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