Lecture 7: Orogeny, Continental Dynamics, and Regional Metamorphism

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Lecture 7 Orogeny, Continental Dynamics, and
Regional Metamorphism

• Questions
• What is the general age and tectonic structure of
  continents?
• Why are the mobile belts on continental margins
  so wide, when oceanic plate boundaries are so
  narrow? What is this telling us about the
  rheology of continental lithosphere?
• What is the relationship between orogenic events
  and regional metamorphism, and what can you learn
  by studying metamorphic rocks?
• Tools
• Continuum and fracture mechanics
• Metamorphic petrology and thermodynamics (again)

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Lecture 7 Continents and Orogeny

• There is a general large-scale structure of
  continents
• Old stable cores surrounded by younger deformed
  belts

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Continents and Orogeny

• Stable continental regions, undeformed since
  precambrian time, are called cratons
  (particularly if Archean in age). Where
  precambrian crystalline (i.e., igneous and
  metamorphic) rocks are exposed, that part of the
  craton is called a shield (example Canadian
  shield).

• Where the craton is covered by a relatively
  flat-lying undeformed sequence of paleozoic and
  later sediments, it is called a platform. Parts
  of platforms may experience prolonged subsidence
  and accumulate thick sedimentary basins. In
  between basins there may be regions (arches or
  domes) that have long stood relatively high and
  accumulated little sediment.

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Continents and Orogeny

• The rest of continental area is made up of
  orogenic or mobile belts. These typically bound
  cratonic regions in the interior of aggregate
  continents and surround the cratons around most
  of the margins of each continent, where
  collisions, subduction, and rifting most often
  occur.

• Near the edges of platforms are found two other
  types of sedimentary basins that originated as
  parts of orogenic belts and became incorporated
  into the craton by later stabilization. These
  include
• orogenic foredeeps formed during orogenic events
  and filled with sediment shed off an orogenic
  mountain belt and
• passive continental margin sequences (example,
  Gulf Coast) .

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Continents and Orogeny

• To a certain extent, the distinction between
  craton and mobile belt is arbitrary, and relates
  only to the age since the last deformation event.
  It is nevertheless useful because once a mobile
  belt is stabilized, it can preserve details of
  geologic history for very long times.

Note this triple-junction here
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Continents and Orogeny

• The rocks making up orogenic belts are a
  combination of juvenile materials (new
  mantle-derived components) and reworked rocks
  from older terranes (from deformation in situ or
  by erosion and redeposition). Major continental
  provinces can be defined by age of deformation,
  rather than the age of the rocks as such (may be
  the same). Since not all the material in a new
  mobile belt is new, young mobile belts can be
  seen to truncate and incorporate parts of older
  mobile belts.

Here it is again
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Continents and Orogeny

• Orogenic belts can be thousands of kilometers
  wide (examples Himalaya-Tibet-Altyn Tagh system
  North American cordillera), which shows that the
  simple plate tectonic axiom of rigid plates with
  sharply defined boundaries is not that useful in
  describing continental dynamics.
• Really, rigid plate dynamics applies best to
  oceanic lithosphere only.

• Why do continents deform in a distributed fashion
  over wide zones? Because continental crust and
  lithosphere are relatively weak. And why is
  that? Well go through the long answer

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Rheology at Plate Scale

• It is possible to find clear examples where
  obviously weak mechanical properties of crust
  contribute directly to distributed deformation,
  as in this picture of the Zagros fold-and-thrust
  belt, which is full of salt (the dark spots are
  where the salt layers have risen as buoyant,
  effectively fluid blobs called diapirs or salt
  domes (the image is 175 km across).
• Broadly speaking, we can understand the
  difference between continents and oceans in this
  regard by considering the strength of granitic
  (quartz-dominated) and ultramafic
  (olivine-dominated) rock as functions of pressure
  and temperature

• This requires us to go into continuum mechanics,
  which describes how materials deform (strain) in
  response to applied forces (stress).

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Continuum Mechanics stress

• Stress is force per unit area applied to a
  particular plane in a particular direction.
  Generally (assuming no unbalanced torques),
  stress is a symmetric second-rank tensor with 6
  independent elements

• The diagonal elements are normal stresses the
  off-diagonal elements are shear stresses

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Continuum Mechanics stress

• We can always find a coordinate system in which
  the stress tensor is diagonal, which defines the
  stress ellipsoid, whose axes are the principal
  stresses s1, s2, s3.
• By convention, s1 is the maximum compressive
  (positive) stress, s2 is the intermediate stress,
  and s3 is the minimum compressive or maximum
  tensile (negative) stress.
• The trace of the stress tensor is independent of
  coordinate system and is three times the mean
  stress
• sm (s11s22s33)/3 (s1s2s3)/3.
• IF AND ONLY IF the three principal stresses are
  equal and the shear stresses are all zero, we
  have a hydrostatic state of stress and the mean
  stress equals the pressure.
• The stress tensor minus the diagonal mean stress
  tensor is the deviatoric stress tensor.
  Differential stress, s1-s3, however, is a scalar.

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Continuum Mechanics strain

• Strain, on the other hand, is the change in shape
  and size of a body during deformation. We exclude
  rigid-body translation and rotation from strain
  only change in shape and change in size count

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Continuum Mechanics strain

• Strain is always expressed in dimensionless
  terms.
• So a change in length L of a line can be
  expressed by e DL/L.
• A change in volume V is expressed as DV/V.
• A shear strain can be expressed by the
  perpendicular displacement of the end of a line
  over its length g D/L or by an angular strain
  tan y D/L.
• In general, strain, like stress, is a second-rank
  tensor (e) with six independent elements
• (in this case the antisymmetric component of
  deformation went into rotation, rather than the
  force balance argument for stress).
• It can also be expressed by a principal strain
  ellipse in a suitable coordinate system and be
  decomposed into volumetric strain and shear
  strain.
• The strain rate, or strain per unit time, is
  usually expressed .

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Continuum Mechanics constitutive relations

• The relationship between stress and strain or
  strain rate for a material is called the
  constitutive relation and depends in form on the
  deformation mechanism and in parameters on the
  material in question.

• Deformation can be either recoverable or
  permanent. Recoverable deformation is described
  by a time-independent strain-stress relation
  when the stress is removed, the strain returns to
  zero. This includes elastic deformation and
  thermal expansion. Permanent deformation includes
  plastic and viscous flow or creep as well as
  brittle deformation (faulting, cracking, etc.)
  and requires a time-dependent constitutive
  relation (perhaps expressing the relationship
  between stress and strain rate instead of strain).

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Continuum Mechanics constitutive relations

• Generally speaking, at low stresses solid
  materials respond elastically, up to some yield
  stress where plastic deformation or brittle
  failure begins.
• We usually describe deformation of a fluid-like
  material with no yield strength as viscous and
  deformation of a solid above the yield stress as
  plastic (particularly when it is accommodated by
  motion of dislocations in the solid lattice).
• Seismology is all about elastic deformation below
  the yield stress geology, on the other hand, is
  all about permanent deformations, plastic or
  brittle.
• The constitutive relationship for elastic
  deformation is Hookes Law strain is
  proportional to stress. For a simple
  one-dimensional spring, this is F kx. For a
  general three-dimensional material,
• where the fourth-rank elasticity tensor C has,
  for the most general material, 21 independent
  elements. For a material that is isotropic, i.e.
  its properties are independent of direction or
  orientation, there are only two independent
  elasticity parameters (such as Bulk Modulus K
  and Shear Modulus m or Youngs modulus E and
  Poissons ratio n).

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Continuum Mechanics constitutive relations

• The constitutive relation for simple Newtonian
  viscous flow is
• where h is the viscosity (which usually has an
  Arrhenius relationship to temperature
  ).
• For plastic deformation of solids, there are two
  broad classes of creep
• dislocation creep, accommodated by motion of
  defects through the crystals, which tends to
  follow a power law, e.g.,
• diffusion creep, which often uses grain
  boundaries to move material around and so depends
  on the grain size of the rock
• At any particular condition, fastest mechanism
  dominates, so dislocation creep takes over at
  high stress.

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Continuum MechanicsPlastic strength of rocks

• For our purposes, the key aspect of these laws is
  the exponential temperature dependence of plastic
  strength (differential stress s1-s3 at a given
  strain rate), and the pre-exponential terms which
  differ from one mineral to another. NOTE olivine
  is strong, quartz and plagioclase are medium,
  salt is very weak

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Continuum Mechanics Brittle Failure

• To complete a first-order understanding of the
  strength of crust and lithosphere, we need to
  venture into brittle rheology and fracture
  mechanics (briefly).
• Whereas plastic flow is strongly temperature
  dependent (weaker at high T), brittle deformation
  is strongly pressure dependent (stronger at high
  P), since (1) most crack modes effectively
  require an increase in volume and (2) sliding is
  resisted by friction, which is proportional to
  normal stress.
• Preview since P and T increase together along a
  geotherm, any rock will be weaker with regard to
  brittle deformation at the surface of the earth
  and weaker with regard to plastic flow at large
  depth the boundary between these regimes is
  called the brittle-plastic or brittle-ductile
  transition. Whichever mode is weaker controls the
  strength of the rock under given conditions.
  Please note Brittle-ductile transition is NOT
  the same as lithosphere-asthenosphere boundary!

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Continuum Mechanics Brittle Failure

• To talk about fracture strength, we need the
  all-important Mohr Diagram, which is a plot of
  shear stress (st) vs. normal stress (sn) resolved
  on planes of various orientations in a given
  homogeneous stress field.
• Start with two dimensions. Consider a plane of
  unit area oriented at an angle Q to the principal
  stress axes s1 and s2. At equilibrium, force (not
  stress!) balance requires

Which we can solve for sn and st
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Continuum Mechanics Brittle Failure

• This is the equation of a circle in the (sn, st)
  plane, with origin at ((s1s2)/2, 0) and diameter
  (s1s2)
• Note (s1s2)/2 is the mean stress, and (s1s2)
  is the differential stress!
• If we plot the states of stress resolved on
  planes of all orientations in two dimensions for
  a given set of principal stresses, then we get a
  Mohr Circle

-sn (tension)
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Continuum Mechanics Brittle Failure

• In three dimensions, all the possible (sn, st)
  points lie on or between the Mohr circles
  oriented in the three principal planes defined by
  pairs of principal stress directions
• So what? Well, experiments that break rocks show
  that the fracture criteria can be plotted in Mohr
  space also. The result is a boundary called the
  Mohr Envelope between states where the rock
  fractures and where it does not. The Mohr
  envelope shows both the conditions where fracture
  occurs and the preferred orientation of fractures
  relative to s1.

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Continuum Mechanics Brittle Failure

• For s1 5To, (To tensile strength) many
  materials follow a Coulomb fracture criterion, a
  linear Mohr envelope at positive s1. In the Earth
  overburden pressure means s1 is always
  compressive.
• Coulomb fracture is defined by
• st So sntanf
• where So is the shear strength at zero normal
  stress (aka cohesive strength) and f is the angle
  of internal friction.
• An empirical modification is Byerlees Law, a
  two-part linear fracture envelope that works for
  many rocks. Another common behavior is the
  Griffith criterion, which is a parabolic Mohr
  envelope.

The bottom line of Coulomb fracture behavior for
our purposes is that is shows that the fracture
strength of rocks increases (linearly) with
mean stress or effective pressure (why effective
pressure? Because pore pressure pushing out on
the rock exerts a negative effect on mean stress
and therefore weakens the rock).
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Continuum Mechanics Overall Strength envelopes

• If we map the temperature-dependent plastic
  strength and the pressure-dependent brittle
  strength of rocks onto a particular geotherm
  (i.e. temperature-depth curve), we have a
  prediction of the strength of the crust and
  lithosphere as a function of depth.

• For the oceanic case (6 km of basaltic crust on
  top of olivine-rich mantle) and the continental
  case (30 km of quartz-rich crust on top of
  olivine-rich mantle), it looks like this

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Continuum Mechanics Conclusion

• So, why are oceanic plates rigid but continents
  undergo distributed deformation?
• Because continental crust is thick and quartz has
  a weak plastic strength. Although the thermal
  gradient in continents is lower, and at large
  depth the lithosphere is colder and stronger,
  what really matters is that we do not encounter
  olivine, which is strong in plastic deformation,
  until larger depth and therefore much higher
  temperature under continents.
• We can also understand how strain concentration
  to plate boundaries works
• Mid-ocean ridges are weak because adiabatic rise
  of asthenosphere brings the hot, weak plastic
  domain almost to the surface the brittle layer
  is only 2 km thick
• Subduction zones may be weak because high fluid
  pressures lower the mean stress across their
  faults and promote brittle behavior to large
  depths.

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Regional Metamorphism

• One major consequence of continental deformation
  is regional metamorphism.
• Orogenic events drive vertical motions and
  departures from stable conductive geothermal
  gradients. Shallow crust is deeply buried under
  nonhydrostatic stress and undergoes coupled
  chemical reaction and ductile deformation. The
  same event at later stages may uplift deep crust
  into mountain ranges where erosion can unroof it
  for geologists to view.
• Generally, in map view the surface will expose
  rocks of a variety of metamorphic grades (i.e.,
  peak P and T), either because of differential
  uplift or because igneous activity heated rocks
  close to the core of the orogeny. The sequence of
  metamorphic grades exposed across a terrain is
  called the metamorphic field gradient and is
  characteristic of the type of orogeny.
• we have already seen the blueschist path of
  low-T, high-P metamorphism leading to eclogite
  facies, associated with the forearc of subduction
  zones.
• In the arc itself, the dominant process is
  heating by large scale igneous activity, and we
  see a relatively high-T path leading to granulite
  facies.
• In collisional mountain belts, burial is dominant
  and what results is an intermediate P-T path
  called the Barrovian sequence

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Regional Metamorphism Facies and Zones
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• Metamorphic conditions can be defined by zones,
  the appearance or disappearance of particular
  minerals in rocks of a given bulk composition.
  The line on a map where a mineral appears is
  called an isograd, and ideally expresses equal
  metamorphic grade. Thus, along a field gradient
  in pelitic rocks (Al-rich metasediments, from
  shaly protoliths), Barrow defined the following
  sequence of isograds, which corresponds to a
  particular P-T path in experiments on phase
  stability in pelitic compositions.

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Regional Metamorphism Facies and Zones
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• However, in different bulk compositions, the same
  mineral (though probably of different
  composition) appears under different conditions,
  so zones are not very general
• a mineral isograd recognizable in the field is
  not necessarily a surface of constant metamorphic
  grade.

Pelitic Rocks
Basaltic Rocks
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Regional Metamorphism Facies and Zones
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• This leads to the concept of a metamorphic
  facies, which is meant to express a given set of
  conditions independent of composition.
  Confusingly, however, the facies are generally
  named for the assemblage typical of basaltic
  rocks equilibrated at the relevant conditions.

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Regional Metamorphism Facies and Zones
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Facies are bounded by a network of mineral
reactions it gets complicated
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Mineral reactions and geothermobarometry

• Some mineral reactions precisely indicate
  particular P-T conditions, especially those
  involving pure phases.
• Thus the andalusite-kyanite-sillimanite triple
  point and univariant reactions are based on the
  stable structures of the pure aluminosilicate
  (Al2SiO5) phases. No other constituents dissolve
  in these minerals, so nothing except kinetics
  affects the reactions.
• Most reactions involve phases of variable
  composition and hence it is necessary to measure
  phase compositions and use thermodynamic
  reasoning to interpret the results in terms of P
  and T.
• A metamorphic assemblage can be bracketed into a
  given region of P-T space using the mineral
  reactions that bound the stability of the
  observed assemblage. Continuous mineral reactions
  involving solutions are used to quantify T or P.
• A reaction that is very T-sensitive and
  relatively P-insensitive makes a good
  geothermometer. A reaction that is P- sensitive
  and relatively T- insensitive makes a good
  geobarometer. A combination of (at least) two
  such reactions yields a thermobarometer, an
  estimate of T and P.

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Mineral reactions and geothermobarometry

• Many important metamorphic reactions are
  dehydration or decarbonation reactions like
• Talc 3 Enstatite Quartz H2O
• Mg3Si4O10(OH)2 3 MgSiO3 SiO2 H2O
• Muscovite Quartz Sillimanite Orthoclase
  H2O
• KAl2(AlSi3)O10(OH)2 SiO2 Al2SiO5 KAlSi3O8
  H2O
• Dolomite Quartz Diopside 2 CO2
• CaMg(CO3)2 SiO2 CaMgSi2O6 2 CO2

• For pure minerals and fluids, these reaction
  boundaries can be precisely defined
  experimentally. However, the conditions at which
  they actually occur are affected by several
  factors
• Solid solution, e.g. the presence of Fe (as a
  component in enstatite and diopside) and of Na
  (as a component of orthoclase), affects the
  reaction equilibria.
• The activity of components in the fluid
  drastically affects the reaction. This includes
  both the presence or absence of a free vapor
  phase, and the composition of the H2OCO2 fluid
  that may be present.

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Mineral reactions and geothermobarometry
As an example, consider the reaction Muscovite
Quartz Sillimanite Orthoclase H2O In
the absence of Na, the only variable phase in the
system in the vapor. The diagram shows the
reaction for a pure-H2O system, in which the
partial pressure of H2O equals the total
pressure. It also shows the location of the
reaction when the vapor is 50 CO2. If the vapor
were an ideal solution of CO2 and H2O, the
partial pressure of H2O would then be half the
total pressure and the curve would move up by a
factor of two. In fact, the vapor is not quite
ideal, so this is only an approximation, as shown.
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Mineral reactions and geothermobarometry

• Consider a reaction such as
• Mg-garnet Fe-biotite Fe-garnet Mg-biotite
• Mg3Al2Si3O12 KFe3(AlSi3)O10(OH)2
  Fe3Al2Si3O12 KMg3(AlSi3)O10(OH)2
• At equilibrium we can write a relationship
  between the reaction constant and the
  thermodynamic properties of the pure mineral end
  members

which shows that DSo expresses the T dependence
and DVo expresses the P dependence of the
equilibrium. The Clapeyron Slope (?T/?P)K
DVo/DSo tells you whether the reaction is going
to be sensitive to P, T, or both. DHo, on the
other hand, determines the spacing of equal K
contours, and so the sensitivity of the reaction
compared to analytical precision.
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Mineral reactions and geothermobarometry

• For garnet-biotite Fe-Mg exchange,
• DVo should be small, since Fe and Mg fit in the
  same sites with little volume strain of the
  lattice.
• DSo should be relatively big because of Fe-Mg
  ordering phenomena.
• Indeed, the calibrated geothermometer equation in
  this case is
• 3RTlnK 12454 cal (4.662 cal/K)T (0.057
  cal/bar)P

• So a measured K of 0.222, for example
• If at 5 kbar, implies T 661 C
• If at 10 kbar, implies T 682 C
• Relative to typical T uncertainty of 50 C
  quoted for most geothermometers, this is indeed
  insensitive to pressure.
• The opposite case could be, e.g., Ca exchange
  between garnet and plagioclase, which has a big
  volume change due to coupled Ca-Al subsitution
  and so is a good barometer.

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