1. Bernhard Steinberger Mantle evolution and dynamic topography of the African Plate Deutsches GeoForschungsZentrum, Potsdam and Physics of Geological Processes, Univ. Oslo and Center for Advanced Studies, Oslo

2. Understanding the mantle contribution to surface uplift and subsidence over time on a large scale Motivation

3. Dynamic topography influences which regions are below sea level, and at what depth, and therefore where sediments and related natural resources may form Before attempting to compute uplift and subsidence in the geologic past, we must first understand present-day dynamic topography Present-day topography

4. Dynamic topography influences which regions are below sea level, and at what depth, and therefore where sediments and related natural resources may form Before attempting to compute uplift and subsidence in the geologic past, we must first understand present-day dynamic topography Present-day topography + 200 m

5. Dynamic topography influences which regions are below sea level, and at what depth, and therefore where sediments and related natural resources may form Before attempting to compute uplift and subsidence in the geologic past, we must first understand present-day dynamic topography Present-day topography minus 200 m

6. Outline Mantle flow models based on seismic tomography Dynamic topography for present-day – computation and comparision with observations Inferring uplift and subsidence in the past from backward-advection of density anomalies and plate reconstructions

7. Seismic tomography S-wave models (here: tx2007 of Simmons, Forte and Grand)

8. Seismic tomography S-wave models (here: tx2007 of Simmons, Forte and Grand) Conversion factor ~ 0.25 (Steinberger and Calderwood, 2006) – 4 % velocity variation ~ ~ 1 % density variation Remove lithosphere

9. Seismic tomography Converted to density anomalies Conversion factor ~ 0.25 (Steinberger and Calderwood, 2006) – 4 % velocity variation ~ 1 % density variation Remove lithosphere

10. Computation of dynamic topography radial viscosity structure based on mineral physics and optimizing fit to geoid etc. (Steinberger and Calderwood, 2006)‏ Computation of dynamic topography through topography kernels (above: stress- free upper boundary; below: normal-stress- free with zero horizontal motion)

11. Actual topography What to compare computations to for present-day

12. Actual topography MINUS Isostatic topography What to compare computations to for present-day

13. Actual topography MINUS Isostatic topography Non-isostatic topography = What to compare computations to for present-day

14. Comparision non-isostatic vs. dynamic topography TX2007 tomography Lithosphere removed (cutoff 0.2%)

15. Non-isostatic topography What to compare computations to for present-day

16. Non-isostatic topography MINUS Thermal topography What to compare computations to for present-day

17. Non-isostatic topography residual topography MINUS Thermal topography = What to compare computations to for present-day

18. Comparision residual vs. dynamic topography TX2007 tomography Lithosphere removed (cutoff 0.2%) Sea floor cooling removed

19. Comparision residual vs. dynamic topography TX2007 tomography Lithosphere not removed Sea floor cooling removed

20. Correlation globally Correlation on African plate Correlation and ratio of dynamic vs. residual topography Ratio globally Ratio on African plate Best fit (in terms of variance reduction)

21. Correlation globally Correlation on African plate Correlation and ratio of dynamic vs. residual topography Ratio globally Ratio on African plate Best fit (in terms of variance reduction) Further improvements by combination with surface tomography models, or...

22. Correlation globally Correlation on African plate Correlation and ratio of dynamic vs. residual topography Ratio globally Ratio on African plate Best fit (in terms of variance reduction) Mixing tomography models – here: Princeton P and S models PRI-P05 PRI- S05

23. TOPOS362D1 J362D28-P 4 6 TX2007 S20RTS 9 1 4 6 6 4 SAW24B16 SAW642AN PRI-S05 PRI-P05 Harvard Princeton Berkeley «smean» 2 8 7 3 East West 6 4

24. Further improvements possible by using other lithosphere models Best results when using lithosphere thicknesses from Rychert et al. (based on seismic observations of Lithosphere-Asthenosphere-Boundary) where data are available...

25. Further improvements possible by using other lithosphere models Best results when using lithosphere thicknesses from Rychert et al. (based on seismic observations of Lithosphere-Asthenosphere-Boundary) Where data are available -- and the lithosphere model TC1 of Irina Artemieva (based on heat flow) elsewhere

26. Comparision residual vs. dynamic topography MIX-A tomography Lithosphere from Rychert et al. (2010) and Artemieva (2006) Sea floor cooling removed

27. How much of the discrepancy is due to errors in observation-based “residual topography” and how much due to errors in modelled “dynamic topography”? What are the regional differences in this discrepancy? How does the agreement depend on spherical harmonic degree? Instead of looking at dynamic topography “in isolation” we hope to gain insight through also considering the geoid: Can we match the “expected” correlation and ratio of geoid and topography?

28. Model prediction for no-slip surface Model prediction for free-slip surface Geoid / uncorrected topography Geoid / residual topography In degree range 16 to 31 → expect high correlation → expect geoid-topography ratio around 0.01 residual topography too high above degree 10, too low below degree 6 ?

29. In degree range 16 to 31 → expect high correlation → expect geoid-topography ratio around 0.01 Higher correlation indicates better residual topography model

30. In degree range 16 to 31 → expect high correlation → expect geoid-topography ratio around 0.01 Ratio about 1.4 % indicates better residual topography model 958871.1945

31. Joint consideration with geoid indicates that discrepancies are, to a larger degree, caused by inaccuracies of residual topography model (e.g. inappropriate crustal model) 95887 1.19 45 geoid-topography ratio Geoid / residual topography Model predictions

51. Congo Afar South Africa Kufra Chad Taoudeni

52. Congo Afar South Africa Kufra Chad Taoudeni

53. Congo Afar South Africa Kufra Chad Taoudeni

54. Congo Afar South Africa Kufra Chad Taoudeni

55. Congo Afar South Africa Kufra Chad Taoudeni

56. Congo Afar South Africa Kufra Chad Taoudeni

57. Congo Afar South Africa Kufra Chad Taoudeni

58. Congo Afar South Africa Kufra Chad Taoudeni

59. Afar Congo South Africa Kufra Chad Taoudeni

60. Conclusions → Present-day dynamic topography computed from mantle density anomalies inferred from tomography → Need to “cut out” lithosphere → Better fit through «mixing» tomography models → Further improved fit with lithosphere models based on thermal and (where available) seismic data → Joint consideration of geoid and topography indicates that much of the remaining misfit is due to errors in residual topography. → Past dynamic topography through combining plate reconstructions in absolute reference frame with backward-advected density and flow → Problem: signal decays back in time → Possible solution (partially): adjoint methods