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Stress distribution and plate boundary force associated with collision mountain ranges
Tectonophysics, 182 (1990) 193-209 Elsevier Science Publishers
193
B.V., Amsterdam
Stress distribution and plate boundary force associated with collision mountain ranges M.H.P. Bott Department of Geological Sciences, University of Durham, South Road, Durham DHI 3LE (United Kingdom) (Received
January
23,199O;
accepted
April 23, 1990)
ABSTRACT Bott, M.H.P., 1990. Stress distribution 182: 193-209
and plate boundary
force associated
with collision
mountain
ranges.
Tectonophysics,
Tectonic stresses associated with collision mountain ranges are studied by finite element modelling. Large horizontal deviatoric tension is produced in the strong elastic core of the upper crust by the topographical loading and the associated crustal root. Equally significant is the effect of the dense downbulge of cool lithospheric mantle produced by plate convergence, as recently observed beneath the Alpine region. This dense slab with its associated downflexure produces compression. This compression is 25% or less of the theoretical value computed from the density-moment function because of the finite width of the slab. The actual state of upper crustal stress is a superimposition of root-produced tension and slab-produced compression. An asymmetrically located deep slab produces large compressions at one edge of a mountain belt co-existing with large tensions towards the other side of the range, leading to mountain building at one edge and extensional tectonics elsewhere. The stresses produced by the dense slab support and accentuate the crustal root, in opposition to the self-inflicted root erosion. When the upper crust is thrust-faulted, the sinking slab produces a collision slab pull force of about 1.2 x lOI N/m (depending on slab sire) which is an essential factor with ridge push in initiating and developing mountain ranges. Surface downflexure produced by slab downpull may give rise to wide borderland sedimentary basins such as the PO basin.
Introduction
seismology (Miller et al., 1982). Werner and Kissling (1985) and Schwendener and Mueller (1985)
Collision mountain ranges such as the Alps and the Himalaya form at convergent plate margins with continental lithosphere on both sides. Con-
used
vergence
positive
of the plates
causes
crustal
thickening
and associated isostatic uplift of the mountain range. In order to accommodate the lithospheric convergence, the cool topmost mantle (subcrustal lithosphere) must also thicken and sink downwards as it is subducted into the underlying mantle. Observational evidence for a massive deepseated lithospheric root beneath the Alpine arc has recently come from seismic and gravity studies, as summarized by Mueller and Panza (1986). The seismic evidence comes from teleseismic travel-time residuals (Baer, 1980), surface wave studies (e.g. Panza et al., 1980) and deep explosion 0040-1951/90/$03.50
0 1990 - Elsevier Science Publishers B.V
seismic
anomaly tracted
caused
control
to
calculate
by the crustal
this from the Bouguer residual
anomaly
the
structure, anomaly
attributable
gravity and sub-
to obtain
a
to the deep
lithospheric root in the upper mantle. According to Schwendener and Mueller (1985), the residual amplitude is about 100 mGa1 and its width is 500 km. They attributed it to a large deep-seated positive density anomaly of 50 kg/m3 of cross section about 150 X 150 km’. This would be consistent with a region of cool lithosphere having an average temperature 500 K below that of the adjacent asthenosphere. Mueller and Panza (1986) suggested that the sinking material may be symmetrical, with subduction of mantle lithosphere from both sides forming a bivergent south of the Alpine axis.
zone, offset
to the
194
M.H.P.
Although spheric obtained, the
direct evidence
root beneath Bird (1978)
lithospheric
account
for
Lyon-Caen lithospheric
for a deep cold litho-
the Himalaya suggested
mantle thermal
of the features
has yet to be
plate. Brunet
conveniently stress.
horizontally
delamination
of
oriented
to
deviatoric
of
plate
the
orogeny. a deep down-
(1986) similarly
Assuming and
component
of
principal
the
stresses
are
vertically,
the average
stress in the strong layer is equal to half
the tectonic
force divided
by the thickness
of the
layer. The tectonic force originates from the densitydepth distribution through the lithosphere and
attributed the downflexing of the plates meeting in the Pyrenees to the formation of a cold litho-
beneath
spheric
and is almost
root.
eliminates
bending
Indian
and Molnar (1985) suggested root to explain the observed
flexing of the Indian
tion
BOIT
strong
it. It is concentrated layer
as a result
upwards
of viscoelastic
independent
into
the
relaxation
of the thickness
of the
If the dimensions of the crustal root and the thickness of the mantle part of the continental
strong layer (Kusznir and Bott, 1977). F, in an infinitely wide structure, in local isostatic equi-
lithosphere
librium
are known,
it should
be possible
to
in relation
to a standard
estimate the dimensions of the deep lithospheric root from simple geometric considerations. How-
sity-depth
can be calculated
from
ever, such a calculation
depth
Ap(z)
is likely
to be an under-
estimate for two reasons. First, an oceanic subducting slab may already exist at the time of the initial collision. Second, uplift and erosion will progressively reduce the crustal root. The most important local stresses
in erogenic
distribution
the density F,=
distribution
/0
moment
lithospheric
to which
it is referenced,
the anomalous using
function
den-
density-
the equation
(Dahlen,
for
1981):
LgrApdz
(2)
where g is gravity
and L is the depth
to the base
belts are produced by surface and subsurface loading. There are two opposing stress systems of this type. The surface loading of the mountains and
of the anomalous densities. This paper uses finite element analysis to study the combined stresses produced by the crustal root
the associated root horizontal deviatoric
and the mantle slab. Some new insights are obtained into the mechanism of mountain building.
crust
(Bott,
of thickened crust produce tension in the strong upper
1971, p. 231; Artyushkov,
contrast, the deep, dense associated downflexing horizontal compressive strong near-surface layer
1973). In
lithospheric root and its of the surface produce deviatoric stress in the (Fleitout and Froidevaux,
Some problems which are examined are as follows. How can compression affect a region such as the Himalayas while tension occurs in a central uplifted region root supported?
such as Tibet? How is a crustal How does the viscosity distribu-
1982; Mueller and Panza, 1986). The actual state of stress in the strong layer of the upper crust is
tion in the mantle affect ment? What plate boundary
the combined effect of these two opposite stress systems together with bending and other local and
The numerical models presented demonstrate the critical importance of deep mantle lithospheric
regional stresses such as due to ridge push. The state of stress in the strong layer of the upper crust can be conveniently expressed in terms of tectonic force F, (Fleitout and Froidevaux, 1983). F, is defined as the difference between the horizontal and vertical principal pressures integrated with respect to depth z through the strong layer. Thus
slabs in the compressional tectonics of the orogen and in contributing to the plate driving mechanism. They also show that simple stress computations based on the density moment function in equation (2) grossly overestimate the tectonic force produced by a deep slab of realistic dimensions. Finite
element
method
the tectonic developforces are developed?
applied
to erogenic
model-
ling
F, = where
/ 0 ‘bxx - G> dz T is the thickness
(1) of the layer. The integra-
Isoparametric quadrilateral and triangular elements have been used to model the continental
TECTONIC
STRESSES
ASSOCIATED
WITH
FINITE ELEMENT
COLLISION
GRID
MOUNTAIN
RANGES
195
(MODELS 1 TO 5)
650 Distance
Fig. 1. The finite element grid used for Models the grid, down to 420 km depth or shallower,
2000
(km)
1 to 5. Models 6 and 7 use the central is shown in the illustration
800 km of this grid. Only the central
of the models (Figs. 3-8);
this region is outlined
800 km of by a thick
line.
lithosphere a collision
puter programmes an earlier version method
propriate assigned values of viscosity. A fault is included in Model 7 using the dual node technique (Goodman et al., 1968; Mithen, 1980). In
and upper mantle to 650 km depth at mountain belt of ideal type. The comused have been developed from written by Waghorn (1984). The
used is also described
in greater
Bott et al. (1989). A symmetrical
preference
been assumed
detail by
lar
two-dimensional
grid 2000 km wide (Fig. 1) with the mountain
belt
the strong, otherwise
TABLE
cool layer of the upper lithosphere, are viscoelastic
that the principal
it has
stress perpendicumodel
average of the two in-plane
principal
for viscoelastic
plane
is the
stresses. This
media
within
the
deviatoric
stresses
are equal and op-
posite, so that only one of them needs to be shown in the figures.
ap-
1
Values of depth
extent of layers,
Layer
anomalous
density,
Young’s
modulus,
Poisson’s
used in the standard
ratio and viscosity
Layer
Depth
Density
Young’s
Poisson’s
Viscosity
number
extent
(kg/m3)
modulus
ratio
(Pa s)
( X 10”
(km) Upper
formulation,
two-dimensional
two in-plane
but
with
strain
Earth than plane strain, although the results for the two formulations do not differ greatly. The
6 and 7. The uppermost 20 crust is elastic representing
the elements
to the
is more realistic
at the centre has been used for Models 1 to 5, and the central 800 km of this grid has been used for asymmetrical Models km of the continental
to the plane
Pa)
crust
1
o-
20
0.0
9.00
0.27
elastic
Lower crust
2
20-
35
0.0
9.00
0.27
1023
Crustal
3
35-
65
9.00
0.27
1023
4
35-100
0.0
17.50
0.27
1023
17.50
0.27
1023
17.50
0.27
10Z3
root
Lithospheric
mantle
- 400.0 a
Slab interior
5
loo-300
Slab flanks
6
loo-300
+ 50.0 b + 25.0 b
Asthenosphere
7
100-400
0.0
11.50
0.27
loZ’
Transition
8
400-650
0.0
28.00
0.27
lo=
sub-continental
density-depth
zone
* The anomalous a 0.0 in Model 2. b 0.0 in Model 1.
density
is referenced
to the standard
models
distribution
at the edges of the models.
*
Anomalous erenced neath
densities
within
to a standard the normal
continental
edges of the models. are immaterial
a crustal
The standard
loading.
variations
regions
and
region
of
+ 25 kg/m3.
a dense +50
mantle
kg/m3
The mountain
at the
constraining
values
ment.
consist
layer.
of -400
the models
a central
the
results.
This
been
used
in the
regions
of
range is modelled
The
tematic
by a
1989), and
this
been
allowed
for by displace-
of 1O23 Pa s has of the lithosphere
near
layer has not been included
with
flanking
Peltier,
BOTT
to zero vertical
value
for the viscosity
the elastic
of
basal nodes
A uniform
assumed
and sub-
and
has to some extent
density
slab
and
four (Mitrovica
increase
be-
stresses depend
root with an anomalous
kg/m3
density
of surface
The anomalous
and
are ref-
profile
lithosphere
since the deviatoric
only on the lateral surface
the models
density-depth
M.H.P.
and is unlikely simple
surface
weak
been below plastic
as it overcomplicates to have much effect on viscosity
standard
structure
models,
but
study of the effect of varying
has a sys-
the viscosity
surface load in Airy equilibrium with the root. Mechanical properties used in the models pre-
below the lithosphere, and within the lower crust, has been carried out and is described in the fol-
sented in the figures are given in Table 1 and Fig. 2. Elastic properties are approximately consistent with the seismic velocity-depth distributions, and
lowing two sections. With the two-order of magnitude variation of viscosity, it has been necessary to use 1000 time increments of 500 year each to
variation of their values within the likely range has minimal effects on the results. The value of viscosity in the mantle below the lithosphere down to 650 km is 10” Pa s based on post-glacial recovery studies. Beneath 650 km the viscosity may increase
approach dynamic equilibrium in 0.5 Ma. It should be pointed out that the process of reaching equilibrium in the models is not of geological significance as it would be in post-glacial studies. The
by a factor
between
about
_-----
thirty
(Hager,
erogenic belt evolves on a much longer timescale and the results merely show the state of stress, the
1984)
(I) UlJper crust Elastic 72F LotGFc?GtT iYE; ___-_-_--.___ 13) Roce&OE+23
_------
(4) Lithospherlc ------
_____----
- - - - - - - - - - - - - -
I.OE+23
mantle
/ (6) /(51 SLab/ (611
l.OE+2l
(7) upper mantle
(8)
transl
t roll zone
0 1st ante
600 Fig. 2. The layering,
Plant le
viscosity
(floating
I. OE+21
1400
(km)
point, in Pa s) and density
(fixed point, in kg/m3)
structure
of Model 3.
TECTONIC
STRESSES
lithospheric
ASSOCIATED
deformation,
rate for the specified The vertical surface
is restricted
Basal nodes
the viscous
and at 35 km which pressures
are applied
senting
ridge push is applied
where
Model
g 6
The stresses produced by the crustal root and the dense sinking lithosphere (referred to as the
dis-
mantle
1 represents
Moho
equilibrium
depth.
7A where
a 30 km thick
separately. crustal
with a mountain
root
Model in Airy
range modelled
by a
edges
surface load (Fig. 3). The base of the lithosphere
repre-
at a constant
depth
dense
slab,
at the edges of the
1:
slab) are first examined
at the surface
a pressure
MODEL -7 -
distribution due to crustal root
Stress
lithosphere.
to the vertical
in Model
in
horizontal
forces proportional
is the normal
except
and
nodes of the lithosphere are constrained horizontally to determine the collision suction force.
6 and 7 where this
are applied
3RP
strain
to zero vertical
boundary
197
RANGES
the central
to zero
to the upper
displacement
lithosphere,
beneath
are constrained Isostatic
MOUNTAIN
distribution.
except in Models
constraint
Zero
and
density
is constrained
displacement,
to vertical
COLLISION
line of nodes
point
placement.
WITH
the
CRUSTAL
mantle
(Table
edge
ROOT,
of 100 km and so that
1) are all assumed
layers
there
is
is no
5, 6, 7 and
to have a viscosity
8 of
NO SLAB
0 _
-400 Deviatoric
-
I I I I I I I I I
Stress
100
MPa
. . . . .!.!!_K_t_!!_l.!. . . . _______________--------------- -_ _z
0
1
.
.
.
_
_
_z
-I-
_>-
_
/ . ~ .
. .\ . * - -----_--------------1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
---------_-____-------------_420
t-
600
Distance
Devlatorlc 0
3 I e, E
(km)
1400
Stress
100
_._ _. -_. . ____--------___---------------. . , .. ----------------...
--. -
--.
_
_
...
._
...
-.\
. .
MPa
.
IFGO 800 Fig. 3. Model 1 with - 400 kg/m3 no mantle the second
Distance crustal
slab. Broken lines represent in-plane
deviatoric
root but no mantle
tensile deviatoric
stress is equal in magnitude
above, and an enlarged
slab. Mechanical
(km) properties
1200 are as shown in Table 1 except that there is
stress and solid lines denote compressive but opposite
version of the central
in sign. The surface
400 km of the lithosphere
stress on the scale shown. Note that
vertical
displacement
is shown beloT,.
profile
is displayed
198
M.H.P.
102r Pa s. The model fects of the mountain Airy
model
is a sufficiently
for the purposes be associated loading. Large
represents
of this paper.
(2) in a very wide mountain
ef-
surface
approximation
Similar
towards
stresses will
root related
horizontal
deviatoric
and
upper
crust
the succeeding
stress nearest
the other in-plane
tension
Model
to thrust
as shown
to the horizontal
deviatoric opposite
occurs
diagrams,
the same
indicates
that
layer should
the tend
a value of 145 MPa, so that the value in 1 is 71% of the between
theoretical
the theoretical
value. and
The
modelled
values is explained
in
ing rise to slow equilibrium creep associated with dissipation of the root of finite width. The stresses
the
are proportional
is shown,
A broken
range having
loading
in
line
by small ongoing
to the density
and approximately
stress being equal in
in sign.
and subsurface
stress in the 20 km thick elastic
difference
Fig. 3. In this and
magnitude
good
with a flexural
the 20 km thick elastic deviatoric
the isolated
range and its Airy root. The
BOTT
proportional
contrast
stresses
giv-
of the root
to its thickness.
Figure 3 shows that small vertical displacements of a few tens of metres have developed.
denotes tension and a solid line denotes compression. A single stress value is shown for each ele-
These are associated
ment, which is the average value of the stress calculated at the gauss points. This effectively
ring in the lower crust, which gives rise to slight central subsidence and flanking uplifts. In order
eliminates bending stress in the elastic layer ciated with flexure. The maximum average toric stress observed in the central elements orogen is 104 MPa (1.04 kbar). If the elastic
to assess the creep more accurately, the creep vectors during the final timestep of 500 yrs have been determined. These show that the slow creep flow is tending to dissipate the root structure.
in the upper crust is thinner, then stress is proportionately larger.
assodeviaof the layer
the deviatoric
with the ongoing
creep occur-
Over a 500 yr time step, the crust thins by about 45 mm (90 m/My) and the root widens by about 173 mm (346 m/My). Over a substantial time period this slow creep would be expected to erode the root significantly. The creep rate is inversely
The large deviatoric tensions are produced by the combined effect of the surface loading of the mountains and the upthrust of the low density root. The stresses are concentrated upwards into the strong elastic layer near the surface as the stresses in the underlying viscoelastic lower crust relax (Kusznir and Bott, 1977). Theoretical calculation of the density moment function using eqn.
proportional to viscosity, so that lowered viscosity in the crustal root and underlying mantle would increase the rate of subsurface erosion of the root. The effect of varying the viscosities within Model 1 has been studied systematically. The
TABLE 2 The effect of varying the viscosity below the lithosphere and within the lower crust in Model 1 * Model
Viscosity (Pa s)
Deviatoric
Tectonic
stress
force
Layer: 1
2
3
4
5
6
7
8
(MPa)
(X lo’* N/m)
1A
elastic
1023
1023
1023
1%
l:zl
1:*1
1%
104.2
4.223
1
elastic
1023
1023
1023
1B
elastic
1023
1023
1023
1c
elastic
1023
1023
1D
elastic
1023
1023
1
elastic
1023
1E
elastic
102’
103.5
4.196
1022
102.9
4.114 4.239
102’
102’
102’
1023
IO23
1023
lo*’
IO*’
104.0
1023
1022
1022
1022
1022
99.1
4.019
1023
1023
102’
lo*’
IO*’
lo*’
103.5
4.196
IO2’
102’
102’
10**
lo*’
1021
98.8
4.110
* The table shows the values of viscosity for each of the eight layers (Table 1 and Fig. 2), the deviatoric stress in the central elastic elements and the tectonic force at the centre of the 20 km thick elastic layer for a selection of model variants. Italic denotes variation from standard Model 1.
TECTONIC
STRESSES
tectonic
force and deviatoric
the elastic
ASSOCIATED
layer
are shown
beneath
the
lithosphere
sphere.
The results
and deviatoric very slightly beneath
has
show
root by at least two orders 1E). Scaling
model
factor leaves the results
been
provided
the time
modelled and
by
that
the tectonic
that
creased
assuming
by the same
crustal
variations
force
the model
factor.
root are thus robust
(Model
in the model by the
same constant
The
unchanged
is run
is in-
results
for the
with respect
to wide
in rheology.
layer are only
by (1) variation
the lithosphere
of magnitude
all the viscosities
2. A zero viscosity
stress in the elastic modified
199
RANGES
on the base of the litho-
Stress distribution due to mantle slab
of viscosity
over a much wider range
than is likely to apply (Models decrease
of these
elements
conditions
MOUNTAIN
stress at the centre of
in Table
the underlying
free boundary
COLLISION
for a selection
variants removing
WITH
of the viscosity
MODEL
-7
Model
1A to lD), and (2)
in the lower 2:
crust
MANTLE
2 (Fig.
bivergent
and SLAB,
4) represents
subducting
slab
a 200 km thick
beneath
an
erogenic
NO ROOT
G
0
_---------------------
u
: -400 : : -800
-
E-1 200 a
-
-
Deviatoric
-
Stress
-----------------__--------___
MPa
-------_ 1 IIll ,I: -
c--
*
,,,
.
‘( . \
---_
.
.
-
*
.
\\\.
.
.
.
-
-
c
a
-:
-
-
-
, ---
I-
----_-_____
100
--
,,
\/
.
.
.
,
.
.
.
-\
-
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
600
0 I st ante
Devlatorlc
(km)
1400
Stress
100
MPa
0 c
7
----
-v
-
--
,___,
--2--\
.
’
_c
/
\ \
42 \
k
*..
deformation.
Mechanical
vertical
displacement
profile
properties
of the surface
mantle
/
-
slab but no low density
are as shown is shown
‘/
.
-----__--__-~
-
Distance
Fig. 4. Model 2 with 200 km thick high density surface
r
//
GO 800
in Table
above,
1 except
’
...
/
-\ 1200
(km) crustal
root, showing
for absence
and an enlargement below.
\
\
\ \/
.
\
___,_--_------C_-___---_,_
deviatoric
of the low density
of the central
stress distribution
and
of the crustal
root. The
400 km of the lithosphere
is shown
M.H.P.
belt. The low density
crustal
load are not included
in the model so that the slab
order of magnitude larger than the bending stresses associated with the downflexure, which have been
effect can be studied
in isolation.
determined
structure
The rheological
is the same as that of Model 1 except for
the high viscosity maximum
gravity
comparable positive crustal
root and the surface
BO’IT
of the slab. anomaly
in amplitude
Bouguer effects
and Mueller,
The slab
of + 78 mGa1 which is
anomaly
1985). This suggests
Model 2 is of realistic
ated
downflexure
slab
produces
surface
over the Alps after all removed
of the crust. an
but are not pre-
value
The high density
downflexure
of
the
1130 m at the centre
extent well beyond
the confines
of the
deep load (Fig. 4).
size.
The magnitude
of the tectonic
force (and devia-
toric stress) in the 20 km thick elastic layer is much smaller than that derived from the density moment function using eqn. (2). The theoretical
The most conspicuous stresses in Model 2 (Fig. 4) are the large almost horizontal deviatoric compressions which dominate the elastic layer. These are of the type originally postulated by Fleitout and Froidevaux (1982). They extend laterally some distance beyond the erogenic belt, where they increasingly deviate from the horizontal. The maximum deviatoric compression, averaged over an
crepancy infinitely
element,
finite
are almost
isostatic
of maximum
with lateral
(Schwendener that the slab in
is 112 MPa. These stresses
points
sented. The large deviatoric compressions originate from the high density of the slab and the associ-
gives a
and width to the residual
have been
at the Gauss
value at the centre is 19.6 X 10” N/m whereas the actual value (Table 3) is 4.6 X lOI N/m which is only 24% of the theoretical value. The dis-
an
arises because wide structure
width.
The
deeper
the theory assumes an whereas the slab is of the
slab
extends
with
TABLE 3 The effect of varying in the standard Model 2 (1) the viscosity below the lithosphere (Models 2A to 2E and 2G to 2J), (2) the depth extent of the slab (Models 2F and 2G), and (3) the viscosity of the lower crust and crustal root (Models 2K to 2M) * Model
Depth extent
Viscosity (Pa s)
Deviatoric
Tectonic
stress
force
Vertical displ.
(MPa)
(X lOI N/m)
(m)
- 117.4
- 4.886
1185
- 115.0
- 4.746
1163
- 112.3
- 4.649
1130
(km)
Layer: 2
3
4
5
6
2A
200
lo23
1023
1023
IO22
10J2
2B
200
lo*’
1023
lo23
1023
102’
2
200
10Z3
102’
102’
1023
102’
2c
200
lo23
102’
1023
1023
1023
102’
10021 ,o*‘.5
- 110.0
- 4.558
1111
2D
200
1023
1023
102’
1023
1023
102’
1022
- 104.9
- 4.343
1069
2E
200
1023
1023
1023
1023
1023
102’
1022.3
- 98.0
- 3.962
992
- 57.9
I
8
0
:,*I
0
2F
100
1o23
1023
1023
102’
102’
102’
102’
2
200
102’
1023
lo*’
1oz3
102’
102’
102’
- 2.414
578
-112.3
- 4.649
1130
2G
300
102’
1023
1023
102’
102’
102’
102’
- 164.9
-6.812
1660
2H
300
102’
1023
lo*’
102’
1023
102’
102’ 5
- 158.6
- 6.533
1596
21
300
lo*’
1023
102’
1023
1023
102’
1022
- 141.7
- 5.824
1435
25
300
1023
1023
1023
1023
1023
102’
J022.S
- 106.1
- 4.368
1092
2
200
1023
1023
1023
1023
102’
102’
1021
- 112.3
- 4.649
1130
2K
200
10Z2
1022
1oz3
1023
102’
102’
102’
- 96.6
- 3.989
1365
2L
200
102’
102’
1023
1023
1oz3
102’
102’
- 59.8
- 2.565
1501
2M a
200
102’
102’
lo*’
102’
lo23
102’
102’
- 105.8
-4.313
1267
* The table shows the depth extent of the slab, the values of viscosity (Pa s) for layers 2 to 8 (Table l), layer 1 being elastic, the deviatoric stress in the central elastic elements, the tectonic force at the centre of the 20 km thick elastic layer and the maximum vertical displacement at the surface for a selection of model variants. Italic denotes variation from standard Model 2. a In Model 2M the two order of magnitude reduction in viscosity
in the lower crustal layer 2 is restricted to the region above the
crustal root. Elsewhere layer 2 has the normal Iithospheric viscosity of 102’ Pa s.
TECTONIC
STRESSES
respect with
ASSOCIATED
to its width,
WITH
the stronger
the theoretical
value
concentrated
up into
viscous
with ongoing deforms
internally.
the stresses somewhat There which
The
force is layer,
in the slab and the
These
are associated
as the slab sinks
slowly
and
It can also be seen (Fig. 4) that
in the elastic beyond
layer
extend
laterally
the edges of the slab.
are two other
deserve
force.
the high level elastic above.
creep
the discrepancy
of the tectonic
stresses remain
lithosphere
MOUNTAIN
of tectonic
result is that only a fraction and significant
COLLISION
features
mention.
However, stricted
if the
deviatoric
root, the reduction This indicates bordering despite
regions the much
linearly
mantle
above the edges of the slab, decreasing towards the centre. The principal stresses are orientated diagonally beneath the flanks of the erogenic belt. The associated creep reach 1.4 X lo-l6 sst, to thicken
strain rates, which locally are causing the crustal root
at an average
500 yr (52 m/My)
and
rate of about to narrow
26 mm in
at about
120
mm in 500 yr (240 m/My). Thus the deep-seated slab has the effect of accentuating the root, opposing the erosion of the root seen in Model 1. (2) Prominent sub-horizontal compressive stress of up to 27 MPa affects slab, causing
the upper
part
it to be shortened
of the mantle
horizontally
and
stretched vertically as it sinks. The associated strain rates are up to 1.5 X lo-l6 s-l.
creep
The effects of varying and
slab
investigated
depth
extent
the viscosity in
systematically.
in Table 3. Larger variations
Model
distribution 2 have
The results
been
are shown
in the viscosity
below
the lithosphere than are likely to apply in practice have a relatively minor effect on the stresses in the elastic layer and the surface downflexure (Models 2A to 2E). As the sub-lithospheric mantle becomes stiffer, the stress and downflexure is slightly reduced as a result of increased support for the slab from below. The most significant when the viscosity tion zone exceeds
reduction
occurs
assigned to the mantle transi1O22 Pa s (Model 2E). This
effect becomes stronger when the slab reaches the top of the transition zone (Model 25). A more significant reduction of the stress and tectonic force of about 50% occurs when the viscosity of the lower crust and crustal root are reduced by two orders of magnitude (Model 2L).
weaker
is re-
10% (Model
2M).
stress can be through
viscosity
the
lower crust,
lower crust
in the oro-
3 also shows that the stress
force in the elastic layer increase
extent
of the root, but rather
(Models
transition
within
into account,
increase
Symmetrical
with
less than
2F and 2G). The shallowing
the olivine-spine1 stantially
topmost
region
layer above the
upwards
of higher
genie belt itself. Table and tectonic
the viscoelastic
and
is only about
transferred
not been taken
crust
viscosity
that the compressive
substantially
stresses of up to 28 MPa which do not relax affect lower
reduced
to the root and the crustal
the depth
of the stress field
(1) Significant
201
RANGES
the slab has
but this would
the downpull
of sub-
of the slab.
models with crustal root and mantle
slab Ideally the cross-sectional area of the mantle slab could be estimated from the amount of lithospheric shortening indicated dimensions. For the crustal
by the crustal root root in the models
here, a bivergent slab of 160 km width should have a vertical extent of about 120 km. As pointed out earlier, mountain duction
progressive range,
uplift
and
and likelihood
slab is present
erosion
that a relict
at the onset
of the sub-
of collision,
suggest that the slab will be bigger than this. The residual positive Bouguer anomaly over the Alps is consistent (Fig.
with a 200 km bivergent
5) shows
the deviatoric
and surface displacement crustal
root
as in Model
slab. Model
stress
for the combination 1 and
3
distribution, of a
a 200 km thick
mantle slab as in Model 2. The deviatoric stress distribution in the elastic upper crust results from the superimposition of sub-horizontal tension caused by the crustal root (Model 1C) and the more wide-reaching compression caused by the slowly sinking slab (Model 2). If the viscosity structure of the separate root and slab models
is identical,
then the superimposition
of the stresses and displacements is effectively linear, as is to be expected theoretically. As a result of this superimposition, the stresses are almost negligible in the upper crust of the erogenic belt, with root-produced tension almost exactly cancelling the slab-produced compression. Moderate sub-horizontal compression affects the flanks
202
M.H.P. BOTT
.5
MODEL
3: ROOT ANG 200 km SLAB
0
-__-_----
-----------
22
: -4Ocl E 4 -800
-
$--1200 Deviatorlc
G 0
-
Stress
. . _ _ _-_-_-___--___-----, e
liil!l!l!lt . -1 - -_ 2 - -- . %. , * * , 7
, . ,_-_------.
f
320 ,600
Distance
T.___L_’
__-*_-_
,------.
100 MPa
.
1400
(km)
100 MPa
O?
__------ 2 , ,
_-_-_-_---------------.i
CL
...
*
.
1..
s
..-
-
-
\
/
\
-....---------------
*,
-c *
.
.
I
.’
...
.
.
I_
*
*.*
..\
...
2 1
’
-
-
’
f
f
*.*
loot
MODEL 0 E _u
3RP: RIDGE PUSH
___---_
_c u a
/
,
’
_--------_-_-----
/ ’
czfi I
...
.
..,
.
Fig. 5. Model
’
incorporates
and
supplemental
an enlarged compression
-
version
slab and low density of the centrat
caused
effect of ridge push in continental
_..
-
Distance
3 with 200 km thick dense mantle (above),
,
0’
by an 8 MPa normal
lithosphere.
crustal
400 km below. pressure
’
\
,..
.
II
_..
1200
(km) root, showing
deviatoric
stress distribution,
Model
3RP (also
across
the edge of the lithosphere
See Table 1 and Fig. 2 for viscosities
of the mountain belt and the bordering regions because of the wider lateral extent of the compression produced by the slab. Significant deviator& stresses which do not relax occur in the viscoelastic region beneath 20 km depth in the vicinity of the crustal root and the mantle slab. These stresses are a combination of
-
.
\. ..*
800 deformation
...
-..
.._
1001
. _--------_
_---_-_------
...
%*
100 MPa
INCLUDED
enlarged)
and anomalous
shown
surface
at the bottom to represent
the
densities.
those developed by the crustal root as it tends to dissipate (Model 1) and by the slab as is extends vertically and sinks (Model 2). Within the crustal root region the two processes oppose each other. The crustal root tends to dissipate itself slowly while it is being supported and accentuated by the creep associated with the sinking slab. The stresses
TECTONIC
within
STRESSES
WITH
COLLISION
the slab itself are almost
entirely
the sinking,
ASSOCIATED
MOUNTAIN
related
as can be seen by comparing
and 3, which have almost In all the
previous
identical models,
to
Model 3RP has been constructed to include norma1 pressure on both edges of the elastic upper
Models 2
lithosphere to represent ridge push. The ridge push force related to 60 Ma old oceanic lithosphere is
slab stresses. zero
pressure
is
of the order
applied at the edges consistent with lithostatic pressure. The contribution to the stresses from ridge
push
has
been
ignored.
To
remedy
203
RANGES
of 2.0 to 2.8 x lo’*
1981; Fleitout much smaller
this,
N/m
(Dahlen,
and Froidevaux, 1983). The value is by about 2.0 x lOI* N/m in con-
-2 MODEL Y
C
4:
ROOT
AND
100
km
SLAB
0
aI
6
-400 : ‘: -800 cn -
0eviatoric
-
0
u
-1
Stress
r . . -----------_-_-----------------
I _
_
_..
lllllll~ ...
...
...
.
.
,,
T Y ,. ------_-_-__
-I
I
*.
w
E-
.
.
0
.
.
MODEL
0
I
100
MPe-
1
.
--------____ .
.
.
. . . . . .
220
&
.:
_
5:
ROOT
AND
300
km
SLAB
----------_-_-_--___
F -400 E al -800 : -CL-1200
-
2 -1600 eviatoric
420 600
Stress
D I st ante
(km)
1400
Fig. 6. Above: Model 4 with 100 km thick slab. Below: Model 5 with 300 km thick slab. Otherwise as Model 3 (Fig. 5). showing deviatoric stresses and surface displacements.
204
M.H.P.
tinental
lithosphere
sity-depth within
because
of the different
so that
its value
should
be
of 0.0 to 0.8 X lOi
N/m.
In
function
the range
Model 3RP the highest value within been used, being represented of 8 MPa across small about
8-12
lated
The normal
horizontal
MPa
affects
the
occurs
below
elastic
Comparison
identical
6 (Fig.
7) includes
dimensions
and
a sinking
properties
slab
of
to that
of
of
mountain
range (as viewed
horizontal
deviatoric
layer
in the creep re(Fig. 5, bottom).
ridge push force thus does not appear
models otherwise have the same densities as Model 3 (Table 1).
of Models
Model
A
to be a major factor in producing compression in erogenic belts in comparison with the sinking slab. To cover the range of possible slab dimensions, deviatoric stresses for mantle slabs of 100 and 300 km vertical extent are shown in Models 4 and 5 (Fig. 6). These viscosities and
such a situation subduction may continue to occur from one side only rather than being bivergent.
Models 2 and 3, but it is laterally displaced so that the axis of the slab underlies the right edge of the
pressure
compression
and a small increase
compression
this range has
by a normal
the 100 km thick lithosphere.
superimposed
throughout
den-
BOTT
3 to 5 shows that the size
and the tension placed
interfere
compression
The
due to the slab dis- j
due to the root are laterally
with respect
do not
in the diagrams).
to each other, to the
same
and thus they
extent
as in
the
previous models. Consequently both the tensions and compressions in the upper crust reach substantially larger values than in Model 3. The maximum element averaged tension is 59 MPa beneath the left part of the mountain range, and the maximum compression of 94 MPa occurs in the right borderland above the slab. There are some other interesting features of Model 6. As the horizontal stresses in the elastic
of the mantle slab has a strong influence on the magnitude of the upper crustal stresses. Compression in the upper crust dominates Model 5 which
upper sional
has a 300 km thick slab, whereas significant upper crustal tensions characterize Model 4 with its 100
tated stresses occupy the central region of the mountain range. The effect of the asymmetry on
km thick slab. Deviatoric stresses in the crustal root region and in the upper part of the slab are largest in Model 5 and smallest in Model 4. As indicated in Table 3, the surface deformation is
the creep processes in the crustal root region also notable. The root beneath the left flank
nearly proportional to the depth extent of the slab, but raised viscosity below 400 km more strongly affects the deeper slabs. These models demonstrate the importance of the mantle slab in producing compression in mountain belts and their flanks. They also show that tension in the central region may coexist with compression affecting the flanks.
Asymmetrical
model
The symmetrical models presented above, with the mantle slab vertically below the crustal root, are a special case. A more general situation may involve a slab asymmetrically located beneath one flank of the collision mountain range. Such asymmetry may occur when a collision mountain belt develops from prior subduction of oceanic lithosphere at the pre-collision continental margin. In
crust change from tensional to comprestowards the right flank, obliquely orien-
is is
being thinned and eroded but beneath the right flank above the slab it is being supported in approximate equilibrium. Over a sufficiently long time period, a significantly will develop. The maximum surface
asymmetric downflexure
crustal
root
of 1140 m
occurs over the centre of the slab. In the symmetrical models, the downflexure of the borderland regions is minimal, but in the asymmetrical Model 6 the downflexing mainly affects the low-lying borderland where the depression of the surface may give rise to a sedimentary basin. A similar depression
is produced
in the geodynamic
models
of Werner (1985) which are based on a layered viscous structure. In Model 6, water and sediment loading has not been included. However, if a 1.0 to 1.5 km deep depression is filled by sediment, the additional load will give rise to a sedimentary basin about 4-5 km thick having a horizontal dimension of 100-200 km. In contrast, the crustal root will be associated with local uplift in response to progressive erosion of the mountain range.
TECTONIC
STRESSES
ASSOCIATED
WITH
MODEL
-2
a
n
COLLISION
MOUNTAIN
205
RANGES
6: ROOT AND 200 km OFFSET
Deviatoric
Stress
SLAB
-
llllllllil
100 MPa i
320 Dist: ce
0 0 2 Y
100 l"l?a ___ _._ ---,--,-_,--~~---~,-_ -
*..
'. ,
/
Distance
255 Fig. 7. Model
(km)
6 with 200 km slab asymmetrically displacement
located
with reference
(above) and an enlargement
--________-_-__ . .
\
\
655
(km)
to the crustal
below. Properties
root,
showing
deviatoric
stresses,
surface
as for Model 3.
Clearly the slab downpull provides an important mechanism for producing wide foreland sedimentary basins adjacent to mountain ranges, such as the PO basin south of the Alps. The existence of such depressions needs to be taken into account in flexural studies of erogenic belts as was recognised
been used for simplicity in the models, but in reality a narrower dipping slab may occur.
by Brunet (1986). They may otherwise be interpreted erroneously solely in terms of surface litho-
It was pointed out earlier (p. 204) that the ridge
spheric loading. The scenario represented
by Model 6 is obvi-
ously relevant to the Himalayan-Tibetan region and to the Alps, with the dense slab displaced towards the south in both regions. The Alps and Himalaya may have developed in this way because of subduction occurring on the south side prior to the collision. A wide slab with vertical sides has
Faulted model: collision plate boundary force
push force as developed in continental lithosphere is likely to give rise to a relatively small compression which has a negligible effect in comparison with the stresses produced by the root and the slab. It is difficult to see how the small residual ridge push effect in continental regions could by itself overcome the tension produced by an orogenie crustal root. The resolution of this enigma comes from the recognition that the sinking slab
M.H.P.
206
beneath
a collision
plate boundary The plates (Fig. crust
slab
to converge cuts
across
only
act
thrust
beneath
develops
fault
435 m horizontally
across
2 u
period
the thrust
MODEL 0
Model
7 has the
and 163 m vertically,
horizontal
convergence
The convergence
yielding
rate
of 0.81
rate is 10.3 mm/yr
ing the first four time steps but decays mm/yr after 0.5 Ma. Model 7 clearly
such
which
the Moho.
mm/yr.
the
throughout
as the deviatoric
over the modelled
displacements
a
an average to cause
the lithosphere.
a major
but is locked
centrates
can
a zero shear stiffness
progressively
produces
when a plane of weakness
8) includes
been assigned
range
force in its own right.
sinking
as a fault
mountain
BO’TT
dur-
to 0.38 demon-
strates that the dense sinking slab can cause plate convergence. The modelled rates are an order of magnitude
The fault
slower
than
that there are regions
stress con-
actual
of 0.5 My. The
erogenic
In order
over 0.5 My are
observed
of greater
rates
suggesting
weakness
beneath
belts.
to- annul
7: ROOT AND OFFSET SLAB WITH FAULT, _-____-__---------
the shearing
stress
on the
EDGES FREE
$ -400 Z -800 m 2 E-1200
-
0
Deviatorlc
__
Stress
100 MPa
320 MODEL
7A: EDGES FIXED 100 MPa
320 Distance
0
Fig. 8. Model 7, as Model 6 except that a fault with zero shear strength slab. The fault is locked edges, and deviatoric
beneath
stresses
the Moho.
are shown
Deviatoric
stresses
(km)
800
cuts the crust beneath
and surface
displacement
the edge of the orogen
(above)
are shown
below for Model 7A which has nodes at both edges of the lithosphere horizontal
displacement.
above the deep
for Model 7 with free constrained
to zero
TECTONIC
fault
STRESSES
plane,
forces
ASSOCIATED
equivalent
are applied
but
Model Regions
crustal
fault plane, a high
is of necessity
almost
and if this is relieved angle
thrust
would
with
are
stress below
the
parallel
to the
by further
fault-
be expected
to
Model 7A is used to estimate the magnitude of the collision slab pull force, referenced to continental
lithosphere,
by
of the lithosphere
placement
(Fig.
constraining
the
edge
to zero horizontal
dis-
8, bottom).
building
ean. There
of initiation
on closure
is no difficulty
initiating
compression,
subducted
oceanic
ent mountain
of collision
of the adjacent
oc-
in understanding
however,
lithosphere
the
if pre-existing
underlies
the incipi-
belt.
Discussion
similarly
develop.
nodes
mountain
stress is
the fault plane.
tension
The large compressive
plane
supin the
in comparison
except just beneath
of upper
enhanced.
ing,
result
tension
207
sphere raises the problem
These
crust associ-
6 (Fig. 7) is that the compressive
greatly reduced
fault
The
deviatoric
RANGES
boundary
nodes.
but they also produce
horizontal plates.
MOUNTAIN
opposite
of the upper
ated with the faulting, adjacent
COLLISION
at the dual fault
give rise to local flexure plementary
WITH
This model
is other-
wise identical to Model 7. In comparison with Model 7 where deviator% stresses die out towards the edges, a significant plate interior deviatoric tension is developed out to the edges in Model 7A. The integrated stress difference across the lithosphere at the edges of the model then yields the value of the tectonic force, which is found to be about 1.2 x lOi N/m. This force combines with the residual ridge push force to drive the plate
A difficulty
with all the models
studied
is that
the slab sinks too slowly to account for convergence rates of lo-70 mm/yr such as are characteristic
of the Alpine-Himalayan
belt.
The
litho-
spheric support for the sinking slab appears to be too stiff. A reduction in lithospheric viscosity would
help. However,
that sinking
the simplest
explanation
.is
is aided by some form of subduction
fault which separates from the lithosphere
the sinking
part of the slab
above and adjacent
to it. This
situation could readily develop from pre-existing subduction of oceanic lithosphere at the time of continental collision. It could give rise to an asymmetrically located slab, and would favour continuation of one-sided rather than bivergent subduction.
This situation
has not been
the present exploratory paper, cated by the results obtained. Bott et al. (1989) studied
modelled
but is clearly
in indi-
the effect of locking
ing.
and unlocking a normal subduction fault. When the fault is locked, the surface downflexing and
A plate with an ocean ridge on one side and a collision mountain range on the opposite side is
compression much greater
driven
same situation
convergence
which produces
by a combination
the mountain
of the ridge
build-
push
and
associated with slab downpull than when the fault is unlocked. probably
applies in collision
collision tinental
slab pull forces. When referenced to conlithosphere, the collision slab pull force
tain ranges.
When the fault is locked,
is impeded
and
appears
to dominate,
lithosphere
eanic
lithosphere
but
referenced
to old oc-
the ridge push force dominates.
the downpull
is maximum
sion and downflexing.
on
producing When
are The
moun-
slab sinking the overlying
large compres-
subsidence
is facili-
In reality, an ideal two-dimensional plate of this type is driven by the difference between these two
tated by an unlocked
fault, downflexure
pression
as the more rapidly
boundary forces referenced to the same type of lithosphere. According to the calculations here, a net force of about 1.8 X lOi N/m probably applies. A larger net force may apply when the sinking slab is bigger than in Model 7, and/or when an unusually large ridge push develops from a hot spot oceanic region such as Iceland. The relatively small compression associated with ridge push as developed in continental litho-
slab is more strongly supported from below. Variation in the state of a subduction fault can thus lead to vertical motion of the surface and variation of stress, with the greatest compression associated with the maximum regional downflexing. Further longer term variations should be associated with the progressive development of the sinking slab, as it sinks towards the mantle transition zone and through it.
are reduced
and comsinking
208
M.H.P.
Conclusions
(5) If the slab is asymmetrically situated beneath one flank, then large compressions affect
(1) The tectonic and surface tain
belt
element
stress produced
loading
at a modelled
has been analysis.
studied An upper
into which stress concentrates thick,
and beneath
tributions
BOTT
(Tables
by subsurface collision
moun-
by viscoelastic
finite
crustal
elastic
tensions opposite
layer
is taken to be 20 km
this appropriate l-3)
this flank and the adjacent
viscosity
are assigned.
dis-
The models
borderland,
affect the mountain side. This situation
Himalayan-Tibetan mountain
region,
building
and extensional the northern
occurs
collapse
interior
range towards the is relevant to the where at the
(Dewey,
compressional southern region.
have been run for 1000 time steps of 500 yrs each
situation,
to approach
slab may give rise to a major sedimentary
dynamic
equilibrium.
Ongoing
creep
the borderland
of the lithosphere
associated
edge
1988) dominates
of the uplifted
downflexing
while large
In this
above the basin
with large negative
in
free-
strains of up to about 1.5 x lo-i6 s-l occur in the crustal root and slab regions and are associated with moderate creep stresses which do not relax. (2) Two primary stress systems of independent
air and Bouguer anomalies. Creep may cause an asymmetrical crustal root to develop, with thickening beneath the active mountain building and
origin can be identified, in addition to secondary bending stress. The surface and subsurface loading arising from the mountain range and its Airy crustal root produces deviatoric tension of about
thinning in the extensional region. (6) The faulted Model 7 demonstrates that plate convergence, albeit slow, is produced. By horizontally constraining the nodes at the edges of the
100 MPa in the local upper crust. The associated creep strains cause the crustal root to thin and
lithosphere
widen very slowly, but significantly. 200 km thick
deep
slab
of cool,
In contrast, dense
a
sinking
lithospheric mantle and its associated surface downflexure produce horizontal deviatoric compression of very similar magnitude (110 MPa) but rather wider lateral extent. Creep stresses produced by the slowly sinking slab support and enhance the crustal root, thus opposing its selferosion. (3) The tectonic force produced by the crustal root is about 70% of the theoretical value computed from the density moment function because of its finite width. The discrepancy is even greater for the tectonic force in the elastic layer produced by the mantle slab, which is only about 25% of the theoretical value. stress and tectonic
Thus simple computation of force using the density moment
in Model 7, it is shown
thick slab produces about 1.2 x lOi* boundary
that a 200 km
a collision slab pull force of N/m. Without this plate
force, normal
ridge push would be inad-
equate to initiate or form range because of its weak
a collision mountain development in con-
tinental lithosphere. (7) An inadequacy of the models with simple unfaulted bivergent subduction is the slow rate of sinking of the slab and convergence of the plates when the upper crust is faulted. This suggests that subduction may characteristically be one-sided with a subduction fault along the original upper surface of the slab. Such a situation would readily develop from pre-existing subduction of oceanic lithosphere at the onset of collision, and would account for the compressive initiate the mountain building, asymmetry
of the present
stress required to and the inherited
Alpine-Himalayan
belt.
function given in eqn. (2) can lead to serious error when applied to features of finite width.
Acknowledgements
(4) If the slab lies symmetrically beneath the crustal root, then the root-produced tension and slab-produced compression tend to cancel each other out in the upper crust of the mountain range. Whether tension or compression wins depends on the size of the slab and the viscosity distribution of the upper mantle and the transition zone.
The work was mostly carried out during tenure of a Visiting Fellowship at Geophysics Division, D.S.I.R., Wellington, New Zealand. I am grateful to the Director, Dr. F.J. Davey, for financial support and facilities and to the Royal Society for a New Zealand Fellowship covering travelling expenses. I thank Dr. D.J. Woodward for help and
TECTONIC
STRESSES
ASSOCIATED
support
in many
ried
out
in
COLLISION
ways. I am grateful
Stern and Derek the manuscript.
WITH
Woodward
MOUNTAIN
to Drs Tim
for critically
reading
The final computations the
Durham
RANGES
were car-
University
Computer
209
Kusznir,
N.J. and Bott, M.H.P.,
the upper
lithosphere
creep. Tectonophysics, Lyon-Caen,
H.
and
evolution
by underlying
in
visco-elastic
43: 247-256.
Molnar,
flexure of the Indian
Centre.
1977. Stress concentration
caused P.,
plate,
1985.
Gravity
anomalies,
and the structure,
of the Himalaya
and Ganga
support
basin.
and
Tectonics,
4:
513-538.
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H., Mueller,
geodynamics Artyushkov,
E.V., 1973. Stresses
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in the lithosphere
inhomogeneities.
caused
by
Res.,
78:
J. Geophys.
7675-7708. Baer,
M., 1980. Relative
events
travel
at the new
Geophys.,
Swiss
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Ann.
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1971. The interior
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Arnold,
London,
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M.H.P.
and
continental
Dean,
D.S., 1972. Stress systems
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D., 1985. A two-dimensional
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ime at subduction
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Kissling,
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193
B.V., Amsterdam
Stress distribution and plate boundary force associated with collision mountain ranges M.H.P. Bott Department of Geological Sciences, University of Durham, South Road, Durham DHI 3LE (United Kingdom) (Received
January
23,199O;
accepted
April 23, 1990)
ABSTRACT Bott, M.H.P., 1990. Stress distribution 182: 193-209
and plate boundary
force associated
with collision
mountain
ranges.
Tectonophysics,
Tectonic stresses associated with collision mountain ranges are studied by finite element modelling. Large horizontal deviatoric tension is produced in the strong elastic core of the upper crust by the topographical loading and the associated crustal root. Equally significant is the effect of the dense downbulge of cool lithospheric mantle produced by plate convergence, as recently observed beneath the Alpine region. This dense slab with its associated downflexure produces compression. This compression is 25% or less of the theoretical value computed from the density-moment function because of the finite width of the slab. The actual state of upper crustal stress is a superimposition of root-produced tension and slab-produced compression. An asymmetrically located deep slab produces large compressions at one edge of a mountain belt co-existing with large tensions towards the other side of the range, leading to mountain building at one edge and extensional tectonics elsewhere. The stresses produced by the dense slab support and accentuate the crustal root, in opposition to the self-inflicted root erosion. When the upper crust is thrust-faulted, the sinking slab produces a collision slab pull force of about 1.2 x lOI N/m (depending on slab sire) which is an essential factor with ridge push in initiating and developing mountain ranges. Surface downflexure produced by slab downpull may give rise to wide borderland sedimentary basins such as the PO basin.
Introduction
seismology (Miller et al., 1982). Werner and Kissling (1985) and Schwendener and Mueller (1985)
Collision mountain ranges such as the Alps and the Himalaya form at convergent plate margins with continental lithosphere on both sides. Con-
used
vergence
positive
of the plates
causes
crustal
thickening
and associated isostatic uplift of the mountain range. In order to accommodate the lithospheric convergence, the cool topmost mantle (subcrustal lithosphere) must also thicken and sink downwards as it is subducted into the underlying mantle. Observational evidence for a massive deepseated lithospheric root beneath the Alpine arc has recently come from seismic and gravity studies, as summarized by Mueller and Panza (1986). The seismic evidence comes from teleseismic travel-time residuals (Baer, 1980), surface wave studies (e.g. Panza et al., 1980) and deep explosion 0040-1951/90/$03.50
0 1990 - Elsevier Science Publishers B.V
seismic
anomaly tracted
caused
control
to
calculate
by the crustal
this from the Bouguer residual
anomaly
the
structure, anomaly
attributable
gravity and sub-
to obtain
a
to the deep
lithospheric root in the upper mantle. According to Schwendener and Mueller (1985), the residual amplitude is about 100 mGa1 and its width is 500 km. They attributed it to a large deep-seated positive density anomaly of 50 kg/m3 of cross section about 150 X 150 km’. This would be consistent with a region of cool lithosphere having an average temperature 500 K below that of the adjacent asthenosphere. Mueller and Panza (1986) suggested that the sinking material may be symmetrical, with subduction of mantle lithosphere from both sides forming a bivergent south of the Alpine axis.
zone, offset
to the
194
M.H.P.
Although spheric obtained, the
direct evidence
root beneath Bird (1978)
lithospheric
account
for
Lyon-Caen lithospheric
for a deep cold litho-
the Himalaya suggested
mantle thermal
of the features
has yet to be
plate. Brunet
conveniently stress.
horizontally
delamination
of
oriented
to
deviatoric
of
plate
the
orogeny. a deep down-
(1986) similarly
Assuming and
component
of
principal
the
stresses
are
vertically,
the average
stress in the strong layer is equal to half
the tectonic
force divided
by the thickness
of the
layer. The tectonic force originates from the densitydepth distribution through the lithosphere and
attributed the downflexing of the plates meeting in the Pyrenees to the formation of a cold litho-
beneath
spheric
and is almost
root.
eliminates
bending
Indian
and Molnar (1985) suggested root to explain the observed
flexing of the Indian
tion
BOIT
strong
it. It is concentrated layer
as a result
upwards
of viscoelastic
independent
into
the
relaxation
of the thickness
of the
If the dimensions of the crustal root and the thickness of the mantle part of the continental
strong layer (Kusznir and Bott, 1977). F, in an infinitely wide structure, in local isostatic equi-
lithosphere
librium
are known,
it should
be possible
to
in relation
to a standard
estimate the dimensions of the deep lithospheric root from simple geometric considerations. How-
sity-depth
can be calculated
from
ever, such a calculation
depth
Ap(z)
is likely
to be an under-
estimate for two reasons. First, an oceanic subducting slab may already exist at the time of the initial collision. Second, uplift and erosion will progressively reduce the crustal root. The most important local stresses
in erogenic
distribution
the density F,=
distribution
/0
moment
lithospheric
to which
it is referenced,
the anomalous using
function
den-
density-
the equation
(Dahlen,
for
1981):
LgrApdz
(2)
where g is gravity
and L is the depth
to the base
belts are produced by surface and subsurface loading. There are two opposing stress systems of this type. The surface loading of the mountains and
of the anomalous densities. This paper uses finite element analysis to study the combined stresses produced by the crustal root
the associated root horizontal deviatoric
and the mantle slab. Some new insights are obtained into the mechanism of mountain building.
crust
(Bott,
of thickened crust produce tension in the strong upper
1971, p. 231; Artyushkov,
contrast, the deep, dense associated downflexing horizontal compressive strong near-surface layer
1973). In
lithospheric root and its of the surface produce deviatoric stress in the (Fleitout and Froidevaux,
Some problems which are examined are as follows. How can compression affect a region such as the Himalayas while tension occurs in a central uplifted region root supported?
such as Tibet? How is a crustal How does the viscosity distribu-
1982; Mueller and Panza, 1986). The actual state of stress in the strong layer of the upper crust is
tion in the mantle affect ment? What plate boundary
the combined effect of these two opposite stress systems together with bending and other local and
The numerical models presented demonstrate the critical importance of deep mantle lithospheric
regional stresses such as due to ridge push. The state of stress in the strong layer of the upper crust can be conveniently expressed in terms of tectonic force F, (Fleitout and Froidevaux, 1983). F, is defined as the difference between the horizontal and vertical principal pressures integrated with respect to depth z through the strong layer. Thus
slabs in the compressional tectonics of the orogen and in contributing to the plate driving mechanism. They also show that simple stress computations based on the density moment function in equation (2) grossly overestimate the tectonic force produced by a deep slab of realistic dimensions. Finite
element
method
the tectonic developforces are developed?
applied
to erogenic
model-
ling
F, = where
/ 0 ‘bxx - G> dz T is the thickness
(1) of the layer. The integra-
Isoparametric quadrilateral and triangular elements have been used to model the continental
TECTONIC
STRESSES
ASSOCIATED
WITH
FINITE ELEMENT
COLLISION
GRID
MOUNTAIN
RANGES
195
(MODELS 1 TO 5)
650 Distance
Fig. 1. The finite element grid used for Models the grid, down to 420 km depth or shallower,
2000
(km)
1 to 5. Models 6 and 7 use the central is shown in the illustration
800 km of this grid. Only the central
of the models (Figs. 3-8);
this region is outlined
800 km of by a thick
line.
lithosphere a collision
puter programmes an earlier version method
propriate assigned values of viscosity. A fault is included in Model 7 using the dual node technique (Goodman et al., 1968; Mithen, 1980). In
and upper mantle to 650 km depth at mountain belt of ideal type. The comused have been developed from written by Waghorn (1984). The
used is also described
in greater
Bott et al. (1989). A symmetrical
preference
been assumed
detail by
lar
two-dimensional
grid 2000 km wide (Fig. 1) with the mountain
belt
the strong, otherwise
TABLE
cool layer of the upper lithosphere, are viscoelastic
that the principal
it has
stress perpendicumodel
average of the two in-plane
principal
for viscoelastic
plane
is the
stresses. This
media
within
the
deviatoric
stresses
are equal and op-
posite, so that only one of them needs to be shown in the figures.
ap-
1
Values of depth
extent of layers,
Layer
anomalous
density,
Young’s
modulus,
Poisson’s
used in the standard
ratio and viscosity
Layer
Depth
Density
Young’s
Poisson’s
Viscosity
number
extent
(kg/m3)
modulus
ratio
(Pa s)
( X 10”
(km) Upper
formulation,
two-dimensional
two in-plane
but
with
strain
Earth than plane strain, although the results for the two formulations do not differ greatly. The
6 and 7. The uppermost 20 crust is elastic representing
the elements
to the
is more realistic
at the centre has been used for Models 1 to 5, and the central 800 km of this grid has been used for asymmetrical Models km of the continental
to the plane
Pa)
crust
1
o-
20
0.0
9.00
0.27
elastic
Lower crust
2
20-
35
0.0
9.00
0.27
1023
Crustal
3
35-
65
9.00
0.27
1023
4
35-100
0.0
17.50
0.27
1023
17.50
0.27
1023
17.50
0.27
10Z3
root
Lithospheric
mantle
- 400.0 a
Slab interior
5
loo-300
Slab flanks
6
loo-300
+ 50.0 b + 25.0 b
Asthenosphere
7
100-400
0.0
11.50
0.27
loZ’
Transition
8
400-650
0.0
28.00
0.27
lo=
sub-continental
density-depth
zone
* The anomalous a 0.0 in Model 2. b 0.0 in Model 1.
density
is referenced
to the standard
models
distribution
at the edges of the models.
*
Anomalous erenced neath
densities
within
to a standard the normal
continental
edges of the models. are immaterial
a crustal
The standard
loading.
variations
regions
and
region
of
+ 25 kg/m3.
a dense +50
mantle
kg/m3
The mountain
at the
constraining
values
ment.
consist
layer.
of -400
the models
a central
the
results.
This
been
used
in the
regions
of
range is modelled
The
tematic
by a
1989), and
this
been
allowed
for by displace-
of 1O23 Pa s has of the lithosphere
near
layer has not been included
with
flanking
Peltier,
BOTT
to zero vertical
value
for the viscosity
the elastic
of
basal nodes
A uniform
assumed
and sub-
and
has to some extent
density
slab
and
four (Mitrovica
increase
be-
stresses depend
root with an anomalous
kg/m3
density
of surface
The anomalous
and
are ref-
profile
lithosphere
since the deviatoric
only on the lateral surface
the models
density-depth
M.H.P.
and is unlikely simple
surface
weak
been below plastic
as it overcomplicates to have much effect on viscosity
standard
structure
models,
but
study of the effect of varying
has a sys-
the viscosity
surface load in Airy equilibrium with the root. Mechanical properties used in the models pre-
below the lithosphere, and within the lower crust, has been carried out and is described in the fol-
sented in the figures are given in Table 1 and Fig. 2. Elastic properties are approximately consistent with the seismic velocity-depth distributions, and
lowing two sections. With the two-order of magnitude variation of viscosity, it has been necessary to use 1000 time increments of 500 year each to
variation of their values within the likely range has minimal effects on the results. The value of viscosity in the mantle below the lithosphere down to 650 km is 10” Pa s based on post-glacial recovery studies. Beneath 650 km the viscosity may increase
approach dynamic equilibrium in 0.5 Ma. It should be pointed out that the process of reaching equilibrium in the models is not of geological significance as it would be in post-glacial studies. The
by a factor
between
about
_-----
thirty
(Hager,
erogenic belt evolves on a much longer timescale and the results merely show the state of stress, the
1984)
(I) UlJper crust Elastic 72F LotGFc?GtT iYE; ___-_-_--.___ 13) Roce&OE+23
_------
(4) Lithospherlc ------
_____----
- - - - - - - - - - - - - -
I.OE+23
mantle
/ (6) /(51 SLab/ (611
l.OE+2l
(7) upper mantle
(8)
transl
t roll zone
0 1st ante
600 Fig. 2. The layering,
Plant le
viscosity
(floating
I. OE+21
1400
(km)
point, in Pa s) and density
(fixed point, in kg/m3)
structure
of Model 3.
TECTONIC
STRESSES
lithospheric
ASSOCIATED
deformation,
rate for the specified The vertical surface
is restricted
Basal nodes
the viscous
and at 35 km which pressures
are applied
senting
ridge push is applied
where
Model
g 6
The stresses produced by the crustal root and the dense sinking lithosphere (referred to as the
dis-
mantle
1 represents
Moho
equilibrium
depth.
7A where
a 30 km thick
separately. crustal
with a mountain
root
Model in Airy
range modelled
by a
edges
surface load (Fig. 3). The base of the lithosphere
repre-
at a constant
depth
dense
slab,
at the edges of the
1:
slab) are first examined
at the surface
a pressure
MODEL -7 -
distribution due to crustal root
Stress
lithosphere.
to the vertical
in Model
in
horizontal
forces proportional
is the normal
except
and
nodes of the lithosphere are constrained horizontally to determine the collision suction force.
6 and 7 where this
are applied
3RP
strain
to zero vertical
boundary
197
RANGES
the central
to zero
to the upper
displacement
lithosphere,
beneath
are constrained Isostatic
MOUNTAIN
distribution.
except in Models
constraint
Zero
and
density
is constrained
displacement,
to vertical
COLLISION
line of nodes
point
placement.
WITH
the
CRUSTAL
mantle
(Table
edge
ROOT,
of 100 km and so that
1) are all assumed
layers
there
is
is no
5, 6, 7 and
to have a viscosity
8 of
NO SLAB
0 _
-400 Deviatoric
-
I I I I I I I I I
Stress
100
MPa
. . . . .!.!!_K_t_!!_l.!. . . . _______________--------------- -_ _z
0
1
.
.
.
_
_
_z
-I-
_>-
_
/ . ~ .
. .\ . * - -----_--------------1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
---------_-____-------------_420
t-
600
Distance
Devlatorlc 0
3 I e, E
(km)
1400
Stress
100
_._ _. -_. . ____--------___---------------. . , .. ----------------...
--. -
--.
_
_
...
._
...
-.\
. .
MPa
.
IFGO 800 Fig. 3. Model 1 with - 400 kg/m3 no mantle the second
Distance crustal
slab. Broken lines represent in-plane
deviatoric
root but no mantle
tensile deviatoric
stress is equal in magnitude
above, and an enlarged
slab. Mechanical
(km) properties
1200 are as shown in Table 1 except that there is
stress and solid lines denote compressive but opposite
version of the central
in sign. The surface
400 km of the lithosphere
stress on the scale shown. Note that
vertical
displacement
is shown beloT,.
profile
is displayed
198
M.H.P.
102r Pa s. The model fects of the mountain Airy
model
is a sufficiently
for the purposes be associated loading. Large
represents
of this paper.
(2) in a very wide mountain
ef-
surface
approximation
Similar
towards
stresses will
root related
horizontal
deviatoric
and
upper
crust
the succeeding
stress nearest
the other in-plane
tension
Model
to thrust
as shown
to the horizontal
deviatoric opposite
occurs
diagrams,
the same
indicates
that
layer should
the tend
a value of 145 MPa, so that the value in 1 is 71% of the between
theoretical
the theoretical
value. and
The
modelled
values is explained
in
ing rise to slow equilibrium creep associated with dissipation of the root of finite width. The stresses
the
are proportional
is shown,
A broken
range having
loading
in
line
by small ongoing
to the density
and approximately
stress being equal in
in sign.
and subsurface
stress in the 20 km thick elastic
difference
Fig. 3. In this and
magnitude
good
with a flexural
the 20 km thick elastic deviatoric
the isolated
range and its Airy root. The
BOTT
proportional
contrast
stresses
giv-
of the root
to its thickness.
Figure 3 shows that small vertical displacements of a few tens of metres have developed.
denotes tension and a solid line denotes compression. A single stress value is shown for each ele-
These are associated
ment, which is the average value of the stress calculated at the gauss points. This effectively
ring in the lower crust, which gives rise to slight central subsidence and flanking uplifts. In order
eliminates bending stress in the elastic layer ciated with flexure. The maximum average toric stress observed in the central elements orogen is 104 MPa (1.04 kbar). If the elastic
to assess the creep more accurately, the creep vectors during the final timestep of 500 yrs have been determined. These show that the slow creep flow is tending to dissipate the root structure.
in the upper crust is thinner, then stress is proportionately larger.
assodeviaof the layer
the deviatoric
with the ongoing
creep occur-
Over a 500 yr time step, the crust thins by about 45 mm (90 m/My) and the root widens by about 173 mm (346 m/My). Over a substantial time period this slow creep would be expected to erode the root significantly. The creep rate is inversely
The large deviatoric tensions are produced by the combined effect of the surface loading of the mountains and the upthrust of the low density root. The stresses are concentrated upwards into the strong elastic layer near the surface as the stresses in the underlying viscoelastic lower crust relax (Kusznir and Bott, 1977). Theoretical calculation of the density moment function using eqn.
proportional to viscosity, so that lowered viscosity in the crustal root and underlying mantle would increase the rate of subsurface erosion of the root. The effect of varying the viscosities within Model 1 has been studied systematically. The
TABLE 2 The effect of varying the viscosity below the lithosphere and within the lower crust in Model 1 * Model
Viscosity (Pa s)
Deviatoric
Tectonic
stress
force
Layer: 1
2
3
4
5
6
7
8
(MPa)
(X lo’* N/m)
1A
elastic
1023
1023
1023
1%
l:zl
1:*1
1%
104.2
4.223
1
elastic
1023
1023
1023
1B
elastic
1023
1023
1023
1c
elastic
1023
1023
1D
elastic
1023
1023
1
elastic
1023
1E
elastic
102’
103.5
4.196
1022
102.9
4.114 4.239
102’
102’
102’
1023
IO23
1023
lo*’
IO*’
104.0
1023
1022
1022
1022
1022
99.1
4.019
1023
1023
102’
lo*’
IO*’
lo*’
103.5
4.196
IO2’
102’
102’
10**
lo*’
1021
98.8
4.110
* The table shows the values of viscosity for each of the eight layers (Table 1 and Fig. 2), the deviatoric stress in the central elastic elements and the tectonic force at the centre of the 20 km thick elastic layer for a selection of model variants. Italic denotes variation from standard Model 1.
TECTONIC
STRESSES
tectonic
force and deviatoric
the elastic
ASSOCIATED
layer
are shown
beneath
the
lithosphere
sphere.
The results
and deviatoric very slightly beneath
has
show
root by at least two orders 1E). Scaling
model
factor leaves the results
been
provided
the time
modelled and
by
that
the tectonic
that
creased
assuming
by the same
crustal
variations
force
the model
factor.
root are thus robust
(Model
in the model by the
same constant
The
unchanged
is run
is in-
results
for the
with respect
to wide
in rheology.
layer are only
by (1) variation
the lithosphere
of magnitude
all the viscosities
2. A zero viscosity
stress in the elastic modified
199
RANGES
on the base of the litho-
Stress distribution due to mantle slab
of viscosity
over a much wider range
than is likely to apply (Models decrease
of these
elements
conditions
MOUNTAIN
stress at the centre of
in Table
the underlying
free boundary
COLLISION
for a selection
variants removing
WITH
of the viscosity
MODEL
-7
Model
1A to lD), and (2)
in the lower 2:
crust
MANTLE
2 (Fig.
bivergent
and SLAB,
4) represents
subducting
slab
a 200 km thick
beneath
an
erogenic
NO ROOT
G
0
_---------------------
u
: -400 : : -800
-
E-1 200 a
-
-
Deviatoric
-
Stress
-----------------__--------___
MPa
-------_ 1 IIll ,I: -
c--
*
,,,
.
‘( . \
---_
.
.
-
*
.
\\\.
.
.
.
-
-
c
a
-:
-
-
-
, ---
I-
----_-_____
100
--
,,
\/
.
.
.
,
.
.
.
-\
-
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
600
0 I st ante
Devlatorlc
(km)
1400
Stress
100
MPa
0 c
7
----
-v
-
--
,___,
--2--\
.
’
_c
/
\ \
42 \
k
*..
deformation.
Mechanical
vertical
displacement
profile
properties
of the surface
mantle
/
-
slab but no low density
are as shown is shown
‘/
.
-----__--__-~
-
Distance
Fig. 4. Model 2 with 200 km thick high density surface
r
//
GO 800
in Table
above,
1 except
’
...
/
-\ 1200
(km) crustal
root, showing
for absence
and an enlargement below.
\
\
\ \/
.
\
___,_--_------C_-___---_,_
deviatoric
of the low density
of the central
stress distribution
and
of the crustal
root. The
400 km of the lithosphere
is shown
M.H.P.
belt. The low density
crustal
load are not included
in the model so that the slab
order of magnitude larger than the bending stresses associated with the downflexure, which have been
effect can be studied
in isolation.
determined
structure
The rheological
is the same as that of Model 1 except for
the high viscosity maximum
gravity
comparable positive crustal
root and the surface
BO’IT
of the slab. anomaly
in amplitude
Bouguer effects
and Mueller,
The slab
of + 78 mGa1 which is
anomaly
1985). This suggests
Model 2 is of realistic
ated
downflexure
slab
produces
surface
over the Alps after all removed
of the crust. an
but are not pre-
value
The high density
downflexure
of
the
1130 m at the centre
extent well beyond
the confines
of the
deep load (Fig. 4).
size.
The magnitude
of the tectonic
force (and devia-
toric stress) in the 20 km thick elastic layer is much smaller than that derived from the density moment function using eqn. (2). The theoretical
The most conspicuous stresses in Model 2 (Fig. 4) are the large almost horizontal deviatoric compressions which dominate the elastic layer. These are of the type originally postulated by Fleitout and Froidevaux (1982). They extend laterally some distance beyond the erogenic belt, where they increasingly deviate from the horizontal. The maximum deviatoric compression, averaged over an
crepancy infinitely
element,
finite
are almost
isostatic
of maximum
with lateral
(Schwendener that the slab in
is 112 MPa. These stresses
points
sented. The large deviatoric compressions originate from the high density of the slab and the associ-
gives a
and width to the residual
have been
at the Gauss
value at the centre is 19.6 X 10” N/m whereas the actual value (Table 3) is 4.6 X lOI N/m which is only 24% of the theoretical value. The dis-
an
arises because wide structure
width.
The
deeper
the theory assumes an whereas the slab is of the
slab
extends
with
TABLE 3 The effect of varying in the standard Model 2 (1) the viscosity below the lithosphere (Models 2A to 2E and 2G to 2J), (2) the depth extent of the slab (Models 2F and 2G), and (3) the viscosity of the lower crust and crustal root (Models 2K to 2M) * Model
Depth extent
Viscosity (Pa s)
Deviatoric
Tectonic
stress
force
Vertical displ.
(MPa)
(X lOI N/m)
(m)
- 117.4
- 4.886
1185
- 115.0
- 4.746
1163
- 112.3
- 4.649
1130
(km)
Layer: 2
3
4
5
6
2A
200
lo23
1023
1023
IO22
10J2
2B
200
lo*’
1023
lo23
1023
102’
2
200
10Z3
102’
102’
1023
102’
2c
200
lo23
102’
1023
1023
1023
102’
10021 ,o*‘.5
- 110.0
- 4.558
1111
2D
200
1023
1023
102’
1023
1023
102’
1022
- 104.9
- 4.343
1069
2E
200
1023
1023
1023
1023
1023
102’
1022.3
- 98.0
- 3.962
992
- 57.9
I
8
0
:,*I
0
2F
100
1o23
1023
1023
102’
102’
102’
102’
2
200
102’
1023
lo*’
1oz3
102’
102’
102’
- 2.414
578
-112.3
- 4.649
1130
2G
300
102’
1023
1023
102’
102’
102’
102’
- 164.9
-6.812
1660
2H
300
102’
1023
lo*’
102’
1023
102’
102’ 5
- 158.6
- 6.533
1596
21
300
lo*’
1023
102’
1023
1023
102’
1022
- 141.7
- 5.824
1435
25
300
1023
1023
1023
1023
1023
102’
J022.S
- 106.1
- 4.368
1092
2
200
1023
1023
1023
1023
102’
102’
1021
- 112.3
- 4.649
1130
2K
200
10Z2
1022
1oz3
1023
102’
102’
102’
- 96.6
- 3.989
1365
2L
200
102’
102’
1023
1023
1oz3
102’
102’
- 59.8
- 2.565
1501
2M a
200
102’
102’
lo*’
102’
lo23
102’
102’
- 105.8
-4.313
1267
* The table shows the depth extent of the slab, the values of viscosity (Pa s) for layers 2 to 8 (Table l), layer 1 being elastic, the deviatoric stress in the central elastic elements, the tectonic force at the centre of the 20 km thick elastic layer and the maximum vertical displacement at the surface for a selection of model variants. Italic denotes variation from standard Model 2. a In Model 2M the two order of magnitude reduction in viscosity
in the lower crustal layer 2 is restricted to the region above the
crustal root. Elsewhere layer 2 has the normal Iithospheric viscosity of 102’ Pa s.
TECTONIC
STRESSES
respect with
ASSOCIATED
to its width,
WITH
the stronger
the theoretical
value
concentrated
up into
viscous
with ongoing deforms
internally.
the stresses somewhat There which
The
force is layer,
in the slab and the
These
are associated
as the slab sinks
slowly
and
It can also be seen (Fig. 4) that
in the elastic beyond
layer
extend
laterally
the edges of the slab.
are two other
deserve
force.
the high level elastic above.
creep
the discrepancy
of the tectonic
stresses remain
lithosphere
MOUNTAIN
of tectonic
result is that only a fraction and significant
COLLISION
features
mention.
However, stricted
if the
deviatoric
root, the reduction This indicates bordering despite
regions the much
linearly
mantle
above the edges of the slab, decreasing towards the centre. The principal stresses are orientated diagonally beneath the flanks of the erogenic belt. The associated creep reach 1.4 X lo-l6 sst, to thicken
strain rates, which locally are causing the crustal root
at an average
500 yr (52 m/My)
and
rate of about to narrow
26 mm in
at about
120
mm in 500 yr (240 m/My). Thus the deep-seated slab has the effect of accentuating the root, opposing the erosion of the root seen in Model 1. (2) Prominent sub-horizontal compressive stress of up to 27 MPa affects slab, causing
the upper
part
it to be shortened
of the mantle
horizontally
and
stretched vertically as it sinks. The associated strain rates are up to 1.5 X lo-l6 s-l.
creep
The effects of varying and
slab
investigated
depth
extent
the viscosity in
systematically.
in Table 3. Larger variations
Model
distribution 2 have
The results
been
are shown
in the viscosity
below
the lithosphere than are likely to apply in practice have a relatively minor effect on the stresses in the elastic layer and the surface downflexure (Models 2A to 2E). As the sub-lithospheric mantle becomes stiffer, the stress and downflexure is slightly reduced as a result of increased support for the slab from below. The most significant when the viscosity tion zone exceeds
reduction
occurs
assigned to the mantle transi1O22 Pa s (Model 2E). This
effect becomes stronger when the slab reaches the top of the transition zone (Model 25). A more significant reduction of the stress and tectonic force of about 50% occurs when the viscosity of the lower crust and crustal root are reduced by two orders of magnitude (Model 2L).
weaker
is re-
10% (Model
2M).
stress can be through
viscosity
the
lower crust,
lower crust
in the oro-
3 also shows that the stress
force in the elastic layer increase
extent
of the root, but rather
(Models
transition
within
into account,
increase
Symmetrical
with
less than
2F and 2G). The shallowing
the olivine-spine1 stantially
topmost
region
layer above the
upwards
of higher
genie belt itself. Table and tectonic
the viscoelastic
and
is only about
transferred
not been taken
crust
viscosity
that the compressive
substantially
stresses of up to 28 MPa which do not relax affect lower
reduced
to the root and the crustal
the depth
of the stress field
(1) Significant
201
RANGES
the slab has
but this would
the downpull
of sub-
of the slab.
models with crustal root and mantle
slab Ideally the cross-sectional area of the mantle slab could be estimated from the amount of lithospheric shortening indicated dimensions. For the crustal
by the crustal root root in the models
here, a bivergent slab of 160 km width should have a vertical extent of about 120 km. As pointed out earlier, mountain duction
progressive range,
uplift
and
and likelihood
slab is present
erosion
that a relict
at the onset
of the sub-
of collision,
suggest that the slab will be bigger than this. The residual positive Bouguer anomaly over the Alps is consistent (Fig.
with a 200 km bivergent
5) shows
the deviatoric
and surface displacement crustal
root
as in Model
slab. Model
stress
for the combination 1 and
3
distribution, of a
a 200 km thick
mantle slab as in Model 2. The deviatoric stress distribution in the elastic upper crust results from the superimposition of sub-horizontal tension caused by the crustal root (Model 1C) and the more wide-reaching compression caused by the slowly sinking slab (Model 2). If the viscosity structure of the separate root and slab models
is identical,
then the superimposition
of the stresses and displacements is effectively linear, as is to be expected theoretically. As a result of this superimposition, the stresses are almost negligible in the upper crust of the erogenic belt, with root-produced tension almost exactly cancelling the slab-produced compression. Moderate sub-horizontal compression affects the flanks
202
M.H.P. BOTT
.5
MODEL
3: ROOT ANG 200 km SLAB
0
-__-_----
-----------
22
: -4Ocl E 4 -800
-
$--1200 Deviatorlc
G 0
-
Stress
. . _ _ _-_-_-___--___-----, e
liil!l!l!lt . -1 - -_ 2 - -- . %. , * * , 7
, . ,_-_------.
f
320 ,600
Distance
T.___L_’
__-*_-_
,------.
100 MPa
.
1400
(km)
100 MPa
O?
__------ 2 , ,
_-_-_-_---------------.i
CL
...
*
.
1..
s
..-
-
-
\
/
\
-....---------------
*,
-c *
.
.
I
.’
...
.
.
I_
*
*.*
..\
...
2 1
’
-
-
’
f
f
*.*
loot
MODEL 0 E _u
3RP: RIDGE PUSH
___---_
_c u a
/
,
’
_--------_-_-----
/ ’
czfi I
...
.
..,
.
Fig. 5. Model
’
incorporates
and
supplemental
an enlarged compression
-
version
slab and low density of the centrat
caused
effect of ridge push in continental
_..
-
Distance
3 with 200 km thick dense mantle (above),
,
0’
by an 8 MPa normal
lithosphere.
crustal
400 km below. pressure
’
\
,..
.
II
_..
1200
(km) root, showing
deviatoric
stress distribution,
Model
3RP (also
across
the edge of the lithosphere
See Table 1 and Fig. 2 for viscosities
of the mountain belt and the bordering regions because of the wider lateral extent of the compression produced by the slab. Significant deviator& stresses which do not relax occur in the viscoelastic region beneath 20 km depth in the vicinity of the crustal root and the mantle slab. These stresses are a combination of
-
.
\. ..*
800 deformation
...
-..
.._
1001
. _--------_
_---_-_------
...
%*
100 MPa
INCLUDED
enlarged)
and anomalous
shown
surface
at the bottom to represent
the
densities.
those developed by the crustal root as it tends to dissipate (Model 1) and by the slab as is extends vertically and sinks (Model 2). Within the crustal root region the two processes oppose each other. The crustal root tends to dissipate itself slowly while it is being supported and accentuated by the creep associated with the sinking slab. The stresses
TECTONIC
within
STRESSES
WITH
COLLISION
the slab itself are almost
entirely
the sinking,
ASSOCIATED
MOUNTAIN
related
as can be seen by comparing
and 3, which have almost In all the
previous
identical models,
to
Model 3RP has been constructed to include norma1 pressure on both edges of the elastic upper
Models 2
lithosphere to represent ridge push. The ridge push force related to 60 Ma old oceanic lithosphere is
slab stresses. zero
pressure
is
of the order
applied at the edges consistent with lithostatic pressure. The contribution to the stresses from ridge
push
has
been
ignored.
To
remedy
203
RANGES
of 2.0 to 2.8 x lo’*
1981; Fleitout much smaller
this,
N/m
(Dahlen,
and Froidevaux, 1983). The value is by about 2.0 x lOI* N/m in con-
-2 MODEL Y
C
4:
ROOT
AND
100
km
SLAB
0
aI
6
-400 : ‘: -800 cn -
0eviatoric
-
0
u
-1
Stress
r . . -----------_-_-----------------
I _
_
_..
lllllll~ ...
...
...
.
.
,,
T Y ,. ------_-_-__
-I
I
*.
w
E-
.
.
0
.
.
MODEL
0
I
100
MPe-
1
.
--------____ .
.
.
. . . . . .
220
&
.:
_
5:
ROOT
AND
300
km
SLAB
----------_-_-_--___
F -400 E al -800 : -CL-1200
-
2 -1600 eviatoric
420 600
Stress
D I st ante
(km)
1400
Fig. 6. Above: Model 4 with 100 km thick slab. Below: Model 5 with 300 km thick slab. Otherwise as Model 3 (Fig. 5). showing deviatoric stresses and surface displacements.
204
M.H.P.
tinental
lithosphere
sity-depth within
because
of the different
so that
its value
should
be
of 0.0 to 0.8 X lOi
N/m.
In
function
the range
Model 3RP the highest value within been used, being represented of 8 MPa across small about
8-12
lated
The normal
horizontal
MPa
affects
the
occurs
below
elastic
Comparison
identical
6 (Fig.
7) includes
dimensions
and
a sinking
properties
slab
of
to that
of
of
mountain
range (as viewed
horizontal
deviatoric
layer
in the creep re(Fig. 5, bottom).
ridge push force thus does not appear
models otherwise have the same densities as Model 3 (Table 1).
of Models
Model
A
to be a major factor in producing compression in erogenic belts in comparison with the sinking slab. To cover the range of possible slab dimensions, deviatoric stresses for mantle slabs of 100 and 300 km vertical extent are shown in Models 4 and 5 (Fig. 6). These viscosities and
such a situation subduction may continue to occur from one side only rather than being bivergent.
Models 2 and 3, but it is laterally displaced so that the axis of the slab underlies the right edge of the
pressure
compression
and a small increase
compression
this range has
by a normal
the 100 km thick lithosphere.
superimposed
throughout
den-
BOTT
3 to 5 shows that the size
and the tension placed
interfere
compression
The
due to the slab dis- j
due to the root are laterally
with respect
do not
in the diagrams).
to each other, to the
same
and thus they
extent
as in
the
previous models. Consequently both the tensions and compressions in the upper crust reach substantially larger values than in Model 3. The maximum element averaged tension is 59 MPa beneath the left part of the mountain range, and the maximum compression of 94 MPa occurs in the right borderland above the slab. There are some other interesting features of Model 6. As the horizontal stresses in the elastic
of the mantle slab has a strong influence on the magnitude of the upper crustal stresses. Compression in the upper crust dominates Model 5 which
upper sional
has a 300 km thick slab, whereas significant upper crustal tensions characterize Model 4 with its 100
tated stresses occupy the central region of the mountain range. The effect of the asymmetry on
km thick slab. Deviatoric stresses in the crustal root region and in the upper part of the slab are largest in Model 5 and smallest in Model 4. As indicated in Table 3, the surface deformation is
the creep processes in the crustal root region also notable. The root beneath the left flank
nearly proportional to the depth extent of the slab, but raised viscosity below 400 km more strongly affects the deeper slabs. These models demonstrate the importance of the mantle slab in producing compression in mountain belts and their flanks. They also show that tension in the central region may coexist with compression affecting the flanks.
Asymmetrical
model
The symmetrical models presented above, with the mantle slab vertically below the crustal root, are a special case. A more general situation may involve a slab asymmetrically located beneath one flank of the collision mountain range. Such asymmetry may occur when a collision mountain belt develops from prior subduction of oceanic lithosphere at the pre-collision continental margin. In
crust change from tensional to comprestowards the right flank, obliquely orien-
is is
being thinned and eroded but beneath the right flank above the slab it is being supported in approximate equilibrium. Over a sufficiently long time period, a significantly will develop. The maximum surface
asymmetric downflexure
crustal
root
of 1140 m
occurs over the centre of the slab. In the symmetrical models, the downflexure of the borderland regions is minimal, but in the asymmetrical Model 6 the downflexing mainly affects the low-lying borderland where the depression of the surface may give rise to a sedimentary basin. A similar depression
is produced
in the geodynamic
models
of Werner (1985) which are based on a layered viscous structure. In Model 6, water and sediment loading has not been included. However, if a 1.0 to 1.5 km deep depression is filled by sediment, the additional load will give rise to a sedimentary basin about 4-5 km thick having a horizontal dimension of 100-200 km. In contrast, the crustal root will be associated with local uplift in response to progressive erosion of the mountain range.
TECTONIC
STRESSES
ASSOCIATED
WITH
MODEL
-2
a
n
COLLISION
MOUNTAIN
205
RANGES
6: ROOT AND 200 km OFFSET
Deviatoric
Stress
SLAB
-
llllllllil
100 MPa i
320 Dist: ce
0 0 2 Y
100 l"l?a ___ _._ ---,--,-_,--~~---~,-_ -
*..
'. ,
/
Distance
255 Fig. 7. Model
(km)
6 with 200 km slab asymmetrically displacement
located
with reference
(above) and an enlargement
--________-_-__ . .
\
\
655
(km)
to the crustal
below. Properties
root,
showing
deviatoric
stresses,
surface
as for Model 3.
Clearly the slab downpull provides an important mechanism for producing wide foreland sedimentary basins adjacent to mountain ranges, such as the PO basin south of the Alps. The existence of such depressions needs to be taken into account in flexural studies of erogenic belts as was recognised
been used for simplicity in the models, but in reality a narrower dipping slab may occur.
by Brunet (1986). They may otherwise be interpreted erroneously solely in terms of surface litho-
It was pointed out earlier (p. 204) that the ridge
spheric loading. The scenario represented
by Model 6 is obvi-
ously relevant to the Himalayan-Tibetan region and to the Alps, with the dense slab displaced towards the south in both regions. The Alps and Himalaya may have developed in this way because of subduction occurring on the south side prior to the collision. A wide slab with vertical sides has
Faulted model: collision plate boundary force
push force as developed in continental lithosphere is likely to give rise to a relatively small compression which has a negligible effect in comparison with the stresses produced by the root and the slab. It is difficult to see how the small residual ridge push effect in continental regions could by itself overcome the tension produced by an orogenie crustal root. The resolution of this enigma comes from the recognition that the sinking slab
M.H.P.
206
beneath
a collision
plate boundary The plates (Fig. crust
slab
to converge cuts
across
only
act
thrust
beneath
develops
fault
435 m horizontally
across
2 u
period
the thrust
MODEL 0
Model
7 has the
and 163 m vertically,
horizontal
convergence
The convergence
yielding
rate
of 0.81
rate is 10.3 mm/yr
ing the first four time steps but decays mm/yr after 0.5 Ma. Model 7 clearly
such
which
the Moho.
mm/yr.
the
throughout
as the deviatoric
over the modelled
displacements
a
an average to cause
the lithosphere.
a major
but is locked
centrates
can
a zero shear stiffness
progressively
produces
when a plane of weakness
8) includes
been assigned
range
force in its own right.
sinking
as a fault
mountain
BO’TT
dur-
to 0.38 demon-
strates that the dense sinking slab can cause plate convergence. The modelled rates are an order of magnitude
The fault
slower
than
that there are regions
stress con-
actual
of 0.5 My. The
erogenic
In order
over 0.5 My are
observed
of greater
rates
suggesting
weakness
beneath
belts.
to- annul
7: ROOT AND OFFSET SLAB WITH FAULT, _-____-__---------
the shearing
stress
on the
EDGES FREE
$ -400 Z -800 m 2 E-1200
-
0
Deviatorlc
__
Stress
100 MPa
320 MODEL
7A: EDGES FIXED 100 MPa
320 Distance
0
Fig. 8. Model 7, as Model 6 except that a fault with zero shear strength slab. The fault is locked edges, and deviatoric
beneath
stresses
the Moho.
are shown
Deviatoric
stresses
(km)
800
cuts the crust beneath
and surface
displacement
the edge of the orogen
(above)
are shown
below for Model 7A which has nodes at both edges of the lithosphere horizontal
displacement.
above the deep
for Model 7 with free constrained
to zero
TECTONIC
fault
STRESSES
plane,
forces
ASSOCIATED
equivalent
are applied
but
Model Regions
crustal
fault plane, a high
is of necessity
almost
and if this is relieved angle
thrust
would
with
are
stress below
the
parallel
to the
by further
fault-
be expected
to
Model 7A is used to estimate the magnitude of the collision slab pull force, referenced to continental
lithosphere,
by
of the lithosphere
placement
(Fig.
constraining
the
edge
to zero horizontal
dis-
8, bottom).
building
ean. There
of initiation
on closure
is no difficulty
initiating
compression,
subducted
oceanic
ent mountain
of collision
of the adjacent
oc-
in understanding
however,
lithosphere
the
if pre-existing
underlies
the incipi-
belt.
Discussion
similarly
develop.
nodes
mountain
stress is
the fault plane.
tension
The large compressive
plane
supin the
in comparison
except just beneath
of upper
enhanced.
ing,
result
tension
207
sphere raises the problem
These
crust associ-
6 (Fig. 7) is that the compressive
greatly reduced
fault
The
deviatoric
RANGES
boundary
nodes.
but they also produce
horizontal plates.
MOUNTAIN
opposite
of the upper
ated with the faulting, adjacent
COLLISION
at the dual fault
give rise to local flexure plementary
WITH
This model
is other-
wise identical to Model 7. In comparison with Model 7 where deviator% stresses die out towards the edges, a significant plate interior deviatoric tension is developed out to the edges in Model 7A. The integrated stress difference across the lithosphere at the edges of the model then yields the value of the tectonic force, which is found to be about 1.2 x lOi N/m. This force combines with the residual ridge push force to drive the plate
A difficulty
with all the models
studied
is that
the slab sinks too slowly to account for convergence rates of lo-70 mm/yr such as are characteristic
of the Alpine-Himalayan
belt.
The
litho-
spheric support for the sinking slab appears to be too stiff. A reduction in lithospheric viscosity would
help. However,
that sinking
the simplest
explanation
.is
is aided by some form of subduction
fault which separates from the lithosphere
the sinking
part of the slab
above and adjacent
to it. This
situation could readily develop from pre-existing subduction of oceanic lithosphere at the time of continental collision. It could give rise to an asymmetrically located slab, and would favour continuation of one-sided rather than bivergent subduction.
This situation
has not been
the present exploratory paper, cated by the results obtained. Bott et al. (1989) studied
modelled
but is clearly
in indi-
the effect of locking
ing.
and unlocking a normal subduction fault. When the fault is locked, the surface downflexing and
A plate with an ocean ridge on one side and a collision mountain range on the opposite side is
compression much greater
driven
same situation
convergence
which produces
by a combination
the mountain
of the ridge
build-
push
and
associated with slab downpull than when the fault is unlocked. probably
applies in collision
collision tinental
slab pull forces. When referenced to conlithosphere, the collision slab pull force
tain ranges.
When the fault is locked,
is impeded
and
appears
to dominate,
lithosphere
eanic
lithosphere
but
referenced
to old oc-
the ridge push force dominates.
the downpull
is maximum
sion and downflexing.
on
producing When
are The
moun-
slab sinking the overlying
large compres-
subsidence
is facili-
In reality, an ideal two-dimensional plate of this type is driven by the difference between these two
tated by an unlocked
fault, downflexure
pression
as the more rapidly
boundary forces referenced to the same type of lithosphere. According to the calculations here, a net force of about 1.8 X lOi N/m probably applies. A larger net force may apply when the sinking slab is bigger than in Model 7, and/or when an unusually large ridge push develops from a hot spot oceanic region such as Iceland. The relatively small compression associated with ridge push as developed in continental litho-
slab is more strongly supported from below. Variation in the state of a subduction fault can thus lead to vertical motion of the surface and variation of stress, with the greatest compression associated with the maximum regional downflexing. Further longer term variations should be associated with the progressive development of the sinking slab, as it sinks towards the mantle transition zone and through it.
are reduced
and comsinking
208
M.H.P.
Conclusions
(5) If the slab is asymmetrically situated beneath one flank, then large compressions affect
(1) The tectonic and surface tain
belt
element
stress produced
loading
at a modelled
has been analysis.
studied An upper
into which stress concentrates thick,
and beneath
tributions
BOTT
(Tables
by subsurface collision
moun-
by viscoelastic
finite
crustal
elastic
tensions opposite
layer
is taken to be 20 km
this appropriate l-3)
this flank and the adjacent
viscosity
are assigned.
dis-
The models
borderland,
affect the mountain side. This situation
Himalayan-Tibetan mountain
region,
building
and extensional the northern
occurs
collapse
interior
range towards the is relevant to the where at the
(Dewey,
compressional southern region.
have been run for 1000 time steps of 500 yrs each
situation,
to approach
slab may give rise to a major sedimentary
dynamic
equilibrium.
Ongoing
creep
the borderland
of the lithosphere
associated
edge
1988) dominates
of the uplifted
downflexing
while large
In this
above the basin
with large negative
in
free-
strains of up to about 1.5 x lo-i6 s-l occur in the crustal root and slab regions and are associated with moderate creep stresses which do not relax. (2) Two primary stress systems of independent
air and Bouguer anomalies. Creep may cause an asymmetrical crustal root to develop, with thickening beneath the active mountain building and
origin can be identified, in addition to secondary bending stress. The surface and subsurface loading arising from the mountain range and its Airy crustal root produces deviatoric tension of about
thinning in the extensional region. (6) The faulted Model 7 demonstrates that plate convergence, albeit slow, is produced. By horizontally constraining the nodes at the edges of the
100 MPa in the local upper crust. The associated creep strains cause the crustal root to thin and
lithosphere
widen very slowly, but significantly. 200 km thick
deep
slab
of cool,
In contrast, dense
a
sinking
lithospheric mantle and its associated surface downflexure produce horizontal deviatoric compression of very similar magnitude (110 MPa) but rather wider lateral extent. Creep stresses produced by the slowly sinking slab support and enhance the crustal root, thus opposing its selferosion. (3) The tectonic force produced by the crustal root is about 70% of the theoretical value computed from the density moment function because of its finite width. The discrepancy is even greater for the tectonic force in the elastic layer produced by the mantle slab, which is only about 25% of the theoretical value. stress and tectonic
Thus simple computation of force using the density moment
in Model 7, it is shown
thick slab produces about 1.2 x lOi* boundary
that a 200 km
a collision slab pull force of N/m. Without this plate
force, normal
ridge push would be inad-
equate to initiate or form range because of its weak
a collision mountain development in con-
tinental lithosphere. (7) An inadequacy of the models with simple unfaulted bivergent subduction is the slow rate of sinking of the slab and convergence of the plates when the upper crust is faulted. This suggests that subduction may characteristically be one-sided with a subduction fault along the original upper surface of the slab. Such a situation would readily develop from pre-existing subduction of oceanic lithosphere at the onset of collision, and would account for the compressive initiate the mountain building, asymmetry
of the present
stress required to and the inherited
Alpine-Himalayan
belt.
function given in eqn. (2) can lead to serious error when applied to features of finite width.
Acknowledgements
(4) If the slab lies symmetrically beneath the crustal root, then the root-produced tension and slab-produced compression tend to cancel each other out in the upper crust of the mountain range. Whether tension or compression wins depends on the size of the slab and the viscosity distribution of the upper mantle and the transition zone.
The work was mostly carried out during tenure of a Visiting Fellowship at Geophysics Division, D.S.I.R., Wellington, New Zealand. I am grateful to the Director, Dr. F.J. Davey, for financial support and facilities and to the Royal Society for a New Zealand Fellowship covering travelling expenses. I thank Dr. D.J. Woodward for help and
TECTONIC
STRESSES
ASSOCIATED
support
in many
ried
out
in
COLLISION
ways. I am grateful
Stern and Derek the manuscript.
WITH
Woodward
MOUNTAIN
to Drs Tim
for critically
reading
The final computations the
Durham
RANGES
were car-
University
Computer
209
Kusznir,
N.J. and Bott, M.H.P.,
the upper
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creep. Tectonophysics, Lyon-Caen,
H.
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Molnar,
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1977. Stress concentration
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plate,
1985.
Gravity
anomalies,
and the structure,
of the Himalaya
and Ganga
support
basin.
and
Tectonics,
4:
513-538.
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