Transcript Lecture 6: Igneous classification, mid

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 triplejunction 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: HimalayaTibet-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? We’ll 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:
és11 s12 s13 ù
s = êês12 s 22 s 23 úú
êës13 s 23 s 33 úû
• 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 = (s11+s22+s33)/3 = (s1+s2+s3)/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 e˙ .
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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 Hooke’s Law: strain
is proportional to stress. For a simple one-dimensional spring, this is F = –kx.
For a general three-dimensional material,
s ij = Cijkle kl
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
[Young’s modulus E and Poisson’s ratio n]).
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Continuum Mechanics: constitutive relations
• The constitutive relation for simple Newtonian viscous flow is
s = he˙
where h is the viscosity (which usually has an Arrhenius
relationship to temperature: lnh µ1/T ).
• 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.,
-Qö
æ
e˙ = Cos expè ø
RT
– diffusion creep, which often uses grain boundaries to move
material around and so depends on the grain size of the rock:
3
Ds
-Qö
æ
n expè RT ø , n = 2 or 3
d
– At any particular condition, fastest mechanism dominates, so
dislocation creep takes over at high stress.
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e˙ = Co
Continuum Mechanics:
Plastic 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 preexponential 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:
s1 cosQ = s n cosQ + st sin Q
s 2 sin Q = s n sin Q - s t cosQ
Which we can solve for sn and st:
sn =
s1 + s 2 s 1 - s 2
2
st =
+
2
s1 - s 2
2
cos2Q
sin 2Q
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Continuum Mechanics: Brittle Failure
s1 + s 2 s 1 - s 2
s1 - s 2
sn =
+
cos2Q st =
sin 2Q
2
2
2
• This is the equation of a circle in the (sn, st) plane, with origin at ((s1+s2)/2,
0) and diameter (s1–s2)
• Note: (s1+s2)/2 is the mean stress, and (s1–s2) 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
Byerlee’s 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 pressuredependent 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 olivinerich mantle) and
the continental
case (30 km of
quartz-rich crust
on top of olivinerich 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
• 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
• 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
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
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 Tinsensitive 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 H2O+CO2 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
(
)
(
)
K = Gt Bi
( aFe )( aMg )
Gt
Bi
aMg
aFe
RT ln K = DGo = DH o - TDS o + PDV o
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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