by Willy Fjeldskaar IRIS
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Transcript of by Willy Fjeldskaar IRIS
by
Willy FjeldskaarIRIS
Modelling techniqueModelling technique
Glacial isostasyGlacial isostasy
Iceload dataIceload data
Calibration dataCalibration data
Development 2006Development 2006
Glacial isostasyGlacial isostasy
The earth’s crust The earth’s crust may…be considered may…be considered as a slowly flexible as a slowly flexible sheet of solid rock sheet of solid rock floating on a viscous floating on a viscous substratumsubstratum
Nansen, 1928Nansen, 1928
A layered viscous Earth with an elastic, uniformly thin
lithosphere(Fjeldskaar & Cathles, 1991)
Asthenosphere
Lithosphere
Upper mantle
Lower mantle
670km
ModelModel
distance (km)
thic
kne
ss (
m)
subs
iden
ce (
m)
load
Isostatic response Isostatic response
Lithosphere as lowpass filter
Decomposition of ice loadDecomposition of ice load
Differencebetween two timesteps
Load removal
20 000 BP 15 000 BP
Ice load I(t, k)
Ice extent and thickness during the last
20 000 years
The glaciation rate from one time step to the next
is assumed constant
)()()(k
kIkoFg
The isostatic equilibrium displacements
by flexure Fo(k) due to a harmonic ice load I(k)
are achieved by subsidence:
where is the density of the mantle, g is the gravity,
k is the wave number, and (k) is the "lithosphere filter" :
( ) ( )4k kgD k1
Nadai, 1950where D(k) is the flexural rigidity
Equilibrium displacementEquilibrium 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.
Transient displacementTransient displacement
Relaxation time
The Exponential Decay of Beer Foam
Relaxation timeRelaxation 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)
Order no k = 2r/ – 1/2
4000 km 400 km
Relaxation timeRelaxation time
Uplift historyUplift history
1) present rate of uplift
0
0,5
1
1,5
2
-12 -10 -8 -6 -4 -2 0Time (thousand years BP)
Trøndelag2) 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)
0 1 2 3 4 5 6 7
40
60
80
100
120
140
Viscosity (1019 Pa s)
Viscosity vs. thickness
A uniform mantle viscosity of 1021 Pa s.
Observed uplift
Best-fit model
Modelling uplift of SvalbardModelling uplift of Svalbard
Bjørnøya
Hopen
Kongsøya
Storøya
Wilhelm- øya
-40
-20
0
20
40
60
-14 -12 -10 -8 -6 -4 -2 0 2
Bjørnøya
Asthenosphereuniform
Age (1000 years BP)
Sea level changesSea level changesSea level changesSea level changes
0
20
40
60
80
100
-10 -8 -6 -4 -2 0
Agardhbukta
observedasthenosphereuniform
Age (1000 years BP)
-10
0
10
20
30
40
50
60
-10 -8 -6 -4 -2 0
Bellsund
observedasthenosphereuniform
Age (1000 years BP)
-20
0
20
40
60
-10 -8 -6 -4 -2 0
Daudmannsøyraobservedasthenosphereuniform
Age (1000 years BP)
-10
0
10
20
30
40
50
60
-10 -8 -6 -4 -2 0
Erdmannflya
observedasthenosphereuniform
Age (1000 years BP)
0
20
40
60
80
100
120
-10 -8 -6 -4 -2 0
Hopen
observedasthenosphereuniform
Age (1000 years BP)
0
20
40
60
80
100
120
-10 -8 -6 -4 -2 0
Kongsøya
observedasthenosphereuniform
Age (1000 years BP)
0
20
40
60
80
100
120
-10 -8 -6 -4 -2 0
Negerdalen
observedasthenosphereuniform
Age (1000 years BP)
-10
0
10
20
30
40
50
60
-10 -8 -6 -4 -2 0
Prins Oscars land
observedasthenosphereuniform
Age (1000 years BP)
-10
0
10
20
30
40
50
60
-10 -8 -6 -4 -2 0
Storøya
observedasthenosphereuniform
Age (1000 years BP)
0
20
40
60
80
100
120
-10 -8 -6 -4 -2 0
Svartknausflya
observedasthenosphereuniform
Age (1000 years BP)
0
20
40
60
80
100
120
-10 -8 -6 -4 -2 0
Wilhelmøya
observedasthenosphereuniform
Age (1000 years BP)
Hopen
Kongsøya
Storøya
Wilhelm- øya
Sea level changesSea level changesSea level changesSea level changes
A flexural rigidity of 2 x 1023 Nm (te = 25 km)
and a uniform mantle viscosity of 1021 Pa s
Svalbard rheologySvalbard rheology
The post-glacial shoreline displacement on Svalbard
indicates a high viscosity mantle
The post-glacial shoreline displacement on Svalbard
indicates a high viscosity mantle
Crustal thickness
F(kx, ky, t) = e-t (kx,ky)/(kx, ky)-1
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
Lateral uniform:
Lateral varying:
(kx, ky) = 1 + D (kx, ky) k4/g
Developing modelDeveloping model
ImplementationImplementation
TestingTesting