PART II. Deformation of plates 1. Overview : Questions ! 2. - - PowerPoint PPT Presentation

PART II. Deformation of plates

• 1. Overview: Questions !
• 2. Feedbacks and localization: 1) grainsize, 2) temperature, 3) segregation of melt/

fluids / weak phases. (This week !)

• 3. Strength Envelopes: Background, successes, failures... Alternatives?
• 4. Viscoelasticity: Cheese/Some thermodynamics/Earth

Part II: Rheology & Dynamics

• 1. Stress, strain, forms of suffering (4-1)
• 2. Viscoelasticity, Thermodynamics (4-6)
• 3. Shear Zones (4-8)
• 4. Thermal structure & strength profiles (4-13)
• 5. Strength profiles 2. (4-15)

ToDo 4: 1-D Thermal profiles ToDo 3: 0D shear zones/ wires ToDo 5: Strength Profiles Part II: Rheology & Dynamics

• 1. Localization(4-6)
• 2. Thermal structure & strength profiles (4-13)
• 3. Viscoelasticity, Thermodynamics (4-15)

ToDo 4: 1-D Thermal profiles ToDo 5: Strength Profiles OVER AMBITIOUS:

• 1. How does the lithosphere deform? How does the response to forces

depend on the cause of the forces? i.e. the time scale of the change in the force?

• 2. What are the appropriate ways to think about the boundary conditions
• f regional deformation (gravitational or constant force, constant velocity,

constant energy) ?

• 3. How do we extrapolate micro-mechanisms to plate-scale processes ? At

what length scale is deformation “homogeneous” ? How, why and where does deformation localize?

• 4. What are the principles that determine the patterns of lithospheric

deformation (at different depths/thermodynamic conditions) ? To what extent is understanding these patterns a deterministic problem?

• 5. How do we describe (mechanically, not kinematically) deformation in

the Earth ?

• 6. What are the structures and dynamics that lie beneath the seismogenic

regions? How do we infer processes at depth from the patterns of seismicity?

• 1. Overview: Questions

Why does Earth have plates?

potential feedbacks in viscosity: c. d.

Geochemistry Geophysics Geosystems G

3

G

3

uniform and moderate yield stress: strain rate weakening, melt weakening + asthenosphere:

η(T) η(σ) η(d) η(φ)

VISCOSITY DOWNWELLING + WATER! temperature stress grain size melt

442

• M. R, Drury et al.

PAGEOPH,

Lanzo ~ ~ Sierra Alpujata

my/onites

~ 4km C

mylon/#es I 4 km

~i Bouchera

~i ,~.'-~ Balmuccla Erro-Tobbio

d ~ f 2kin

Figure l Schematic maps of structural domains and foliation trajectories in upper mantle peridotite massifs. Arrows show azimuth of stretching lineations. Three main types of structural domain can be recognised, coarse-granular domains, tectonite domains and mylonile domains. Tectonite domains form the largest

fraction of most massifs. (a) Shamah massif, Oman, after CEUI-ENEER

et al. (1988); (b) Lanzo, W. Alps,

after BOVDIER (1978); (C) Sierra Alpujata, Spain, after TUBIA and CuEvAs (1987); (d) Beni Bouserra, Morrocco, after REUBER

et al. (1982); (e) Balmuccia,

• W. Alps, after BOUDIER

et al. (1984); (f) Mount

Tugello block of the Erro-Tobbio peridotite, Ligurian Alps, after VISSEI~S

et al. (1991).

are not always the "wall rock" of tectonite shear zones. In the case of the Ronda massif (VAN DER WAL and VISSERS, 1991) the coarse-granular microstructure

• verprints high-pressure tectonite and mylonite shear zones. This composite domain
• f high-pressure tectonites, mylonites and granular peridotites then forms the wall

rock to a later tectonite shear zone developed at lower pressures (VAN DER WAL and VISSERS, 1991). Mylonitic peridotites occur as sub-planar zones in massifs and xenoliths with widths from 0.005 to 1000 metres (NICOLAS and POIRIER, 1976; BROD~E, 1980; REVBER et al., 1982; KRUHL and VOLL, 1978/79; BOUDIER et al., 1988; NORREL and HARPER, 1988; DRURY et al., 1990; HOOGERDUIJN STRATING et al., 1991). In kimberlite xenoliths mylonitic microstructures are developed in two distinct rock types (HARTE, 1983). "High temperature" xenoliths deformed at 1200-1600~ are homogeneously deformed, although, most of these xenoliths are only tens of centimetres in diameter. "Cold xenoliths" deformed at lower temperatures of 800-1100~

• ften contain very narrow shear zones (BoULIER and NICOLAS, t973;

PAGeoph, 1991

PAGEOPH, Vol. 137, No. 4 (1991) 0033-4553/91/040439 2251.50 + 0.20/0 9 1991 Birkh~iuser Verlag, Basel

Shear Localisation in Upper Mantle Peridotites

MARTYN R. DRURY, 1 REINOUD L. M. VISSERS, 2 DIRK VAN DER WAL, 2

and EILARD H. HOOGERDUIJN STRATING 2

Abstract--Upper mantle peridotite bodies at the earth's surface contain relict structures and

microstructures which provide direct information on the role and the mechanisms of shear localisation in the upper mantle. Deformation which occurred at high temperatures (T > 950 _+ 50~ is relatively homogeneous within domains ranging in scale from a few kilometres to a few tens of kilometres. Below 950 + 50~ strain is localised into centimetre to several hundred metre wide shear zones which commonly contain hydrated mylonitic peridotites. The microstructures developed in the peridotites suggest there is a correlation between the occurrence of shear localisation and the occurrence of strain softening and brittle deformation processes. The most important strain softening processes are inferred to be structural and reaction induced softening. Structural softening processes include dynamic recrys- tallisation and strain-induced transitions from dislocation creep to some form of grain-size-sensitive (GSS) creep. Reaction induced softening is related to the formation of fine grained polyphase reaction products which deform by GSS creep and the formation of weak sheet silicates such as phlogopite, chlorite, talc and antigorite. From experimental studies these softening processes and brittle deformation processes are inferred to occur mainly at temperatures less than about 910 _+ 160~ This temperature range is inferred to be a significant rheological transition in the upper mantle. Below 910 _+ 160~ deformation during orogenesis may be accommodated by an anastomosing network of hydrated mylonitic shear zones with a distinct, perhaps weak, rheology. At higher temperatures strain is accommodated in much wider deformation zones. On the scale of the lithosphere the degree of localisation may be different to that determined at the scale of the peridotite massif. An anastomosing network of hundred metre wide mylonitic shear zones forming 0.05-0.3 by volume fraction of the mantle lithosphere at T < 950~ could accommodate inhomogeneous or homogeneous bulk deformation depending on the spatial distribution and ordering of the mylonite zones. The higher temperature deformation at deeper levels in the mantle could be markedly inhomogeneous being concentrated in shear zones with widths in the range of 2-20 kin, alternatively these zones may widen significantly during deformation, resulting in a decrease in the degree of localisation with increasing bulk strain. Key words: Deformation, localisation, softening, mantle, peridotite, olivine.

Introduction

It is well established that shear localisation is an important process during deformation in the upper and middle crust (WroTE et al., 1980; BREWER et al., Research School of Earth Sciences, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia. 2 Department of Geology, Institute of Earth Sciences, State University of Utrecht, PO Box 80.021, 3508 TA Utrecht, The Netherlands.

Continental geotherms, constrained by P-T estimates of xenolith equilibration (McKenzie, Jackson & Priestley, EPSL 2005)

Density, pressure and temperature (from Equations of state and thermal conductivity)

• 1. Thermal structure and strength profiles

Strain localisation in the subcontinental mantle — a ductile alternative to the brittle mantle

• J. Precigout a,⁎, F. Gueydan a, D. Gapais a, C.J. Garrido b, A. Essaifi c

Tectonophysics 445 (2007) 318–336

Return to this image:

• 1. Localization (grain size, temperature, other...)
• 1. Very basic (my level) introduction to thermodynamics of

irreversible processes (non-equilibrium thermodynamics) (and a note on the wattmeter?)

• 2. Localization by grain size reduction:

Observations of the Stack of Glencoul (Kohlstedt & Weathers, 1979), application and interpretation of the wattmeter and piezometer.

• 3. Localization by thermal feedback. Simple model, more complex

models...

• 4. Localization by melt segregation: rocks, experiments, theory.
• 5. Interactions of feedbacks...

(amplifying and damping situations)

• 1. Intro to non-equilibrium, irreversible thermodynamics

Work Heat System Surroundings System

dU = dpQrev + dpW dpQrev = TdS dpW = −PdV + (σdε) dU = TdS − PdV

U = internal energy Q = heat flow S = entropy W = work dp = path-dependent, inexact differential T, P = intensive state variables S, V, U, H, F, G = extensive state variables

Enthalpy: H = U + PV dH = TdS + V dP H = H(S, P) Helmholtz Free Energy: F = U − TS dF = −SdT − PdV F = F(T, V ) Gibbs Free Energy: G = H − TS dG = −SdT + V dP G = G(T, P)

The thermodynamic potentials (whose gradients are forces) ( for mechanical problems, use G, F ; because the entropy is subtracted ? )

System Reservoir System Reservoir

Reversible entropy change

i

dSe = dQrev T (the Φ

dQ = dQ =

C = dQ dT dQ = TdS ( )

dS = dSi + dSe dSe = dQrev T (the external flow of entropy) dSi = Φd T (the internal source of entropy) Φd = (σijεij)d(the viscous energy dissipation) dSi = dWd T dWtot = dWstored=st + dWdiss=d dWd = dWtot − dWst

Irreversible entropy change

Joule’s expts: relation between work and heat Entropy generator (above, entropy is generated inside; here, entropy is generated in the reservoir, by heat flow:

The recrystallized grain size represents the budget of energy being stored in grain boundaries and energy dissipated by flow. total work/dt = energy stored + energy dissipated in creation

• f new GB

fraction of dislocation creep all diffusion creep + net grain growth/dt = growth rate + reduction rate

Paleowattmeters: A scaling relation for dynamically recrystallized grain size

Nicholas J. Austin* Brian Evans*

GEOLOGY, April 2007

=

• f1(d, σ) = ˙

d+ + ˙ d− = Kg exp (−Qg/RT) d1−p

p

− d2

cγ σλ ˙

εdis f2(d, σ) = ˙ εdif(d) + ˙ εdis(σ) = A1d−p exp(−Q1/RT) + A2σn exp(−Q2/RT)

• 1. Observation: The Stack of Glencoul !...
• 2. Localization by grain size reduction (and by thermal

feedback?)

• 2. Localization by grain size reduction:

120 m 50 m 10 m 1 m 0 m

? grain elongation shows gradual strain localization (and thus strain rate enhancement) :

from: “Atlas” localization by gradual grain size reduction ? (wattmeter) localization by formation of new grains at constant rxl grain size, and gradual increase in the volume fraction of new small grains (Glencoul, FB hypothesis)

Observation Interpretation

Piezometer: Wattmeter: Piezometer: Wattmeter: drx arx drx arx d0 “Typical” Mylonite: Stack of Glencoul: stress stress strain rate stress stress strain rate distance distance d0

. σε The paleowattmeter may also explain the pro- gressive reduction in recrystallized grain size from shear-zone margin to core (i.e., from proto- mylonite to ultramylonite). If the average grain size at a given position in the shear zone is a func- tion of stress only, then the stress within the shear zone is inferred to increase toward the core. If grain size refl ects the local power dissipated, then, for constant stress conditions, those regions with higher strain rates will have smaller grain sizes. Paleowattmeters: A scaling relation for dynamically recrystallized grain size

Nicholas J. Austin* Brian Evans*

GEOLOGY, April 2007

• 3. Shear heating instabilities

System System adiabatic: isothermal: ˙ ε = Aσn

c exp(−Q/RT)

Φd = σc ˙ ε ˙ T = Φd ρcp to solve: ε =

• t

˙ εdt T =

• t

˙ Tdt constant stress:

0.01 0.02 1200 1220 1240 time (years) Temperature (C) Olivine, =100 MPa, d=15 µm 0.01 0.02 0.5 1 1.5 time (years) Strain 0.01 0.02 100 200 300 400 time (years) Dissipation (Pa/s) 0.01 0.02 0.06 0.08 0.1 0.12 time (years) dislocation/diffusion 500 1000 1100 1120 1140 time (years) Temperature (C) Olivine, =30 MPa, d=1000 µm 500 1000 2 4 time (years) Strain 500 1000 2 4 6x 10

time (years) Dissipation (Pa/s) 500 1000 400 500 600 time (years) dislocation/diffusion

Experimental conditions: Warm Lithosphere conditions:

• 4. Localization by Melt/Fluid/Weak phase segregation
• Fig. 25. An aerial IR photograph of part of the Oman ophiolite near

Muscat, adapted from Braun & Kelemen (2002). Here we show only the trace of the dunites (light grey) surrounded by harzburgite (dark grey).The morphological similarities to our experiments (namely that smaller bands tend to join with larger bands at different angles) should be noted. tes, e

• ndi-

ing e e ;

mantle: crust:

c d Shearing Melt Out of the Earth: An Experimentalist’s Perspective on the Influence

• f Deformation on

Melt Extraction

David L. Kohlstedt1 and Benjamin K. Holtzman2

• Annu. Rev. Earth Planet. Sci. 2009. 37:561–93

50 μm

b a

20º

a b

a b c

Increasing shear stress

500 μm

c

What is the feedback ?

• D. Stevenson, GRL, 1989

η(φ) ∇P ∇ dφ

direct shear:

500 m

PI-1020, olivine + chromite + 4% MORB, = 3.5, = 30 - 60 MPa

lenses (melt- depleted) networks (melt-rich bands)

"anastomosing networks"

• D. Stevenson, GRL, 1989

η(φ) ∇P ∇ dφ

c

• livine + 3% MORB

alignment, no segregation strong segregation

Zimmerman et. al., 1999

฀฀c฀฀k

• k = permeability

฀ solid viscosity ฀฀fluid viscosity

c >> th c = th ~

compaction length

Holtzman et al., 2003: experimental demonstration of stress-driven segregation in simple shear: Oman dunites (after Braun + Kelemen)

1000 2000 100 200 300 400 500

Band spacing, δs (μm) Compaction length,

a b

δc (μm) Band spacing, δs (μm) Compaction length, δc (μm)

• Olv. + chr. + 2% MORB
• Olv. + chr. + 6% MORB
• Olv. + chr. + 12% MORB
• An. + MORB
• Olv. + albite

m=0.15 m=0.30 1000 2000 100 200 300 400 500

• Olv. + chr. + 4% MORB

The angle of the bands is a function of the stress exponent, n

Magma dynamics: coupled two-phase flow

Katz et al., Nature 2006:

η(φ, ˙ ǫ) = η0eα(φ−φ0) ˙ ǫ

1−n n

II

Non-newtonian constitutive relation, with stress exponent, n

α β abvb (1-ab)vn

vt

vt vb vt (b) (c) (d)

1 3

v1 v3

B

α

v

1

v

3

N

β

(a)

α

(1-ab)*L ab*L

hb hn ht

Viscous Energy Dissipation and Strain Partitioning in Partially Molten Rocks

BENJAMIN K. HOLTZMAN1*, DAVID L. KOHLSTEDT1 AND JASON PHIPPS MORGAN2

(a)

esis The gle lower

• f

and . han- en stress this with

• f

we and evolve. the the to first

R.A. Parsons et al. / Earth and Planetary Science Letters 267 (2008) 548–557

surface tension stores energy, that then drives relaxation

• f the structures when the applied stress is removed.

current questions: similar to the processes that control grain size, during melt segregation, the system stores energy in a structure (i.e. energy stored as surface tension in the melt bands, and at the same time, is minimizing entropy production rate by segregating and strain partitioning between melt-rich and melt-poor regions (and minimizing stress gradients in the system)

dSi = dWd T dWtot = dWstored=st + dWdiss=d dWd = dWtot − dWst

in disl., grain bdy + melt dist. in diff creep + x*disl creep in bands + lenses

d

Bands 1 mm

γ=1

Bands 1 mm

c

b

r=0 r=R

R H

R a d i a l s e c t i

• n

r

Tangential section

HGG,"'

=&(0,!"#$%&>,&(,#%$//

intuition: all aspects of the microstructure (grain size, melt fraction) evolve with segregation (space and time), and all the rheological processes depend

• n stress... so we would expect the segregation rate

to increase with increasing stress, strain rate or energy input into the system.

dγ dS dt = dS dγ (˙

γ)˙ γ ??

h r

(a)

h r

R H tangential section

radial section

r

• d
• S. front

df df

bands

(b)

1 mm

• b )

(c) (d)

Primary observation: migration of segregation front

h r

(a)

h r

R H tangential section

r a d i a l s e c t i

• n

r

• d
• S. front

df df

bands

(b)

1 mm

• b )

(c) (d)

• f )
• Band front position

2 constant strain rate expts. show evidence for different segregation rates in the “macroscopic” rheological data:

For the lower strain rate, weakening (i.e. segregation)

• ccurs at higher

strain, consistent with γc decreasing with decreasing stress. high strn. rate low strn. rate (and grain size is constant, so peak stress is not defined by gs reduction)

scaling from laboratory to earth conditions:

ts = length scale (m) velocity (m/s)

f v V ð Þ ¼ kf m r r r r rP rf g h i

permeability (higher in mantle) feedbacks: melt dist & grain size (both evolving functions of stress) pressure gradient (lower in mantle) feedbacks: evolving function of length scale, constitutive relation (melt dist., strain rate dist.) and surface tension resisting force.

2) Spiegelman, 2003: (linear stability analysis) melt effect on viscosity alone does not lead to low angle (20 degree) bands 3) Katz et al., 2006: (LSA + PDE) localization due to stress-dependent viscosity stabilizes lower angle bands 4) Takei & Holtzman, 2009: anisotropic viscosity due to aligned melt pockets adds a driving force for segregation, stabilizing low angles. 5) Butler, 2008 (PEPI): comparison of rates of stress-driven segregation to buoyancy driven extraction In simple or general shear, the pressure gradients become more complex; Magma Dynamics theory has helped: Can stress-induced organization occur quickly enough to be important in melt-transport and deformation processes ?

• 5. Interacting feedbacks (amplifying and damping)

d T S