Why does the Nazca plate slow down since the Neogene? Supplemental Information

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1 GSA DATA REPOSITORY Why does the Nazca plate slow down since the Neogene? Supplemental Information Javier Quinteros a,b,, Stephan V. Sobolev a,c a Deutsches GeoForschungsZentrum GFZ, Telegrafenberg, Potsdam, Germany, Section 2.5. b Dept. of Computer Sciences, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina c Institute of Physics of the Earth, Moscow, Russia Equations and Numerical model An improved version of the code SLIM-3D (Popov and Sobolev, 2008; Quinteros and Sobolev, 2012) was used to run all experiments. The finite element method (FEM) was used to solve the governing equations. Namely, the conservation of momentum and conservation of energy σ ij x j + ρ g = 0 (1) ρc p DT P Dt = κ 2 T P + r. (2) where σ ij is the Cauchy stress tensor, ρ is density, g is gravity acceleration, C p is heat capacity, κ is thermal conductivity, D Dt is the material time derivative, T P is the potential temperature and r is the volumetric heat sources. Adiabatic heating, which is approximated as a linear function depending on depth (0.3 C.km 1 ), is added to the potential temperature (T p ) and consistently included in the calculation of pressure, density and viscosity. Corresponding author. Fax: address: javier@gfz-potsdam.de (Javier Quinteros) Preprint submitted to Geology June 11, 2012

2 The effects of compressibility are coupled with the constitutive equation by means of ( Dp Dt = K vi α DT ). (3) x i Dt Here K is the bulk modulus and α is the thermal expansion. In the same way, volumetric deformations were followed by corrections in the calculation of density by means of the Murnaghan approach. Total deviatoric strain rate ( ε ij ) is additively decomposed in an elastic, viscous and plastic term. Namely, ε ij = ε el ij + ε vis ij + ε pl ij = ˆτ ij 2G + τ ij + γ Q (4) 2µ eff τ ij where G is the elastic shear modulus, µ eff is the effective viscosity, ˆτ ij is the objective stress rate tensor, γ is the plastic multiplier and Q is the plastic potential function. Numerical integration of stresses was calculated by means of the Hughes-Winget scheme (Hughes and Winget, 1980) for the trial stresses, while a predictor-corrector procedure (Simo and Taylor, 1985) was applied to update deviatoric stresses considering plasticity. Viscosity is stress and temperature dependent. Three different types of creep were included, following the approach of Kameyama et al. (1999). Effective viscous strain rate was additively decomposed into three different types of creep mechanisms (diffusion, dislocation and Peierls), namely Strain rate due to diffusion creep was defined as ε (v) eff = ε d + ε n + ε p. (5) ε d = B d τ II e H d RT, (6) dislocation, power-law creep as ε n = B n τ n IIe Hn RT, (7) and Peierls creep as [ ε p = B p e Hp RT ( 1 τ II τp ) q ], (8)

3 where τ II is the square root of the second invariant of the deviatoric stress, R is the gas constant, B d, B n, B p are creep parameters and τ p is Peierls stress. H d, H n, H p are the activation enthalpies for each creep, which are defined as H j = E j + P.V j (9) for j {d, n, p} and being E the activation energy, P the pressure and V the activation volume. A yield stress (350 MPa or 500 MPa) was also applied in transition zone and lower mantle. Finally, effective viscosity was calculated as µ eff = τ II 2 ε (v) eff. (10) Thermal expansivity was considered to decrease from the upper mantle ( /K) to the transition zone ( /K) and to increase again below the 660 km boundary ( /K) (Steinberger and Calderwood, 2006). Clapeyron slope for olivine-spinel is 2.0 MPa/K, while at the spinel-perovskite transformation boundary ranges from -0.5 to -1.5 MPa/K (e.g. Katsura et al., 2003; Fukao et al., 2009). Different friction coefficient values have been tested for the reference model (from 0.02 (low) to 0.05 (high)). The Murnaghan approach is used to calculate density and volumetric corrections are also taken into account. We used wet olivine parameters for the rheology in the upper mantle (Hirth and Kohlstedt, 2003). For the mantle transition zone and the shallower lower mantle, we used values which have been shown to be consistent with global data from subduction zones and seismic images (Steinberger and Calderwood, 2006; Billen, 2008; Quinteros et al., 2010). All the experiments were run with a grid of 450 x 230 elements with finer resolution 200 km around the trench in horizontal direction and from the surface to a depth of 150 km. Average size of an element in this region is km 2.

4 Experiments We show in Table S-1 a list with the experiments run for this article. Some of these were run with an upper plate which included an orogen similar to the Andes, in order to check its influence on the convergence velocity and the evolution of the slab in the deeper mantle. A schematic view of the setup used in all the experiments can be seen in Fig. S-1. Figs. S-2, S-3 and S-4 show the convergence rate from the experiments that have not been shown in the manuscript.

5 Denomination Slab age Clapeyron slope Viscosity in LM Overriding velocity Max. viscosity Yield stress Friction coeff. 660 km in MTZ and LM ref My (*) 3 cm/yr ref My cm/yr ref1-40s 40 My and 2 cm/yr ref1-40s My and 2 cm/yr ref My cm/yr ref2-40s 40 My and 2 cm/yr ref2-40s My and 2 cm/yr ref My cm/yr ref My cm/yr ref My (*) 3 cm/yr ref2-40s500-fr3 40 My and 2 cm/yr ref2-40s500-fr4 40 My and 2 cm/yr ref2-40s500-fr5 40 My and 2 cm/yr Table S-1: List of experiments run. The most important input parameters are shown. (*) viscosity value given is the one on the shallower part, while deeper the value increases with an activation volume of 3 cm 3. ref2-40s500 is our preferred case.

6 Figure S-1: Setup of the model and parameters used in our set of experiments. The viscosity profile for our simulations is shown in the inlet. At the beginning of the experiments the slab is pushed at low velocity in order to mimic the long lasting oblique or near parallel subduction in Central and Northern Chile. After a coherent thermal state is achieved, the slab develops dynamically driven by gravitational instability.

7 Figure S-2: Convergence velocity for the experiments ref1-40, ref1-40s and ref1-40s500. Abrupt acceleration in the end of the experiments are related to bending of the slab in MTZ due to interaction with lower mantle Guillaume et al. (2009). All the parameters related to these experiments can be seen in Table S-2.

8 Figure S-3: Convergence velocity for the experiments ref2-40, ref3-40, ref4-40 and ref-50. All the parameters related to these experiments can be seen in Table S-2.

9 Figure S-4: Convergence velocity for the reference model with friction coefficients ranging from 0.02 to All the parameters related to these experiments can be seen in Table S-2.

10 Material ρ K G log(b d ) E d V d log(b n) E n n V n log(b p) E p τ φ c α C p k A Crust Mantle Lith.mantle Lith.slab Oc.gabro Cont.gabro Sediments Eclogite Table S-2: Model parameters used for the set of experiments. ρ: density, K: Bulk modulus, G: Shear modulus, B j : Pre-exponential factor, E j : Activation energy, V j : Activation volume, where the subscript j {d : difussion creep, n :dislocation creep, p :Peirls creep}, n: exponential constant in dislocation creep, τ p: Peierls stress, φ: friction coefficient, c: cohession strength, α: thermal expansion, C p: heat capacity, k: heat conductivity and A: radiogenic heat production. (Mackwell et al., 1998; Kameyama et al., 1999; Hirth and Kohlstedt, 2003)

11 References Billen, M. I., Modeling the dynamics of subducting slabs. Annual Review of Earth and Planetary Sciences 36 (1), Fukao, Y., Obayashi, M., Nakakuki, T., Stagnant slab: A review. Annual Review of Earth Planetary Science 37, Guillaume, B., Martinod, J., Espurt, N., Variations of slab dip and overriding plate tectonics during subduction: Insights from analogue modelling. Tectonophysics 463 (1 4), Hirth, G., Kohlstedt, D. L., Rheology of the upper mantle and the mantle wedge: A view from the experimentalists. In: Eiler, J. (Ed.), Inside the Subduction Factory. Vol. 138 of Geophysical Monograph. American Geophysical Union, pp Hughes, T. J. R., Winget, J., Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. International Journal for Numerical Methods for Engineering 15, Kameyama, M., Yuen, D. A., Karato, S., Thermal-mechanical effects on low-temperature plasticity (the Peierls mechanism) on the deformation of a viscoelastic shear zone. Earth and Planetary Science Letters 168, Katsura, T., Yamada, H., Shinmei, T., Kubo, A., Ono, S., Kanzaki, M., Yoneda, A., Walter, M. J., Ito, E., Urakawa, S., Funakoshi, K., Utsumi, W., Postspinel transition in Mg2SiO4 determined by high P-T in situ X-ray diffractometry. Physics of the Earth and Planetary Interiors 136 (1 2), Mackwell, S. J., Zimmerman, M. E., Kohlstedt, D. L., High temperature deformation of dry diabase with application to tectonics on Venus. Journal of Geophysical Research 103 (B1), Popov, A. A., Sobolev, S. V., Slim3d: A tool for three-dimensional thermomechanical modeling of the lithospheric deformation with elasto-visco-plastic rheology. Physics of the Earth Interiors 171,

12 Quinteros, J., Sobolev, S. V., Constraining kinetics of metastable olivine in Marianas slab from seismic observations and dynamic models. Tectonophysics (0), Quinteros, J., Sobolev, S. V., Popov, A. A., Viscosity in transition zone and lower mantle. Implications for slab penetration. Geophysical Research Letters 37, L Simo, J. C., Taylor, R. L., Consistent tangent operators for rateindependent elasto-plasticity. Computer Methods in Applied Mechanics and Engineering 48, Steinberger, B., Calderwood, A., Models of large-scale viscous flow in the Earth s mantle with constraints from mineral physics and surface observations. Geophysics Journal International 167,