Lecture 7: Continents and Orogeny

1. Lecture 7: Continents and Orogeny There is a general large-scale structure of continents: Old stable cores surrounded by younger deformed belts

2. Continents and Orogeny Where the craton is covered by a relatively flat-lying undeformed sequence of paleozoic and later sediments, it is called a platform. Within the platform, there may be roughly circular or oval regions that experienced prolonged subsidence and accumulated thick sedimentary basins. In between basins there may be regions that have long stood relatively high and accumulated little sediment. If roughly linear, these are arches; if roughly circular, these are domes

3. Continents and Orogeny 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) .

4. Continents and Orogeny

5. Continents and Orogeny

6. Continents and Orogeny

7. Rheology at Plate Scale

8. 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:

9. 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.

10. 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

11. 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 .

12. Continuum Mechanics: constitutive relations 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).

13. Continuum Mechanics: constitutive relations

14. Continuum Mechanics: constitutive relations

15. 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 pre-exponential terms which differ from one mineral to another. NOTE: olivine is strong, quartz and plagioclase are medium, salt is very weak

16. 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.

17. 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:

18. Continuum Mechanics: Brittle Failure 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:

19. 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 states where it does not. The Mohr envelope shows both the conditions where fracture occurs and the preferred orientation of fractures relative to s1.

20. 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.

21. Continuum Mechanics: Overall Strength envelopes 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:

22. 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.

23. 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

24. 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.

25. Regional Metamorphism: Facies and Zones However, in different bulk compositions, the same mineral (though probably of different composition if you go to the trouble of a microprobe analysis) 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.

26. 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.

27. 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.

28. 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

29. Mineral reactions and geothermobarometry

30. 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

31. 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