1. Investigating Large-Scale Mantle Heterogeneity using the Thermochemical Extension of CitcomS Allen K. McNamara Department of Geological Sciences Arizona State University Thanks to: Shijie Zhong, Carolina Lithgow-Bertelloni, Thorsten Becker, Ed Garnero, Jeroen Ritsema, Chuck Meertens

2. 1.Why thermochemical mantle models? 2.Conceptual models based on previous work 3.Goal and Method 4.Fluid dynamical studies on thermochemical convection in a spherical geometry 5.Thermochemical convection using Earth’s recent plate velocity history

3. Observations that hint at compositional heterogeneity in the mantle  Seismic tomography  Raypath studies  Normal mode studies (e.g. Ishii and Tromp, 1998, 2004)  Geochemistry  Heat budget arguments

4. Pacific AmericaAfricaAsia Ritsema et al. (1999, 2004)

5. Bunge et al. (2002) Ritsema et al. (1999, 2004)

6. (Ni and Helmberger, 2003)

8. Wang and Wen (2004)

9. Ishii and Tromp (1999, 2004) Shear velocity Bulk sound velocity Density

10. Davaille (2003) Superplumes (unstable upwelling structures) Higher viscosity dense layer Lower viscosity dense layer

11. Olson and Kincaid (1991)

12. Tackley (1998, 2002)

13. Jellinek and Manga (2004)

14. McNamara and Zhong (2004)

15. Kellogg et al. (1999) Jellinek and Manga (2004) Tackley (1998, 2000) Davaille (2002)

16. Important Questions 1.Do thermochemical piles exist? Can geodynamics reveal whether their existence can be constrained? 2.If dense piles exist:  What is their volume?  What is their intrinsic density?  What is their rheology?  Are they passive or active convection features?  Are they stable or unstable?  Are they primordial or are they being renewed. 3. If dense piles exist, can we use them as tools (when compared to observations) to constrain:  Depth-dependent thermal conductivity and expansivity  Lower mantle viscosity  Earth’s recent plate history

17. Challenges Large parameter range - viscosity formulation, density contrast and volume of dense material, depth-dependent parameters, phase changes, extended Boussinesq features (viscous dissipation, adiabatic heating/cooling), compressibility, mode of heating (internal, core), initial condition, plate tectonics. Numerical capabilities Of course its unlikely that we can answer all of these questions, but we may be able to ‘chip away’ at them by designing numerical experiments to test specific hypotheses.

18. CitcomS (Zhong et al., 2000) Boussinesq Approximation Parallel 12/24 processors 1 - 3 million elements 10-30 million tracers

19. Tracer Advection Ratio Tracer Method (e.g. Tackley and King, 2003) Non-standard aspects of tracer advection in CitcomS 1. Finding which element a tracer is in.  use a finer “regular” mesh (e.g. van Keken and Ballentine (1998), McNamara et al. (2003)) 2. Interpolation of tracer velocity  Difficult for CitcomS elements  Transform coordinates using gnomonic transformation  Ci Ci # of tracers C element =

20. Elements are bounded by great circle planes. Element boundaries are not related to coordinate system.

21. If the cross products of a boundary vector and a vector pointing to a tracer is in the positive r direction for all 4 boundaries, the tracer is in the element. But this is slow.

22. Superimpose a very fine regular grid which is aligned with the spherical coordinate system

23. Map the regular mesh to the real CitcomS mesh before the first timestep

24. Interpolating velocity of a tracer First, transform the great circle plane boundaries to rectangular boundaries using gnomonic transformation. This can be done and saved before the first timestep.

25. u= v= Gnomonic Projection – great circles transform to straight lines

26.  Determine u and v for the tracer.  Split upper and lower surfaces into 2 triangles each and determine which one the tracer is in.  Using standard shape function methods for triangular elements, interpolate velocity for the tracer within each triangle.  Weight by distance to upper and lower surfaces. u v

27. First step: Generalized fluid dynamical experiments Investigate thermochemical convection in a spherical geometry Parameters to investigate: viscosity formulation, density contrast, volume of dense material. Hypothesis: Thermochemical convection in a spherical rheology lead to the formation of a few, large piles of dense material.

28. Isoviscous B=0.8 compositiontemperature

29. Isoviscous B=0.7 compositiontemperature

30. Temperature Dependent B=0.8 compositionLog viscosity

31. Temperature Dependent B=0.7 compositionresidual

32. temperaturecomposition

34. Temperature Dependent B=0.5

35. composition Temperature and Depth Dependent B=0.8

37. compositionLog viscosity T, C (100x) dependent B=0.7

38. compositionresidual T, C (500x) dependent B=0.7

39. composition temperature T, C (500x) dependent B=0.6

42. Some conclusions from more-general fluid dynamical experiments  Temperature-dependence leads to hot, weak piles that form a ridge-like pattern (similar to Cartesian studies!)  Low density contrasts lead to unstable, doming structures (similar to Cartesian studies!)  Depth-dependent viscosity leads to large, ridge-like linear piles  Addition of compositional rheology leads to long-lived, stable rounded dome structures (similar to Cartesian studies?)  Rheology plays the largest role. The spherical geometry does not.

43. Hypothesis Earth’s recent (last 119 million years) subduction history acts to guide thermochemical structures into 2 piles beneath Africa and the Pacific with trends similar to that observed in the tomography and ray path studies. Assumptions Stable dense piles exist. (not in a state of overturn) Temperature-dependence of rheology dominates (negligible compositional-dependence)

44. Plate Velocities (Lithgow-Bertelloni and Richards, 1998) 119 Million Years (11 stages) Approach similar to Bunge et al. (1998, 2002)

45. Internal and bottom heating Temperature dependence of viscosity - 10 4 contrast Depth dependence of viscosity (weak upper mantle, 30x jump at 660, linear increase to 300 at CMB) Earth-like convective vigor (Ra > 10 8 defined by upper mantle viscosity) viscosity ~ 3 x10 20 in upper mantle, ~10 23 deep lower mantle

46. 10 22 10 23 10 21 10 20 Viscosity profile

47. Control Case #1 Thermochemical Convection with no plate motions

48. Control Case #2 Isochemical Convection with plate motions

52. (figure courtesy of Chuck Meertens, GEON)

53. History is important 11 stages Present day velocities – 119 million years

54. Example: Viscosity Profile Depth-dependent Jump at 660 Straight viscosity profile

55. Initial condition 2D profile Stage 1 – 60myr Stage 1 – 120myr

56. Conclusions The general morphology of thermochemical piles in Cartesian and spherical geometries is similar. Temperature and depth-dependent rheology lead to the formation of large, linear, passive piles Recent plate history leads to the development of:  2 nearly antipodal piles beneath Africa and the Pacific  A linear NW-SE trending structure beneath Africa  A set of overlapping ridges beneath the Pacific A decent reference model starting point? Next steps:  Investigate the error associated with unknown initial condition at 119 Ma  Put geodynamical results through a tomographic filter to better correlate spatially with tomography  Determine whether we may place reliable constraints upon lower mantle viscosity and dense component density and volume. Are the “error bars” are small enough for this work to tell us something useful?

57. Next Step: put results through a ‘tomographic filter’ and produce correlation charts. B volume B Find the controlling parameters. Create charts such as these for the different controlling parameters Viscosity profile 1Viscosity profile 2 75 % 50 % 25 %