The influence of phase boundary deflection on velocity anomalies of stagnant slabs in the transition zone

GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 18, 1965, doi:10.1029/2003gl017754, 2003 The influence of phase boundary deflection on velocity anomalies of stagnant slabs in the transition zone K. Chambers 1 Department of Geology, University of Durham, UK R. N. Pysklywec Department of Geology, University of Toronto, Canada Received 15 May 2003; revised 9 July 2003; accepted 14 August 2003; published 27 September 2003. [1] Although the behavior of subducted slabs in the mantle transition zone remains uncertain, images from seismic tomography provide insight into a rather complex geodynamic evolution of slabs in this region. Using a numerical mantle convection model we consider in more detail the dynamics of subducted slabs around an endothermic phase change at 660 km depth. The timedependent temperature fields from the flow simulation are used to derive perturbations from a radially stratified seismic velocity model. We find that the positive velocity anomalies of the cold descending slabs may be significantly decreased at the phase change owing to the slab-induced downward phase boundary deflection and associated velocity discontinuity across the boundary. The slab may be completely or partially rendered seismically undetectable, depending on the amount of phase boundary deflection. The results have implications for the seismic interpretation of the dynamics of subducted slabs interacting with a phase transition. INDEX TERMS: 7207 Seismology: Core and mantle; 8120 Tectonophysics: Dynamics of lithosphere and mantle general. Citation: Chambers, K., and R. N. Pysklywec, The influence of phase boundary deflection on velocity anomalies of stagnant slabs in the transition zone, Geophys. Res. Lett., 30(18), 1965, doi:10.1029/2003gl017754, 2003. 1. Introduction [2] Despite the importance of subduction in plate scale mantle flow [Davies and Richards, 1992] many of the details concerning the behavior of subducted lithosphere in the mantle remain uncertain. Particularly enigmatic is the behavior of subducted slabs in the transition zone. The primary observational constraints on the dynamics of subducting slabs at the phase boundary comes from images produced by seismic tomography [Grand, 1994; van der Hilst, 1995; Bijwaard et al., 1998; Fukao et al., 2001]. These tomographic models show variably slabs that deflect at 660 km depth, penetrate through to the coremantle boundary, or are discontinuous with gaps in their seismic velocity anomaly. 1 Now at Department of Earth Sciences, University of Oxford, Parks Rd., Oxford, OX1 3PR, UK. Copyright 2003 by the American Geophysical Union. 0094-8276/03/2003GL017754 SDE 9-1 [3] The transition zone is bounded by the polymorphic transformation of a-olivine to b-olivine at around 410-km depth, and the breakdown of g-olivine at around 660 km depth (henceforth the 410 and 660). These phase transformations are believed to be associated with significant density and seismic velocity increases [Fei et al., 1991; Helffrich, 2000; Chudinovskikh and Boehler, 2001; Shim et al., 2001], and may have important thermodynamic effects on mantle material passing through. [4] The endothermic nature of the 660 phase change causes the phase boundary to be deflected downwards when cold material (e.g. a subducting slab) impinges on the boundary [Christensen and Yuen, 1984; Christensen and Yuen, 1985]. Due to the density increase associated with the phase change, sinking lithosphere has reduced negative buoyancy in the region of the deflected phase boundary. This has been suggested as one mechanism for producing stagnant lithosphere in the transition zone [Ringwood, 1991]. An alternative mechanism is a viscosity jump associated with the 660 phase change. This would resist transfer of material across the boundary and affect the orientation and shape of an impinging slab [Gurnis and Hager, 1988]. Trench roll-back and other geodynamical processes have also been suggested as mechanisms for the creation of horizontal slabs around 660 km depth [van der Hilst, 1995; Christensen, 2001]. However, these processes can only produce a temporarily horizontal slab in the transition zone. To create quasistagnant lithosphere, interaction with a phase or viscosity boundary is required. [5] Here, we use forward modelling to consider in more detail the seismic expression of a subducting slab near the 660 km endothermic phase transition. The models are designed to highlight the effects of phase changes on the modelled seismic velocity anomalies of subducted lithosphere. Accordingly, the results of this study should be interpreted in terms of the seismic manifestation of subducted lithosphere in the mantle rather than as a fully realistic simulation of mantle convection in the Earth. 2. Modelling Slab Dynamics in the Transition Zone [6] The convection model (Figure 1) is based on spherical axisymmetric solutions to the coupled equations which govern flow in an infinite Prandtl number, anelastic fluid [Solheim and Peltier, 1990; Solheim and Peltier, 1994; Pysklywec and Mitrovica, 2000]. The model utilises the

SDE 9-2 CHAMBERS AND PYSKLYWEC: TRANSITION ZONE SLAB VELOCITY ANOMALIES Figure 1. A Geometry for the convection model. Subsequent plots consider only the area surrounding the slab as indicated by the box. The slab was configured to initially extend to 360 km depth, have width of 100 km, and dip 30. B Temperature and viscosity profiles through the model prior to the introduction of the slab. (g 660 ). Most independent measurements of g 660 place it in the range 1.9 to 4.5 MPaK 1 [Akaogi and Ito, 1993; Bina and Helffrich, 1994; Chudinovskikh and Boehler, 2001; Shim et al., 2001]. In the numerical experiments we adopt two values for g 660 within this range: 2.9 and 3.8 MPaK 1. We also present an illustrative model run which used a (probably unrealistic) g 660 value of 6.9 MPaK 1 to demonstrate the effect of extremely large discontinuity deflections. Where a 410-km phase change was included a Clapeyron slope of +2.9 MPaK 1 was used [Bina and Helffrich, 1994; Helffrich, 2000]. [10] Figure 2 shows the results from three model runs. In all the numerical experiments the cold dense slab descends essentially vertically, but is hindered by the thermodynamic effects of the 660 phase change. In model A, with the lowest Clapeyron slope the slab is retained for the least time at the phase boundary and hence penetrates furthermost into the lower mantle. The model B shows a slab that ponds at the phase transition for about 40 Myr longer than that in model run A. The slab in model run C does not reach the lower mantle in the time frame considered in Figure 2. characteristic scales of Pysklywec and Mitrovica [2000]. Temperature (T) was nondimensionalised using T T b T c where T b is the surface temperature (300 K), and T c is the temperature difference across the mantle (5600 K). [7] For the experiments a background mantle state was generated by running the model for 40 Gyr at progressively higher Rayleigh numbers until 1.5 10 8 was reached (based on an upper mantle reference viscosity of 5 10 20 Pas and characteristic temperature T c = 5600K). The high Rayleigh number was required in order to obtain realistic flow velocities (1 2 cm/yr) in the mantle. A slab was introduced into the background field by setting the temperature field to lithospheric values over a slab shaped region (Figure 1). [8] Depth and temperature dependence for viscosity h (r, T 0 ) are incorporated into the model using the approach of Zhong and Gurnis [1994]: s 1 hðr; T 0 T Þ ¼ h r e 0 s 1 þs 2 1þs 2 ð1þ Where r is the radius and T 0 is the laterally varying nondimensional temperature. The radial viscosity profile (h r ) is based on joint inferences from postglacial rebound and mantle convection [Mitrovica and Forte, 1997]. The temperature dependence parameters s 1 and s 2 were taken as 2.5 and 0.5, respectively. These values were chosen to give an order of magnitude increase in viscosity through the 150 km thick lithosphere. Although this temperature dependence of viscosity is weaker than that in the Earth, it effectively produces strong subducting slabs [Pysklywec and Mitrovica, 2000] and does not exceed the numerical limitations of the finite difference convection model. [9] The only parameter modified between model runs was the Clapeyron slope for the 660 km phase transition Figure 2. Temperature fields from the model using different values for g 660. A 2.9, B 3.8, and C 6.9 MPaK 1. Models were run for 250 Myr with 80% internal heat generation. A used a phase change at 410-km. Trials (not shown here) found this to have little effect on the slab so it was omitted from B and C. The phase transitions occur over a depth range of 25 km, the centre of the phase change (i.e., 50% of each phase present) is shown as a line on each plot. Non-dimensional density changes for the 410 and 660 phase changes were taken as 0.07 and 0.08, respectively, [Fei et al., 1991]. Latent heating by the 660 km phase change is dependent on g 660 ; resulting values in the models were 59.2, 77.6, and 141.0 kj/kg in A, B and C respectively.

CHAMBERS AND PYSKLYWEC: TRANSITION ZONE SLAB VELOCITY ANOMALIES SDE 9-3 Figure 3. Lateral perturbations to a spherically symmetric P wave velocity model, derived from temperature fields of Figure 2 using equation 2. The values here are expressed as a percentage of the appropriate velocity in the 1-D reference model PREM [Anderson and Dziewonski, 1981]. [11] In all the models, the retention of a slab at the phase boundary is due to deflection of the phase boundary. The magnitude of phase boundary deflection, and hence the duration of slab ponding above the phase boundary, increases with the magnitude of the 660 Clapeyron slope. velocity distribution used. Q is also dependent on temperature and this would need to be taken into account in a more rigorous determination of seismic velocity. is the parameter set that is generally solved for by an inversion of travel-time data in seismic tomography. The velocity perturbations generated for a grid point in the model can be considered to be what would be seen if it was possible to invert for velocity anomalies independently, with the same resolution as the convection model. [14] Figure 3 shows P-wave velocity perturbations from a spherically symmetric velocity model derived from the temperature fields of Figure 2. A parallel calculation of the S-wave velocity perturbations (not shown here) demonstrated similar behaviour to the P-wave anomalies. These velocity perturbations roughly mimic the temperature plots from which they were derived. In particular, the velocity anomaly of each slab is distinct from the background. [15] Notably, there is a distinct evolution in the slab s velocity anomaly as it passes through the phase change. Above and below the 660 phase change the slab is clearly visible. However, during the stage when the slab is ponded at or actively penetrating through 660 km depth its seismic anomaly diminishes due to the downward deflection of the phase boundary. In the model where the slab descent has been inhibited by a downward deflection of the phase boundary (C), the slab has no velocity anomaly in this region. While in A and B, where the slab has penetrated into the lower mantle (due to a lower g 660 ) it is visible, except for a gap where the slab is interacting with the discontinuity. dv [13] v r 3. Velocity Anomalies of Ponded Slab Material [12] We used an exponential relationship to calculate velocity anomalies from the axisymmetric temperature fields, as this allows for the effects of anelasticity on the temperature derivative of seismic velocity. A similar approach, but in the opposite sense, was adopted by Cadek et al. [1994], to convert velocity anomalies to temperature fields. Relative perturbation from a radially symmetric model dv v r was calculated using equation 2. dv ¼ e lðtr;q ð Þ TrÞ þ d 410 þ d 660 1 ð2þ v r v r v r Where q is the azimuthal angle from the pole, and T r is the radially averaged temperature (in Kelvin). v r is a spherically symmetric velocity model [PREM, Anderson and Dziewonski, 1981], which contains seismic discontinuities at 410 and 660 km depth of 0.23 kms 1 and 0.49 kms 1 for P waves. These are interpreted as being related to the olivine pph hase transitions and so are added or subtracted in regions where the phase boundary is deflected (d 410 and d 660 ). The deflection was determined from the middle of the finite width phase transition in the numerical models. For l, the temperature derivative of velocity in terms of @lnv @T 0, we adopted values from Karato [1993] except for the upmost 200 km of the mantle which was taken as uniform. The values of Karato [1993] were based on the radial distribution of intrinsic attenuation (Q) by Widmer et al. [1991]. However, this is not entirely self consistent with the radial Figure 4. A cross section through the tomographic model of van der Hilst [1995] (reproduced with permission). The image shows a seismically fast anomaly (green/blue) interpreted as a subducting slab underneath Tonga (outlined by the dashed lines). The white circles represent Earthquake hypocentres and the question mark refers to an area of low resolution in the model. The image shows a clear region of seismically slow material (yellow/red) in the middle of the subducting slab just below 660 km depth. The feature is well resolved as the model utilises a variable cell size with layers 15 km thick between 590 and 730-km depth. We interpret this feature as possibly being related to the slabinduced downward deflection of the 660 km phase boundary, as our models predict. The colour scale is saturated at 3 and +2%.

SDE 9-4 CHAMBERS AND PYSKLYWEC: TRANSITION ZONE SLAB VELOCITY ANOMALIES Essentially, the temperature and phase related velocity changes counteract each other to produce a net velocity anomaly of zero in the region of the phase boundary deflection. [16] The magnitudes of the velocity perturbations calculated here (5 6%) are greater than those derived in tomographic inversions (<3%) [Grand, 1994; van der Hilst, 1995; Bijwaard et al., 1998; Fukao et al., 2001]. The temperature anomaly of the slab in our models ( 1100 K) is in order with values estimated from measured discontinuity deflections ( 900 1000 K at 410 km) [Collier et al., 2001]. So, differences are attributed to the lower resolution of tomographic inversions, which could result from larger cell sizes, non-uniform ray sampling, and non-independence between cells. This means that high amplitude short wavelength perturbations to velocity, observed in the models, would be averaged out. 4. Conclusions: Invisible Slabs at 660 km [17] The modelling results (Figure 3) suggest a subducting slab s velocity anomaly can be significantly reduced in the region of a deflected phase boundary. The velocity reduction due to the downward deflection of the phase boundary counteracts the velocity increase from the slabs colder temperatures. Velocity jumps at the phase boundary consistent with the spherically symmetric velocity model PREM [Anderson and Dziewonski, 1981] are sufficient to render portions of a ponded slab in the transition zone seismically undetectable. [18] This may be observed in Figure 4 which shows a cross section through the tomographic model of van der Hilst [1995] (reproduced with permission) which images a region of slower material just below 660 km depth within a seismically fast anomaly interpreted as the Tonga slab. The cold slab depressing the 660 phase boundary, and so lowering the velocity anomaly in these cells could create this type of slab gap, as the velocity models derived here predict. [19] The slab will only be completely hidden where the phase boundary is significantly deflected (>75 km). This only occurs in model C which uses an unrealistically steep g 660. Collier and Helffrich [1997], have measured 40 km depressions of the 660 discontinuity, in the vicinity of subducting slabs. This is more consistent with models A and B which show gaps in the slab s velocity anomaly. Accordingly, the amount of deflection should determine the amount of gap in the slab s velocity anomaly. [20] It would be also be expected that the reflection coefficient of the seismic discontinuity would be reduced where lithosphere is ponded above the boundary. This has been observed by Revenaugh and Sipkin [1994] who found that low reflection coefficients for the 660 km discontinuity correlated with topographic depressions of the discontinuity, using ScS reverberations. Reflections from the discontinuity would be further complicated where the slab has a gap in its velocity anomaly as it passes through the phase change. [21] We assume that the phase change may play a significant role in the formation of ponded slabs observed in tomographic images. Other flow inhibiting effects, such as a large viscosity increase near 660 km depth, may also contribute to this effect with less required deflection of the phase boundary. Alternatively, it may be possible that horizontal slabs at the base of the transition zone are simply snap-shots of horizontal sinking bodies rather than ponded lithosphere. However, the global frequency of such events [Fukao et al., 2001] would reduce the likelihood of this possibility. [22] Acknowledgments. We thank Mike Kendall and Glenn Milne for helpful suggestions and the contributions of two anonymous reviewers. We also thank Miaki Ishii for her clarification of the conversion of temperature to seismic velocity and Rob van der Hilst for the use of his tomographic image. KC benefited from NERC grant NER/S/M/2001/06673 in relation to this work. RNP was funded by the Natural Sciences and Engineering Research Council of Canada. References Akaogi, M., and E. Ito, Refinement of enthalpy measurement of MgSiO 3 perovskite and negative pressure-temperature slopes for perovskiteforming reactions, Geophys. Res. Lett., 20, 1839 1842, 1993. Anderson, D. L., and A. M. Dziewonski, Preliminary reference Earth model, Phys. Earth Planet. Inter., 25, 297 356, 1981. Bijwaard, H., W. Spakman, and E. Engdahl, Closing the gap between regional and global travel time tomography, J. Geophys. Res., 103, 30,055 30,078, 1998. Bina, C., and G. R. 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CHAMBERS AND PYSKLYWEC: TRANSITION ZONE SLAB VELOCITY ANOMALIES SDE 9-5 Solheim, L. P., and W. R. Peltier, Heat transfer and the onset of chaos in a spherical, axisymmetric, anelastic model of whole mantle convection, Geo. Astro. Fluid Dyn., 53, 205 255, 1990. Solheim, L. P., and W. R. Peltier, Avalanche effects in phase transition modulated thermal convection: A model of the Earth s mantle, J. Geophys. Res., 99, 6997 7018, 1994. van der Hilst, R., Complex morphology of subducted lithosphere in the mantle beneath the Tonga trench, Nature, 374, 154 157, 1995. Widmer, R., G. Masters, and G. Freeman, Spherically symmetric attenuation within the Earth from normal mode data, Geophys. J. Int., 104, 541 553, 1991. Zhong, S., and M. Gurnis, Role of plates and temperature-dependent viscosity in phase change dynamics, J. Geophys. Res., 99, 15,903 15,917, 1994. K. Chambers, Department of Earth Sciences, University of Oxford, Parks Road, Oxford, OX1 3PR, UK. (kitc@earth.ox.ac.uk) R. N. Pysklywec, Department of Geology, University of Toronto, 22 Russel Street, Toronto, Ontario M5S 3B1, Canada. (russ@geology. utoronto.ca)