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Lecture 7: Orogeny, Continental Dynamics, and Regional Metamorphism


Consider a plane of unit area oriented at an angle Q to the principal stress ... Plastic strength of rocks Continuum Mechanics: Brittle Failure Continuum ... – PowerPoint PPT presentation

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Title: Lecture 7: Orogeny, Continental Dynamics, and Regional Metamorphism

Lecture 7 Orogeny, Continental Dynamics, and
Regional Metamorphism
  • Questions
  • What is the general age and tectonic structure of
  • 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)

Lecture 7 Continents and Orogeny
  • There is a general large-scale structure of
  • Old stable cores surrounded by younger deformed

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
  • 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.

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
  • 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
  • orogenic foredeeps formed during orogenic events
    and filled with sediment shed off an orogenic
    mountain belt and
  • passive continental margin sequences (example,
    Gulf Coast) .

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
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
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

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).

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

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
  • 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.

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

Continuum Mechanics strain
  • Strain is always expressed in dimensionless
  • 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
  • The strain rate, or strain per unit time, is
    usually expressed .

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).

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
  • 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).

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.

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

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!

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
Continuum Mechanics Brittle Failure
  • This is the equation of a circle in the (sn, st)
    plane, with origin at ((s1s2)/2, 0) and diameter
  • 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)
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.

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
  • 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

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).
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

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

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
  • 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
  • In collisional mountain belts, burial is dominant
    and what results is an intermediate P-T path
    called the Barrovian sequence

Regional Metamorphism Facies and Zones
  • 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.

Regional Metamorphism Facies and Zones
  • 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

Pelitic Rocks
Basaltic Rocks
Regional Metamorphism Facies and Zones
  • 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.

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

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
  • KAl2(AlSi3)O10(OH)2 SiO2 Al2SiO5 KAlSi3O8
  • 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
  • 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.

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.
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

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.
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
  • 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
  • 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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