ESS 250: MARS
Dave Paige / Francis Nimmo
ESS 250 Winter 2003
Lecture Outline
• Bulk structure and composition
– Geochemical constraints
– Geophysical constraints
• Properties of the crust and lithosphere
– Density, thickness, rigidity
– Magnetic properties
• Evolution of Mars through time
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Bulk Structure and Composition
•
•
•
•
•
•
Cosmochemical arguments
SNC meteorites
Remote sensing
In situ measurements
Mass and Moment of inertia
(Seismology)
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Cosmochemical constraints
• The solar photosphere and
carbonaceous chondrites (CI) have essentially the same
composition
• In the absence of any other
information, we can assume
that all solar system bodies
started with roughly this
composition
Basaltic Volcanism Terrestrial Planets, 1981
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SNC meteorites
• Shergotty, Nakhla, Chassigny (plus
others)
• What are they?
– Mafic rocks, often cumulates
• How do we know they’re from Mars?
2.3mm
– Timing – most are 1.3 Gyr old
– Trapped gases are identical in
composition to atmosphere measured by
Viking. QED.
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McSween, Meteoritics, 1994
What do the SNC’s tell us?
• Assume the abundances of a few
key elements e.g. Mg, Si, Al
(using geophysical,
cosmochemical and
observational constraints)
• Then use ratios to infer
abundances of other elements
• Without the SNC’s, we would
have to simply assume an Earthlike or CI-like mantle
Mars
Earth
Dreibus and Wanke, Meteoritics, 1985
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What do the SNC’s tell us? (cont’d)
Estimated bulk Martian mantle
iron
volatiles
Note that
Al,Mg,Mn
are assumed
chondritic
chalcophiles
1. Mars is iron-rich
relative to Earth
2. Mars is volatilerich relative to
Earth
3. Mars is depleted in
chalcophile
(sulphur-loving)
elements
Dreibus and Wanke, Meteoritics, 1985
These observations provide information about the manner in
which Mars accreted, and the likely composition of the core
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Remote Sensing Observations (1)
• K,U,Th are naturally radioactive and emit gamma rays as they decay
• Other elements may emit gamma rays due to excitation by incoming
cosmic rays
• The energy of these gamma rays is characteristic of the element
emitting them
• So an orbiting gamma ray spectrometer can estimate the abundances
of near-surface elements
Initial results from
Odyssey GRS showing
variations in nearsurface potassium
concentrations
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http://photojournal.jpl.nasa.gov/catalog/PIA04255
Remote Sensing (2)
• Different minerals have different thermal infrared spectra, controlled mainly by the
characteristic bond energies
• These energies can be measured remotely by an
infra-red spectrometer, and the surface
mineralogy determined
• Doing so is very tricky, mainly because the
effects of the CO2 atmosphere and atmospheric
dust have to be subtracted
• There is some ground-truth from Earth which
suggests that the technique can work
• It has been proposed that there are two types of
mineralogy present: a “basaltic” type and an
“andesitic” type. The latter is significant
because andesites on Earth are associated with
subduction zones.
• One problem with the data is that IR emissions
come from the top few microns, so it is not
clear what the subsurface is doing
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“basalt”
“andesite”
Bandfield et al, Science 2000
Using MGS-TES data
In Situ Measurements
APXS
Mars Pathfinder, 1997
•Pathfinder measured rock and soil
compositions using an Alpha
Proton X-Ray Spectrometer
(APXS)
•This works by irradiating a
sample with Alpha particles and
detecting the particles/radiation
given off
•The instrument appears not to
have been properly calibrated (!),
so the results have been subject to
revision
•The two Viking landers (1976) employed similar technology but
only on soil samples (not rocks).
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Results
From Wanke et al.,
Space Sci. Rev.,
2001
As well as the
calibration problems,
the rock surfaces
appear to be sulphurrich due to a kind of
“desert varnish”, so
the surface does not
reflect the interior
composition
The “soil-free rock” may be enriched in silica relative to basalts??
The soil looks like a mixture of basaltic (shergotty-like) material plus
this more silica-rich end-member
Silica-rich rocks are important because on Earth they are often (but
not always) associated with subduction (e.g. andesites)
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Moment of Inertia
• I = S m r2   r 2dV
• r is perpendicular distance
from axis
• I of sphere = 0.4 MR2
• Objects with mass
concentrated in centre have
I/MR2 < 0.4
• So I tells us about internal
structure
• Normally, we measure C, the
maximum MoI
r
m
C = max. moment of inertia
A = min. moment of inertia
I = (A + B + C)/3
How do we measure it?
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Obtaining the MoI
How do we get moment of inertia (C)? Three steps:
1) Obtain (C-A) from observations of orbiting spacecraft
2) Obtain (C-A)/C from observations of planetary precession
3) Use 1) and 2) to obtain C
1) Gravitational potential of a planet is given by
GM GMR 2
2
V 

J
(
3
sin
  1)
2
3
r
2r
CA
where J 2 
MR 2
r
R

So observations of the spacecraft orbit* give us J2
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*The rate at which the node precesses
Obtaining the MoI (cont’d)
2) Rate of planetary precession depends on (C-A)/C
Axis precesses
Sun
torques
Spin axis wobbles (precesses) with time
This is due to gravitational torques on a
non-spherical (flattened) object
The magnitude of the torque depends on
C-A (larger flattening = bigger torque)
But the response to the torque goes as 1/C
(larger MoI=smaller response to torque)
So the period of the precession is
proportional to (C-A)/C
3) Precession gives us (C-A)/C, measuring J2 gives us (C-A)
So we can obtain C directly
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MoI of Mars
• Inferred value of C is 0.3662 +/- 0.0017
• This is less than 0.4, so Mars has its mass concentrated
towards the centre – suggests an iron core
• Details of the structure depend on what elements are present,
but suggest a core radius 1300km-2000km
Models of Martian interior
from Bertka and
Fei, Science 1998.
They use various different
core compositions
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A liquid core (?)
• Just like the Earth, Mars experiences solid-body tides due to
the gravitational attraction of the Sun
• The response to these tides depends on the interior structure of
the planet
• In particular, a planet with a (partially) liquid core will deform
more than a planet with a solid, rigid core
• Because the shape of the planet affects its gravitational
potential, the tidal deformation of the planet can be measured
by observing the changes in spacecraft orbit
• The dimensionless response of the gravity field to the tides is
given by the tidal Love number k2.
Sun
Liquid core
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2
Solid core
(small k2)
A liquid core (?) cont’d
• Yoder et al. (Science 2003) have obtained a Love number which is
only consistent with an at least partially molten liquid core
Edge-on orbit
Love
Number
Angle to Sun
Face-on orbit
• Is this surprising? Maybe not, since the SNC evidence suggests
that there is a lot of sulphur in the core, and sulphur is a very good
antifreeze
• What does this mean about the Martian geodynamo? (see later)
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Gravity
• Variations in surface gravity cause
spacecraft orbit to vary
• Orbit variations cause doppler shift in
radio signals to Earth
• Doppler shift can be used to infer
line-of-sight (LOS) velocity changes
• With enough observations, the LOS
velocity changes can be used to
reconstruct the gravity field
Line-of-sight
(LOS) to Earth
z
spacecraft
surface
The importance of gravity measurements is that they provide one of
the few ways of inferring the subsurface properties of Mars.
Seismology is another (better) way, but it is not a priority for current
NASA Mars exploration
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Gravity (cont’d)
• Requires enormous precision (detect mm/s variations in
velocity, orbital velocity is km/s)
• Main limitation is spacecraft altitude (determined by
atmosphere, ~200km for Mars)
• Gravity signals are attenuated by a factor of
exp (- k z)
• where k is the wavenumber (=2p/l) and z is the spacecraft
altitude
• So it is hard to detect gravity signals with wavelengths shorter
than the spacecraft altitude
• Same goes for magnetic signals
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Gravity Map
• Tharsis Montes have
obvious signals
• Big basins show small
signals (compensated)
• Utopia & Isidis Basins
are mascons (see later)
• Dichotomy is not
obvious
• Anomalies in S
highlands are small
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topography
Free-air gravity
From Zuber et al., Science 2000
Gravity Signals
• There are two end-member cases which are easy:
• 1) Crust/lithosphere has no strength (isostatic compensation).
Here surface loads are supported by lateral variations in crustal
thickness or density
“Airy
Isostasy”
crust
mantle
1 >  2
“Pratt
Isostasy”
• To a first approximation, isostatically compensated terrain
produces no gravity anomaly at all, Dg~0
• 2) Completely rigid crust. Here the surface load gives rise to a
gravity anomaly Dg = 2 G p  h
h
where G is the gravitational constant,

 is density and h is thickness
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Gravity Signals (cont’d)
• A rigid load of thickness 1km and density contrast 1000 kg/m3
produces a gravity anomaly of 42 mGal
• 1 mGal = 10-5 m s-2. MGS gravity accuracy is a few mGal.
• So large gravity anomalies (100’s mGal) imply rigidly
supported loads, small gravity anomalies imply isostatically
supported loads
• So we can use gravity to infer how loads are supported on
other planets
• In order to understand this use of gravity, we need to
understand how loads are supported by the lithosphere . . .
load
lithosphere
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How are loads supported?
• A very useful model for how loads are supported assumes that
the lithosphere is elastic
• Elastic materials deform according to the following equation:
4
d w
D 4  gw  L( x)
dx
(A)
• Here D is the rigidity, w is the deflection,  is the density contrast
between mantle and surface and L is the load
• The rigidity can be expressed as an effective elastic thickness Te
3
e
ET
D
12(1   2 )
• Here E is Young’s modulus and  is Poisson’s ratio
• Te is measured in km and is a more intuitive measure than D
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How are loads supported? (2)
If you assume a sinusoidal load, then you can use equation (A) to
infer whether a load is closer to isostatic or rigid support.
If the rigidity is very low or the load wavelength is long, you get
(Airy) isostatic support; if the rigidity is very large or the load
wavelength short, you get rigid support.
The crossover from rigidly-supported to isostatically-supported
depends on the quantity
1

Dk 
1 

 Dg 
where D is the rigidity (see above), k is the load wavenumber, D is
the density contrast between mantle and crust and g is acceleration
due to gravity. How do we derive this?
This quantity gives the deflection due to a load, relative to the
isostatic deflection (it is small for large D, =1 if D=0).
4
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Examples
gravity
• Large impact basins are generally
isostatically compensated – low
rigidity
sediments
dense
lavas
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• Big volcanoes are mainly flexurally
supported
• Some impact basins were flooded with
dense lavas after the lithosphere cooled
and strengthened, resulting in large
positive gravity anomalies over
negative topography - mascons
Back to Gravity . . .
• Isostatic loads produce small gravity anomalies; rigidly supported
loads produce large gravity anomalies
• Short wavelength loads are rigidly supported; long wavelength
loads are isostatically supported
• The crossover wavelength depends on the rigidity of the lithosphere
• So the gravity as a function of wavelength contains information on
how loads are supported
• We form a quantity called the admittance, Z(k), which is the ratio of
the gravity to the topography at a particular wavelength:
Z(k) = g(k) / h(k)
• We can plot the calculated admittance from real data and compare it
to theoretical predictions to infer the rigidity, density and thickness
of the crust/lithosphere
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Theoretical Admittance
• At very short wavelengths, the admittance will be 2pG mGal/km
(why?). So the short-wavelength admittance gives us the surface
density  directly.
• The crossover wavelength from rigidly-supported to isostaticallysupported depends on the rigidity D.
Admittance depends on crustal thickness and Te
Admittance
depends on crustal
thickness,
membrane stresses
and convection
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Admittance constant,
depends on crustal
density (2pG)
From McKenzie et
al. EPSL 2002
At this wavelength, Dk4/Dg=1, giving the crossover from
isostatically-supported to rigidly supported
Theoretical Admittance (cont’d)
• The admittance changes slightly with crustal thickness: a
larger crustal thickness gives rise to a slightly higher
admittance (why?)
• There are tradeoffs between Te, crustal thickness and  which
make it difficult to estimate all three properties (although  can
be uniquely determined using short-wavelength data). Why
might this not be possible in practice?
• If there are subsurface loads, the non-uniqueness problem
becomes worse. The presence of subsurface loads gives rise to
incoherence between the gravity and topography.
• On a small planet such as Mars, the sphericity of the body is
important in the elastic deformation equations
• Finally, convection can be an important source of topography
at long wavelengths (and has a characteristic admittance).
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Admittance results (1)
We calculate the admittance by taking the ratio of the observed
gravity to topography as a function of wavelength: Z(k)=g(k)/h(k)
We compare the results with theoretical predictions to infer Te,  etc.
McKenzie et al., EPSL 2002
McGovern et al., JGR 2002
Spherical harmonic degree
Different approaches produce broadly
similar results, giving us confidence in
the underlying technique
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Admittance results (2)
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Small Te
Decreasing age
• Young features (e.g. Olympus
Mons) have very large elastic
thicknesses (Te > 100 km)
• Older features have lower elastic
thicknesses
• This may reflect a decline in heat
flux with time, like the increase in
rigidity with age for oceanic
plates on Earth
• The very longest wavelength
behaviour is difficult to interpret
e.g. we can’t tell whether Tharsis
is supported by convection or by
variations in crustal thickness
Large Te
McGovern et al., JGR 2002
Te and heat flux
• Terrestrial oceans show a
(rough) correlation between
plate age and Te
• This is (presumably) because
older plates are colder and
more rigid
• A good rule of thumb is that
the depth to the 600oC
isotherm gives you Te
• So by measuring Te we can
infer the heat flux
• The method works much less
well on terrestrial continents,
because of the thick crust
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Watts & Zhong
GJI, 2000
Crustal thickness
• We can use the admittance approach to infer the crustal
thickness, but there are tradeoffs with Te and density which
means the uncertainties are large
• An alternative is to assume a mean crustal thickness and use
gravity and topography to calculate the crustal thickness
variations. This is the approach of Zuber et al., Science, 2000
and does not require any assumptions about rigidity.
• They assume a mean value of 50km, so that the largest impact
basins would not penetrate to the mantle
Observed gravity
Observed topography
Assumed mean
crustal thickness
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Inferred crustal
thickness variation
Crustal thickness (2)
• If there are crustal thickness variations, these produce pressure
gradients which drive flow in the lower crust
• The rate of flow depends on the crustal rheology, temperature
and thickness
• To preserve the observed Martian topography, crustal flow
must not have been significant over 4 Gyr
Nimmo & Stevenson (2001)
• Given estimates of crustal
heat flux and rheology, this
approach places upper
bounds on the crustal
thickness of ~100km (thicker
crust produces more rapid
flow)
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Observed topo.
Model topo.
(decays with time)
Magnetism
• Spatial resolution limited in same way as gravity (e-kz term)
• E.g. terrestrial mid-ocean ridge stripe width ~10km, so they
cannot be detected by spacecraft at altitude ~400km
• Magnetic fields are similar to gravity fields, but interpretation is
complicated by fact that magnetization is a vector quantity
(while mass is a scalar)
• Magnetic field (vector) is measured in units of nT (nano-Tesla)
• The Earth’s magnetic field intensity (at the surface) is appx.
40,000 nT (varies spatially, slowly varies in time)
• Crustal magnetism is due to induced magnetization (from
background field) and remanent magnetization (acquired when
the rock last cooled below its Curie temperature)
• Typical crustal magnetic anomalies are ~100 nT
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Magnetism (cont’d)
• Gravitational and magnetic potentials differ because magnetic
fields are generated by dipoles
+p/2

r
Magnetic
r
Gravity
d
-p/2
 0 m cos 
W
4p r 2
M
M
U G
r
Magnetic dipole moment m=dp
Note lack of directional term
0 is a constant (but depends on which units you use . . .)
Magnetization of a material is its magnetic moment per unit volume
(SI units A/m)
Note that dipole mag. field (=dW/dr) falls off as the cube of distance
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Magnetic Observations
• From the early Mars spacecraft, we know that Mars does not
have a global magnetic field like the Earth’s
• A big surprise of MGS was that there are large, local magnetic
anomalies present
From Acuna et al,
Science 1999
Note the peculiar
projection
Largest terrestrial
magnetic anomalies
are ~100nT at similar
altitudes
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Comparison with Earth
• Amplitude of crustal magnetic
anomalies is ~10 times bigger on
Mars than Earth. Why?
• Power spectra give information on
wavelength-dependence of field
• Slope of crustal component of power
spectrum for Mars suggests mean
depth of magnetization ~50km
• Young MOR basalts have
magnetizations up to ~30 A/m, but
with age this reduces to ~5 A/m
• These magnetizations require layer
thicknesses of 15-100 km to explain
the observed anomalies
Mars lacks
core field
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Magnetic power spectra for Earth
and Mars
Slope gives depth to
top of Earth’s core
Mars
Mars crustal anomalies bigger
Earth
Voorhies et al., JGR 2002
Stripes?
• A potentially very significant discovery – magnetic stripes on
Earth are the best signature of plate tectonics
• Did Mars have ancient plate tectonics?
• NB the map projection accentuates the stripeyness!
•They look rather
different from terrestrial
stripes – larger
wavelength, larger
amplitude
•If there were shorterwavelength stripes, we
couldn’t see them
(limitations of spacecraft
altitude again).
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Connerney et al.,
Science 1999
What use are they?
• The fact that the large impact basins do not show any magnetic
anomalies suggests that the Martian dynamo was not operating
at the time these basins formed (~4 Gyr B.P.)
• The ancient Martian meteorite ALH84001 does show
magnetization, suggesting that the Martian dynamo operated
early in Mars’ history, and then stopped (see later)
• The depth of the anomalies tells us something about the
temperature structure of the crust (parts of the crust that
exceed the Curie Temperature will not retain magnetisation)
• How do we estimate the depth of the anomaliess?:
– Power spectral approaches (see before) ~50km
– Effects of impact craters (big ones show demagnetization, small ones
don’t – critical size depends on thickness of magnetized layer) ~50km
– Layer must be thick enough to produce correct amplitude – depends on
the magnetization of the material (see before) ~15-100km
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Evolution of Mars
•
•
•
•
•
What constraints do we have?
Te varies with age – can be linked to changing heat flux
Magnetic field operated early on, then stopped
Present-day state of core (at least partially molten)
Present-day crustal thickness (but how and when it formed is
uncertain)
• Volcanism – voluminous early on, but has carried on at a
reduced rate to the present day (difficult to quantify)
• Atmospheric isotopes – 40Ar contains degassing record,
integrated over Martian history
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Modelling Martian Evolution
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temperature
top b.l.
depth
• Convecting system consists
of adiabatic interior and
conductive boundary layers
• Heat transported across
conductive boundary layers
(e.g. core-mantle boundary
(CMB), lithosphere)
• Thickness of boundary
layers depends on the (Tdependent) mantle viscosity
• Radioactive heat sources
decay with time
• Mantle and core thermal
evolution can be tracked
adiabat
bottom b.l.
this region determines
the core heat flow
CMB
Core Behaviour (1)
• The core needs to be convecting in order to produce a dynamo
• The maximum heat flux it can get rid of without convection
occurring is given by the adiabat:
kgT
F
Cp
• Here k is conductivity,  is thermal expansivity, g is
acceleration due to gravity, T is temperature and Cp is specific
heat capacity. Typical Martian value ~15 mW m-2
• The heat flux out of the core is controlled by the mantle’s
ability to remove heat
• If the heat flux out of the core drops below the critical value F
then core convection will stop and the dynamo will cease
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Core Behaviour (2)
• If there is a solid inner core, convection can also be driven by
latent heat and chemical buoyancy as the inner core freezes
• For Mars, we know that the core is at least partly liquid
• Under Martian conditions, the adiabat and iron melting curve are
almost parallel (see below)
• So it is likely that the entire core is liquid
• Note the effect that sulphur has on the core melting temperature
Iron melting curves
and adiabat. Solid
inner core arises when
the adiabat and the
melting curve cross.
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adiabat
Figure courtesy Pierre Williams
Typical Martian Evolution
• Convection without plate tectonics (“stagnant lid”) is rather
inefficient at getting rid of heat – Mars cools slowly
• Surface heat flux tracks heat production by radiogenic elements
• Core heat flux drops rapidly – difficult to sustain a geodynamo
for ~0.5 Gyr
Adiabatic heat flux
Core heat flux
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Nimmo and Stevenson, JGR 2000
Sustaining a geodynamo?
• To sustain a geodynamo we need some way of increasing the
heat flux out of the core. Several possibilities:
• 1) Plate tectonics – mantle cools faster, which means that more
heat is extracted from the core. When plate tectonics stops, the
geodynamo will also cease. Unfortunately, not clear that plate
tectonics ever happened . . .
• 2) Potassium in the core – acts as an additional heat source.
But the half-life of potassium is long (1.25 Gyr) – means that
the dynamo lasts too long
• 3) A hot core – when the core differentiates it is likely to end
up hotter than the mantle (gravitational energy). A hot core
will increase the core heat flux temporarily, and can sustain a
geodynamo for 0.5 Gyr.
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Summary
• SNC chemistry and surface measurements can be used to infer
bulk and surface composition of Mars
• Observations of spacecraft orbit and planetary precession can
be used to derive moment of inertia and thus internal structure
• Gravity and topography can be used to infer lithospheric
rigidity, density and crustal thickness (admittance technique)
• Variations in lithospheric rigidity with time can be used to
infer change in heat flux
• Magnetic observations give indication of depth of magnetized
layer and suggest dynamo only lasted for first ~0.5 Gyr
• Sustaining a dynamo for this length of time may require either
a hot core or an episode of plate tectonics
• Both gravity and magnetic resolution are limited by the
altitude of the spacecraft
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