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I II
n
! y ! c
field x
Multi-Scale Dynamics and Rheology of Mantle Convection with PlatesLaura Alisic (alisic@gps.caltech.edu), Michael Gurnis (Seismological Laboratory, Caltech),
Georg Stadler, Omar Ghattas (ICES, University of Texas at Austin), Carsten Burstedde (Rheinische Friedrich-Wilhelms-Universität Bonn)
Key Points Global Plate Motions and Plateness Regional Plate Motions
Model Constraints Microplates and Trench Rollback
C.
15 cm/yr
C.
15 cm/yr
C.
15 cm/yr
0.00
0.25
0.50
0.75ω deg/Ma
0.7
0.8
0.9
1.0plateness
0.00
0.25
0.50
0.75ω deg/Ma
0.7
0.8
0.9
1.0plateness
0.00
0.25
0.50
0.75ω deg/Ma
0.00
0.25
0.50
0.75
1.00plateness
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
−18 −17 −16 −15 −14
eII[1/s]
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
−18 −17 −16 −15 −14
eII[1/s]
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
−18 −17 −16 −15 −14
eII[1/s]
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
−18 −17 −16 −15 −14
eII[1/s]
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
−18 −17 −16 −15 −14
eII[1/s]
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
−18 −17 −16 −15 −14
eII[1/s]
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
160˚
160˚
170˚
170˚
180˚
180˚
190˚
190˚
−40˚ −40˚
−30˚ −30˚
−20˚ −20˚
−10˚ −10˚
−18 −17 −16 −15 −14
eII[1/s]
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
310˚
310˚
320˚
320˚
330˚
330˚
340˚
340˚
350˚
350˚
−70˚ −70˚
−60˚ −60˚
−50˚ −50˚
−18 −17 −16 −15 −14
eII[1/s]
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
130˚
130˚
140˚
140˚
150˚
150˚
160˚
160˚
10˚ 10˚
20˚ 20˚
30˚ 30˚
−18 −17 −16 −15 −14
eII[1/s]
2.0
2.5
3.0
3.5
Str
ess e
xp
on
en
t
0 200 400 600 800 1000 1200
Yield stress (MPa)
PAC normalized velocity, constraint = 1
1
0.0
0.5
1.0
1.5
2.0normvel
2.0
2.5
3.0
3.5
Str
ess e
xponent
0 200 400 600 800 1000 1200
Yield stress (MPa)
Net surface rotation, constraint = 0.13
0.13
0.1
3
0.0
0.1
0.2
degMy
2.0
2.5
3.0
3.5
Str
ess e
xponent
0 200 400 600 800 1000 1200
Yield stress (MPa)
GLOB P2, constraint = 1
1
0.80
0.84
0.88
0.92
0.96
1.00P2
2.0
2.5
3.0
3.5
Str
ess e
xp
on
en
t
0 200 400 600 800 1000 1200
Yield stress (MPa)
GLOB normalized velocity, constraint = 1
1
0.0
0.5
1.0
1.5
2.0normvel
2.0
2.5
3.0
3.5
Str
ess e
xp
on
en
t
0 200 400 600 800 1000 1200
Yield stress (MPa)
Global average shallow strain rate
−15
−16.0
−15.5
−15.0
−14.5
−14.0eII[1/s]
2.0
2.5
3.0
3.5
Str
ess e
xponent
0 200 400 600 800 1000 1200
Yield stress (MPa)
Marianas1 rollback
8.7
0
5
10
15cm/yr
0
10
20
Rollb
ack (
cm
/yr)
0 5 10 15 20 25
Subducting plate velocity (cm/yr)
Marianas1
2.0
2.5
3.0
3.5
n
0
10
20
Rollb
ack (
cm
/yr)
0 5 10 15 20 25
Subducting plate velocity (cm/yr)
Marianas1
0
200
400
600
800
1000
1200σy(MPa)
2.0
2.5
3.0
3.5
Str
ess e
xp
on
en
t
0 200 400 600 800 1000 1200
Yield stress (MPa)
NewHebrides1 rollback
13.5
0
10
20
30cm/yr
0
10
20
30
40
50
60
Ro
llba
ck (
cm
/yr)
0 5 10 15
Subducting plate velocity (cm/yr)
NewHebrides1
2.0
2.5
3.0
3.5
n
0
10
20
30
40
50
60
Ro
llba
ck (
cm
/yr)
0 5 10 15
Subducting plate velocity (cm/yr)
NewHebrides1
0
200
400
600
800
1000
1200σy(MPa)
2.0
2.5
3.0
3.5
Str
ess e
xp
on
en
t
0 200 400 600 800 1000 1200
Yield stress (MPa)
Sandwich1 rollback
11.1
0
5
10
15
20cm/yr
0
10
20
30
40
50
60
Rollb
ack (
cm
/yr)
0 5 10 15 20 25
Subducting plate velocity (cm/yr)
Sandwich1
2.0
2.5
3.0
3.5
n
0
10
20
30
40
50
60
Ro
llba
ck (
cm
/yr)
0 5 10 15 20 25
Subducting plate velocity (cm/yr)
Sandwich1
0
200
400
600
800
1000
1200σy(MPa)
2.0
2.5
3.0
3.5
Str
ess e
xponent
0 200 400 600 800 1000 1200
Yield stress (MPa)
PAC P2, constraint = 1
0.80
0.84
0.88
0.92
0.96
1.00P2
Model 104yield stress = 100 MPastress exponent = 3.0
Model 109yield stress = 1200 MPastress exponent = 3.75
Model 107yield stress = 800 MPastress exponent = 3.0
Convective Stresses
• Global dynamic models of mantle convection with plates, using Rhea with adaptive mesh re�nement allowing for local resolution of 1 km
• Composite viscosity with di�usion creep (linear), dislocation creep (nonlinear), and yield stress
• Models have narrow plate boundaries, sharply de�ned slabs in the upper mantle, and tomography structure in the lower mantle
• Yield stress and stress exponent are varied: Strength and nonlinearity
• Models are tested with suite of constraints: Plate motions, plateness, minimum shallow slab strain rate from seismic moment release, state of stress from CMT stress axes
• We study regional dynamics: Microplate motions and trench rollback as function of yield stress and strain rate
• Stress exponent strongly a�ects model results
• Emerging pattern: Yield stress important when low (< 200MPa). When yield stress is high, convective stress becomes more important and yield stress has no impact anymore
New Hebrides
Sandwich
Marianas
Figure 1. Typical global viscosity �eld. (a) Cut through the Paci�c (PAC), Marianas (MAR) and Philippine (PS) plates. (b) Zoom-in on the Marianas slab, with nonlinear e�ects visible in the mantle wedge and slab hinge. (c) Further zoom-in on the mesh around the weak zone at the Marianas trench, as indicated by the white box in (b), with a highest resolution of ~1 km.
Black: Rhea surface velocity. Green: NNR-NUVEL1A velocity.
Plate motions �t observations reasonably well. PAC plateness is lowest at boundaries and in southwest corner.
Plate motions are signi�cantly slower, plateness worse. PAC plate is more stuck due to higher yield stress. Section ro-tation poles are more spread out, indicating more internal deformation.
All plates speed up signi�-cantly, plateness improves. The e�ect of increase in nonlinear-ity (and therefore strain local-ization) is larger than the e�ect of increase in yield stress.
Copper color scale: plateness, measure of rigidity of Paci�c plate. Dots: section rotation poles for PAC.
New Hebrides rolls back su�ciently. Tonga and Marianas do not roll back fast enough, and Scotia even shows trench advance.
Increase in yield stress slows plates down, es-pecially the major plates.
Increase in stress expo-nent causes higher strain rates and larger plate velocities. All mi-croplates now roll back rapidly.
Black: Rhea velocities. White: NNR-NUVEL1A and velocities from Bird(2003).
Background: surface strain rate.
Figure 3: Model quantities as function of stress ex-ponent and yield stress, with contours denoting constraints. (a) PAC normalized velocity; (b) Global average normalized plate velocity; (c) PAC plateness; (d) Global average plateness; (e) Net surface rota-tion; (f) Global average shallow strain rate.
Figure 2: Left: Global plate motions and plate-ness. Right: Regional plate motions and sur-face strain rate.
Figure 4: Left: Trench rollback as function of stress exponent and yield stress, contour denotes constraint. Center: Trench rollback as function of subducting plate velocity, color coded by yield stress; dotted lines denote plate velocity constraints, shallow slab strain rate constraint shown as solid contour. Right: Trench rollback as function of subducting plate velocity, color coded by stress exponent.
Tonga-FijiScotia Marianas
Rollback, subducting plate ve-locity and strain rate con-straints lie close. Models with moderate to high stress expo-nents and yield stress match the constraints.
Strain rate constraint is never reached. Only models with high stress exponent come close to matching rollback and subducting plate velocity constraints.
The three constraints coincide well, and models with moder-ate stress exponent �t the constraints. The Marianas mi-croplate shows unusually sus-tained e�ect of yield stress, even for high yield stresses.
Figure 5: Schematic of the behaviour of a resulting quantity, e.g. plate velocity, as function of stress exponent (n) and yield stress (σy). Dotted lines show contours, which are closer together for higher stress exponent. The transition stress between domains I and II is de-noted as the convective stress, σc.
Domain I:Yield stress and stress ex-ponent both have strong in�uence on the quantity.
σmax = σy < σc
Yield stress limits strength of material.
Domain II: Yield stress has no bearing on the result, only the stress expo-nent has e�ect.
σmax = σc < σy
Convective stress determines bulk ambient stresses, yield stress a�ects only localized areas with high ambient stress.
(a) (b)
(c) (d)
(e) (f)
PAC
PS
MAR
(a)
(b) (c)
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