Dynamic topography, phase boundary topography and latentheat release

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Dynamic topography, phase boundary topography and
latent-heat release
Bernhard Steinberger
Center for Geodynamics, NGU, Trondheim, Norway
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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 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
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• 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
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• 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
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Actual topography
What to compare computations to for present-day
Spherical harmonic expansion of observed
topography to degree 31
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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
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Actual topography
Non-isostatic topography

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

MINUS Thermal topography
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residual topography, l1-31
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residual topography, l1-31
residual topography, l1-31 Values above sea
level multiplied with factor 1.45, because
dynamic topography is computed for
global seawater coverage
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residual topography, l1-12, above sea level
mulitiplied with 1.45
residual topography, l1-31
residual topography, l1-31 Above sea level
multiplied with 1.45
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residual topography, l1-12
RMS amplitude 0.52 km
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residual topography, l1-12, our model
RMS amplitude 0.52 km
Correlation coefficient 0.74
Model by Panasyuk and Hager (2000)
RMS amplitude 0.52 km
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residual topography, l1-12, our model
RMS amplitude 0.52 km
Correlation coefficient 0.86
Model by Kaban et al. (2003)
RMS amplitude 0.64 km
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Positive Clapeyron slope
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l31
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)
l2
l31
l2
Kr,l(z)
l31
l2
l31
l2
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• 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
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• 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
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• Dynamic topography
• Spectral method (Hager and
• OConnell, 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
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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
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Predicted 410 topography Thermal effect
only RMS amplitude 4.81 km With other tomography
models 2.85 to 7.43 km
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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
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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)
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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
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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
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Summary of results with thermal effect only
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• Summary of results with thermal effect only
• Predicted dynamic topography bigger than observed

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• Summary of results with thermal effect only
• Predicted dynamic topography bigger than observed
• Predicted topography 660 smaller than observed

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• 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

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• 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

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• 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

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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
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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
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For divariant phase change, amount of
displacement depends on flow speed
660 km
410 km
410 km
660 km
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For divariant phase change, amount of
displacement depends on flow speed
V
660 km
410 km
410 km
660 km
Z
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Computed flow speed Depth 410 km
Computed flow speed Depth 660 km
Density model inferred from S20RTS (Ritsema et
al., 2000)
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Phase boundary displacement due to latent heat
depth 410 km
depth 660 km
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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!)

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

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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)

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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

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Combine dynamic topography with sea level curve
to compute inundation
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Heine et al., in preparation
Present-day
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64 Ma
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41 Ma
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31 Ma
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13 Ma
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8 Ma
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3 Ma
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Dynamic topography on New Jersey Margin
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• Outlook Understanding of present-day dynamic
  topography
• A multi-disciplinary approach is required,
  including, but not limited to the following
  aspects
• Improving both seismic and geodynamic models of
  phase boundary topography
• Improving mantle density models, in particular in
  the lithosphere
• More realistic and laterally variable rheology,
  in particular in the lithosphere
• Regional computations

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• Past mantle structure cannot be fully recovered
  by simple backward-advection
• A global mantle reference frame through geologic
  times is required to relate computed uplift and
  subsidence to geological observations