Towards dynamically constraining
subduction-zone parameters
from
surface-topography characteristics
Fabio Crameri(1), Keely O’Farrell(1), Paul J. Tackley(2) and Carolina R. Lithgow-Bertelloni(1)
(1) University College London
(2) ETH Zurich
www.fabiocrameri.ch
MOTIVATION
WE SHOULD!
Surface topography is one of the few direct
measurements we have that constrains the dynamics
in the Earth’s interior.
WE CAN!
We can now model mantle convection with both a
free surface (Crameri et al., 2012a) and realistic,
single-sided subduction (Crameri et al., 2012b).
WE DO!
We investigate here the link between surfacetopography characteristics and the diverse,
topography-controlling subduction parameters
(Figure 1).
RESULTS & CONCLUSIONS
§ We observe a deep back-arc depression at low
angles, and a deep trench at high angles. Slabs
with a low dip angle transfer stresses more
efficiently through the thinner mantle wedge to the
upper plate, whereas slabs with a high dip angle
transfer stresses mostly along the slab (Figure 2).
Figure 2: Effect of variable slab dip shown as close-ups of surface topography (top) and
effective viscosity (bottom).
§ All models (with different subduction parameters)
show a consistent systematic behaviour when slab
dip varies (Figure 3). This allows us to predict the
long-wavelength surface topography (in the range
of the parameter uncertainty) at a certain dip-angle
and possibly in turn, to constrain the subduction
parameters from the observed or reconstructed
topography.
Figure 3: Effect of shallow-slab dip angle on topography characteristics for models with
different subduction parameters.
➥ 1. A young convergent boundary (low slab
dip, low slab-mantle buoyancy contrast and
weak plate) is likely to have low-amplitude
fore-bulge, trench and volcanic arc, but a
deep and voluminous back-arc basin.
§ Slab dip strongly controls all topographic features
(Figure 5).
§ Slab buoyancy has a strong control on the trench
depth and the back-arc depression.
§ Radial mantle viscosity gradient has a strong
control on trench depth.
§ Plate strength strongly controls the island arc
height and the extent of the back-arc depression.
➥ 2. Shallow slab dip and slab buoyancy
have main control on topographic
amplitudes.
• Models with a fixed (i.e., free-slip) surface produce
unnatural normal stresses at the top model
boundary above a subduction zone leading to
unnatural topographic artefacts (Figure 4).
Figure 5: Potential of individual subduction parameters to change each topography feature
within a typical, Earth-like range. Values are given in percentage of plate thickness.
➥ 3. Models without a free surface do NOT
reproduce correct topography!
Figure 1: (a,b) Observed and (c) modelled surface
topography and characteristic features
PHYSICAL MODEL
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Visco-plastic rheology; Boussinesq approximation (Ra = 106; Eact = 240 kJmol-1; Vact = 0 m3mol-1)
Diffusion creep (Arrhenius law)
Composite yield stress: brittle (Byerlee, Drucker Prager) and ductile (constant) yield stress
Purely internal heating
Boundaries: isothermal at 300 K (top), zero flux (bottom & sides), free-slip (all)
Sticky-air layer approximates a free surface (Matsumoto and Tomoda (1983); Schmeling et al., 2008; Crameri et al., 2012, GJI)
Weak crustal layer implemented on top of the plate (Lenardic & Kaula, 1994; Gerya et al., 2008, Crameri & Tackley, 2015)
BAD: Back-arc depression
IA: Island arc
TR: Trench
FB: Forebulge
NUMERICAL MODEL
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Calculated by StagYY (Tackley 2008)
Finite difference/volume multigrid code
Non-diffusive tracers track composition (i.e. sticky air and weak crust) and topography
2-D, 2:1 aspect-ratio, Cartesian domains
Resolution: nx×nz = 512×256, plus 5× vertical refinement
Models are run for >100 time steps and for 2 Ma
Post-processed and visualised by StagLab (www.fabiocrameri.ch/software)
Figure 4: Free surface versus a free-slip surface
REFERENCES
Crameri, F., et al. (2012a), Geophys. J. Int., 189(1).
Crameri, F., et al. (2012b), Geophys. Res. Lett., 39(3).
Crameri, F., and P. J. Tackley (2015), J. Geophys. Res., 120(5)
Gerya, T. V., et al. (2008), Geology, 36(1)
Lenardic, A., and W. M. Kaula (1994), Geophys. Res. Lett., 21(16)
Matsumoto, T., and Y. Tomoda (1983), J. Phys. Earth, 31(3)
Schmeling, H., et al. (2008), Phys. Earth Planet. Int., 171(1-4)
Tackley, P. J. (2008), Phys. Earth Planet. Int., 171(1-4)