ESS 250 Winter 2003
Dave Paige / Francis Nimmo
ESS 250: MARS
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
ESS 250 Winter 2003
Bulk Structure and Composition• Cosmochemical arguments• SNC meteorites• Remote sensing• In situ measurements• Mass and Moment of inertia• (Seismology)
ESS 250 Winter 2003
Cosmochemical constraints• The solar photosphere and
carbonaceous chondrites (C-I) 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
ESS 250 Winter 2003
SNC meteorites• Shergotty, Nakhla, Chassigny (plus
others)• What are they?
– Mafic rocks, often cumulates• How do we know they’re from Mars?
– Timing – most are 1.3 Gyr old– Trapped gases are identical in
composition to atmosphere measured by Viking. QED.
McSween, Meteoritics, 1994
2.3mm
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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 Earth-like or CI-like mantle
Mars
Earth
Dreibus and Wanke, Meteoritics, 1985
ESS 250 Winter 2003
What do the SNC’s tell us? (cont’d)
Dreibus and Wanke, Meteoritics, 1985
Note thatAl,Mg,Mnare assumed chondritic
Estimated bulk Martian mantle
volatiles
chalcophiles
1. Mars is iron-rich relative to Earth
2. Mars is volatile-rich relative to Earth
3. Mars is depleted in chalcophile (sulphur-loving) elements
These observations provide information about the manner in which Mars accreted, and the likely composition of the core
iron
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Remote Sensing Observations (1)
http://photojournal.jpl.nasa.gov/catalog/PIA04255
• 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 fromOdyssey GRS showingvariations in near-surface potassium concentrations
ESS 250 Winter 2003
Remote Sensing (2)“basalt”
“andesite”
Bandfield et al, Science 2000Using MGS-TES data
• Different minerals have different thermal infra-red 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
ESS 250 Winter 2003
In Situ Measurements
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
APXS
•The two Viking landers (1976) employed similar technology but only on soil samples (not rocks).
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ResultsFrom Wanke et al.,Space Sci. Rev.,2001
As well as the calibration problems, the rock surfaces appear to be sulphur- rich 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-memberSilica-rich rocks are important because on Earth they are often (but not always) associated with subduction (e.g. andesites)
ESS 250 Winter 2003
Moment of Inertia• I = m r2 • 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
C = max. moment of inertiaA = min. moment of inertia
rm
How do we measure it?
I = (A + B + C)/3
dVr 2
ESS 250 Winter 2003
Obtaining the MoIHow do we get moment of inertia (C)? Three steps:1) Obtain (C-A) from observations of orbiting spacecraft2) Obtain (C-A)/C from observations of planetary precession3) Use 1) and 2) to obtain C
1) Gravitational potential of a planet is given by
)1sin3(2
223
2
Jr
GMRr
GMV
where22 MRACJ
r
R
So observations of the spacecraft orbit* give us J2 *The rate at which the node precesses
ESS 250 Winter 2003
Obtaining the MoI (cont’d)2) Rate of planetary precession depends on (C-A)/C
Sun
torques
Axis precesses Spin axis wobbles (precesses) with timeThis is due to gravitational torques on a non-spherical (flattened) objectThe 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 andFei, Science 1998.They use various different core compositions
ESS 250 Winter 2003
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.
SunSolid core(small k2)
Liquid core (large k2)
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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
Face-on orbit
Angle to Sun
Love Number
• 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)
ESS 250 Winter 2003
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
surface
spacecraft
Line-of-sight(LOS) to Earth
z
• With enough observations, the LOS velocity changes can be used to reconstruct the gravity field
The importance of gravity measurements is that they provide one ofthe few ways of inferring the subsurface properties of Mars.Seismology is another (better) way, but it is not a priority for currentNASA Mars exploration
ESS 250 Winter 2003
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 (=2) 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
From Zuber et al., Science 2000
topography
Free-air gravity
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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
crust
mantle
1 >2“AiryIsostasy”
“PrattIsostasy”
• To a first approximation, isostatically compensated terrain produces no gravity anomaly at all, g~0
• 2) Completely rigid crust. Here the surface load gives rise to a gravity anomaly g = 2 G h where G is the gravitational constant, is density and h is thickness
h
ESS 250 Winter 2003
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 . . .
loadlithosphere
ESS 250 Winter 2003
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
4
xLgwdx
wdD
• 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
)1(12 2
3
eETD
• Here E is Young’s modulus and is Poisson’s ratio• Te is measured in km and is a more intuitive measure than D
(A)
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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
14
1
g
Dk
where D is the rigidity (see above), k is the load wavenumber, 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).
ESS 250 Winter 2003
Examples• Large impact basins are generally
isostatically compensated – low rigidity
gravity
sediments • Big volcanoes are mainly flexurally supported
denselavas
• Some impact basins were flooded with dense lavas after the lithosphere cooled and strengthened, resulting in large positive gravity anomalies over negative topography - mascons
ESS 250 Winter 2003
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 2G mGal/km
(why?). So the short-wavelength admittance gives us the surface density directly.
• The crossover wavelength from rigidly-supported to isostatically-supported depends on the rigidity D.
Admittance depends on crustal thickness and Te
Admittance depends on crustal thickness, membrane stresses and convection
At this wavelength, Dk4/g=1, giving the crossover fromisostatically-supported to rigidly supported
From McKenzie et al. EPSL 2002
Admittance constant, depends on crustal density (2G)
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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).
ESS 250 Winter 2003
Admittance results (1)We calculate the admittance by taking the ratio of the observedgravity 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
ESS 250 Winter 2003
Admittance results (2)• 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
McGovern et al., JGR 2002
Small TeLarge Te
Decreasing age
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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
Watts & ZhongGJI, 2000
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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
Inferred crustal thickness variation
Assumed mean crustal thickness
ESS 250 Winter 2003
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
• 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)
Observed topo.
Model topo.(decays with time)
Nimmo & Stevenson (2001)
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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
ESS 250 Winter 2003
Magnetism (cont’d)• Gravitational and magnetic potentials differ because magnetic
fields are generated by dipoles
20 cos
4 rmW
r
MGU
d+p/2
-p/2
r
M
r
Magnetic dipole moment m=dp0 is a constant (but depends on which units you use . . .)
Magnetic Gravity
Note lack of directional term
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
ESS 250 Winter 2003
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
Magnetic power spectra for Earth and Mars
Voorhies et al., JGR 2002
Earth
MarsSlope gives depth totop of Earth’s core
Mars crustal anomalies bigger
Mars lackscore field
• 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
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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!
Connerney et al.,Science 1999
•They look rather different from terrestrial stripes – larger wavelength, larger amplitude•If there were shorter-wavelength stripes, we couldn’t see them (limitations of spacecraft altitude again).
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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
ESS 250 Winter 2003
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
ESS 250 Winter 2003
Modelling Martian Evolutiontemperature
dept
h
top b.l.
bottom b.l.
adiabat
CMB
this region determinesthe core heat flow
• 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 (T-dependent) mantle viscosity
• Radioactive heat sources decay with time
• Mantle and core thermal evolution can be tracked
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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:
pCgTkF
• 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
ESS 250 Winter 2003
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
Figure courtesy Pierre Williams
adiabatPure iron melting
Fe+14 wt% S melting
Iron melting curves and adiabat. Solid inner core arises when the adiabat and the melting curve cross.
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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
Core heat flux
Adiabatic heat flux
Nimmo and Stevenson, JGR 2000
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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.
ESS 250 Winter 2003
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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