Lithospheric structure and dynamics
Lecture 6 - Composition and rheology of the
lithosphere in northern Europe
Lecturer: David Whipp
david.whipp@helsinki.fi
4.11.2015
Lithospheric structure & dynamics
www.helsinki.fi/yliopisto
2
Goals of this lecture
•
Look at several methods for determining the thickness of the
lithosphere in northern Europe
•
Discuss the strength of the lithosphere with two examples
from Fennoscandia
3
Part 1 - Composition of the lithosphere
•
Although the lithosphere is the most accessible portion of the
Earth for us, we’re really only able to explore a small fraction
of it
•
•
•
How thick is typical continental lithosphere?
How deep have we drilled?
Fortunately we can use several geological/geophysical methods
to study the composition and structure of the lithosphere
•
Thermal modelling, seismology, electrical methods, mantle
xenoliths, etc.
4
Composition of the lithosphere
•
Although the lithosphere is the most accessible portion of the
Earth for us, we’re really only able to explore a small fraction
of it
•
•
•
How thick is typical continental lithosphere?
How deep have we drilled?
Fortunately we can use several geological/geophysical methods
to study the composition and structure of the lithosphere
•
Thermal modelling, seismology, electrical methods, mantle
xenoliths, etc.
5
The lithosphere, a reminder
•
As noted in lecture 1, the lithosphere can be defined in several
ways
•
Elastic/rheological lithosphere: The part of the crust and
upper mantle that can support elastic stresses of a given
size for a given time. Its base may be close to the “brittleductile” transition. Also known as the flexural, mechanical or
rheological lithosphere.
•
Seismic lithosphere: The region of high seismic velocity
overlying the low-velocity zone in the upper mantle
•
Thermal lithosphere: The relatively cool upper layer of
crust and mantle above the convecting asthenosphere.
Typical temperature cut-off: ~1300°C
6
The lithosphere, a reminder
•
As noted in lecture 1, the lithosphere can be defined in several
ways
•
Electrical lithosphere: The region of crust and mantle of
relatively low conductance above the region of relatively
high conductivity that corresponds to the seismic lowvelocity zone
•
Petrological lithosphere: The chemical boundary layer of
crust and upper mantle that is relatively depleted in basaltic
components compared to the underlying asthenosphere.
Depletion of Fe, Al and Ca is typical, as well as depletion of
Ti, Zr and Y.
7
Exploring the thermal lithosphere
•
The flux of heat at the Earth’s surface is a key observation that
can be used to constrain the thermal field in the lithosphere
•
A common approach is to use thermal models to calculate
the thermal field in the lithosphere from basic physics, and then
compare derived quantities such as the surface heat flow to
observations
•
Although this perhaps sounds straightforward, thermal models
are highly non-unique. What does this mean?
•
Non-uniqueness: There are many possible combinations of
model input values that can produce the same results
(predicted heat flow values, for example)
8
Exploring the thermal lithosphere
•
The flux of heat at the Earth’s surface is a key observation that
can be used to constrain the thermal field in the lithosphere
•
A common approach is to use thermal models to calculate
the thermal field in the lithosphere from basic physics, and then
compare derived quantities such as the surface heat flow to
observations
•
Although this perhaps sounds straightforward, thermal models
are highly non-unique. What does this mean?
•
Non-uniqueness: There are many possible combinations of
values/parameters that produce similar results
(predicted heat flow values, for example)
9
Heat transfer equation, also a reminder
•
In shield areas, heat transfer can be modelled using the heat
conduction equation with heat production
@T
r
·
(krT
)
+
A
=
⇢c
p
@t
where ! is thermal conductivity, " is temperature, # is
volumetric heat production, $ is rock density, %& is specific heat
and ' is time
•
•
Rates of tectonic activity and erosion/sedimentation are
generally slow here, so we can ignore advection
Typically in shield areas we can also assume the thermal field is
close to a thermal equilibrium state at the lithospheric scale,
reducing our heat transfer equation to the steady-state version
r · (krT ) + A = 0
10
How does it work?
•
To determine temperature from either equation, they must be
solved analytically or numerically by applying appropriate
boundary conditions
•
Let’s consider a 1D thermal solution with a constant
temperature boundary condition at the Earth’s surface, and
constant heat flux boundary condition at depth…
11
0°
10°
20°
A
Profiles
70°
30°
70°
Seismological
Thermal
Geodynamical
Thermal modelling in
Fennoscandia
Mantle lithosphere
Seismological station
Magnetotelluric station
65°
65°
•
Now that we have a sense of
how things work in 1D, let’s
consider the thermal field in
Fennoscandia in 2D
•
We’ll look at three profiles
across this region (green lines)
FKF
B 3/4
BHRF
60°
60°
NRA0
•
•
•
KONO
OG8
C
TTL
G
DB
-43
DK88
ML2
B
B
NE02
ML3
55°
ATK
NE03
C‘
A
A‘
55°
BA
•
BA
ML1
Baltic shield (A-Aʹ)
Danish basin (B-Bʹ)
North German basin (C-Cʹ)
What do we expect to see?
B‘
Balling, 2013
C
10°
20°
12
0°
10°
20°
A
Profiles
70°
30°
70°
Seismological
Thermal
Geodynamical
Thermal modelling in
Fennoscandia
Mantle lithosphere
Seismological station
Magnetotelluric station
65°
65°
•
Now that we have a sense of
how things work in 1D, let’s
consider the thermal field in
Fennoscandia in 2D
•
We’ll look at three profiles
across this region (green lines)
FKF
B 3/4
BHRF
60°
60°
NRA0
•
•
•
KONO
OG8
C
TTL
G
DB
-43
DK88
ML2
B
B
NE02
ML3
55°
ATK
NE03
C‘
A
A‘
55°
BA
•
BA
ML1
Baltic shield (A-Aʹ)
Danish basin (B-Bʹ)
North German basin (C-Cʹ)
What do we expect to see?
B‘
Balling, 2013
C
10°
20°
13
Heat flow (mW/m2)
100
N
80
S
60
40
qs
20
a)
40
Heat flow
qm
250
0
500
750
1000
1250
1500
Archean
0
Depth (km)
Svecofennian
TIB
0
200
400
600
50
100
1000
150
150
1200
200
Isotherms
Depth (km)
•
The thermal lithosphere
thickness varies from ~250
km in the north to <150
km in the south
•
You have seen this
example already in the
previous lectures on heat
flow
250
300
300
0
15
20
40
10
7.5
Temp. gradient
60
0
17.5
20
12.5
40
5
60
80
80
0
Depth (km)
Surface heat flow values
are fairly low
200
1400
250
d)
•
50
800
100
20
25
40
Heat flow
60
80
0
A’
Caledonides
Baltic shield
20
1750 km
A
c)
80
60
0
b)
100
0
250
30
35
40
20
40
20
500
0
55
45 50
Balling, 2013
750
1000
1250
1500
1750 km
60
80
14
Heat flow(mW/m2)
100
80
60
N
S
60
40
40
qm
20
B
Depth (km)
100
200
STZ
Danish
Basin
RingkøbingFyn High
500 km
North German Basin
200
400
600
800
50
0
B’
0
50
1000
1200
1400
100
100
Isotherms
150
0
20
10
Depth (km)
400
300
Danish basin
20
Heat flow
Sveconorwegian
0
20
22.5 25 27.5
20
30
15
12.5 10
40
50
Temp. gradient
c) 60
0
20
d) 60
50
60
30
40
Heat flow
Balling, 2013
0
Thermal lithosphere is ~100 km thick
across the profile
20
35
50
•
10
40
30
Heat flow values are more typical for
continental lithosphere
0
70 65 75
60
55
50
45
10
•
10
30
40
150
0
30
17.5
40
Depth (km)
80
qs
a) 0 0
b)
100
100
200
300
400
500 km
50
60
15
SW
NE
100
Heat flow (mW/m2)
100
80
80
qs
60
60
40
40
qm
20
a)
0
Heat flow
0
100
C
200
400
200
400
600
20
0
500 km
C’
TTZ/STZ
North German Basin
0
0
800
1000
50
Depth (km)
300
50
1200
100
100
Asthenosphere
b)
Isotherms
0 80
Depth (km)
50 30
High surface heat flow values across
basin
•
Thermal lithospheric thickness
increases from ~75 km in south to
almost 200 km in north
0
60 50 70
40
35
50
35
30
100
100
Asthenosphere
150
c)
200
40
200
•
150
150
200
North German basin
150
Heat flow
0
100
Balling, 2013
200
300
400
200
500 km
16
Summary of observations
•
Heat flow variations across Fennoscandia correlate with
variations in the thickness of the thermal lithosphere
•
•
•
High heat flow → Thin thermal lithosphere
Low heat flow → Thick thermal lithosphere
Moho temperatures are quite variable for each profile
17
63°
60°
P-wave traveltime residuals
Two types of station P-wave travelt
Seismological
were calculated: station relative resid
constraints
tion absolute residuals (Fig. 6.7). The
sidual is the difference between the ob
NORSAR array
time of the P-phase and the predicted
HFC2
a standard Earth model for which th
Seismology is another
erence model (Kennett and Engdahl,
important source of data
plied. Since observations from the va
about the thickness and
arrays cover different time periods
structure of the lithosphere
station procedure was applied for th
tion of relative residuals. Permanen
fors (HFC2, Fig. 6.6) was selected as
Variations
in seismic
wavequality
This
station has
very good
velocities
and statio
thepropagation
whole period
of temporary
Permanent
structural
are and 2009
which
is here reflections
between 1996
CALAS
MAGNUS
particularly
useful
for
studying
Relative
P-residuals
determined
us
SCANLIPS
CENMOVE
the large-scale properties of
relation procedures (complemented b
DanSeis
Tor
the lithosphere
ity control and manual fine-tuning a
P33 and P35) are generally very accu
°
8
1
15°
12°
within ± 0.1 s, and reflect P-wave v
Balling, 2013
18
tions
below
the
study
area.
Absolut
1000 1500 2000 m
•
57°
•
54°
51°
3°
6°
0
9°
500
Balling, 2013
Variations
in
relative
63°
P-wave travel times
63°
63°
60°
60°
60°
•
57°
57°
54°
54°
9°
15°
12°
51°
3° (a)
6°
51°
3°
18°
9°
12°
(a)
6°
15°
9°
18°
12°
P-wave residuals relative to
permanent station HFC2 (red
5star)
7°
indicate P-wave velocities
vary significantly in the
lithosphere and upper mantle
across southern Norway and
Sweden, and northern
54°
Denmark
51°
(b)
3°
18°
15°
6°
9°
12°
(b)
15°
19
P-wave velocity variations from regional
relative tomography
Chapter 6
76
A
0
200
400
E
A’
600
400
200
0
800
1000
E’
1200
C
C’
0
100
100
100
200
200
200
300
300
300
400
400
400
500
500
500
600
600
600
100 - 200 km
63
B
0
200
400
600
B
A’
100
57
300
400
500
600
D
0
C’
D’
B’
60
200
600
200
400
600
800
D’
100
200
300
C
400
54
500
600
D E‘
51
0
400
A E
B’
800
200
6
12
18
1
Balling, 2013
20
100 - 200 km
100 - 200 km
63°
60°
60°
57°
57°
54°
54°
51°
51°
0°
6°
12°
18°
0°
6°
•
In the tomographic
calculations based on both
the relative and absolute Pwave velocities we observe
relatively slow velocities in
southern Norway and the
Danish and North German
basins
•
Velocities in most of Sweden
and northern Norway are
relatively fast
18°
12°
(a)
(c)
Relative
Absolute
200 - 300 km
200 - 300 km
63°
63°
60°
60°
57°
57°
54°
54°
51°
0°
P-wave velocity
variations
63°
51°
6°
12°
(b)
18°
0°
6°
12°
(d)
18°
Balling, 2013
21
10°
5°
15°
+ 1 - 2%
Cal
n
edo
–1%
–1 - 2%
Implications
s
e
d
+ 1%
•
d
l
e
i
Sh
OG
60°
i
SG
ic
t
l
a
B
+ 2 - 3%
•
DB
–2%
STZ
•
55°
–2%
TT
Z
NGB
5°
ences (Cammerano et al. 2003; Lee, 2003; Schu
and Lesher, 2006; Hieronymus et al. 2007; H
eronymus and Goes, 2010). Large differenc
in upper-mantle seismic velocity, such as tho
observed in the present area, mainly seem to
caused by temperature differences. The abo
studies
compositional
differences
f
Bothindicate
the thermal
models and
Plikely upper-mantle petrology to be of minor i
60°
wave velocities/tomography suggest
portance and may only account for velocity var
the lithosphere is relatively thin
tions of up to about 1%.
near
the Danish
and North
The
combined
information
fromGerman
seismic tom
basins,
as in southern
graphy
and as
thewell
surface-wave
and thermal studi
Norway
discussed
above clearly indicate a lithosphere
reduced thickness beneath Denmark and adjace
Inofcontrast,
Balticand
shield
parts
northernthe
Germany
the North Sea an
lithosphere
appearsmost
thick
apparently
also beneath
of southern Norw
compared to the adjacent areas of southern Sw
Rifting can explain the thin
den. The generally narrow upper-mantle veloc
55°
lithosphere
near
transition
outlined
in the
Figs.Danish
6.9 andand
6.10 is th
North German
basins,
but southern
interpreted
to form the
southwestern
bounda
Norway
less obvious
of thick
BalticisShield
lithosphere. In the southe
part of the area this boundary runs along (an
close to) the STZ and seems to follow the easte
22
Balling,boundary
2013
of a branch of significant Late Carbo
10°
15°
Mantle xenoliths and xenocrysts
Chapter 6
S
0
50
Kuopio
Kaavi
Kuhmo
Svecofennian
crust
2.1-1.85 Ga
S-Kuusamo
Lentiira
N-Kuusamo
N
Archean crust
3.5-2.6 Ga
Moho
Layer A
•
Layer B
100
c. 2.7-2.8 Ga
c. 3.3 Ga
Depth (km)
Diamond in
150
Layer B
200
Metasomatised
c. 2.0 Ga
Layer C
Metasomatised
1.9 Ga
Regenerated
1.2 and 0.36 Ga
Mantle xenoliths and
xenocrysts from eastern
Finland are sourced from
65-250 km depth, all from
within the mantle
lithosphere of an Archean
craton
250
0
300
100 km
Asthenosphere
Balling, 2013
Cross-section of Baltic Shield lithosphere along a c. 600 km long transect in the south-central Finland kims, showing Archean Karelian province and the boundary to the Palaeoproterozoic Svecofennian province.
nen and O´Brien (2009). Location is shown in Fig. 6.1. Layered structure of lithospheric mantle is interpreted
23
Mantle xenoliths and xenocrysts
Chapter 6
S
0
50
Kuopio
Kaavi
Kuhmo
Svecofennian
crust
2.1-1.85 Ga
S-Kuusamo
Lentiira
N-Kuusamo
N
Archean crust
3.5-2.6 Ga
Moho
Layer A
•
Layer A: Fine-grained
garnet-spinnel
harzburgites
•
Layer B: Harzburgites,
lherzolites, wehrlites,
websterites. Low-Ca,
high-Cr garnets.
•
Layer C: No subcalcic
harzburgite garnets, less
depleted lherzolitic
pyropes
c. 2.7-2.8 Ga
c. 3.3 Ga
Diamond in
Depth (km)
This data suggests the
mantle has a peridotite
composition, but is stratified
Layer B
100
150
Layer B
200
Metasomatised
c. 2.0 Ga
Layer C
Metasomatised
1.9 Ga
Regenerated
1.2 and 0.36 Ga
250
0
300
•
100 km
Asthenosphere
Balling, 2013
Cross-section of Baltic Shield lithosphere along a c. 600 km long transect in the south-central Finland kims, showing Archean Karelian province and the boundary to the Palaeoproterozoic Svecofennian province.
nen and O´Brien (2009). Location is shown in Fig. 6.1. Layered structure of lithospheric mantle is interpreted
24
Archean amalgamated craton - c. 3.5-2.6 Ga
Comparison of results using diff
physical methods
Formation of stratified
In an interesting recent study, Jones e
mantle
Continental break-up - c. 2.0 Ga
compare results of the determination o
sphere-asthenosphere boundary (LAB
ropean areas by applying of differen
cal methods. Three independent data
depth to the LAB are analysed statisti
sphere
from receiver funct
Thisthickness
is one possible
P-residuals/anisotropy
and fromof ma
explanation for stratification
rics.the
Allmantle
three data
sets agree in showin
lithosphere
cant and rapid variation in lithospheric
across the Trans-European Suture Zon
ter 1 and 2; Figs. 1.1; 2.1). For Precambr
Obviously,
this isShield,
challenging
to sei
including
the Baltic
the two
demonstrate
methods
yield generally consistent res
mean lithospheric thickness of 170-180
pared to the deeper electromagnetic resu
250 km. For Phanerozoic Europe, inc
Danish and North German areas, anoth
of results, receiver functions and electr
25
are consistent with a mean lithospheric
•
Closure of the Svecofennian sea - c. 1.90 Ga
•
Svecofennian arc complex
Layer A
Balling, 2013
Layer C
Ophiolites
Part 2 - Rheology of the lithosphere
•
The composition and temperature of the lithosphere have
major implications for how the lithosphere will deform over
geological time scales
•
Rheology
The science of the flow characteristics of materials.
•
For most geologists
A term that describes the deformational behavior of materials,
regardless of whether the deformation occurs by flow, fracture
or other mechanisms.
26
Elasticity
n
or
Twiss and Moores, 2007
s
n
or
s
E or 2G
•
/"
•
Stress is proportional to
strain
For 1-D normal stress
xx = E"xx
•
"n or "s
"n or "s
( : Young’s modulus (1D)
) : Shear modulus (1D)
If stress → 0, strain → 0
(recoverable)
xx
= E"xx
27
Elasticity
n
or
Twiss and Moores, 2007
s
n
or
s
E or 2G
•
/"
•
Stress is proportional to
strain
For 1-D normal stress
xx = E"xx
•
"n or "s
"n or "s
( : Young’s modulus (1D)
) : Shear modulus (1D)
If stress → 0, strain → 0
(recoverable)
xx
= E"xx
28
Perfectly plastic behavior
Twiss and Moores, 2007
s
s
•
•
Constant stress required for
deformation
•
No deformation prior to
exceeding yield stress
•
Infinite deformation if applied
stress equals (or exceeds)
yield stress
⇢
<
=
y
y
no deformation
failure; infinite deformation
Nonrecoverable
y
y
"˙s
"¯s
y
29
Perfectly plastic behavior
Twiss and Moores, 2007
s
s
•
•
Constant stress required for
deformation
•
No deformation prior to
exceeding yield stress
•
Infinite deformation if applied
stress equals (or exceeds)
yield stress
⇢
<
=
y
y
no deformation
failure; infinite deformation
Nonrecoverable
y
y
"˙s
"¯s
y
30
(Linear) Viscous deformation
•
n
In simple shear,
⌧
s
= ⌘˙
n
* Dynamic viscosity
Shear stress proportional to shear
strain rate
•
In general,
⌧
= 2⌘ "˙
"˙n
"¯n
deviatoric stress is proportional to
strain rate
•
For linear viscous (Newtonian)
materials, * is constant
•
Nonrecoverable
Twiss and Moores, 2007
31
(Linear) Viscous deformation
•
n
In simple shear,
⌧
s
= ⌘˙
n
* Dynamic viscosity
Shear stress proportional to shear
strain rate
•
In general,
⌧
= 2⌘ "˙
"˙n
"¯n
deviatoric stress is proportional to
strain rate
•
For linear viscous (Newtonian)
materials, * is constant
•
Nonrecoverable
Twiss and Moores, 2007
32
Nonlinear viscous deformation
•
•
Most rocks do not behave as
Newtonian viscous materials
Why not?
Two main reasons:
•
Temperature dependence
⌘ = A exp (Q/RT )
0
K
#0 is the pre-exponent constant,
, is the activation energy, - is the
universal gas constant and "K is
temperature in Kelvins
Viscous strength of quartz
← Increasing Temperature
•
d
z
Stüwe, 2007
33
Nonlinear viscous deformation
•
Most rocks do not behave as
Newtonian viscous materials
•
•
Why not?
Two main reasons:
•
•
Nonlinearity
⌧
sn = Ae↵ ˙
/ is the power law exponent and
#eff is a material constant in Pa/4s
Twiss and Moores, 2007
Many rocks deform 8 times as fast
when stress is doubled
34
Strength of the lithosphere
•
Defining the strength of the lithosphere is challenging and
estimates are quite variable
•
What do we consider strong?
•
•
•
•
Frictional plasticity?
High viscosity?
Large elastic thickness?
All three are possible sources of “strength” in the lithosphere
and we’ll now focus on a few examples of these concepts
applied to Fennoscandia
35
Strength of the lithosphere
•
Defining the strength of the lithosphere is challenging and
estimates are quite variable
•
What do we consider strong?
•
•
•
•
Frictional plasticity?
High viscosity?
Large elastic thickness?
All three are possible sources of “strength” in the lithosphere
and we’ll now focus on a few examples of these concepts
applied to Fennoscandia
36
experiments, contrasting the expected
behaviors of representative dry and wet
lower crust and mantle combinations
(adapted from Mackwell et al., 1998).
This figure is included not because such
profiles should be taken literally, but to
illustrate the effect of small amounts of
water onThe
creepBrace-Goetze
strength.
Lithospheric
strength envelopes
•
lithosphere is a
popular
reference
If significant
strength
resides only in
the seismogenic
the continental
model,layer
butof many
lithosphere, it would not be surprising if
are at the
regionalother
patterns options
of active faulting
surface were
dominated by the strength
possible
IMPLICATIONS
of the crustal blocks and the interactions
between them. The strength of the faults
Jelly
sandwich
themselves
is then
presumably a limiting
factor in crustal behavior, but remains
very uncertain
Scholz, 2000).
A(e.g.,
- Brace-Goetze
Maggi et al. (2000b) suggested that the
heights of mountains and plateaus
Bthe
- Wet
LC
correlate with
strength
of their
bounding forelands, with higher
mountains
requiringbrûlée
greater support.
Crème
The large buoyancy force needed to
support Tibet is equivalent to average
C - Wet
deviatoric stresses
of ~120UM
MPa if
contained within the 40-km-thick elastic
layer of India,
exceeding
the
Dgreatly
- Wet
LC, UM
average stress drops observed in
earthquakes
37
Jackson,
2002 of 1–10 MPa. But the faults
in the Himalayan foreland are not
•
•
•
•
•
•
Lithospheric strength in
the Fennoscandian shield
Kaikkonen et al., 2000
•
The study area is eastern Finland and
northern Estonia, crossing the region
of maximum Moho depth in Finland
•
The goal is to define the present-day
strength envelopes of the
lithosphere in central Fennoscandia
38
Lithospheric strength in
the Fennoscandian shield
Kaikkonen et al., 2000
•
The study area is eastern Finland and
northern Estonia, crossing the region
of maximum Moho depth in Finland
•
The goal is to define the present-day
strength envelopes of the
lithosphere in central Fennoscandia
39
Heat flow in
Fennoscandia
•
Rock viscosity is strongly
temperature dependent, so a good
estimate of crustal temperatures is
important for any model trying to
define the “strength” of the
lithosphere
•
Heat flow is variable and generally
low in Fennoscandia
w density distribution in our study area Ž58–718N, 17–348E.. Data Žshown as dots. has been taken from the database
Kaikkonen et al., 2000
ndell et al. Ž1992..
40
and wet rheologies. Temperatures of 58C at the
surface and of 11008C at the lithosphere–asthenosphere boundary were used as the boundary condi-
Fig. 6c Ždry. and d Žwet.. The figures show
two features, the weak ductile lower crust
with a varying thickness and the deepening
Lithospheric thermal model
Kaikkonen et al., 2000
Fig. 4. Temperature Ž8C. cross-section based on the calculated 1-D geotherms along the BALTIC–SKJ profile.
•
The thermal lithosphere increases in thickness from <150 km
in the south to > 200 km in the zone of largest Moho
thickness
•
What do you think about the “steps” in the thermal field
of this model?
41
and wet rheologies. Temperatures of 58C at the
surface and of 11008C at the lithosphere–asthenosphere boundary were used as the boundary condi-
Fig. 6c Ždry. and d Žwet.. The figures show
two features, the weak ductile lower crust
with a varying thickness and the deepening
Lithospheric thermal model
Kaikkonen et al., 2000
Fig. 4. Temperature Ž8C. cross-section based on the calculated 1-D geotherms along the BALTIC–SKJ profile.
•
The thermal lithosphere increases in thickness from <150 km
in the south to > 200 km in the zone of largest Moho
thickness
•
What do you think about the “steps” in the thermal field
of this model?
42
and wet rheologies. Temperatures of 58C at the
surface and of 11008C at the lithosphere–asthenosphere boundary were used as the boundary condi-
Fig. 6c Ždry. and d Žwet.. The figures show
two features, the weak ductile lower crust
with a varying thickness and the deepening
Lithospheric thermal model
Kaikkonen et al., 2000
Fig. 4. Temperature Ž8C. cross-section based on the calculated 1-D geotherms along the BALTIC–SKJ profile.
•
This study uses a 1D thermal model with two crustal layers
•
•
Constant temperature at the surface and at infinite depth
Different solutions are applied across the model for the
different geological regions
43
Model rheologies P. Kaikkonen et al.r Physics of the Earth and Planeta
Table 2
A layered petrological model mainly used in the calculations
Upper crust
Middle crust
Lower crust
Mantle
Dry
Wet
granite
granite,
felsic
granulite or
anorthosite
diabase
olivine
granite
granite or diorite
diorite
olivine
Kaikkonen et al., 2000
•
temperature values between the old Archaean Žcold.
Rheological
models use
several common
typesThe
and
Žwarmerrock
. units.
and the younger
Proterozoic
include
simulation
and wet conditions
uncertainties
in of
thedry
temperature
values as a function
of depth can be rather large, depending mainly on
the validity of the surface HFD values used in the
geotherm calculations. For example, an increase of
the surface HFD by an amount of 10 mWrm2
tions
1997.
metho
geoth
both
spheri
are sli
mal m
sophis
Ž1997
Th
calcul
not s
lower
and u
larly w
culate
44
‘sandw
Model predictions
45
Fig. 5. The strength envelopes ŽMPa. in the points a–f Žsee Fig. 1. along the BALTIC–SKJ profile. Strength envelopes were calculated
with the way
in this paper
Kaikkonen
etpresented
al., 2000
Žthick line. and based on the MC simulation of the geotherms ŽJokinen and Kukkonen, 1997. Žthin line.. Comparison of the strength envelopes is presented at the six sites Ža–f.
Model predictions
Where is the “strength” in this model?
46
Fig. 5. The strength envelopes ŽMPa. in the points a–f Žsee Fig. 1. along the BALTIC–SKJ profile. Strength envelopes were calculated
with the way
in this paper
Kaikkonen
etpresented
al., 2000
Žthick line. and based on the MC simulation of the geotherms ŽJokinen and Kukkonen, 1997. Žthin line.. Comparison of the strength envelopes is presented at the six sites Ža–f.
Model predictions
Where is the “strength” in this model?
47
Fig. 5. The strength envelopes ŽMPa. in the points a–f Žsee Fig. 1. along the BALTIC–SKJ profile. Strength envelopes were calculated
with the way
in this paper
Kaikkonen
etpresented
al., 2000
Žthick line. and based on the MC simulation of the geotherms ŽJokinen and Kukkonen, 1997. Žthin line.. Comparison of the strength envelopes is presented at the six sites Ža–f.
Dry models
Model predictions
48
Fig. 5. The strength envelopes ŽMPa. in the points a–f Žsee Fig. 1. along the BALTIC–SKJ profile. Strength envelopes were calculated
with the way
in this paper
Kaikkonen
etpresented
al., 2000
Žthick line. and based on the MC simulation of the geotherms ŽJokinen and Kukkonen, 1997. Žthin line.. Comparison of the strength envelopes is presented at the six sites Ža–f.
Wet models
Dry models
Model predictions
49
Fig. 5. The strength envelopes ŽMPa. in the points a–f Žsee Fig. 1. along the BALTIC–SKJ profile. Strength envelopes were calculated
with the way
in this paper
Kaikkonen
etpresented
al., 2000
Žthick line. and based on the MC simulation of the geotherms ŽJokinen and Kukkonen, 1997. Žthin line.. Comparison of the strength envelopes is presented at the six sites Ža–f.
Wet models
Dry models
Model predictions
Fig. 5 Ž continued ..
Kaikkonen et al., 2000
50
ILS
ICS
Integrated crustal/
lithospheric strength
•
Integrated crustal strength (ICS)
and integrated lithospheric
strength (ILS) values provide a
single scalar value for the
strength of the crust or
lithosphere
•
ICS is smaller than ILS, as
expected and both have their
highest values in the same
general region
g. 8. ICS ŽTNrm. for compressional wet Ža. and dry Žb. rheology and ILS ŽTNrm. for compressional wet Žc. and dry Žd. rheology in the
ntral Fennoscandian Shield. Dots show the calculations points.
Wet
Dry
Kaikkonen et al., 2000
51
Earthquakes in
Fennoscandia
•
We’ve seen predictions that the
“strength” of the lithosphere is largely
in the crust in Fennoscandia
•
•
The mantle lithosphere is only
“strong” under extension here
What is the general anticipated stress
field in Finland?
Kaikkonen et al., 2000
52
Earthquakes in
Fennoscandia
•
We’ve seen predictions that the
“strength” of the lithosphere is largely
in the crust in Fennoscandia
•
•
The mantle lithosphere is only
“strong” under extension here
In general, what kind of stress field is
anticipated in Finland?
Kaikkonen et al., 2000
53
Earthquakes in
Fennoscandia
•
We’ve seen predictions that the
“strength” of the lithosphere is largely
in the crust in Fennoscandia
•
•
The mantle lithosphere is only
“strong” under extension here
Earthquake foci generally are found only
within the brittle part of the
lithosphere, so the observed seismicity
is consistent with the predictions from
the lithospheric strength profiles
Kaikkonen et al., 2000
54
The effective elastic thickness in Fennoscandia
Another measure of lithospheric
“strength” is the elastic strength
•
The elastic lithosphere will bend when
loaded, and can be modeled as flexure
of an elastic beam or plate using the
following equation
3.12 Deformation of Strata Overlying an Igneou
•
d4 w
D 4 + (⇢m
dx
⇢c )gw = q(x)
where 6 is the flexural rigidity, 7 is the
flexural displacement, $m and $c are the
mantle and crust densities, 8 is
gravitational acceleration and 9(:) is the
vertical load distribution on the plate
Turcotte and Schubert, 2014
55
The effective elastic thickness in Fennoscandia
•
3.12 Deformation of Strata Overlying an Igneou
The flexural rigidity 6 of the beam/plate
represents its resistance to bending or
strength
ETe3
D=
12(1 ⌫ 2 )
where "; is the effective elastic
thickness, and ( and < are material
properties called Young’s modulus and
Poisson’s ratio, respectively
•
Turcotte and Schubert, 2014
The effective elastic thickness "; is the
equivalent thickness of an elastic beam/
plate as a model of the lithosphere
56
B10409
Calculations of Te in Fennoscandia
PÉREZ-GUSSINYÉ ET AL.: ELASTIC THICKNESS FROM SPECTRAL METHODS
B10409
Pérez-Gussiné et al., 2004
57
B10409
Calculations of Te in Fennoscandia
PÉREZ-GUSSINYÉ ET AL.: ELASTIC THICKNESS FROM SPECTRAL METHODS
B10409
Pérez-Gussiné et al., 2004
58
Summary of observations
•
The lithosphere in Fennoscandia although seismically relative
inactive appears to have strength only in the crust according to
lithospheric strength profiles
•
The elastic thickness in Fennoscandia is much larger, suggesting
both the crust and mantle lithosphere are “strong”
59
Part 3 - Rheology of the upper mantle
6.10 Postglacial Rebound
435
•
In Fennoscandia, we’re in a unique
position to study the flow of the
uppermost mantle in response to glacial
unloading following the last ice age
•
Glacial isostatic adjustment (or
postglacial rebound) is modulated by the
viscosity of the upper mantle, allowing us
to directly link uplift velocities to mantle
flow
•
As you’ll see, this has implications for the
lithosphere as well
and Schubert,
.14Turcotte
Subsidence
due to 2014
glaciation and the subsequent postglacial
.
60
Modelling glacial isostatic adjustment
•
Essentially, two components are needed to model glacial
isostatic adjustment:
•
•
A rheological model for the lithosphere and upper mantle
An ice thickness model
61
Modelling glacial isostatic adjustment
•
van der Wal et al. (2013) used a 3D spherical Earth model with
a 2° x 2° horizontal resolution to model glacial loading and
unloading in Fennoscandia
•
In their model, the upper 35 km was crust (elastic) and a
viscous mantle down to 400 km with an olivine rheology that
varies with depth
•
The olivine rheology has variable grain size and can be
calculated for either wet or dry conditions
62
Thermal models considered
•
•
UMT1: Based on surface heat
flow
•
UMT2: Based on a recent highresolution lithospheric model
by Gradmann et al. (2013)
•
UMT3: Based on seismic
velocity anomalies
Downloaded from http://gji.oxfordjournals.org/ at Hulib on November 3, 2015
van der Wal et al., 2013
Three different thermal models are
considered:
63
Thermal models considered
•
•
UMT1: Based on surface heat
flow
•
UMT2: Based on a recent highresolution lithospheric model
by Gradmann et al. (2013)
•
UMT3: Based on seismic
velocity anomalies
Downloaded from http://gji.oxfordjournals.org/ at Hulib on November 3, 2015
van der Wal et al., 2013
Three different thermal models are
considered:
64
68
Ice thickness model
W. van der Wal et al.
van der Wal et al., 2013
Figure 3. Ice thickness of the plastic ice model at six different time steps.
•
Ice thickness is calculated using known ice sheet boundaries
with depth.
Therefore,
is not possible to use t
and records of changes in ice sheet
volume
overit time
to independently constrain mantle rheology.
Our
65
based on assumptions about mantle viscosity, whic
Constraints on upper mantle viscosity
•
GIA model with composite 3-D rheology
temperature
and
wet/dry
bothBoth
UMT1 and
UMT3, while the
wet rheology
lowers viscos
hereconditions
shown only for UMT1.
have a strong effect on
Maps of the effective viscosity are shown in Fig. 6 for a m
the
which
has calculated
a reasonable fit effective
to uplift rates viscosity
and sea level.of
Grey sh
areasthe
haveupper
viscosity mantle
larger than 1025 Pas, for which viscous d
mation was shown to be negligible over the glacial cycle (Barnh
et al. 2011a). Viscosity at a depth of 315 km is not shown bec
viscosity at that depth is nearly constant for UMT1, as can be
in Figs 1 and 5. Although the GIA induced stress also influence
Theviscosity,
rangetheofpattern
mantle
effective
in Fig.temperatures
6 resembles that of the UM
temperature
maps
in Fig. 1 such
as the transition
from cold to
is quite
narrow
at depth
for the
areas going from east to west, and patches of hot areas to the n
thermalof model
UMT1, but varies
and southwest
Fennoscandia.
•
van der Wal
al.,different
2013
Figure 5. Depth profiles of viscosity below Fennoscandia
for et
four
combinations of parameters. Each colour brackets the lateral variation in
viscosity found in the region underneath the maximum ice extent according
to our ice model.
depending on the rheological
of olivine
3.2 properties
Relative sea level
RSL data for sites from the Tushingham & Peltier (1991) data
are used. Sites with less than four data points, or which span
than 4 ka, or which do not show a clear trend were removed, as
as some inconsistent sea level data points, which can not be fi
66
a smooth curve. The locations of the sites used here are
show
Fig. 7.
Changes in relative sea level
W. van der Wal et al.
van der Wal &
et Peltier
al., 2013
gure 7. Location of the RSL sites from the Tushingham
(1991)
abase that are used in misfit analysis. The selection of sites is described
he text.
agnifies the misfit so that it can be dominated by the misfit of one
more data points. This is particularly true for ‘outliers’ resulting
•
•
in viscosity profiles resulting from the different tem
(Fig. 5). Thirdly, wet rheology results in the smallest
agrees with the finding of Barnhoorn et al. (2011a
Model
also viscosities.
be compared
rheologyresults
results in can
acceptable
It is surprisi
rheology
such as UMT3/dry/10
leads to compara
to
a database
of changesmm
in relative
the UMT1/wet/10
mmnorthern
model. Possibly
the large spread
sea
level across
Europe
for UMT3 models at depths below 200 km contribute
For the UMT1 wet rheologies, the change in misfit from
grain size is small, indicating that the contribution
dependent (diffusion) creep is small. Still, misfit genera
Inwith
this
case, the
from
a that the U
increasing
grain data
size. Itare
can also
be seen
compilation
by Tushingham
and of UMT
which can be considered
a local improvement
very small
improvement in fit of the best-fitting dry an
Peltier
(1991)
models.
For comparison, Fig. 8 also contains the misfit fo
used 1-D viscosity profile VM2 (Peltier 2004). We use
(2007)’s approximation of this profile in the finite ele
upper-mantle viscosity of 9 × 1020 Pa s, and lower-man
of 3.6 × 1021 Pa s. The VM2 approximation perform
67
any of the models (wet versus dry and grain size).
On
might not be surprising that the addition of independen
Changes in relative sea level
71
GIA model with composite 3-D rheology
•
Downloaded from http://gji.oxfordjournals.org/ at Hulib
Model predictions
match observed
changes in relative sea
level quite well for a
number of sites,
particularly for wet
olivine rheologies
van der Wal et al., 2013
Relative sea level (RSL) curves for three different GIA models at the sites used in the misfit analysis: (i) the model that best-fitting sea level data
68
Changes in relative sea level
71
GIA model with composite 3-D rheology
•
Downloaded from http://gji.oxfordjournals.org/ at Hulib
Model predictions
match observed
changes in relative sea
level quite well for a
number of sites,
particularly for wet
olivine rheologies
van der Wal et al., 2013
Relative sea level (RSL) curves for three different GIA models at the sites used in the misfit analysis: (i) the model that best-fitting sea level data
69
Predicted surface uplift velocities
Observed maximum
GIA model with composite 3-D rheology
uplift rate
73
•
For the “hotter” thermal
models, rapid surface uplift
is only observed for dry
olivine
•
The wet olivine rheology
combined with the coldest
thermal model still only
produces roughly half of
the observed maximum
uplift velocity
Downloaded from ht
rates for varying grain sizes. (a) UMT1 (plastic ice model and ICE-5G),
VM2
with plastic ice model. (b) UMT3
vanUMT2,
der Wal
etprofile
al., 2013
G), UMT4 and VM2 profile with plastic ice model. The grey bar shows the observed maximum uplift rate of 10.1 mm yr–1 with
et al. 2007).
70
ximum uplift rates are too small. This is in
Barnhoorn et al. (2011a) that wet rheology
sity values in agreement with previous GIA
namic simulations were performed there
ging of effective viscosities in Barnhoorn
and time does not necessarily correspond
y that is ‘felt’ by the GIA process. The
n the GIA model be improved so that the
ment with the measured uplift rate? Two
ussed: modifying the ice loading history,
creep. The uplift rates with the ICE-5G
in Fig. 12. Maximum uplift rates for this
w those with the plastic ice model, because
ss is smaller than for the plastic ice model.
m ice height has been shown to increase
e of creep parameters (van der Wal et al.
tion is found for models with 1-mm grain
uplift rates cannot be reached.
4 D I S C U S S I O N A N D C O N C LU S I O N S
Model fits
relative
level and
uplift rates
Tableto
3 summarizes
the fit of sea
various combinations
of parameters.
For our ice model, the best fit to sea level data is found for a wet rheTable 3. Overview of fit of models with respect to historic sea levels and
present-day uplift rate.
UMT1
UMT2
UMT3
VM2
Wet, 10 mm
Dry, 4 mm
Dry, 10 mm
Wet, 10 mm
Wet, 10 mm
RSL (one-norm misfit)
Uplift rate (mm yr–1 )
3.4 (3rd best)
4.1
5.0
3.3 (best)
3.4 (2nd best)
5.6
3.0 (too low)
6.9 (OK)
9.0
3.0 (too low)
5.5 (low)
9.7
Lower is better
~10.1 mm/a is observed
van der Wal et al., 2013
•
Although these models are sophisticated and simulate a
number of important processes related to glacial isostatic
adjustment, there are clearly some issues
•
Most notably, the relative sea level data is best fit with a wet
olivine mantle rheology, but the predicted uplift rates in
those models are too low
71
Implications for the lithosphere
y Science Letters 388 (2014) 71–80
•
Another recent modelling study
looked at the potential magnitude
of fault throw related to glacial
unloading
•
In this work, the authors used a
layered 2D (visco)elastic model of
the crust and mantle
•
Variables include the position and
dip angle of a fault, ice thickness and
width, crust and lithospheric
thickness and mantle viscosity
73
Fig. 2. Structure of the model showing location of faults (note
that et
only
fault
Steffen
al.,one
2014
is active in a model). Springs represent elastic foundations, triangles represent the
fixed degree of freedom, and the red lines show faults in the crustal layer. The ice
sheet (grey body on top of the model) follows a parabolic shape and, except for
Fig. 4(a, b), does not undergo any change in horizontal dimensions during a glacial
period. (For interpretation of the references to color in this figure legend, the reader
is referred to the web version of this article.)
size increases in the following layers and is 200 km in the lower
part of the lower mantle. Due to model limitations by the software
72
30 km, 40 km, 50 km, 60 km
HS: 7·1020 Pa s (UM), 20·1021 Pa s (LM)
RF3: 6 · 1020 Pa s (UM), 4.5 · 1021 Pa s (LM)
VM1: 5 · 1020 Pa s (UM), 2.4 · 1021 Pa s (LM)
30◦ , 45◦ , 60◦
−1000 km, −500 km, 0 km, 500 km, 1000 km
0.4
0 MPa
0.4
8 km
0 MPa
Fault throw as a function of dip and location
Steffen et al., 2014
Fig. 3. Fault slip for the reference model at different locations (0 km, 500 km, and
1000 km) and dip angles (30◦ , 45◦ , and 60◦ ) over time between 90 ka and 130 ka.
The purple line on top presents the amount of ice load applied in the model. The
half-width of the load is 1500 km. The following additional parameters were used:
crustal thickness – 40 km, lithospheric thickness – 160 km, viscosity profile – HS,
•
Fault slip generally occurs
coincident with the end of
deglaciation (100-110 ka)
•
Faults directly beneath the
center of the ice load tend
to slip earlier than those
away from the center (black
versus yellow lines)
•
The largest fault slip occurs
for shallowly dipping faults
73
Potential seismic moment magnitude Mw
•
The magnitude of fault slip
R. Steffen et al. / Earth and Planetary Science Letters 388 (2014) 71–80
predicted in the models would
produce
There likely
are some
remaining great
questionsearthquakes
that need to be
address
in future studies. For example, the model does not incorpora
post-seismic creep that could extend the fault tip to deeper dep
Furthermore, stress accumulations at the fault tip are not co
sidered, so no estimations can be made about current seismic
and when it will end. Our current model contains no lateral va
ations in earth parameters and geometry, as well as no dens
contrast along the fault. Furthermore, several more parameters c
be tested, e.g. magnitude of background stress, depth of fault, po
fluid coefficient in the background stress and along the fault. Ne
ertheless, different effects on the magnitude of fault throw ha
been successfully related to certain parameters. Future investig
tions will incorporate these additional features as well as the e
tension into a 3D model.
•
•
Fig. 6. Moment magnitude determined from the displacement for faults below the
ice-sheet centre without taking into account the length of the fault along the surface (main crosses), and the minimum magnitudes determined using a fault length
of 150 km (end of vertical bar).
cycle temporarily changes a stable tectonic region into a highly
active area characterized by earthquake magnitudes similar to
those found along subduction zones. However, only one earth-
The range here is between
magnitudes calculated without
considering fault length (plus
signs) down to a fault length of
150 km
As you can see, even steeply
dipping faults could slip as a result
of glacial unloading
Acknowledgements
We thank the editor Peter Shearer, Christophe Pascal and
anonymous reviewer for their constructive reviews. We would li
74 Univ
to thank Björn Lund and Peter Schmidt (both from Uppsala
sity), Steffen Abe (RWTH Aachen), Raymond Munier (Swedish N
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earthquakes. Earth and Planetary Science Letters, 388, 71-80.
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75