Mantle evolution and dynamic topography of the African
Plate
Bernhard Steinberger
Deutsches GeoForschungsZentrum, Potsdam
and
Physics of Geological Processes, Univ. Oslo
and
Center for Advanced Studies, Oslo
Motivation
Understanding the mantle contribution to surface uplift and
subsidence over time on a large scale
•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
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

Seismic tomography
S-wave models (here: tx2007 of Simmons, Forte and Grand)
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
Seismic tomography
Converted to density anomalies
•Conversion factor ~
0.25 (Steinberger and
Calderwood, 2006) –
4 % velocity variation
~ 1 % density variation
 Remove lithosphere
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: stressfree upper boundary;
below: normal-stressfree with zero horizontal
motion)
Actual topography
What to compare
computations to for
present-day
Actual topography
MINUS
Isostatic topography
What to compare
computations to for
present-day
Actual topography
What to compare
computations to for
present-day
Non-isostatic topography
MINUS
Isostatic topography
=
Comparision non-isostatic vs.
dynamic topography
TX2007 tomography
Lithosphere removed (cutoff 0.2%)

Non-isostatic topography
What to compare
computations to for
present-day
Non-isostatic topography
MINUS
Thermal topography
What to compare
computations to for
present-day
Non-isostatic topography
What to compare
computations to for
present-day
residual topography
MINUS
Thermal topography
=
Comparision residual vs.
dynamic topography
TX2007 tomography
Lithosphere removed (cutoff 0.2%)
Sea floor cooling removed

Comparision residual vs.
dynamic topography
TX2007 tomography
Lithosphere not removed
Sea floor cooling removed

Correlation and ratio of dynamic vs. residual topography
Best fit (in terms of
variance reduction)
Ratio on
African plate
Ratio
globally
Correlation on
African plate
Correlation
globally
Correlation and ratio of dynamic vs. residual topography
Best fit (in terms of
variance reduction)
Ratio on
African plate
Ratio
globally
Correlation on
African plate
Correlation
globally
Further improvements by combination with surface tomography models, or ...
Correlation and ratio of dynamic vs. residual topography
PRI-P05
Ratio
globally
Best fit (in terms of
variance reduction)
PRIS05
Ratio on
African
plate
Correlation
on African
plate
Correlation
globally
Mixing tomography models – here: Princeton P and S models
TOPOS362D1
J362D28-P
4 6
Harvard Princeton
PRI-S05 PRI-P05
6 4
2 8
East
SAW24B16
SAW642AN
4 6
TX2007 S20RTS
9 1
Berkeley «smean»
7 3
West
6 4
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 ...
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
Comparision residual vs.
dynamic topography
MIX-A tomography
Lithosphere from Rychert et al.
(2010) and Artemieva (2006)
Sea floor cooling removed

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?
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 ?
Geoid /
residual topography
Model
prediction for
no-slip surface
Model prediction
for free-slip
surface
Geoid /
uncorrected
topography
In degree range 16 to 31
→ expect high correlation
→ expect geoid-topography ratio around 0.01
Higher correlation indicates better residual topography
model
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
9
58
87
1.19
45
geoid-topography ratio
Geoid /
residual topography
Joint consideration with geoid
indicates that discrepancies are, to a
larger degree, caused by
inaccuracies of residual topography
model (e.g. inappropriate crustal
model)
9
58
87
1.19
45
Taoudeni
Kufra
Chad
Congo
South
Africa
Afar
Taoudeni
Kufra
Chad
Congo
South
Africa
Afar
Taoudeni
Kufra
Chad
Congo
South
Africa
Afar
Taoudeni
Kufra
Chad
Congo
South
Africa
Afar
Taoudeni
Kufra
Chad
Congo
South
Africa
Afar
Taoudeni
Kufra
Chad
Congo
South
Africa
Afar
Taoudeni
Kufra
Chad
Congo
South
Africa
Afar
Taoudeni
Kufra
Chad
Congo
South
Africa
Afar
Afar
Kufra
Chad
Congo
South Africa
Taoudeni
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