Global scale models of the mantle flow field predicted by synthetic tomography models
Introduction
Understanding the global-scale velocity field associated with convection in Earth's mantle has been a long-standing pursuit in the geophysical community. Such an understanding is essential to constrain plate driving forces, geoid variations, lithospheric stresses and the thermal and compositional structure of the mantle. If plate motions are prescribed at the surface, return flow and mantle tractions can be computed (Hager and O’Connell, 1981). Constraints on the buoyancy-driven component of flow outside subduction zones arrived with the advent of global seismic tomography (e.g., Dziewonski et al., 1977, Dziewonski, 1984, Woodhouse and Dziewonski, 1984) as seismic velocity anomalies were interpreted in terms of density perturbations (e.g., Hager et al., 1985, Hager and Clayton, 1989, Ricard and Vigny, 1989). Subsequently, several models of the large-scale velocity fields of the mantle have been proposed (e.g., Richards and Hager, 1984, Ricard et al., 1984, Ricard et al., 1989, Forte and Peltier, 1987, Forte and Peltier, 1991, Hager and Clayton, 1989, Hager and Richards, 1989, King and Masters, 1992, Forte et al., 1994, King, 1995, Lithgow-Bertelloni and Richards, 1998, Becker and O’Connell, 2001, Forte and Mitrovica, 2001) and have been widely used to investigate upper mantle anisotropy (e.g., Becker et al., 2003, Gaboret et al., 2003, Conrad et al., 2007); geoid undulations (e.g., Cadek and Fleitout, 1999, King and Masters, 1992); surface uplift (e.g., Gurnis et al., 2000); tectonic plate velocities (e.g., Becker and O’Connell, 2001, Conrad and Lithgow-Bertelloni, 2002, Becker, 2006); lithospheric stress field (e.g., Steinberger et al., 2001, Lithgow-Bertelloni and Guynn, 2004) and upper mantle thermal structure (e.g., Cammarano et al., 2003). Comparisons of computed parameters, such as heat flux, plate motions, geoid and lithospheric stresses with the observations help assess the success of the models (e.g., Steinberger and Calderwood, 2006).
The global-scale mantle flow field is typically calculated from the Stokes and continuity equations for a given density distribution and mechanical boundary condition. Currently, one method of deriving such a density structure relies on converting a seismic tomography model into a density field (i.e., buoyancy structure) using relationships from mineral physics. Although widely used, there are several caveats to this method. Firstly, the resolution of seismic tomography models is inherently spatially heterogeneous due to an uneven and incomplete seismic sampling of the mantle (Fig. 1) (e.g., Mégnin et al., 1997). Ritsema et al. (2007) showed that the inhomogeneous data coverage and the damping applied in tomographic inversions result in suppressed short wavelength structures, removal of strong velocity gradients and artificial stretching and tilting of shear-wave velocity anomalies throughout the mantle. As such, if the tomographic model used to derive a density field distorts thermal and chemical heterogeneity in the mantle, the result will be a blurred image of mantle structure (e.g., Schubert et al., 2004, Ritsema et al., 2007, Bull et al., 2009, Schuberth et al., 2009) which could potentially lead to significant misinterpretations and uncertainties when this density field is used to calculate the instantaneous flow field. Secondly, the interpretation of the seismic wavespeeds in terms of density perturbations depends on relations derived from mineral physics (e.g., Karato and Karki, 2001, Stixrude and Lithgow-Bertelloni, 2005). Estimates of the relationship between observed seismic wavespeed anomalies and density defined as:vary from −0.2 to 0.4 for most materials, however there is no clear consensus on how to apply a pressure-dependence to the relationship over the depth of the mantle (e.g., Chopelas, 1992, Karato, 1993, Karato and Karki, 2001, Cammarano et al., 2003). Accordingly, most studies use constant values of the velocity–density relationship as a function of depth. One key issue in interpreting the tomographic model is whether the observed seismic anomalies have a thermal or chemical origin and how to translate that to density. As a result, several different formulations have been used. These include ignoring velocity or density variations in the uppermost 200–300 km of the mantle where the velocity structure is thought to be dominated by chemical heterogeneity (e.g., Jordan, 1978, Thoraval and Richards, 1997, Lithgow-Bertelloni and Silver, 1998), using a constant value for R throughout the upper mantle and allowing R to vary smoothly in the lower mantle (e.g., Forte et al., 1995, Cammarano et al., 2003), using a constant value throughout the entire mantle below 200 km (e.g., Steinberger et al., 2001), imposing near-zero or negative values in the lowermost mantle (e.g., Gurnis et al., 2000, Karato and Karki, 2001, Matas and Bukowinski, 2007), and determining the relationship through probabilistic tomography (e.g., Resovsky and Trampert, 2003). As such, global-scale mantle flow fields derived using this method may be subject to scaling errors that arise from imperfect or insufficient mineral physics data. Although it is possible to use self-consistent thermodynamic calculations (e.g., Stixrude and Lithgow-Bertelloni, 2005) to derive temperature-, pressure- and compositional-dependent seismic wavespeeds throughout the depth of the mantle, such an approach relies upon knowledge of the compositional structure of the mantle. We have used this approach in previous work (Bull et al., 2009); however in this work, we focus on investigating more classical approaches to density-wavespeed conversions.
One way to investigate the method of using seismic observations to derive global-scale 3D models of the mantle flow field is to run joint seismological and geodynamic inversions (e.g., Simmons et al., 2007). Here, we focus on a different approach and use a multi-disciplinary technique developed in previous work (Ritsema et al., 2007, Bull et al., 2009) to investigate the use of seismic tomography observations to mantle flow field models. We investigate how (1) the resolution of the seismic model and (2) the relationship used to interpret wavespeed anomalies in terms of density perturbations affect the calculated flow field. We create a synthetic tomography model from a 3D spherical whole mantle geodynamic convection model using the resolution matrix of the seismic tomography model, S20RTS (Ritsema et al., 1999, Ritsema et al., 2004), as an effective “seismic filter” to capture the variable resolution inherent to seismic tomography. We compare flow patterns of the global mantle flow fields from both the original convection model which serves as the control case and from a similar convection model that differs in that it uses the buoyancy field derived from the synthetic tomography model of the control case as an initial condition.
We find that, to first order, the global velocity field predicted by the synthetic tomography model correlates well with the flow field from the original convection model throughout most of the mantle, however in regions where the resolving power of the seismic model is low, agreement between the models is reduced. We also note that the flow field from the synthetic tomography model is relatively independent of the density–velocity scaling ratio used for the four typical profiles investigated in this work.
Section snippets
Global-scale velocity field from the geodynamics model
Following the general approach of Davies and Bunge (2001), we calculate the global-scale mantle flow field using the 3D spherical finite-element convection code CitcomS (Zhong et al., 2000) to solve an instantaneous Stokes flow calculation for a whole-mantle convection model. For this global circulation model (GCM), we impose a free-slip boundary condition at the surface. To create an initial condition for the GCM we first use CitcomS to solve a time-dependent convection calculation over the
Results
Fig. 3a shows the resulting temperature field (i.e., buoyancy field) derived from the 3D spherical geodynamical calculation (i.e., the GCM) projected onto a Cartesian box. Clusters of upwelling thermal plumes (red color) form beneath the Central Pacific and the African region while downwellings (blue color) are focused along the outer edge of the Pacific basin where lithosphere is subducting. We performed a resolution test using 12 × 96 × 96 × 96 (from 12 × 64 × 64 × 64) elements to verify that the small
Discussion
In this work, we investigated possible caveats associated with using seismic observations to calculate flow fields. As global-scale mantle flow fields are widely used in many aspects of geophysics, such as seismic anisotropy studies (e.g., Becker et al., 2003, Behn et al., 2004), investigations of tectonic driving forces (e.g., Lithgow-Bertelloni and Silver, 1998, Becker and O’Connell, 2001, Conrad and Lithgow-Bertelloni, 2002) it is important to have constraints on the reliability of the
Conclusions
In this work, we investigated several possible caveats associated with using seismic observations to calculate flow fields: (1) the resolving power of the tomographic model may affect the calculated flow field and (2) the relationship used to interpret seismic anomalies in terms of density is not well-constrained over the depth of the mantle.
We find these general conclusions.
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The global-scale mantle velocity flow field predicted by the Tomography-Derived model correlates well with the flow field
Acknowledgements
The authors would like to thank Dr. S.D. King and Dr. C. Beghein for their constructive reviews and insightful comments. Discussions with Dr. A. Clarke, Dr. M. Fouch, Dr. E. Garnero and Dr. J. Tyburczy aided greatly in the creation of the final manuscript. The authors would also like to extend gratitude to Dr. F. Timmes for access to ASU's high performance computing center which was invaluable to this research. The work in this manuscript was supported by grants NSF: EAR-0838565 and NSF:
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