Viscosity in transition zone and lower mantle: Implications for slab penetration

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1 Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 37,, doi: /2010gl043140, 2010 Viscosity in transition zone and lower mantle: Implications for slab penetration J. Quinteros, 1,2 S. V. Sobolev, 1,3 and A. A. Popov 1 Received 4 March 2010; revised 3 April 2010; accepted 13 April 2010; published 13 May [1] The evolution of a subducting slab is strongly influenced by the viscosity of the mantle which it overlies. However, there is still no consensus about the viscosity in the transition zone and shallower lower mantle. We use a numerical self consistent subduction model and run a set of experiments in order to find critical patterns of viscosity that would allow the evolution of the different subduction styles that can actually be found in nature. Our results show that a jump in viscosity of 5 times from transition zone to lower mantle gives the most reasonable results. Optimal values of viscosity in the transition zone are in the range of 3 * Pa s. Higher values would produce piling up of the slab and later sinking or even slab flattening. Lower viscosities result in velocities (>30 cm/yr) that are too high, while the new slab subducts through the upper mantle and transition zone, a phenomenon that is rarely seen in nature. Reduction of the Clapeyron slope, related to the spinel perovskite transition, variations in oceanic crustal thickness and in the age of the slab do not influence much the style of subduction. When overriding velocity is applied to the upper plate, the previously penetrating slab tends to lay at the 660 km boundary but does not substantially change the subduction velocity. Citation: Quinteros, J., S. V. Sobolev, and A. A. Popov (2010), Viscosity in transition zone and lower mantle: Implications for slab penetration, Geophys. Res. Lett., 37,, doi: /2010gl Introduction [2] It is accepted that over a long timescale, mantle behaves like a viscous fluid, while lithosphere can be seen as a brittle layer. However, a viscosity profile throughout the whole mantle is far from being accurate. Different models were proposed to find the best fit viscosity distribution based on the imposition of different sets of constraints (e.g., geoid, Haskell, tomography model) [King, 1995; Steinberger and Calderwood, 2006]. There are some common factors in all the possible profiles: 1) there seems to be a sharp viscosity increment between transition zone (TZ) and lower mantle (LM) and 2) a slow increase in viscosity with depth in the first hundreds of km of LM. [3] Many authors [e.g., Mitrovica and Forte, 2004] agree that the asthenosphere should be the layer with lowest viscosity. However, others claim that the TZ maybe weaker 1 Section 2.5, Deutsches GeoForschungsZentrum, Potsdam, Germany. 2 Department of Computer Sciences, FCEN, UBA, Buenos Aires, Argentina. 3 Institute of Physics of the Earth, Moscow, Russia. Copyright 2010 by the American Geophysical Union /10/2010GL than upper mantle (UM) and LM due to the presence of water stored in wadsleyite or ringwoodite. [4] We considered a range of possible viscosity values for the TZ presented by Steinberger and Calderwood [2006] and tested their feasibility by numerical simulation of a subducting slab. As viscosity values should be compatible with the different types of subduction detected by seismic tomography, in this work we present a set of experiments designed to study and constrain the possible critical patterns of viscosity that could determine the fate of the slab. [5] In the last decades stagnant slabs have been identified in different subduction zones (for a review see Fukao et al. [2009]). The positive Clapeyron slope associated with the olivine spinel phase transition at 410 km favours that the cold slab can go through it, accelerating the subduction process. The opposite situation seems to occur on the spinelperovskite phase transition at 660 km, where the Clapeyron slope is negative and inhibits or slows the subduction [Tackley et al., 1993]. Whether the slab is able to sink beyond this boundary depends, not only on the value of the Clapeyron slope, but also on other factors like absolute velocities of the plates and viscosity of the underlying mantle. [6] The increment on viscosity related to the 660 km boundary is likely present [e.g., Hager, 1984], but its magnitude remains unclear. In numerical experiments, this varies from 0 to 50 times [Čížková et al., 2002; Pysklywec and Ishii, 2005; Kaus et al., 2008; Enns et al., 2005]. 2. Previous Studies [7] Christensen [1996] studied the relationship of trench migration and slab penetration into lower mantle. He was the first who described different types of subduction styles as a function of the kinematically imposed trench retreat. One of the main drawbacks of the kinematic conditions applied is the lack of feedback between the subducted slab and the velocity of subduction that was held constant throughout all the simulations. [8] Čížková et al. [2002] performed a parametric study on rheological weakening in slabs that interact with the 660 km discontinuity. They varied the yield stress (in order to approximate Peierls creep mechanism) and the grain size. They conclude that stress limit is more important than grain size reduction in the evolution of the slab, because it controls the deformation on the outer rigid part of the slab, while grain size only decreases viscosity in the inner part [Karato et al., 2001]. They also claim that further studies should be made on the influence of stepwise viscosity increase at 660 km, among other factors. [9] Enns et al. [2005] investigated the influence of viscosity stratification on the trench migration. They showed that phase transition dynamics and density or viscosity 1of5

2 Figure 1. (a) Numerical model setup and boundary conditions. Subducting slab is 40 My old and is pushed on the left side for 2 My at 15 cm/yr to initiate subduction. (b) Viscosity plot and temperature contour in UM at the beginning of simulation. layering can produce a variety of ponded slab shapes near the 660 km boundary. However, the effects of the Clapeyron slopes for both phase transitions and of the increment of density related to the 410 km boundary were not taken into account. [10] Mishin et al. [2008] studied the penetration of the 660 km boundary by slabs in double subduction systems. They found that penetration is strongly influenced by the convergence rate and the relative movement of the overriding plate, among other factors. 3. Numerical Method and Set Up [11] We used a coupled elasto visco plastic thermomechanical numerical model based on code SLIM 3D [Popov and Sobolev, 2008] to run all experiments. As our set of experiments is inherently 2D, the setup contains only one element on one of the coordinates. The model has true free surface and elastic deformation is included. Realistic rheology was applied to the subducting and overriding plates as well as the upper mantle. In this part of the model, viscosity is stress and temperature dependent. Three different types of creep (diffusion, dislocation and Peierls) are included, following the approach of Kameyama et al. [1999]. In particular, Peierls creep plays a key role to reduce stress in the deep cold slab. A complete list of the parameters used can be found in the auxiliary material. 1 [12] Note that in this model we do not include adiabatic compression. Therefore, temperatures in the model are potential temperatures, i.e., temperatures extrapolated to zero pressure along adiabat. [13] Volumetric deformations are followed by corrections in the calculation of density by means of the Murnaghan approach. Density is increased by 6% at the olivine spinel phase transition [Christensen, 1995] and 8% at the spinelperovskite [Dziewonski and Anderson, 1981]. [14] All phase transition boundaries (gabbro eclogite, coesite stishovite, olivine spinel and spinel perovskite) in this 1 Auxiliary materials are available in the HTML. doi: / 2009GL implementation are dynamic. This means that their position is the result of application of the P T diagram at every timestep for every particle in the domain. Clapeyron slope for olivine spinel transition is considered to be +2.0 MPa/K and 2.5 MPa/K for the spinel perovskite. These values coincide with seismological data [Fukao et al., 2009] and laboratory experiments by Litasov et al. [2005] and Irifune et al. [1998]. [15] Subduction channel was considered as a well lubricated interface with low viscosity and friction coefficient, which favours the development of realistic one sided subduction [Sobolev and Babeyko, 2005; Gerya et al., 2008]. This interface is three elements wide, defined at every time step and restricted to the contact between oceanic and continental material at a depth less than 120 km, treated similarly by Sobolev and Babeyko [2005]. [16] The structure of the overriding plate was also handled as was done by Sobolev and Babeyko [2005]. It consists of a continental crust (40 km) and lithospheric mantle up to a depth of 100 to 140 km. [17] Subducting slab is composed of 7 km of oceanic gabbro and 73 km of oceanic lithospheric mantle. It is considered to have a thermal age of 40 My, but according to Christensen [1996], slab age does not play a key role when determining the style of subduction. Trench motion is allowed and in none of our experiments was imposed neither kinematically nor by another means. [18] No overriding is prescribed in most of our experiments in order to isolate the influence produced by the tested values. However, some experiments where repeated with overriding velocity to estimate the influence on results. [19] The viscosity profile of TZ and LM was represented in a simplified way by means of two parameters: viscosity in TZ and viscosity step at the spinel perovskite phase transition. [20] We focus not only on the more realistic range of 5 to 30 times higher viscosity in LM, according to the results of Steinberger and Calderwood [2006], but also include simulations without a jump to evaluate the differences. The viscosity for TZ considered ranges from to 3 * Pa s as suggested by Steinberger and Calderwood [2006]. 2of5

3 Figure 2. Different styles of subduction detected in the experiments. Viscosity is shown in colours and temperature with contours. A vertical viscosity profile taken at x = 300 km is shown inside every plot. (a) Penetrating slab; (b) penetrating slab with some buckling; (c) piling up and slow sinking after flat slab with late penetration under subduction zone; (d) flat slab. [21] The domain is 1700 km wide and 1300 km deep. Slab is pushed with a constant velocity of 15 cm/yr at the beginning of simulation at its left edge for 2 My to develop the subduction zone and obtain a coherent thermal state. After that moment evolution is driven by gravity. A schematic view of the setup can be seen in Figure 1. [22] Left side of the domain is opened as only hydrostatic pressure boundary conditions were defined. This gives the slab the freedom to move on any direction and with any velocity and assures that subduction will evolve in a selfconsistent way. The top side of the domain is a free surface with zero stress. On the bottom and right side free slip conditions are applied. 4. Results [23] More than 40 experiments have been run and classified in order to find constraints on the viscosity pattern. Examples of the different styles of subduction that were classified based on the experiments are shown in Figure 2, from direct penetration (Figure 2a) to slabs that lay over the 660 km boundary (Figure 2d). [24] Taking Figure 2a as a reference case, one can see in Figure 2b that the increment of viscosity in TZ reduces subduction velocity by about 2 3 times (see Figure 3) and how penetration of a small part of the subducted slab is reaccommodated by slight buckling. [25] A very similar situation (not shown) is obtained if the viscosity step between TZ and LM is increased. Even if this is not enough to stop the subduction, it is actually retarded in LM. If the jump is further increased (Figure 2c) it is more difficult for the head of the slab to sink and this causes folding and piling up of the slab, which slowly reactivates the sinking process. [26] In the last case (Figure 2d) TZ and LM are more viscous and thus offer more resistance to slab penetration. Subduction velocity diminishes to 1 3 cm/yr during almost the whole simulation ( 50 My). At My slab starts folding and velocity increases slightly. Slab flattens even before being close to LM, what delays the contact until 3of5

4 Figure 3. Subduction velocity corresponding to experiments without overriding separated by viscosity in TM; (top) 3 * 10 20, (middle) 10 21, and (bottom) 3 * Pa s. Bold arrows indicate the moment when slab contacts or crosses the 660 km phase transition boundary. Codes in legends indicate the viscosity step. Subduction style is specified next to the lines. See caption in Table 1 for description. 23 My. As subduction continues, many mln. years later a pile is formed and slowly sinks. [27] In all the experiments, subduction accelerates when slab enters TZ. The main cause is the positive Clapeyron slope related to the olivine spinel phase transition, which further increases the density contrast caused by the low temperature. Velocity is reduced when the head of the slab gets closer to the 660 km boundary and after that it becomes stable for the next mln. years (see Figure 3). Depending on the case, one possibility is that subduction can go further but, if subduction velocity is faster than sinking velocity, folding of the slab can occur. In this case, subduction reactivates after folding and velocity increases causing piling up of the slab and slowly sinking of the pile. During this process of piling up and sinking, neither avalanche type nor drastic changes in the lower mantle flux were observed. [28] A summary of the cases without overriding, classified by viscosity in TZ and the jump between TZ and LM, can be seen in Table 1. These were categorized using a similar classification as suggested by Christensen [1996]. [29] It is important to mention that in comparison with Christensen [1996] much less buckling was found. The main cause seems to be the absence of kinematical boundary conditions for the slab. If the subduction velocity were kinematically imposed, slab would not be able to reduce its velocity when hitting the 660 km boundary and would generate spurious buckling. [30] Interestingly, in almost all the experiments, viscosity in TZ was higher than the one in the bottom of UM (Figure 2). [31] Additional experiments to test the influence of other variables show that substantial reduction of Clapeyron slope at 660 km has almost no influence on the results. We also ran experiments with an oceanic crust of 10 and 12 km and Table 1. Summary of Models Without Overriding a Viscosity in TM (in Pa.s) m lm /m tz * * P P P (B) 5 P P (B) RP PIL SP 10 P RP (B) FS PIL SP 20 P RP (B) RP PIL SP F PIL SP 30 P RP PIL SP FS PIL SP F PIL SP a P, straight penetration of slab; RP, retarded penetration; B, buckling; PIL, slab folding and piling up; SP, pile sinking into LM; FS, flat slab, then penetration near subduction zone; F, flat slab. 4of5

5 the subduction styles were not changed, while velocity patterns suffered only minor changes. Inclusion of overriding velocity influenced on the subduction style (more stagnant slabs) but not on the velocity pattern. 5. Conclusions [32] From our results we can conclude that the most reasonable range of viscosity values for the TZ would be (3 * ) Pa s. A value of 3 * is too high to allow a subducting slab to penetrate into the LM with a reasonable velocity if a viscosity step is present. The same situation arises if the viscosity step is greater than 10, in which case a piling up of material next to the LM or flat slabs can be seen, but no direct penetration. It should also be noted that, for higher viscosity jumps, viscosity in LM would be too large under certain combinations. A substantial reduction of the Clapeyron slope at the 660 km boundary did not help to enhance subduction and showed only a small influence over the evolution of the slab. [33] On the other hand, when viscosity in TZ is significantly lower than 3 * Pa s slab accelerates to more than 30 cm/yr while (or before) penetrating the TZ, a phenomenon that is rarely seen in nature. If viscosity step is not present, exaggerated or very high velocity values are also obtained for the most reasonable viscosity. The best results, considering the obtained subduction velocities, were obtained with a step around 5. Even if overriding velocity can change the style of subduction toward more flattened slab, it cannot reduce the exaggerated velocities obtained with the low values of both variables. [34] With a viscosity of 3 * Pa s in TZ, a step between 5 and 10 gives the best velocity patterns, considering that this is a case of fast subduction (15 cm/yr at the beginning). If viscosity is Pa s, the step between TZ and LM should be smaller than 5 in order to get reasonable subduction velocities. These viscosity values are in agreement with those suggested by Billen [2008]. 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