1. Plate tectonics on a hotter Earth: the role of rheology Jeroen van Hunen ETH Zurich, Switzerland in collaboration with: Arie van den Berg (Utrecht Univ) thanks to: Herman van Roermund (Utrecht Univ) Taras Gerya (ETH Zurich)
My presentation deals with the role of rheology in the discussion on the beginning of plate tectonics.

2. Conclusions In a hotter Earth: Numerical modeling illustrates that:
crust was thicker  less slab pull, slower tectonics?
material was weaker  faster tectonics?
Numerical modeling illustrates that:
BasaltEclogite transition can overcome buoyancy problem
For 100 K hotter Earth, subduction resembles present-day’s.
For hotter Earth, slower or no plate tectonics, because:
weaker slabs lead to more slab break-off
weaker, thicker crust leads to more crust separation
Lack of UHPM older than Ma could be due to
weak slabs.
As requested, I’ll start with the conclusions:

3. Consequences of a hotter Earth for plate tectonics
Young Earth was probably hotter than today: estimates K
Consequences:
Weaker mantle due to h(T)
More melting at MORs
(van Thienen et al., 2004)
Earth was hotter in past, because it looses more heat (surface heat flow) than it produces (radioactivity): according geological observations: K in Archean. This has several implications for plate tectonic mechanism:
material weaker, rule-of-thumb: every 100K hotter makes mantle material 10x weaker  guess relative weakness in past. Effect on mantle vigor & strength slabs?
Hotter Earth gave more melting  more crust  gravitational stable oceanic plates  subduction? (Next slide)
More melting at MOR implies thicker basalt & harzburgite layers
more compositional buoyancy
less gravitational instability
(slab pull?  subduction?  plate tectonics?)

4. Model setup 2-D FEM code SEPRAN: mass, momentum & energy conservation
Tracers define composition
Geometry: W x H = 3600 x 2000 km
100 km deep static fault decouples converging plates
phase transitions: mantle (400-D, 670-D), crust (basalteclogite)
rheology: diffusion-, dislocation creep, yielding, material-dependent

5. Numerical modeling results
vsubd (t)
colors =
viscosity
black
basalt
white
eclogite t
NB: color scale, time scale, crustal thickness vs. slab thickness, slab breakoff
viscosity
DTpot = 0 K K K K

6. Numerical modeling results
NB: color scale, time scale, crustal thickness vs. slab thickness, slab breakoff
viscosity
For low DTpot subduction looks like today’s

7. Numerical modeling results
NB: color scale, time scale, crustal thickness vs. slab thickness, slab breakoff
viscosity
For higher Tpot more frequent slab breakoff occurs,

8. Numerical modeling results
NB: color scale, time scale, crustal thickness vs. slab thickness, slab breakoff
viscosity
… or subduction stops completely.

9. Parameter space Investigated model parameters:
crustal strength: (1 or ~0.01 x (Shelton & Tullis, 1981))
mantle wedge relative viscosity: ∆ηmw=0.1 or 0.01
basalt  eclogite reaction kinetics: tbe=1 or 5 Ma
yield strength: 100, 200, or 1000 MPa
fault friction: 0 & 5 MPa (for every 5 cm/yr subduction)
strong depleted mantle material (x100)

10. Higher yield stress 1 GPa: faster subduction in hotter Earth, because slab break-off occurs less frequent

11. Fault friction of 5 MPa (at 5 cm/yr subduction velocity): stabilizing effect

12. Another issue is the buoyancy (gravitational stability): basalteclogite is slow and if too slow, the slab remains buoyant until deep, and the total slab might be buoyant. This doesn’t really stop subduction, but can make it very slow, so that it cannot effectively cool the Earth anymore.
Slow eclogitization may keep plate too buoyant for efficient subduction in a K hotter Earth

13. Summary of results

14. Summary of results no subduction slab breakoff dominates
‘normal’ subduction

15. First appearance of UHPM
Crustal material experiences very high pressure/metamorphism, and
subsequently somehow makes it to the surface again.
Observations:
Oldest Ultra-High Pressure Metamorphism: 600 Ma
Oldest blueschists: Ma
(Possible) mechanism:
At closure of ocean, partial continental subduction
Slab breakoff
Buoyant continental lithosphere back to surface
Suggested causes:
Change in pT conditions due to secular cooling (Maruyama&Liou, 1998)
Preservation problem (Möller et al., 1995)
Stable oceanic lithosphere/absence of subduction (Stern, 2005)
Shallow breakoff prevents ‘rebound’ from UHP (this study)

16. Conclusions In a hotter Earth: Numerical modeling illustrates that:
crust was thicker  less slab pull, slower tectonics?
material was weaker  faster tectonics?
Numerical modeling illustrates that:
BasaltEclogite transition can overcome buoyancy problem
For 100 K hotter Earth, subduction resembles present-day’s.
For hotter Earth, slower or no plate tectonics, because:
weaker slabs lead to more slab break-off
weaker, thicker crust leads to more crust separation
Lack of UHPM older than Ma could be due to
weak slabs.

19. Another issue is the buoyancy (gravitational stability): basalteclogite is slow and if too slow, the slab remains buoyant until deep, and the total slab might be buoyant. This doesn’t really stop subduction, but can make it very slow, so that it cannot effectively cool the Earth anymore.
More crustal decoupling, stronger wedge: crustal delamination + more frequent breakoff stop subduction process

20. Another issue is the buoyancy (gravitational stability): basalteclogite is slow and if too slow, the slab remains buoyant until deep, and the total slab might be buoyant. This doesn’t really stop subduction, but can make it very slow, so that it cannot effectively cool the Earth anymore.
Strong harzburgitic depleted mantle: thermal weakening still more important

21. Buoyancy of an oceanic plate with a thick crust
To see effect of crustal thickness on gravitational stability, look at this plot.
At MOR, crust=basalt/gabbro(UK)/diabase(US)  most stable lithosphere.
At depth (AFTER subduction!!)  phase transition to heavier amphibolite or eclogite  instable lithosphere
Additional problem: phase transition basalteclogite is probably kinetically slow!
Bulk density for a 100-km thick lithosphere with different
crustal thicknesses and compositions (from Cloos, 1993)

22. Alternative tectonic models: magma ocean
So it is not clear whether plate tectonics could have been present in the hotter Earth. We might need to look for alternative models. Here I will discuss a few.
1) Sleep assumed only one type of tectonics (plate tectonics) that can have different modes. In the past, the Earth was too hot to form rigid plates, instead everything was molten  magma ocean. Magma oceans are very effective in cooling the Earth until plates occur. Especially in the early Earth, plate tectonics may have been not effective enough to cool the Earth with all its radioactive heating, and Earth started heating in the mode. After enough heating, we form a magma ocean again. This loop continues until radioactivity is decreased and plate tectonics becomes efficient enough. This is the stage we are in now. After more cooling, plates (and especially MORS) will be too stiff and plate tectonics will stop, and will form a stagnant lid (like on Venus and Mars).
(Sleep, 2000)

23. Alternative tectonic models: crustal delamination (1)
2) Crustal delamination. We saw in the numerical models that subduction might stop or not start at all in the past. In that case, a ‘stagnant lid’ occurs. Melting below it will steadily produce a thicker and thicker crust, until it reaches the thickness of the be transition. If eclogite is formed, it is heavy, and might drip down. Illustrated here.
(Zegers & van Keken, 2001)

24. Alternative tectonic models: crustal delamination (2)
“Subplate
tectonics”
3) Also some mixed mode between convection and plate tectonics might occur: the mantle part of the lithosphere might still convect (always grav. heavy), but the buoyant crust might stay at surface (like foam in a hot pool, and like what happens today when continent try to subduct, e.g. India under Eurasia). This might have formed the socalled ‘granite-greenstone belts’ that are observed around the globe. This mode was called ‘Subplate tectonics’ by Davies.
Also a mixed mode with the dripping in Zegers and van Keken (former slide) might have occurred: “Drip tectonics’.
“Drip
tectonics”
(Davies, 1992)

25. Alternative tectonic models: Flake tectonics (Hoffman & Ranalli, 1988)
Today, continental lithosphere
shows ‘sandwich’ rheology. In past
maybe all plates showed that, with
less plate and more ductile material
in between. The two layers might
have started convecting separately.
(Kohlstedt et al., 1995)

26. Alternative tectonic models: Continental overflow as Archean
tectonic mechanism
Continental overflow might also have occurred: continents grow for some reason, from below, and will collapse at some point, which will give lateral spreading, thereby overriding neighbouring plates that may ‘subduct’ in this way. The hotter-Earth sandwich-rheology again may give the typical ‘ductile flow’ as shown in the plot.
(Bailey, 1999)

27. Alternative tectonic models:
Violent overturns in the mantle could have
produced Archean mantle lithosphere
The Earth may not have been cooling steadily, but episodically (see plot continental formation through time).
Davies proposed a 2-layer convection model: convection is layered (for more details come to my class on physics of mantle and core): 2 layers on top of each other, but sometimes material is exchanged in a ‘flushing’ event, which suddenly add a lot of hot material from the lower mantle into the upper mantle (think about toilet flushing suddenly bringing a lot of water into the toilet). This extra heat gives large-scale melting continent formation, and plate motion.
(McCulloch and Bennett, 1994)
(Davies, 1995)

28. Theory: Cooling the Earth (1)
Surface heat flow qs by radioactivity:
Upper limit: today’s surface heat flow: ~80 mW/m2
More sophisticated estimate: ~40 mW/m2 (McKenzie & Richter, 1981)
In past (‘Hadean’): ~ 4x more radioactivity than today (Van Schmus, 1995)
Early Earth radioactivity produced ~160 mW/m2 surface heat flow
Remaining ~40 mW/m2 from cooling the Earth?
Specific heat Cp of average Earth: ~1 kJ/kg,K (Stacey & Loper, 1984)
qs of 1 mW/m2 cools Earth with 2.57 K/Ga (Sleep, 2000)
For 40 mW/m2: cooling of about 100 K/Ga, upper limit?
Or qs was 2 – 4 times higher than today (very efficient tectonics!), or Earth
heating up instead of cooling down.
If plate tectonics wasn’t there in past, we have a problem:
what did then cool the Earth. (go through simple theory)  if heatflow was 2-4 times higher in past, Earth was cooling slower or even heating up. Geology shows that T was higher in past, so we need extra cooling  we need efficient cooling mechanism also in early Earth

29. initial situations
Model setup (3)
subduction
today
subduction? Y N

30. Model setup (2) density: ρ0=3300 kg/m3 ∆ρbasalt=-500 kg/m3
∆ρeclogite=+100 kg/m3
∆ρHz=-75 kg/m3
phase transitions:
basalt  eclogite (be):
at 40 km depth
in 1 or 5 Ma
400-D & 660-D, equilibrium
rheology:
composite (diffusion + dislocation creep, (Karato & Wu, 1993))
yielding (sy= 100 MPa – 1GPa)
Byerlee's law (sBy=0.2rgz)
Relative mantle wedge viscosity ∆ηmw=0.1 or 0.01

31. Lower yield stress 100 MPa: little effect; again slab breakoff
Another issue is the buoyancy (gravitational stability): basalteclogite is slow and if too slow, the slab remains buoyant until deep, and the total slab might be buoyant. This doesn’t really stop subduction, but can make it very slow, so that it cannot effectively cool the Earth anymore.
Lower yield stress 100 MPa: little effect; again slab breakoff

32. Theory: Cooling the Earth (2)
Opposite scenario:
hotter Earth
 weaker mantle
faster convection
faster cooling
hotter Earth in past
= Urey ratio=fraction of
surface heat flow from
Earth cooling
Simple convection with T-dependent
viscosity gives ‘thermal catastrophe’.
If we look at simple mantle convection, another, opposite problem appears: too much cooling of the Earth. How does that work?
Grey area shows Earth mantle T in past from observations.
Curves show predicted temperatures from simple relationships between cooling and T (cooling=T^alpha, alpha +-0.3)
Cooling is much too rapid in past, if we use reasonable values for today. So T must have been very high to begin with then, unreasonably high: ‘thermal catastrophe’
So it is clear that these theories lack some important ingredients, we don’t fully understand the system yet.
(Korenaga, 2005)

33. Observational evidence for plate tectonics
Tonalite-Trondjemite-Granite
(TTGs) as Archean equivalent of
Cenozoic adakites (formed by
melting of subducting slab)
(Abbott & Hoffman, 1984)
Linear granite-greenstone belts
suggest subduction
(Calvert et al., 1995)
Water was present since the early
Archean (de Wit, 1998)
(Calvert et al., 1995)
Modern plate tectonics can be seen in action (geodesy, seismology, geology), but for ancient tectonics we have to rely on what is frozen in in the lithosphere. Hoping that the freezing itself didn’t change the structures/chemistry too much, we can use these structures to analyze what may have happened in the early Earth.
TTGs: Today we observe adakites in young/hot subduction zones: slab crust melts with little mantle wedge component. Adakite shows similarities with TTG, which was widely formed during Archean: Archean subduction? It is consistent with idea that thick crust in hot Archean mantle could melt, and flat subduction (no interaction with mantle wedge) has been suggested for early Earth.
Linear belts: see map: linear structures clearly present. Age progression: 3.1 Ga (N) to 2.7 Ga (S)  accretion of terrains during subduction. Interpretation of seismic profile (plot below) of read area in map shows N-dipping structures: subducting slabs?
Water: water is probably the main ingredient for plate tectonics: no liquid water on Mars and Venus probably is the reason for absence of plate tectonics there. Water lubricates, and makes faults weaker. An liquid water ocean probably formed very early in Earth history, probably early Archean, so conditions for plate tectonics were okay then. N S

34. Observational evidence against plate tectonics
No ophiolites in Archean (Hamilton, 1998)
No ultrahigh pressure metamorphism (UHPM) older than 600 Ma
(Maruyama & Liou, 1998)
No evidence for Archean rifting, rotation and re-assembly of
continental plates (Hamilton, 1998)
Modern plate tectonics can be seen in action (geodesy, seismology, geology), but for ancient tectonics we have to rely on what is frozen in in the lithosphere. Hoping that the freezing itself didn’t change the structures/chemistry too much, we can use these structures to analyze what may have happened in the early Earth.
Most evidence comes from absence of modern plate tectonics characteristics. Ophiolites (obducting structures instead of subducting)
have not been found in old rocks. Many scientists have their doubts about the oldest one found (2.5 Ga, Kusky et al., 2001), and all others are clearly younger.
Also eclogites and blueschists are even not older than 600 Ma. These are mostly found in continental collision zones (final stage of Wilson cycle): crust is subducted deep, metamorphism into hp-phase occurred, and then these rockes were exhumed again due to attachment to lighter, continental crust. This process apparently didn’t occur in the early Earth. This indicates that even when subduction took place back then, it had different characteristics. Finally, other characteristics such as rifting, plate rotation, and large scale merging of continents has not (yet?) been shown for the early Earth.
(Maruyama & Liou, 1998)