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Dynamic topography, phase boundary topography and latent-heat release

Dynamic topography, phase boundary topography and latent-heat release. Bernhard Steinberger. Center for Geodynamics, NGU, Trondheim, Norway. Prediction of surface uplift and subsidence over time on a large scale is one of the most important outcomes of mantle flow models.

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Dynamic topography, phase boundary topography and latent-heat release

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  1. Dynamic topography, phase boundary topography and latent-heat release Bernhard Steinberger Center for Geodynamics, NGU, Trondheim, Norway

  2. Prediction of surface uplift and subsidence over time on a large scale is one of the most important outcomes of mantle flow models

  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. Actual topography What to compare computations to for present-day Spherical harmonic expansion of observed topography to degree 31

  7. Actual topography MINUS Isostatic topography Computed based on densities and thicknesses of crustal layers in CRUST 2.0 model (Laske, Masters and Reif) http://mahi.ucsd.edu/Gabi/rem.html

  8. Actual topography Non-isostatic topography = MINUS Isostatic topography

  9. Non-isostatic topography

  10. Non-isostatic topography MINUS Thermal topography Computed from the age_2.0 ocean floor age grid (Müller, Gaina, Sdrolias and Heine, 2005) for ages < 100 Ma

  11. Non-isostatic topography residual topography = MINUS Thermal topography

  12. residual topography, l=1-31

  13. residual topography, l=1-31 residual topography, l=1-31 Values above sea level multiplied with factor 1.45, because dynamic topography is computed for global seawater coverage

  14. residual topography, l=1-12, above sea level mulitiplied with 1.45 residual topography, l=1-31 residual topography, l=1-31 Above sea level multiplied with 1.45

  15. residual topography, l=1-12 RMS amplitude 0.52 km

  16. residual topography, l=1-12, our model RMS amplitude 0.52 km Correlation coefficient 0.74 Model by Panasyuk and Hager (2000) RMS amplitude 0.52 km

  17. residual topography, l=1-12, our model RMS amplitude 0.52 km Correlation coefficient 0.86 Model by Kaban et al. (2003) RMS amplitude 0.64 km

  18. Positive Clapeyron slope

  19. l=31 Radial stress kernels Kr,l(z) describe how much a density anomaly lmat a depth z contributes to dynamic topography: Computed for global water coverage: s= 2280 kg/m3 Figure from Steinberger, Marquart and Schmeling (2001) l=2 l=31 l=2 Kr,l(z) l=31 l=2 l=31 l=2

  20. Densities inferred from S-wave tomography -- here: model S20RTS (Ritsema et al., 2000) • Conversion factor ~ 0.25 (Steinberger and Calderwood, 2006) – • 4 % velocity variation ~ • ~ 1 % density variation Depth 300 km 4.8 4.0 3.2 2.4 1.6 0.8 0.0 -0.8 -1.6 -2.4 -3.2 -4.0

  21. Densities inferred from S-wave tomography -- here: model S20RTS (Ritsema et al., 2000) • Disregard velocity anomalies above 220 km depth Depth 200 km 4.8 4.0 3.2 2.4 1.6 0.8 0.0 -0.8 -1.6 -2.4 -3.2 -4.0

  22. Dynamic topography • Spectral method (Hager and • O’Connell, 1979,1981) for • computation of flow and stresses • NUVEL plate motions for surface boundary condition (results remain similar with free-slip and no-slip surface) • Radial viscosity variation only Viscosity profile from Steinberger and Calderwood (2006) RMS amplitude 1.07 km With other tomography models: 0.63 km [Grand] to 1.47 km [SB4L18, Masters et al., 2000]

  23. Dynamic topography RMS amplitude 1.07 km With other tomography models: 0.63 to 1.47 km Correlation 0.33 With other tomography models: 0.30 to 0.53 Residual topography RMS amplitude 0.52 km Other models: 0.47 to 0.64 km

  24. Predicted “410” topography Thermal effect only RMS amplitude 4.81 km With other tomography models: 2.85 to 7.43 km

  25. Predicted “410” topography Thermal effect only RMS amplitude 4.81 km With other tomography models: 2.85 to 7.43 km Correlation 0.37 With computation based on other tomography models: 0.27 to 0.42 Observed “410” topography Gu, Dziewonski, Ekström (2003) RMS amplitude 5.24 km Other models: 3.90 to 5.24 km Correlation between different ”observed” models 0.10 to 0.44

  26. Predicted “660” topography Thermal effect only RMS amplitude 4.57 km With other tomography models: 2.69 to 5.59 km Correlation 0.35 With computation based on other tomography models: 0.06 to 0.35 Correlation with “410”: -0.80 (-0.21 to -0.80 with other models) Observed “660” topography Gu, Dziewonski, Ekstrøm (2003) RMS amplitude 7.31 km Other models: 6.98 to 7.31 km Correlation between different “observed” models 0.33 to 0.50 Correlation with “410”: 0.24 (0.24 to 0.49 with other models)

  27. Predicted TZ thickness variation Thermal effect only RMS amplitude 8.89 km With other tomography models: 5.05 to 11.86 km Correlation 0.51 With computation based on other tomography models: 0.36 to 0.51 Observed TZ thickness variation Gu, Dziewonski, Ekstrøm (2003) RMS amplitude 7.92 km Other models: 6.52 to 7.92 km Correlation between different “observed” models 0.30 to 0.41

  28. Dynamic topography – correlation with predicted TZ thickness variation –0.77 With other tomography models: -0.48 to –0.89 Residual topography - correlation with observed TZ thickness variation –0.17 Other models: -0.17 to 0.02

  29. Summary of results with thermal effect only:

  30. Summary of results with thermal effect only: • Predicted dynamic topography bigger than observed

  31. Summary of results with thermal effect only: • Predicted dynamic topography bigger than observed • Predicted topography “660” smaller than observed

  32. Summary of results with thermal effect only: • Predicted dynamic topography bigger than observed • Predicted topography “660” smaller than observed • “410” and “660” topography correlation predicted negative, observed positive

  33. Summary of results with thermal effect only: • Predicted dynamic topography bigger than observed • Predicted topography “660” smaller than observed • “410” and “660” topography correlation predicted negative, observed positive • TZ thickness and dyn. topography correlation predicted negative, obs. ~ zero

  34. Summary of results with thermal effect only: • Predicted dynamic topography bigger than observed • Predicted topography “660” smaller than observed • “410” and “660” topography correlation predicted negative, observed positive • TZ thickness and dyn. topography correlation predicted negative, obs. ~ zero • Correlations between predicted and observed models not too good

  35. Phase boundary topography by latent heat effects (Christensen, 1998, EPSL) 410 km: Phase boundary with positive Clapeyron slope Latent heat causes HIGHER temperature BELOW 660 km: Phase boundary with negative Clapeyron slope Latent heat causes LOWER temperature BELOW In both cases: Temperature gradient on upstream side Constant temperature on downstream side Boundary displaced in direction of flow

  36. Phase boundary topography by latent heat effects (Christensen, 1998, EPSL) LQ = g cp) = 3.8 km cp = specific heat capacity 410 km: Phase boundary with positive Clapeyron slope Latent heat causes HIGHER temperature BELOW 660 km: Phase boundary with negative Clapeyron slope Latent heat causes LOWER temperature BELOW LQ = 4.4 km In both cases: Temperature gradient on upstream side Constant temperature on downstream side Boundary displaced in direction of flow

  37. For divariant phase change, amount of displacement depends on flow speed 660 km 410 km 410 km 660 km

  38. V= For divariant phase change, amount of displacement depends on flow speed 660 km 410 km 410 km 660 km Z=

  39. Computed flow speed – Depth 410 km Computed flow speed – Depth 660 km Density model inferred from S20RTS (Ritsema et al., 2000)

  40. Phase boundary displacement due to latent heat– depth 410 km depth 660 km

  41. “660” phase boundary displacement Thermal effect Latent heat effect • Predicted topography “660” smaller than observed • Increases by including latent heat effect (but not enough – note different scale!)

  42. Phase boundary displacement due to latent heat– depth 410 km • “410” and “660” topography correlation predicted negative, observed positive • Latent heat effect displaces phase boundaries in same direction and hence contributes towards less negative correlation (but not enough – note different scale!) depth 660 km

  43. Phase boundary displacement due to latent heat – depth 410 km Effect of latent heat effect on dynamic topography depth 660 km

  44. Dynamic topography with thermal effect only Effect of latent heat effect on dynamic topography • Computed dynamic topography bigger than observed • Including latent heat effect reduces dynamic topography (note opposite sense of color scale! - but not enough – note different scale)

  45. Dynamic topography with computed phase boundaries RMS 1.02 km Residual topography RMS 0.52 km Correlation 0.34 • Computed dynamic topography bigger than observed • Including latent heat effect reduces dynamic topography • Including latent heat effect generally somewhat increases correlations (but not by much)

  46. Dynamic topography with computed phase boundaries -- RMS 1.02 km Residual topography -- RMS 0.52 km Correlation 0.34 Dynamic topography with observed phase boundaries -- RMS 0.98 km Correlation 0.26 • Including latent heat effect generally somewhat increases correlations (but not by much) • Replacing computed by observed phase boundary topography in the calculation of dynamic topography generally does not improve results

  47. Combine dynamic topography with sea level curve to compute inundation

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