Plate tectonics generated by nonlinear rheology in mantle

							Plate tectonics generated
by nonlinear rheology in
    mantle convection
 models & application to
    thermo-chemical
         evolution
      Paul J. Tackley, UCLA
  (some parts from Shunxing Xie,
       Stephane Labrosse)
Plan
Review ‘plate problem’ and rheology
3D simulations of mantle convection show
 how pseudo-plastic yielding leads to plate-
 like behavior
Other important effects
  Strain weakening
  Viscosity stratification (asthenosphere)
Application to planetary evolution
From Published Papers

EPSL 157, 9-22, 1998
Geochem., Geophys. Geosystems 2000
 (2 papers)
AGU Plate Motions Monograph 121, 2000
Proc. R. Soc. Lond. A., in press 2002
Viscosity (T) : how much?

exp(E/kT) where E~400 kJ/mol
T from 1600 -> 300 K
=>4x1056 variation

=> RIGID LID!
Expect rigid lid: Earth
unusual ?
Mars: rigid lid
  Had plate tectonics early?
Venus: rigid lid
  Plate tectonics->rigid lid?
  Episodic overturn?
Plates and mantle

‘Traditional’ approach
  2 separate systems
  plates ‘drive’ mantle (plate tectonicists)
  mantle ‘drives’ plates (geodynamicists)
Self-consistent approach
  one system
  same rheology applies everywhere:
   h(T,p,e,C,d,history)
  Rheology
Typical mantle convection models:
  temperature-dependent
  è or è3
Realistic:
  as above plus:
  highly nonlinear @ high stress (yielding)
  history-dependent (e.g., strain weakening)
  dependent on grain-size, composition, volatile content...
  elasticity and brittle failure
Too complicated: what is most important?
Yield strength of
rocks

Increases with confining
 pressure (depth) then
 saturates
Strength profile of oceanic
lithosphere
Lithospheric deformation
Brittle faults: upper part (10-20km?),
 velocity weakening (rate&state-dependent
 friction)
Ductile shear zones: semi-brittle or plastic
 flow, strain weakening
Distributed viscous creep (mantle)
*The strongest part of the lithosphere is
           in a ductile creep regime*
Model
100% internally-heated, RaH=106.
8x8x1 periodic domain
Boussinesq
Newtonian temperature-dependent viscosity
 (≤factor 105)
visco-plastic yield stress:
  either constant with depth (‘ductile’)
  proportional to depth (‘brittle’/’Bylerlee')
  composite (both of the above)
(later) strain-weakening or strain-rate weakening
(no elasticity)
Equations

Boussinesq, infinite Prandtl number

                        
       h i , j  v j,i   P  Ra.Tz
           v                           ˆ

                   yield 
              h
  heff  min  (T),
                    2e 
                        Ý 
                          T
   v  0                     T  v .T
                                 2

                          t
34 MPa


70 MPa


86 MPa

120 MPa


168 MPa


200 MPa


340 MPa
Surface Strain Rate and V
RaH=2e7; YS=50 MPa (2e4)



             QuickTime™ and a
          Anima tion d ecompressor
       are neede d to see this picture.
RaH=2e7; YS=150 MPa (6e4)



             QuickTime™ and a
          Anima tion d ecompressor
       are neede d to see this picture.
By S. Labrosse
Mixed
 internal+basal
 heating
Shows episodic
 merging of              QuickTime™ an d a
                            decompressor
 downwellings      are need ed to see this picture.



Core heat flow
 driven by upper
 boundary layer
Characterizing plate
tectonics
'Plateness': Most deformation focused in
 narrow zones ~15% of surface area
 (Stein)
Significant toroidal motion
Spreading centers: passive, symmetric
Subduction: single-sided
Strike-slip boundaries
Earth’s Tor/Pol
 ratio ~0.3-0.5
 (excluding net
 rotation)
Time-Dependence

 Yield stress
  increases top to
  bottom
Scaling of plate diagnostics
with Yield Stress
Does low viscosity beneath the
lithosphere help?
‘Asthenosphere’
Decouples piecewise continuous plate motion
 from distributed mantle deformation ?
Want to add in such a way that viscosity is
 unchanged elsewhere
Define ‘solidus’ T=T0+A*depth, decrease h by
 factor 10 when T reaches solidus
(in reality getting close to solidus is sufficient)
Varying yield
 strength
Time
 evolution
Greatly improves plate quality
So far…instantaneous rheology


Isn’t history dependence
important? i.e., Strain
weakening, and healing
Strain weakening?
Observed in laboratory
Expected in theory
Evidenced in the field
Mechanisms:
  Dynamic recrystallization => small grains
  Volatile infiltration + reactions
  Viscous dissipation
Provides positive feedback leading to strain
 localization and narrow shear zones
Mantle shear zone in Greenland
X-section thru
shear zone
Simplified 'Damage' evolution
       dD
           A : e  R(T)D
                 Ý
       dt
       h  h undam aged(1 D)
       e.g., R(T) 1/ h (T)
            h  hT,z, e,history 
                       Ý

If A and R very large => strain-rate weakening
Comparison of
various
rheologies
Forms lithospheric shear zones
…works
with more
realistic
viscosity
profile
Instantaneous
flow with
strain rate
weakening.

Simple 2-lyr
model
  Same with
  bigger box




Simple yielding
 doesn’t produce
 plate-like motion
Add SW to time-dep models
…but
doesn’t
have a large
effect on
diagnostics
Divergence:
 Poloidal field
Vorticity:
 Toroidal field
Surface Strain rate




            Divergence   Vorticity
Pol- & Toroidal with depth
Continents aid 1-sided
subduction, but add time-depn
Summary
Successes and failures
Robust successes:
  Linear 'subduction'
  Linear passive spreading centers+rifts
Less Robust successes:
  Toroidal:Poloidal ratio realistic (sometimes)
  1-sided subduction (sometimes)
Failures:
  No focused pure strike-slip margins
Things that 'help'

Buoyant continents (toroidal flow, 1-sided
 subduction)
'melting' (focuses MOR)
Mantle viscosity stratification (?)
Future directions
Greater realism
  Actual rheologies instead of idealized (but not well
   known)
  Higher convective vigor
  Spherical geometry
Use to study planetary thermal and chemical
 evolution
  Direct simulation and
  Calibrate/determine scaling for parameterized
   models
Mantle convection models and
        geochemistry


     Paul J. Tackley and Shunxing Xie

          ESS and IGPP, UCLA
Integrating Geodynamic and Geochemical
Models of Mantle Evolution and Plate
Tectonics
 Motivation
  Gechemistry and dynamics inextricably linked:
    Composition affects density, rheology, heating rate
    Dynamics affects melting, differentiation, mixing
  Test hypothesized chemical models and
   processes in a self-consistent manner
    What works?
    What model(s) produce results that satisfy both
     chemical and physical observational constraints?
Approach
  Add tracking of trace & major element chemistry
   to a numerical convection-plate tectonics code
TEST cartoon models: which ones “work” both
geophysically and geochemically?
     Chemical model
 Major elements:
    2-components: ‘crust’ (basalt/eclogite)<-> ‘residue’ (harzburgite).
    Melts when T reaches solidus (Herzberg et al 2000; Zerr et al 1998) melt
     instantly removed to form surface crust.
    Chemical density variation constant with depth except for basalt->eclogite (2.5%
     in presented models)
 Trace elements:
    207Pb, 206Pb, 204Pb, 143Nd, 144Nd, 147Sm, 235U, 238U, 3He, 4He 36Ar, 40Ar, 40K, 232Th
    Initial concentrations represent mantle after extraction of CC 3.6 Ga ago.
    Radioactive decay
    Partitioning between crust + residue on melting. Coefficients from
     (Hiyagon+Ozima 86) and (Hofmann 88).
    Noble gases outgas on melting (99% in presented models)
Physical model
Compressible anelastic
Cylindrical geometry (2-D)
Viscosity dependent on:
  Temperature (factor 106)
  Depth (factor 10, exponential)
  Stress (yielding gives different lid
   behaviors including “plate-like”)
Mixed basal and internal heating
  Geochemical evolution:
  Focus on 2 cases
 Differing initial conditions:
   Chemically homogeneous
   Chemically layered
       50% of isotopes concentrated into lower 20% of mantle
        3He concentration calculated to give 8 or 35 times atmospheric today
 Not yet Earth-like but display some of proposed processes so
  useful to analyze
   Convective vigor too low (V~0.3 cm/yr, flux~30mW/m2)
   Viscosity too high, rheology less T-dependent that Earth (mantle gets
    too hot, too much melting+differentiation)
Homogeneous start: after 1
and 2 Gyr
      1 Gyr          2 Gyr



C




T
      QuickTime™ and a
   Anima tion d ecompressor
are neede d to see this picture.




      QuickTime™ and a
   Anima tion d ecompressor
are neede d to see this picture.
Homogeneous start
(after 3.6 Gyr)
Layered start: after 200 Myr
and 2.5 Gyr
      QuickTime™ and a
   Anima tion d ecompressor
are neede d to see this picture.




      QuickTime™ and a
   Anima tion d ecompressor
are neede d to see this picture.
Layered start: present day
(3.6 Gyr)
Noble gas outgassing: too much(?)
Ratios in melted material
(last 150 Myr)

3He/4He
Pb ratios in melted material
Thermal evolution strongly affected by
magmatism: simple example

 Calculation takes into account decay of
  radiogenic elements and cooling of the
  core
 Boussinesq, constant viscosity, but:
 Viscosity is strongly dependent on mean
  temperature, realistic activation energy
Isochemical case


                      QuickTime™ and a
                   Anima tion de compressor
                are neede d to se e this picture.




Core cooling reduces it to nearly
 internally-heated convection
with
differentiation
                        QuickTime™ and a
                     Anima tion de compressor
                  are neede d to se e this picture.

Hot layer
 forms at base
Core cooling
 much reduced


                        QuickTime™ and a
                     Anima tion de compressor
                  are neede d to se e this picture.
Heat flow is almost constant
Temperature varies much less
THE END
Yielding generates “plate tectonics”

a low-
 viscosity
 zone
 (asthenosp
 here) helps
 greatly
YS~100
 MPa is
 needed
Goals
‘Complete’ understanding of mantle:plate
 tectonic system
Apply to specific events on Earth
Understand evolution of Earth, Venus,
 Mars, e.g.,
  Early plate tectonics on Mars?
  Episodic plate tectonics on Venus?
  Pre-plate-tectonics regime on Earth?
Rheological Model
 Strongly temperature-dependent viscosity (many orders
  of magnitude)
 +depth-dependent yield stress (brittle)
 +constant yield stress (ductile)
 +strain weakening & healing ('damage')

 No elasticity!