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Dynamic topography, phase boundary topography and latentheat release

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Title: Dynamic topography, phase boundary topography and latentheat release


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 lt 100 Ma
11
Non-isostatic topography
residual topography

MINUS Thermal topography
12
residual topography, l1-31
13
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
14
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
15
residual topography, l1-12
RMS amplitude 0.52 km
16
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
17
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
18
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19
Positive Clapeyron slope
20
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21
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
22
  • 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
23
  • 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
24
  • 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
25
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
26
Predicted 410 topography Thermal effect
only RMS amplitude 4.81 km With other tomography
models 2.85 to 7.43 km
27
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
28
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)
29
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
30
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
31
Summary of results with thermal effect only
32
  • Summary of results with thermal effect only
  • Predicted dynamic topography bigger than observed

33
  • Summary of results with thermal effect only
  • Predicted dynamic topography bigger than observed
  • Predicted topography 660 smaller than observed

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

35
  • 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

36
  • 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

37
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
38
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
39
For divariant phase change, amount of
displacement depends on flow speed
660 km
410 km
410 km
660 km
40
For divariant phase change, amount of
displacement depends on flow speed
V
660 km
410 km
410 km
660 km
Z
41
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42
Computed flow speed Depth 410 km
Computed flow speed Depth 660 km
Density model inferred from S20RTS (Ritsema et
al., 2000)
43
Phase boundary displacement due to latent heat
depth 410 km
depth 660 km
44
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!)

45
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
46
Phase boundary displacement due to latent heat
depth 410 km
Effect of latent heat effect on dynamic topography
depth 660 km
47
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)

48
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)

49
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

50
Combine dynamic topography with sea level curve
to compute inundation
51
Heine et al., in preparation
Present-day
52
64 Ma
53
41 Ma
54
31 Ma
55
13 Ma
56
8 Ma
57
3 Ma
58
Dynamic topography on New Jersey Margin
59
  • 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

60
  • 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
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