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

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”

→ 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)

→ 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

→ 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

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

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 + 200 m 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 Present-day topography - 200 m sea level

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

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

= Actual topography Non-isostatic topography MINUS 11 11

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

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

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

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)

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

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

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

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)‏

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

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

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)

→ “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) - 0.843) actual temperature profile z0 Lithosphere thickness zL 23 23 23

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) - 0.843) z0 C and z0 are treated as variables zL depth 24 24 24

 = 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

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

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

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

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)

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

residual

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

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

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

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)

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

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

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

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