


The topic of VILMA, Viscoelastic Lithosphere and Mantle model, is the reduction of global GRACE, GPS and altimetry data with respect to the glacialisostatic adjustment applying a 3D viscoelastic earth model.
contact: volkerk@gfzpotsdam.de
Temporal Earthgravity variations recently derived from GRACE monthly solutions mainly result from the superposition of annual or semiannual oceanic, atmospheric and hydrological mass movements as well as from the secular dynamics of the earth's interior. The separation of the individual contributions requires the application of advanced filtering and analysis techniques. This is exemplified in northern Europe, where the secular gravity variations are largely caused by the land uplift in response to the disappearance of the last Fennoscandian ice sheet at the end of the Pleistocene.
To model this glacialisostatic adjustment, the earth's interior is represented as a viscoelastic fluid. In realistic computations, lateral variations of the lithosphere thickness and mantle viscosity related to the convective circulation in the earth's interior must be taken into account. For this purpose, a 3D viscoelastic earth model forced by the global deglaciation at the end of the Pleistocene is developed. This model can also be applied to regions with tectonic boundaries, such as Alaska, Antarctica, Iceland, Patagonia and Svalbard, where recent glacial changes are observed.
 Validation of code against analytical 2D code
 Development of tools, scripts for handling of the code
 Parallelisation of code using (OpenMP)
 Modification of formalism for time integration presented by Martinec (2000) to account for nonlinear and anisotropic rheologies
 Integration of nonlinear sealevel equation according to Hagedoorn (2005) to model the effect of moving coast lines
 Implementation of compressibility (Tanaka et al. 2010, submitted)
 Stability problem of compressible continuum
 Participation in COST action ES0701 benchmark of GIA codes (Spada et al. 2010, in prep.)
 Implementation of stressdependent viscosity
 Cooperation with AGIA
 SLIdata handling (Dransch et al. 2010, submitted)
2D version: (axial symmetry of viscoelastic structure and surface load) applied to Iceland plume, Patagonian slab and postseismic adjustment
Hartmann et al., (2007): Improvement in fitting surface gravity and uplift in vicinity of Vatnajökull, Iceland.
Figure shows results of the gravity measuring campaigns in Iceland during 19912000 with error ellipses (grey shading) at different distances from the center of the Vatnajökull ice load and computed gravitychange rate as function of the plume viscosity for a laterally inhomogeneous earth model.
Klemann et al. (2007): Strong asymmetry of uplift and horizontal displacement east and west of South Patagonian Icefield due to material transport in asthenosphere. Slab is impeding material transport towards the Pacific Ocean.
Figure shows presentday displacement of crust and upper mantle due to glacial loading of South Patagonian Icefield located at 60° colatitude.
3D version: (arbitrary lateral viscosity variations in mantle, no restrictions on surfaceload geometry), presription of plate boundaries as 400 kmwide lowviscosity zones separating the elastic plates
• Equipartioning of spheroidal and toroidal surface motion: Motion of plates due to GIA follows the same equipartitioning as motion of plates due to the mantle convection. Note that if a spherically symmetric structure of the Earth is considered there is no toroidal displacement induced by surfacemass loading. Thus, the toroidal component is induced by coupling mechanisms to the spheroidal excitation.
Figure shows degree variances of spheroidalvertical (dotted), spheroidalhorizontal (solid) and toroidalhorizontal (dashed) displacements for 1D (spherically symmetric) and 3D earth model (consideration of plate boundaries and lithosphere thickness variations).
• Assessment of plate rotation vectors for 1D and 3D structure. Due to improved GPS analysis, predicted `GIA corrections' for plate motion are comparable or even larger than the accuracy of their determination due to geodetic methods (state of ITRF (Altamimi et al., 2007)).
Figure shows horizontal presentday GIAinduced surface velocities for rigid plate loations of North America considered in the ITRF2005 for the 1D earth model (left) and 3D earth model (right). Black arrows indicate the induced surface velocities and red arrows the velocities due to a rigid rotation with parameters given at the top of each plot.
GIA induced geocenter motion. It has been shown that the GIA induced contribution to the geocenter motion is most sensitive to lowermantle viscosity. The amplitude due to GIA lies between 0.1 and 1 mm/yr depending on the lowermantle viscosity structure, whereas the direction of the motion is pointing rather stable towards east of Hudson Bay, NA. Because the accuracy of the geodetically determined geocenter motion is only about 1 mm/yr, the interpretation of this signal in terms of GIA demands an improvement by one order of magnitude in the observation techniques.
• Interpretation of results in terms of dynamics of the Earth's interior
• Consideration of lateral viscosity variations derived from mantle tomography
• Implications for the interpretation of gravity variations
• Inversion strategy by assimilation of Sealevel indicators in order to get a consistent model
Figure shows expected lateral variability of viscosity in the lower mantle for a given scaling of shearwave velocity variation to viscosity. Red bars denote the shearwave velocity variation of an averaged tomographic model (Becker & Boschi, 2002).
 Jacoby WR, Hartmann O, Wallner H, Smilde PL, Bürger S, Sjöberg LE, Erlingsson S, Wolf D, Klemann V, Sasgen I 2009. Temporal gravity variations near shrinking Vatnajökull icecap, Iceland. Pure Appl. Geophys., 166: 12831302.
 Klemann V, Ivins ER, Martinec Z, Wolf D 2007. Models of active glacial isostasy roofing warm subduction: The case of the South Patagonian Icefield. J. Geophys. Res., 112: B09405.
 Klemann V, Martinec Z, Ivins ER 2008. Glacial isostasy and plate motions. J. Geodyn., 46: 95103.
 Klemann V, Martinec Z 2009. Contribution of glacialisostatic adjustment to the geocenter motion. Tectonophysics, online.
 Sasgen I, Mulvaney R, Klemann V and Wolf D 2008. Glacialisostatic adjustment and sealevel change near Berkner Island, Antarctica. Pure Appl. Geophys., submitted.
 Tanaka Y, Klemann V and Okuno J, 2009. Application of a numerical inverse Laplace integration to surface loading in a viscoelastic compressible Earth model. Pure Appl. Geophys., 166: 11991216.
 Tanaka Y, Klemann V, Fleming K and Martinec Z 2009. Spectral finite element approach to postseismic deformation in a viscoelastic selfgravitating spherical Earth. Geophys. J. Int., 176: 715739.


