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by Willy Fjeldskaar IRIS Modelling technique Glacial isostasy Iceload data Calibration data Development 2006 Glacial isostasy The earth’s crust may…be considered as a slowly flexible sheet of solid rock floating on a viscous substratum Nansen, 1928 Model Lithosphere Asthenosphere Upper mantle 670km A layered viscous Earth with an elastic, uniformly thin lithosphere (Fjeldskaar & Cathles, 1991) Lower mantle load subsidence (m) thickness (m) Isostatic response distance (km) Lithosphere as lowpass filter Decomposition of ice load Load removal 20 000 BP Ice load I(t, k) Difference between two timesteps 15 000 BP Ice extent and thickness during the last 20 000 years The glaciation rate from one time step to the next is assumed constant Equilibrium displacement The isostatic equilibrium displacements by flexure Fo(k) due to a harmonic ice load I(k) are achieved by subsidence: Fo (k ) I (k ) g (k ) where is the density of the mantle, g is the gravity, k is the wave number, and (k) is the "lithosphere filter" : (k ) 1 kg4 D(k ) Nadai, 1950 where D(k) is the flexural rigidity Transient displacement The elastic lithosphere will speed up the rate of compensation. The subsidence as a function of time t: F(k, t) = Fo(k)e-t(k)/ where is the relaxation time for the viscous fluid mantle below the lithosphere. Relaxation time The Exponential Decay of Beer Foam Relaxation time Relaxation time wavelengths Filtered relaxation time Relaxation time is the time required for a function to decrease to 1/e (36.8%) of the equilibrium value. Relaxation time (40 x 1023 Nm; 70 km) 4000 km 400 km Order no k = 2pr/l – 1/2 Uplift history 1) present rate of uplift 2) palaeo shoreline tilt 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) Viscosity vs. thickness 140 120 100 80 60 40 0 1 2 3 19 4 5 Viscosity (10 Pa s) A uniform mantle viscosity of 1021 Pa s. 6 7 Best-fit model Observed uplift Modelling uplift of Svalbard Sea level changes Storøya Wilhelmøya Kongsøya Hopen Bjørnøya Sea level changes Storøya Wilhelmøya Kongsøya Hopen 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 Crustal thickness Lateral uniform: F(kx, ky, t) = e-t (kx,ky)/(kx, ky)-1 (kx, ky) = 1 + D (kx, ky) k4/g Lateral varying: F(kx, ky, x, y, t) = e-t (kx,ky,x,y )/(kx,ky,x,y)-1 (kx, ky, x, y) = 1 + D(x, y) k4/g Developing model Implementation Testing