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Consideration of material compressibility in GIA modelling*

Consideration of material compressibility in GIA modelling*. Volker Klemann 1 , Yoshiyuki Tanaka 2 , Zdeněk Martinec 3 , Riccardo EM Riva 4. IGS Workshop 2010/Vertical Rates Symposium Jul. 2 , 2010 ( Newcastle Upon Tyne ). (1) GFZ German Research Center for Geosciences, Potsdam

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Consideration of material compressibility in GIA modelling*

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  1. Consideration of material compressibilityin GIA modelling* Volker Klemann1, Yoshiyuki Tanaka2, Zdeněk Martinec3, Riccardo EM Riva4 IGS Workshop 2010/Vertical Rates Symposium Jul. 2, 2010 (Newcastle Upon Tyne) (1) GFZ German Research Center for Geosciences, Potsdam volkerk@gfz-potsdam.de (2) University of Tokyo, Japan (3) DIAS, Dublin, Ireland (4) DEOS, Delft University of Technology, The Netherlands * submitted (Tanaka et al., 2010, GJI)

  2. Overview • Extra terms in field equations • Consequences why it is still an issue • Process of GIA • Model set up • Variance spectrum • Displacement rates

  3. Field equations

  4. Interface conditions

  5. Why compressibility is often not considered? • Compressiblity affects gravitational processes… • become dominant for the viscous long-term behavior • commercial codes are designed for ingeneering (no gravity) • Solution of field equations may result in unphysical behavior • Problems if density increase does not follow self-compaction (Adams-Williamson condition) • Appearance of continuous or infinitely denumerable sets of relaxation modes (Plag & Jüttner 1995 — Cambiotti& Sabadini 2009) • Long-term behavior is described by a compressible fluid • a tricky problem in hydrodynamics (Ralf Greve, pers. Comm.) • Influences flexural rigidity of elastic lithosphere

  6. Earth response to glacial loading (GIA) • Response to glacial loads • Extension: O (1000 km) • Thickness: O (1 km) • Period: O (100 kyr) • Last glaciation terminated 8000 yr BP • Present-day adjustment • Mechanism is the trade off between • elastic flexure of the lithosphere and • buoyant viscous flow of the mantle

  7. Model set up • Parameterisation of elastic parameters in lithosphere and mantle • Model C: • Compressible PREM Model IA: • Shear modulus as model A • Incompressible • Model IB: • Inside lithosphere (Lambeck & Nakiboglu 1984) • Incompressible

  8. Spectral representation

  9. Degree variances

  10. Displacement fieldmodels C and IA Model C - IA

  11. Displacement fieldmodels C and IB Model C - IB

  12. Differences forj > 5 Model C - IB Model C - IA

  13. Summary • Prediction of GIA induced vertical displacement can be modelled applying an incompressible earth model • Horizontal displacement depends much stronger on the lithospheric structure • Adjustment of the flexural rigidity by reduced shear modulus, results in reasonable prediction of horizontal displacement • This simple parameterisation fails if considering low-degree harmonics, which are governed by mantle flow, which depends on the buoyant flow affected by compressibility rather than flexure or shear relaxarion.

  14. Thank you for your attantion • http://www.fifa.com/football

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