1. Dynamic topography Bernhard Steinberger
Deutsches GeoForschungsZentrum, Potsdam
and
Centre for Earth Evolution and Dynamics, Univ. Oslo

2. What is dynamic topography?
Commonly vertical displacement of the Earth's surface generated in response to flow in the Earth's mantle called “dynamic topography”

3. → An effort to determine which part of topography is not due to crustal isostasy or ocean floor cooling 2 1 3 4
Contributions to topography
(1) crustal isostasy (remove)
(2) due to ocean floor cooling (remove)
(3) other contributions within the lithosphere (~ isostatic – include)
(4) beneath the lithosphere (“dynamic” in the proper sense – include)
Key point: Isostatic (3) and dynamic (4) topography very similar for shallow depth and large lateral scales, so don't distinguish for present day. But distinction important for time changes as (3) moves with plates (no change) and (4) doesn't (causes uplift and subsidence)

4. → An effort to determine which part of topography is not due to crustal isostasy or ocean floor cooling 2 1 3 4
Density anomalies (3) and (4) can be inferred from seismic tomography, but lithosphere has also compositional anomalies.
Hence we are concerned with
(a) which part of tomographic anomalies to include and which part not (and also, which tomography model(s) to use)
(b) how to infer topography from the geoid
An important ingredient is a model of lithosphere thickness

5. → An effort to determine which part of topography is not due to crustal isostasy or ocean floor cooling 2 1 3 4
To check the quality of our models, we compare
(A) a model of “residual topography”, obtained by subtracting contributions (1) and (2) from actual topography
(B) a model of topography due to contributions (3) and (4) obtained from seismic tomography (and deciding which parts to include) and subtracting contribution (2).
(C) a model additionally based on the geoid

6. Why is it important to know dynamic topography?
Many areas on Earth within few hundred meters above or below sea level (bright green / light blue on map)
Dynamic topography expected to reach a few hundred meters and hence may influence when and where sediments and natural resources may form
Present-day topography
sea
level
Why is it important to know dynamic topography?
Many areas on Earth within few hundred meters above or below sea level (bright green / light blue on map)
Dynamic topography expected to reach a few hundred meters and hence may influence when and where sediments and natural resources may form
Why is it important to know dynamic topography?
Many areas on Earth within few hundred meters above or below sea level (bright green / light blue on map)
Dynamic topography expected to reach a few hundred meters and hence may influence when and where sediments and natural resources may form
Why is it important to know dynamic topography?
Many areas on Earth within few hundred meters above or below sea level (bright green / light blue on map)
Dynamic topography expected to reach a few hundred meters and hence may influence when and where sediments and natural resources may form

7. Why is it important to know dynamic topography?
Many areas on Earth within few hundred meters above or below sea level (bright green / light blue on map)
Dynamic topography expected to reach a few hundred meters and hence may influence when and where sediments and natural resources may form
Present-day topography m
sea
level

8. Why is it important to know dynamic topography?
Many areas on Earth within few hundred meters above or below sea level (bright green / light blue on map)
Dynamic topography expected to reach a few hundred meters and hence may influence when and where sediments and natural resources may form
Present-day topography m
sea
level

9. Dynamic topography changes ocean basin volume and hence sea level
Figure from Conrad and Husson (Lithosphere, 2009) 9 9

10. Inferring dynamic topography from observations
Actual topography
Inferring dynamic topography from observations
Airy Pratt
MINUS
Isostatic topography
Computed based on densities and thicknesses of crustal layers in CRUST 1.0 model (Laske et al., http:
//igppweb.ucsd.edu/~gabi/crust1.html 10 10

11. = Actual topography Non-isostatic topography MINUS11 11

12. = Non-isostatic topography residual topography MINUS ridge topography
Continents sqrt (200 Ma) topography 12 12

13. How is present-day dynamic topography computed from mantle flow models?
Most important model ingredients: Density and viscosity structure of the mantle
Density inferred from seismic tomography – here: S-wave model tx2007 of Simmons, Forte and Grand

14. Seismic tomography Convert to density anomalies Blue line:
Conversion factor
for thermal anomalies
inferred from mineral
Physics (Steinberger
and Calderwood, 2006)

15. Here: attempt to “remove lithosphere” by setting density anomaly to 0
Here: attempt to “remove lithosphere” by setting density anomaly to 0.2 % wherever, above 400 km depth, inferred density anomaly is positive >0.2 % at that depth and everywhere above
Blue line:
Conversion factor
for thermal anomalies
inferred from mineral
Physics (Steinberger
and Calderwood, 2006)

16. Seismic tomography Convert to density anomalies Blue line:
Conversion factor
for thermal anomalies
inferred from mineral
Physics (Steinberger
and Calderwood, 2006)

17. Mantle viscosity for flow computation I
Use mineral physics to infer viscosity profile based on mantle temperature and
melting temperature profile
Adiabatic temperature profile
T(z): Integrate dT/dz = T(z) a(z) g(z) / C
Thermal
expansivity
specific heat
gravity
Melting
Temperature
Profile Tm

18. Mantle viscosity for flow computation II
In the lower mantle, use strain-stress relationship .
e ~ sn exp(-gTm/T)
hence h (z) ~ exp (-gTm/nT) for constant strain rate
Yamazaki and Karato
(2001): g=12, n=1
Absolute viscosity values
may be different in
Upper mantle
Transition zone
lower mantle
determined by optimizing
fit to various observations

19. Mantle flow computation
Density model based on tomography (here: Simmons, Forte, Grand, 2006)‏
velocity-density scaling based on mineral physics
radial viscosity structure based on mineral physics and optimizing fit to geoid etc. (Steinberger and Calderwood, 2006)‏
Spectral method (Hager and O'Connell, 1979, 1981)‏

20. B: “Dynamic” topography
If viscosity only depends on radius:
Effect of density anomalies δρlmat given depth z and spherical harmonic degree l on topography can be described in terms of topography kernels Kr,l(z):
Beneath air : Δρs= 3300 kg/m3
Geoid kernels described in analogy 3 8 2 5 12 17 23 30
geoid
topography 20 20 20 20 20

21. B: “Dynamic” topography:
Why this is new (and exciting)
(I) Recent tomography models have reached a new quality:
Higher correlation with geoid in a degree and depth range where this is expected, based on kernels and amplitudes

22. B: “Dynamic” topography:
Why this is new (and exciting)
(ii) Based on new tomography models, develop a model of lithosphere thickness (and compare with other models)

23. → “Extract” this isosurface from tomography model
→ Assign isosurface for given temperature TL to be lower boundary of lithosphere
→ “Extract” this isosurface from tomography model
→ Assume “reference temperature profile”
to represent global average
Surface
TemperatureTS
Mantle
Temperature TM
→ choose TL such that
(TL-TS)/(TM-TS)=erf(1)=0.843 TL
reference
profile
A point is inside the lithosphere,
if at that depth and all depths above
T(z) < TL
(T(z)-T0(z))/(TM-TS) < (TL-T0(z))/(TM-TS)
(T(z)-T0(z))/(TM-TS) < erf(1)-erf(z/z0)
vs/vs > C · (erf(z/z0) )
actual
temperature
profile z0
Lithosphere thickness zL 23 23 23

24. A point is inside the lithosphere,
-C · 0.843
A point is inside the lithosphere,
if at that depth and all depths above
vs/vs > C · (erf(z/z0) ) z0
C and z0 are treated as variables zL
depth 24 24 24

25.  = thermal diffusivity
t = ocean floor age
 = thermal diffusivity
For
age_3.6 ocean floor age grid
(Müller, Sdrolias, Gaina and Roest, G3, 2008)
→ determine for each point lithosphere thickness based on tomography model according to above-described procedure
→ find parameters C and z0 such that optimum fit with
is achieved for average thickness at given sea floor age. 25 25 25

26. Schaeffer and Lebedev (2013) C = 9 %, z0 = 60 km theoretical: C = 11 %
SL2013SV:
Schaeffer and Lebedev (2013)
C = 9 %, z0 = 60 km
theoretical: C = 11 % 26 26 26 26

27. scattered wave imaging Artemieva (2006) thermal model
Rychert et al. (2010)
scattered wave imaging
Artemieva (2006) thermal model
This model based on
SL2013 tomography
Priestley and McKenzie (2013)
based on surface wave tomography 27 27 27 27

28. Elastic lithosphere thickness
Audet and Burgmann (2011)
Based on smean tomography

29. 1/q= 1/(heat flow) from Davies
lRF = Rychert
1/q= 1/(heat flow) from Davies
lT = Artemieva
hC = crustal thickness crust1
lST = simple thickness from isovalue 
lSB = this work seismological thickness
Te = elastic thickness from Audet and Burgmann (2011)

30. Sea floor age contribution not subtracted
→ Lithosphere
 = 0.2 %
→ optimized
viscosity
Structure
→ lmax = 31
Correlation 0.77
Ratio 1.08
Sea floor age contribution not subtracted
Residual topography (before spherical harmonic expansion) divided by 1.45 in oceans to account for water coverage 30

32. residual

34. Correlation and ratio of residual and “dynamic” and topography based on various
tomography models.
Pink line = geoid-derived for l>~15

35. How is past dynamic topography computed from mantle flow models?
Backward-advection of density heterogeneities in the flow field

36. Example 1: Recent uplift of southern Africa
Dependence on lateral viscosity variations
B.Sc Thesis Robert Herrendörfer, 2011; Calculations with CitcomS

37. Combined with plate reconstructions to compute
uplift/subsidence in reference frame of moving plate
Example 2: Explaining Sea Level
Curves on the East Coast of
North America
(Müller et al., 2008)

38. Example 3: Explaining marine inundations in Australia (Heine et al

45. Outlook: Coupling mantle convection and lithospheric deformation
Lithospheric code (Finite Elements)
Mantle code (spectral)
Mantle and lithospheric codes are coupled through continuity of velocities and tractions at 300 km.
Sobolev, Popov and Steinberger, unpublished work

46. Self-generated plate boundaries
Sobolev, Popov and Steinberger, unpublished work

47. Conclusions
Recent tomography models (in particular SL2013SV) have high correlation with geoid at intermediate degrees (l~4-50) and shallow depth, indicating substantial improvement
Based on tomography models, we developed models of lithosphere thickness
We investigated correlation between lithosphere thickness models based on various approaches
Rather high correlation between tomography-based and elastic thickness estimate, but elastic lithosphere ~3 times thinner
Improved correlation between residual and „dynamic“ topography ~0.6