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
•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
•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
•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
Actual topography
What to compare computations to
for present-day
Spherical harmonic
expansion of observed
topography to degree 31
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
Actual topography
Non-isostatic topography
MINUS
Isostatic topography
=
Non-isostatic topography
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
Non-isostatic topography
residual topography
MINUS
Thermal topography
=
residual topography, l=1-31
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
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
residual topography, l=1-12
RMS amplitude 0.52 km
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
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
Positive
Clapeyron
slope
l=31
l=2
Radial stress kernels Kr,l(z)
describe how much a
density anomaly lm at a
depth z contributes to
dynamic topography:
l=31
l=2
Kr,l(z)
Computed for global water
coverage:
s= 2280 kg/m3
Figure from Steinberger, Marquart
and Schmeling (2001)
l=31
l=2
l=31
l=2
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
•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
•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
Viscosity profile from
Steinberger and Calderwood (2006)
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
RMS amplitude 1.07 km
With other tomography models:
0.63 km [Grand] to 1.47 km
[SB4L18, Masters et al., 2000]
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
Predicted “410” topography
Thermal effect only
RMS amplitude 4.81 km
With other tomography models:
2.85 to 7.43 km
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
Predicted “660” topography
Thermal effect only
RMS amplitude 4.57 km
With other tomography models:
2.69 to 5.59 km
Correlation with “410”: -0.80
(-0.21 to -0.80 with other models)
Correlation 0.35
With computation based on other
tomography models:
0.06 to 0.35
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)
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
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
Summary of results with thermal effect only:
Summary of results with thermal effect only:
•Predicted dynamic topography bigger than observed
Summary of results with thermal effect only:
•Predicted dynamic topography bigger than observed
•Predicted topography “660” smaller than observed
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
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
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
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
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
For divariant phase change,
amount of displacement depends
on flow speed
660 km
410 km
410 km
660 km
V=
For divariant phase change,
amount of displacement depends
on flow speed
660 km
Z=
410 km
410 km
660 km
Computed flow speed –
Depth 410 km
Computed flow speed –
Depth 660 km
Density model inferred from
S20RTS (Ritsema et al., 2000)
Phase boundary displacement due to latent heat–
depth 410 km
depth 660 km
“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!)
Phase boundary displacement due to latent heat–
depth 410 km
depth 660 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!)
Phase boundary displacement due to latent heat –
depth 410 km
Effect of latent heat effect on
dynamic topography
depth 660 km
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)
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
•Including latent heat effect generally
dynamic topography
somewhat increases correlations (but
not by much)
Dynamic topography with computed phase
boundaries -- RMS 1.02 km
Residual topography -- RMS 0.52 km
Correlation
0.34
Dynamic topography with observed phase
Correlation
boundaries -- RMS 0.98 km
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
Combine dynamic topography with sea level curve to compute
inundation
Heine et al., in
preparation
Present-day
64 Ma
41 Ma
31 Ma
13 Ma
8 Ma
3 Ma
Dynamic topography on New Jersey Margin
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
Outlook II: Time-dependent dynamic topography and plate motions
•Past mantle structure cannot be fully recovered by simple backwardadvection
•A global mantle reference frame through geologic times is required
to relate computed uplift and subsidence to geological observations