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

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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).

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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)

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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)

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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)

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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)

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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).

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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.

ESS 250 Winter 2003

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

ESS 250 Winter 2003

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