Jacqueline Austermann Harriet Lau, Jerry Mitrovica CIDER community workshop, May 6 th 2016 Image credit: Mike Beauregard Towards reconciling viscosity inversions

Inversions of 1D mantle viscosity Seismic relaxation Huang et al. (2016) Panet et al. (2010) Khazaradze et al. (2002) Postglacial rebound Forte & Mitrovica (1996) Lambeck et al. (1996) Lambeck et al. (1998) Peltier (2004) Whitehouse (2012) Ivins (2013) Argus et al. (2014) Convection Hager et al. (1985) Forte & Peltier (1987, 1991) King & Masters (1992) Ricard et al. (1993) Corrieu et al. (1995) Rudolph et al. (2015)

Seismic relaxation Huang et al., 2016 Pre-EQ model 10 mm/yr onward Surface deformation before and after Loma Prieta EQ displacement (mm) Viscoelastic Models (unit: Pa s)

Uplift from previously glaciated regions Far-field relative sea level curves Chan et al. (2011) Long-wavelength geoid, rotational data Ice age observables Far field highstands

Convection observables Ricard et al., 2001; Simmons et al., 2009 Nonhydrostatic component of the geoid Dynamic topography Plate motions Excess ellipticity of the core mantle boundary

Outline 1)At what depth does the increase in mantle viscosity occur? 2)Why do ice age based estimates of lower mantle viscosity differ? 3)Why is there so much variability in the inferred upper mantle viscosity

Image credit: Mike Beauregard Towards reconciling viscosity inversions 1)At what depth does the increase in mantle viscosity occur? 2)Why do ice age based estimates of lower mantle viscosity differ? 3)Why is there so much variability in the inferred upper mantle viscosity?

Convection observables Kaufmann and Lambeck, 2001; Rudolph et al., 2015 Inversion style can dictate at which depth the viscosity increase occurs (including constraints on number of layers and layer depths) King & Masters (1992)Forte & Peltier (1987, 1991)Hager et al. (1985)

Image credit: Mike Beauregard Towards reconciling viscosity inversions 1)At what depth does the increase in mantle viscosity occur? 2)Why do ice age based estimates of lower mantle viscosity differ? 3)Why is there so much variability in the inferred upper mantle viscosity?

Ice age observables Kaufmann and Lambeck, 2000; Argus et al., 2014 Argus et al. (2014) – VM5Lambeck et al. (1998) Lambeck et al. (1996) Forte & Mitrovica (1996) Viscosity profiles from predictions of postglacial rebound. Models are consistent with a viscosity increase at 1000km depth Significant difference in the amount of viscosity increase in the lower mantle

Ice age observables Argus et al., 2015 Sensitivity kernels depend on viscosity itself

Ice age observables Argus et al., 2015 J2 dot - rate of change of the ‘degree 2’ (or long wavelength) zonal geopotential It is a measure of the oblateness of the Earth’s geoid (which changes with the melting of polar ice caps). But it is also sensitive to recent melt. Sensitivity kernels depend on viscosity itself

Ice age observables Argus et al., 2015 Increase in lower mantle viscosity VM5 LM J2 dot - rate of change of the ‘degree 2’ (or long wavelength) zonal geopotential It is a measure of the oblateness of the Earth’s geoid (which changes with the melting of polar ice caps). But it is also sensitive to recent melt.

Ice age observables Argus et al., 2015 Increase in lower mantle viscosity VM5 LM Data estimate without correcting for recent melt J2 dot - rate of change of the ‘degree 2’ (or long wavelength) zonal geopotential It is a measure of the oblateness of the Earth’s geoid (which changes with the melting of polar ice caps). But it is also sensitive to recent melt.

Ice age observables Argus et al., 2015 J2 dot - rate of change of the ‘degree 2’ (or long wavelength) zonal geopotential It is a measure of the oblateness of the Earth’s geoid (which changes with the melting of polar ice caps). But it is also sensitive to recent melt. Using latest IPCC estimates of ice melt we can remove this rate from the observed rate to find the GIA-induced value. Mitrovica et al. (2015) Nakada et al. (2015) Increase in lower mantle viscosity VM5 LM Data estimate with correcting for recent melt

Image credit: Mike Beauregard Towards reconciling viscosity inversions 1)At what depth does the increase in mantle viscosity occur? 2)Why do ice age based estimates of lower mantle viscosity differ? 3)Why is there so much variability in the inferred upper mantle viscosity?

Rheology Transient rheology (Burgers material) Newtonian fluid Viscoelastic (Maxwell fluid) 1d 1s 1 Myr1 kyr free oscillations tides seismic relaxation glacial adjustment mantle convection 1 Gyr1 yr Elastic Anelastic (Kelvin solid)

Location bias in inversions Lithospheric thickness (km) (Conrad and Lithgow- Bertelloni, 2006)

Location bias in inversions 2 -2 S40RTS (Ritsema et al., 2011) at 300km depth

Synthetic inputs: Imposed 1D viscosity model: VM5a (Argus et al., 2014) Imposed ice history: ICE-6G (Argus et al., 2014) Inversion choices: Prior model, starting model = VM5a (Argus et al., 2014) +/- 5 orders of magnitude in standard deviation Quantifying the 3D bias Lau et al., in prep.

Richmond Gulf decay time Fennoscandia Relaxation Spectrum Lau et al., in prep. Quantifying the 3D bias

Richmond Gulf decay time Fennoscandia Relaxation Spectrum To conserve J2 dot average deep mantle dives below Lau et al., in prep. Quantifying the 3D bias

Starting model: Upper mantle viscosity = 0.5 × Pa s Lower mantle viscosity = 5 × Pa s Bias in mid-mantle is 1.5 orders of magnitude Starting model: VM2 (Peltier, 2004) Bias in mid-mantle is 0.5 orders of magnitude Regardless of 1D viscosity profile, a significant geographical biases exist! The 3D bias is non-linear Lau et al., in prep.

Location bias - deglaciation Austermann et al., 2013 BarbadosTahiti Seismic tomography model S40RTS (Ritsema et al., 2011) 2 -2

Conclusions Viscosity models with an increase at 800 – 1200km improve the fit to the geoid (Forte and Peltier, 1987; Rudolph et al., 2915) Postglacial rebound observations are compatible with such models J2-dot is important constraint on lower mantle viscosity and increases its estimate if recent melt is included Inferring mantle viscosity from postglacial rebound introduces a bias in 1D estimates of mantle viscosity, which will tend to over estimate upper mantle viscosity and mid-lower mantle viscosity Locations of seismic relaxation studies are potentially biased low (relative to a 1D viscosity profile) due to their location

CIDER and mantle viscosity Mantle viscosity at CIDER 2014: Rudolph, Lekic and Lithgow-Bertelloni, Science (2015) 2015: ‘Are we looking at the same mantle?’ Advances will require interdisciplinary work! Including cross-disciplinary constraints from mineral physics and geochemistry Compiling and connecting existing local estimates Introducing more sophisticated inversion schemes that allow combining different data types Quantifying uncertainty (covariance) Communicating estimates and their limitations Implications!!!