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Consideration of material compressibility in GIA modelling*

This study explores the impact of material compressibility in GIA modeling, discussing its effects on gravitational processes, commercial codes, and field equations. It investigates why compressibility is often overlooked and the consequences of neglecting it, providing insights into the complexities of long-term Earth responses to glacial loading.

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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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