Dave Paige / Francis Nimmo

1
ESS 250 MARS

• Dave Paige / Francis Nimmo

2
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

3
Bulk Structure and Composition

• Cosmochemical arguments
• SNC meteorites
• Remote sensing
• In situ measurements
• Mass and Moment of inertia
• (Seismology)

4
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
5
SNC meteorites

• Shergotty, Nakhla, Chassigny (plus others)
• What are they?
• Mafic rocks, often cumulates
• How do we know theyre from Mars?
• Timing most are 1.3 Gyr old
• Trapped gases are identical in composition to
  atmosphere measured by Viking. QED.

2.3mm
McSween, Meteoritics, 1994
6
What do the SNCs tell us?
Mars

• 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 SNCs, we would have to simply assume
  an Earth-like or CI-like mantle

Earth
Dreibus and Wanke, Meteoritics, 1985
7
What do the SNCs tell us? (contd)
Estimated bulk Martian mantle

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

volatiles
iron
Note that Al,Mg,Mn are assumed chondritic
chalcophiles
Dreibus and Wanke, Meteoritics, 1985
These observations provide information about the
manner in which Mars accreted, and the likely
composition of the core
8
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 near- surface potassium
concentrations
http//photojournal.jpl.nasa.gov/catalog/PIA04255
9
Remote Sensing (2)

• 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

basalt
andesite
Bandfield et al, Science 2000 Using MGS-TES data
10
In Situ Measurements

• 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
Mars Pathfinder, 1997

• The two Viking landers (1976) employed similar
  technology but only on soil samples (not rocks).

11
Results
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
From Wanke et al., Space Sci. Rev., 2001
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)
12
Moment of Inertia

• I S m r2
• r is perpendicular distance from axis
• I of sphere 0.4 MR2
• Objects with mass concentrated in centre have
  I/MR2 lt 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?
13
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
r
f
where
R
So observations of the spacecraft orbit give us
J2
The rate at which the node precesses
14
Obtaining the MoI (contd)
2) Rate of planetary precession depends on (C-A)/C
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 MoIsmaller response to torque) So
the period of the precession is proportional to
(C-A)/C
Axis precesses
Sun
torques
3) Precession gives us (C-A)/C, measuring J2
gives us (C-A) So we can obtain C directly
15
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
16
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
Solid core (small k2)
Liquid core (large k2)
17
A liquid core (?) contd

• 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)

18
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

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
19
Gravity (contd)

• 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

20
Gravity Map
topography

• 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

Free-air gravity
From Zuber et al., Science 2000
21
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

r1 gt r2
Airy Isostasy
Pratt Isostasy
crust
mantle

• To a first approximation, isostatically
  compensated terrain produces no gravity anomaly
  at all, Dg0
• 2) Completely rigid crust. Here the surface load
  gives rise to a gravity anomaly Dg 2 G p r h
• where G is the gravitational constant,
• r is density and h is thickness

h
r
22
Gravity Signals (contd)

• 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 (100s 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
23
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

(A)

• Here D is the rigidity, w is the deflection, r is
  the density contrast between mantle and surface
  and L is the load
• The rigidity can be expressed as an effective
  elastic thickness Te

• Here E is Youngs modulus and s is Poissons
  ratio
• Te is measured in km and is a more intuitive
  measure than D

24
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
where D is the rigidity (see above), k is the
load wavenumber, Dr 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 D0).
25
Examples
gravity

• Large impact basins are generally isostatically
  compensated low rigidity

• Big volcanoes are mainly flexurally supported

sediments

• Some impact basins were flooded with dense lavas
  after the lithosphere cooled and strengthened,
  resulting in large positive gravity anomalies
  over negative topography - mascons

dense lavas
26
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

27
Theoretical Admittance

• At very short wavelengths, the admittance will be
  2pGr mGal/km (why?). So the short-wavelength
  admittance gives us the surface density r
  directly.
• The crossover wavelength from rigidly-supported
  to isostatically-supported depends on the
  rigidity D.

Admittance constant, depends on crustal density
(2prG)
28
Theoretical Admittance (contd)

• 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 r which make it difficult to estimate all
  three properties (although r 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).

29
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, r 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
30
Admittance results (2)
Large Te
Small Te

• Young features (e.g. Olympus Mons) have very
  large elastic thicknesses (Te gt 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 cant tell whether
  Tharsis is supported by convection or by
  variations in crustal thickness

Decreasing age
McGovern et al., JGR 2002
31
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 Zhong GJI, 2000
32
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

33
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)

Observed topo.
Model topo. (decays with time)
34
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 Earths 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

35
Magnetism (contd)

• Gravitational and magnetic potentials differ
  because magnetic fields are generated by dipoles

q
Magnetic
r
Gravity
p/2
r
d
-p/2
M
Magnetic dipole moment mdp m0 is a constant (but
depends on which units you use . . .)
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
36
Magnetic Observations

• From the early Mars spacecraft, we know that Mars
  does not have a global magnetic field like the
  Earths
• 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
37
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

Magnetic power spectra for Earth and Mars
Slope gives depth to top of Earths core
Mars
Mars crustal anomalies bigger
Earth
Mars lacks core field
Voorhies et al., JGR 2002
38
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 shorter-wavelength stripes, we
  couldnt see them (limitations of spacecraft
  altitude again).

Connerney et al., Science 1999
39
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 dont 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

40
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

41
Modelling Martian Evolution

• 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

temperature
top b.l.
depth
adiabat
bottom b.l.
CMB
this region determines the core heat flow
42
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

• Here k is conductivity, a 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 mantles 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

43
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.
44
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
Nimmo and Stevenson, JGR 2000
45
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.

46
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