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. Ill) sl.)x~s r(~as(m:d)](. :tgroein(,.l, est)e(.ia,lly
l'.r lhe enrirhed 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), ~ivi.g . surl':..e .liviu(' C.ml).sili(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 liho(. H.mlh'aI wet~lheriug l)re('ilfiiai(' It.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 llsui f(,r ihc
Ihl,rllittl llllid(,],'- :lilll I)r..A.IIIoil ] ) a i l I l y ]'(u' ('l)ll:lililiH~ Ihe Fay paliis aiid l i':~vc]-I hno ('llrv('. \::lhial)lt!
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()nlril)ulion i,) lhe (!()nll):ll:tlJ()iis. Tiffs r(!s(!arcli
Wa,s sllpljiil'l('d liv X'.<\SA Iliidl!r (;i'lliil N(IN-70Sl
ali(I Slli)(!i)iilr:i('l (i(1437B ilildi!r (I()nlracl N A ~ I 97(1;I, l)arily iu I)i'(,l)lt, i'al.i(m for ill(, 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(' (]:tlii for lilitilllo
nialeri~tls (at)si I'IL(.I ]. 1~11.,4. 7'I'IIIIN..I /#ll'l'. (~t'IIIjII/],R.
l ' . / . . 87, 32(L
INTERNAL STRUCTURE OF MARS
ANI)ERSON, D. L. (1967a). Phase changes in the
upper mantle. Science 157, 1165 1173.
ANI)EItSON, D. L. (1967b). A seismic equation of
state. Geophys. J. 13, 9-30.
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