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by Willy Fjeldskaar IRIS

How do we model glacial isostasy?. by Willy Fjeldskaar IRIS. Outline. Modelling technique Glacial isostasy Iceload data Calibration data Development 2006. Glacial isostasy.

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by Willy Fjeldskaar IRIS

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  1. How do we model glacial isostasy? by Willy Fjeldskaar IRIS

  2. Outline • Modelling technique Glacial isostasy Iceload data Calibration data • Development 2006

  3. Glacial isostasy The earth’s crust may…be considered as a slowly flexible sheet of solid rock floating on a viscous substratum Nansen, 1928

  4. Model Lithosphere Asthenosphere A layered viscous Earth with an elastic, uniformly thin lithosphere (Fjeldskaar & Cathles, 1991) Upper mantle 670km Lower mantle

  5. Isostatic response load thickness (m) subsidence (m) distance(km)

  6. Forebulge

  7. Lithosphere as lowpass filter

  8. Decomposition of ice load

  9. Ice load

  10. Load removal 15 000 BP 20 000 BP Ice load I(t, k) Difference between two timesteps

  11. Deglaciation history Ice extent and thickness during the last 20 000 years The glaciation rate from one time step to the next is assumed constant

  12. Equilibrium displacement Nadai, 1950

  13. Transient displacement Relaxation time The Exponential Decay of Beer Foam

  14. Relaxation time Relaxation time Filtered relaxation time wavelengths Relaxation time is the time required for a function to decrease to 1/e (36.8%) of the equilibrium value.

  15. Relaxation time (40 x 1023 Nm; 70 km) 4000 km 400 km Order no k = 2pr/l – 1/2

  16. Digital output

  17. Uplift history

  18. Data on post-glacial uplift 1) present rate of uplift 2) palaeo shoreline tilt

  19. Uplift modelling The Earth's response to the deglaciation in Fennoscandia is modelled using a layered viscous model with elastic lithosphere. “The most likely ice model gives a flexural rigidity of 1023 Nm (te = 20 km) at the Norwegian coast, increasing to more than 1024 Nm (te = 50km) in central parts of Fennoscandia” (Fjeldskaar, 1997) (Fjeldskaar & Cathles, 1991)

  20. 140 120 100 80 60 40 0 1 2 3 4 5 6 7 Asthenosphere viscosity Viscosity vs. thickness 19 Pa s) Viscosity (10 A uniform mantle viscosity of 1021 Pa s.

  21. Theoretical present rate of uplift Best-fit model Observed uplift

  22. Modelling uplift of Svalbard

  23. Storøya Wilhelm- øya Kongsøya Hopen Bjørnøya Sea level changes

  24. Storøya Wilhelm- øya Kongsøya Hopen Sea level changes

  25. Svalbard rheology The post-glacial shoreline displacement on Svalbard indicates a high viscosity mantle A flexural rigidity of 2 x 1023 Nm (te = 25 km) and a uniform mantle viscosity of 1021 Pa s

  26. Crustal thickness

  27. Lateral changes

  28. Lateral changes in elastic rheology Lateral uniform: F(kx, ky, t) = e-t a(kx,ky)/t a(kx, ky)-1 a(kx, ky) = 1 + D (kx, ky) k4/rg Lateral varying: F(kx, ky, x, y, t) = e-t a(kx,ky,x,y )/t a(kx,ky,x,y)-1 a(kx, ky, x, y) = 1 + D(x, y) k4/rg

  29. Developing model Implementation Testing Activity 2006

  30. Algorithm

  31. Example 1

  32. Example 2

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