Download Relaxation time

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