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)

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.

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

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.

Regional Metamorphism Facies and Zones

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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.

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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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