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Tectonophysics, 199 1991) 343-314
Elsevier Science publishers B.V., Amsterdam
343
A two level concept of plate tectonics: application to geod~a~cs
L.I. Lobkovsky a and V.I. Kerchman b
y
nstitute of Oceanology The U.S.S.R. Academy
of Scien ces
Moscow ii 7238, USSR
h The Interuniversity Computer Center, Kishinev 279003, USSR
(Received August 15.1989; revised version accepted July 15.1990)
ABSTRACT
Lobkovsky, L.I. and Kerchman, V.I., 1991. A two-level concept of plate tectonics: application to geodynamics. In: L.P.
Zonenshain (Editor), The Achievements of Plate Tectonics in the U.S.S.R. Tectonophysics, 199: 343-374.
A twolevel plate tectonics concept is developed on the basis of data on lithosphere rbeological stratification. This
approach differentiates between crust and subcrust plate ensembles separated by a lower-crust viscoplastic asthenolayer.
Similarly to classical plate tectonics, three types of boundaries are distinguished in the lower layer which do not always
coincide with crust-plate boundaries (especially for continents). Applications of this concept to geodynamics are considered,
and a corresponding quantitative analysis for several important
processes is carried out.
A
quantitative mode1 of mountain
formation and collision-plateau origins is proposed.
Also, a geodynamic model of the evolution of passive margins, taking into
account a lower-crust viscous flow, is considered and its geological consequences are discussed. A mechanism
of
rifting, taking
into consideration rheological lithospheric layering and its vertical movements caused by extension, is developed. Both a
qualitative scheme and quantitative analysis of the slow evolution of intracraton structures of “shield-basin” type, taking into
account erosion and sedimentation processes, are worked through. Also, historical aspects of plate tectonics are discussed from
the point of view of the proposed concept.
Intmduetion
The orthodox theory of plate tectonics seems to
have certain restrictions on its application. Thus,
tectonic processes of a regional scale, that is of
several hundreds of kilometres, cannot be de-
scribed sufficiently well by standard plate-tectonic
models. This is of special concern for the conti-
nents (Molar, 1988; Lobkovsky, 1988a) because,
when one analyses regional processes, those inho-
mogeneities (both horizontal and vertical) and dis-
tributions of intraplate strains which have not
been considered on a global scale (since they have
virtually been averaged) become the main objects
of the research. Since many researchers have been
guided by the idea of scale restrictions imposed on
the plate-tectonic processes, they have put this
above the quantitative study of plate non-rigidity
and patterns of intraplate strains and stresses
(Molnar and Tapponier, 1978; England and Mc-
Kenzie, 1982; Vilotte et al., 1982; Cloetingh et al.,
1984; England et al., 1985; Khain, 1986; Bruhn,
1987; Kirby and Kronenberg, 1987).
As for geomechanics, the analysis of the prob-
lem mentioned is reduced to the description of the
rheological behaviour of lithospheric rocks under
the real P-T conditions and for the various regi-
mes of tectonic strain.
In geodynamics, an “effective strength)* is usu-
ally used as a generalized rheological characteristic
of the lithosphere (Ranalli and Murphy, 1987;
Kirby and Kronenberg, 1987); this may be inter-
preted in different ways, depending upon the
P-T
conditions and mechanisms of rock strain. For the
domain of quasi-elastic strains and brittle fractur-
ing, this characteristic coincides with the defini-
tion of a material strength as used in mechanics
(Byerlie, 1968; Sibson, 1974; Brace and Kohlstedt,
1980). For the ductile (non-linear viscous) flow of
the medium, the notion of “creep strength” has
been introduced (Ranalli and Murphy, 1987;
Kirby, 1983).
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344
L..l. LOBKOVSKY AND ‘4.1. KtRtHMAN
a
Temperature
rengh
b Tempera ure
Fig. 1. Model strength profiles (solid lines): (a) for normal
continental lithosphere with a 15 km thick granitic upper crust
and a 25 km thick mafic lower crust; (b) for normal oceanic
lithosphere with a 5 km thick basaltic upper crust and a 2 km
thick serpentinitic lower crust. Rashed lines denote the geo-
therms for the two cases. The dotted line denotes the strength
envelope. The strain fate is lO_” s-‘.
Ahhough each particular profile of an “effec-
tive strength” compiled from the data of labora-
tory tests, depends upon the assumed composition
of the Earth’s crust and upper mantle, and upon
temperature distributions, deformation rate, water
saturation of the media, and so on, all these pro-
files plainly indicate the main feature of the rheo-
logical s~at~~ca~on of the exosphere; th8t is, the
occurrence of an extremely low strength (viscosity)
of the medium in the lower crust in contrast to the
stronger and more brittle layers of the upper crust
and the subcrustal part of the lithosphere.
As an example, in Fig. la we illustrate a typical
profile of the generalized strength of the litho-
sphere, which is composed of an upper “granitic”
crust (Z) - 15 km thick, a lower “mafic” crust
(II) - 25 km thick and an underlying olivine
mantle (III). This plot has been drawn from a
typical continental geotherm that corresponds to
the average heat flow on the surface; that is, about
50 mW/m* {Morgan and Sass, 1984), in accor-
dance with experimental rheological data (Byerlie,
1968; Brace and Kohlstedt, 1980; Kirby, 1983;
Ranalli and Murphy, 1987), the deformation rate
being constant at C? 1O-‘5 s-j. The envelope line
shows the resistance of the medium to brittle
fracturing (Byerlie, 1968), and corresponds to the
generalized strength of almost the entire upper
crustal layer (I), a small part of a “cold” lower
crust (II’) and a quasi-rigid core of the subcrustal
mantle (III ‘). The main part of the lower crust
(II) - that is, the crustal asthenolayer - shows
ductile properties which may be described by a
creep law (Kriby, 1983). The lower quasi-viscous
lithosphere (III) is a tradition to the mantle
asthenosphere.
The profile of the generalized strength for a
normal oceanic lithosphere has a similar character
(Fig. lb). Here, the lower serpentinite layer of the
oceanic crust is analogous to the crustal
asthenolayer (Raleigh and Paterson, 1965;
Lobkovsky et al., 1986). Note that each particular
profile of a generalized strength (limiting shear
stress) varies considerably from region to region as
the heat regime and tectonic strain of the media
vary (for instance, as the rates of various processes
change in different layers).
The present-day concepts described concerning
the rheological stratification of geological media,
distinguishing quasi-rigid and ductile layers in the
crust, are analogous to the traditional geophysical
concept of the existence of the lithosphere and
asthenosphere in the upper mantle, the concept on
which the orthodox theory of plate tectonics rests.
The understanding of the geodynamic essence of
this analogue has resulted in the fo~ula~on by
Lobkovsky (1987a,b; 1988a,b) of the pfincipaily
new concept of two-level plate tectonics. The main
idea of this concept lies in the recognition of two
main levels (crustal and subcrustal) and in the
introduction of different scales in the conventional
theory of plate tectonics. When global horizontal
motions of several thousands of kilometres (a typi-
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A TWO-LEVEL CONCEPT OF PLATE TECTONICS
345
cal scale) are described, it is the lower subcnustal
(upper-mantle) level of the system that works,
whereas the processes in the upper-crustal level
are subordinate. However, to describe adequately
the majority of the regiond te&m.ic processes, the
typical scales of which are only some hundreds of
kilometres and even less, it is necessary to turn to
the upper-crustal level of the geodynamic model
considered. Within this level, the upper brittle
crustal sublayer is dissected into individual micro-
plates and geoblocks, their dimensions being from
several hundreds to several tens of kilometres.
Such crustal blocks are capable of horizontal dis-
placements over the underlying crustal astheno-
layer relative to the mantle part of the lithosphere.
If one ignores these displacements - in the case
of relatively strong coupling of crustal blocks with
the mantle and at lesser differential stresses - it
is possible to hold to the standard plate-tectonic
constructions. If differential stresses are suffi-
ciently great, as in the case of collision and con-
~nent~-~ft~g zones? the upper-crnstal layer may
move and be deformed independently, to a con-
siderable extent, on the subcrustal layer of the
system due to the developed ductile flow of the
lower crust. One such situation is illustrated in
Fig. 2. A general two-level scheme for the continental c&&ion
of India and Eurasia (after Lobkovsky, 19 8a; see text
for
explanation). I - Upper brittle crust; 2 = lower ductile crust;
3 = subcrustal Lithosphere; 4 = mantle asthenosphere; 5 =
thrust-type (convergent) crusti boundaries; 6 = strikaslip-type
(transform) txustal bounties; 7 = she-ax- elo@ity distributio+x
ill a cross-section of lowex crust; 8 = direetioll of sllbcrustal
lithosphere movement; 9 = subduction zone.
Fig. 2: the continental collision of India and
Eurasia (Lobkovsky, 1988a,b). This shows the
mosaic of the upper-crustal microplates, the rela-
tive
displacements of which are determined both
by the indentation of the Hindustan to Eurasia
boundary (at crustal level) and by the dragging of
crustal blocks by the mantle part of the litho-
sphere7 which is slipping beneath the crust. It is
also determined by the flow of the lower crust
caused by the above-mentioned process. As a re-
sult of the viscous flow of the lower crust, its
material may be forced (injected) into the vicinity
of the suture zone, thus causing thickening of the
lower crust and formation of the roots of the
mount~s and isostatic uplifts of the territory.
The present paper not only gives a quantitative
analysis of the collision process (according to the
scheme mentioned above) (Lobkovsky, 1988a,b;
1990; Khain and Lobkovsky, 3990), but also con-
siders how a two-level concept of plate tectonics
can be applied to some geodynarnic problems. It
describes the evolution of passive continental
margins and the formation of rift zones at their
rear (Lobkovsky, 1989; Lobkovsky and Khain,
1989); it gives the general scheme of continental
rifting at two levels and analyses the geodynamic
behaviour of the crust within cratons with regard
to the ‘~erosion-sedimen~tion-rnet~o~~srn-
flow in the lower crust” rnate~~-circula~on cycle
(Lobkovsky, 1989); finally, it considers some his-
torical aspects of two-level evolution of the litho-
sphere.
Geological-geophysical grounds and general ideas
of a two-level, plate-tectonic concept
First, we briefly consider the factual data that
provide evidence for a two-layered (in first ap-
proximation) rheological structure of the Earths
crust. The results of deep seismic studies, by pro-
jects such as COCORP (Allmendinger et al., 1987),
ECDRS (Choukroune and Garridq 1989) and
EUGENO-S (h4eissner et al., 1987), have allowed
their authors to determine a fine-layered structure
of the lower continental crust. We believe that
such a stratification probabIy originates from the
horizontal flow of ductile mater&I in the Iower-
crustal asthenolayer.
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346
L 1. LOBKOVSKY AND V.I. KEKCHMAN
Considerable progress has been achieved in in-
strumental seismology in the past decade. As a
result, the accuracy with earthquake hypocentres
can be determined has increased by one order of
magnitude (Chen and Molnar, 1983). From the
studies that have been carried out, it turns out that
the hypocentres of continental earthquakes are
predominantly concentrated in the uppermost 20
km of the crust. The lower layer of the continental
crust, which is 15-20 km thick, is virtually
aseismic; earthquake foci appear again only in the
subcrustal horizons of the upper mantle in active
tectonic regions of the Earth. Thus, the lower
Continental crust can be considered to be an
aseismic layer (Chen and Molnar, 1983; Meissner,
1985; Jackson, 1987) and this verifies its astheno-
spheric nature.
A comparison of the observed distribution pat-
terns of earthquake hypocentres in the lithosphere
and the temperature field in the crust and upper
mantle, made for various regions of the Earth, has
shown that seismicity within the continental crust
is limited by about the 3SO” C isotherm, whereas
seismicity in the upper mantle is controlled by the
700 o C isotherm (Chen and Molnar, 1983; Wiens
and Stein, 1983). The temperatures mentioned
correspond to the transition from a quasi-brittle to
ductile deformation regime for the geomaterial of
the crust (at
- 350 o C) and mantle (at - 700 0 C)
obtained in laboratory tests (DeRito et al., 1986;
Jackson, 1987).
The observed pattern of the distribution of
seismicity serves as independent evidence for the
rheological stratification of the Earth’s crust into
the lithosphere and asthenosphere. Note that the
correlation between the heat regime of the litho-
sphere and the character of seismicity in one re-
gion or another allows us to draw conclusions on
the lateral variability of the properties of the
crustal asthenosphere; and on the changes in its
thickness, effective viscosity, etc. in particular.
It follows from a proposed pattern of plate
tectonics (Lobkovsky, 1988a) that the process of
isostatic equilibrium should occur at two levels at
least; namely, at the crustal and hthosphe~c levels.
As for the lateral scales of isostatic compensation
of several tens (or perhaps hundreds) of kilo-
metres, the main role is played by the crustal
asthenosphere, this being verified by analysis of
local isostasy on the continents (McAdoo, 1985).
When the scale is increased to several hundreds of
kilometres, the mantle asthenosphere acquires an
important meaning. The given supposition of a
two-level isostatic compensation is verified by
analysing the isostasy of each particular region.
On the basis of such an analysis, it is possible to
show which part of the isostatic compensation is
taken up by the crust (it is usually 70%) and how
much remains in the mantle lithosphere and
asthenosphere (Artemjev and Kaban, 1987).
The rheologieal statification of the crust and
lithosphere is verified by numerous geological data
concerning their tectonic layering in each particu-
lar region &nipper and Ruzhentsev, 1977; Peive
et al., 1983; Ranalli and Murphy, 1987). Extensive
granite-gneiss allochthons with displacement am-
plitudes of hundreds of kilometres, in the Alpine
belt, Appalachian Mountains and other fold belts,
are the direct geological evidence for the occur-
rence of the lower-crustal asthenolayer (Cook et
al., 1979; Hsii, 1979; Peive et al., 1983).
We shall now formulate some general state-
ments initially proposed by Lobkovsky (1987a,
1988a) which complement the plate-tectonic ap-
proach to a two-level pattern. At each level we
distinguish a geodynamic system with its own
ensemble of plates (~croplates) which, generally
speaking, do not coincide. This is the principal
difference in the proposed model from the ortho-
dox plate-tectonic concept. The system of plates
and microplates of the upper-crustal “deck” coin-
cides with the orthodox plate-tectonic concept (Le
Pichon et al., 1973; Zonenshain and Savostin,
1979). The tectonic system of the lower (mantle>
floor of the lithosphere can be explained by the
occurrence of a quasi-rigid subcrustal layer III’
(Fig. la) dissected into large plates, the size of
which is on the scale of thousands of kilometres.
They are dissected by boundaries of three types, in
a similar manner to the orthodox concept, namely
divergent, convergent and transform.
If these plates and the boundaries between
them coincide (the character of motion included),
the plates may be considered as a monolith and
their boundaries as a common one. In this case,
we can use constructions of conventional plate
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A TWO-LEVEL CONCEPT OF PLATE TECTONICS
341
tectonics: this is true for the most part of the
oceanic lithosphere, since in the oceans, the
governing behaviour is that of the lower subcrustal
lithosphere with a quasi-rigid “core” III’ (- 20-
40 km thick), which is considerably thicker and
stronger compared to the brittle overlying basalt
crust (3-5 km).
If the plates (and their boundaries) of the upper
and lower floors do not ocincide, a more complex
two-level model of tectonics originates, where
various motions of crustal plates (blocks) are pos-
sible relative to each other and relative to the
mantle part of the lithosphere (due to the flow of
a ductile lower-crustal layer). The collision scheme
for such motions is shown in Fig. 2.
A two-level tectonic structure is most distinct
in the continental regions where, in contrast to
oceans, the total strength and thickness of the
upper-crustal brittle layer and the quasi-rigid sub-
crustal core of the lithosphere are comparable. In
this connection, a problem arises as to how to
single out individual plates of the lower level
under the continents, the boundaries of which do
not coincide with the traditional ones.
As for the divergent plate boundaries of the
lower level, it seems most logical to attribute them
to the extensive linear zones of basaltic (alkaline
and tholeiitic) magmatism (Milanovsky, 1975),
which usually occurs long before the rifting in the
system at the upper level and which produces a
complete splitting up of the plates in the tradi-
tional sense. So, for instance, it is known
(Razvalyaev, 1984) that during the past 800 Ma
intrusions of alkaline basalts happened many times
(at around 770-450, 290, 185, 120 and 80 Ma)
along the East African rift system. The periods of
basaltic magmatism alternated with the periods of
secondary alkaline-granitic magmatism (570-450,
185 and 50 Ma) (Razvalyaev, 1984). In addition to
the East African rift system, a spatial coincidence
of the linear zones of alkaline magmatism with rift
structures has been revealed in the Gardar prov-
ince (Greenland), the St. Lawrence rift, the Baikal
rift zone and a number of others. In many cases,
such magmatism occurred before not only the
Cenozoic but also the Mesozoic rifting.
In the framework of a two-level plate-tectonic
concept, it is natural to consider such prolonged
linear zones of alkaline magmatism as divergent
plate boundaries in the lower level. It is difficult
to trace these boundaries through the entire area
of the continents, as the magmatism attributed to
them is not always exposed on the Earth’s surface;
for example, due to the compression regime in the
upper level of the system. As an example of a
divergent plate boundary in the lower level, we
can draw a linear belt extending from the North
Sea to the Lower and Upper Rhine grabens, to the
grabens of the Seine and Rh&e, then continuing
through the Mediterranean (Tunisia strait, grabens
in Pantelleria and Malta), further on into Africa
to the Gulf of Guinea, and along the Cameroon
line into the South Atlantic. The East African rift
system and the East Asian system from Anadyr
Bay to Tungting Hu Lake in Southern China may
be attributed to the same category of divergent
plate boundaries (Lobkovsky and Khain, 1989).
As in orthodox plate tectonics, the divergent seg-
ments of plate boundaries in the lower level might
be connected by lower-layer transform segments,
although there is little direct evidence of this.
The convergent plate boundaries of the lower
level usually occur in collision belts where in-
tracontinental subduction processes develop. Ex-
amples are the Alpine-Himalayas zone of sub-
crustal subduction (Fig. 2) and possible in-
tracontinental subduction beneath the Rocky
Mountains during the Laramide orogeny. As a
rule, lower-level subduction is not marked by mid-
dle- and deep-foci earthquakes, although rare ex-
ceptions occur in individual segments with a nar-
row frontal part (Calabria, Hindu Kush, etc.). The
aseismic behaviour of such subduction zones can
be explained first by the fact that cold hydrated
crust is not subducted, as in the case of the
oceanic plates and, second, by the considerable
frictional heating of the subducted lithosphere (this
mechanism will be considered in detail below).
The aseismic regions of convergent plate
boundaries in the lower level can be revealed using
seismic tomography data. The inclined high-veloc-
ity layers and the Q-factor correspond to such
zones (Spakman, 1986). Post-collisional granitic
magmatism generated by frictional heating may
serve as a geological indicator of collisional sub-
duction (Debon et al., 1986; Lobkovsky, 1988a;
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34x
1, I. LOBKOVSKY AND V.I. KEKCHMAN
Khain and Lobkovsky, 1990; Kerchman and
Lobkovsky, 1990b).
The two-level concept of plate tectonics poses a
general problem, how to recognize the plate
boundaries of the lower layer using the mass of
complex geological and geophysical data availa-
ble, including gravity field, heat flow and geo-
chemical information (in particular, the zones of
mantle helium).
The possible structure of divergent plate
boundaries in the lower layer may be predicted by
analogy with the central parts of slowly expanding
mid-oceanic ridges (Lobkovsky, 1989). Thus, they
should show a bilaterally symmetrical inhomo-
geneity of the subcrustal Lithosphere thickness. An
example of a divergent plate boundary in the
lower level may be the asthenospheric bulge under
the Sayan-Baikal arch uplift and its northeast and
southwest extensions (Rogozhina and Kozhevni-
kov, 1979; Logachev and Zorin, 1988). Another
example of a divergent boundary in the subcrustal
layer is an extension of an anomalous mantle
bulge from the Rio-Grande rift into the inner
parts of the North American continent. In con-
trast to the oceanic divergent boundaries, which
are characterized by extension only, crustal struc-
tures of both extension (Baikal rift) and compres-
sion (the Mongolian Altai, Han-hai, the Gobi AI-
tai and Eastern Sayan) can be located over the
divergent boundaries of the lower level. Within the
African continent, the latter may be represented
by a considerably thinner subcrustal lithosphere
(Fairhead and Reeves, 1977; Kazmin, 1987).
As has been noted above, the divergent
boundaries of the lithospheric lower layer are part
of the global system of plate boundaries. In par-
ticular, they continue from the continental to the
oceanic regions and vice versa. The continuation
of the East Pacific Rise under the crustal layer of
North America in the Basin and Range Province
and the ‘“Cameroon line” that continues the is-
lands of the South Atlantic into the lower-level
extension boundary under West Africa are typical
of this feature (Lobkovsky, 1989).
Plate bound~es of the subcrustal layer seem to
be as stable in time as the principal boundaries of
large oceanic plates, i.e. mid-oceanic ridges and
subduction zones. They can change due to changes
in the mantle convection regime, and also due to
large-scale geodynamie processes which occur at
both levels of the lithosphere (collision, for in-
stance).
A two-level plate-tectonic model allows us to
incorporate the principal mechanisms of rift prop-
agation (Co~tillot, 1982; Martin, 1984). In par-
ticular, the propagation of rifts from oceanic basins
to the upper-crustal layer of continents may be
due to a pre-existing divergent boundary in their
lower layer.
This new view of the plate tectonics of the
lithosphe~c lower layer allows us to consider hot
spots within the continents as zones where mag-
matic activity is localized at triple junctions of
divergent and transform lower-level boundaries,
where the quasi-rigid layer of subcrustal litho-
sphere is completely absent. Examples of such
isolated points are Yellowstone Park in the U.S.A.,
and the volcanic areas of Tibesti, Darfur and
Achaggar in Central and Western Africa (Lobkov-
sky, 1989). The tectonic evolution of the Earth in
the earliest historical stages (Archean and Pro-
terozoic) is of great interest. At present, the majot-
ity of researchers believe that plate-tectonic
processes began on the Earth as late as in the
Proterozoic (Khain and Mikhailov, 1985; Khain
and Bozhko, 1988). According to the concept de-
scribed above, the plate-tectonic regime may begin
when a general cooling of the Earth occurs, the
intensity of mantle convection decreases and, as a
result, a continuous subcrustal layer is formed in
the lithosphere. The quasi-rigid core of the lower
lithospheric layer prevents chaotic motion and
decouples the previously formed massifs of sialic
protocrust from the unsteady convective flow of
the mantle. Such “capturing” of individual proto-
crustal blocks by the lithospheric lower layer may
explain the formation of stable cratons and con-
tinental cores. The mosaic pattern of Archean
permobile tectonics may be explained by the lack
of a quasi-rigid frame in the lower level. Similar
conclusions can be reached about the oceanic
proto-crust. This concept of the evolution of the
Earth’s tectonic regime from a hot chaotic state to
an organized plate-tectonic one by the formation
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A TWO-LEVEL CONCEPr OF PLATE TECTONKS
of a continuous lower-level “skeleton” (frame)
may be applied to the evolution of all terrestrial
planets.
We note that in a two-level plate-tectonic model
the main driving forces are applied to the plates of
the lower level, either by coupling of subcrustal
plates with convective mantle flows or by a “pull-
ing” effect that works on the subducted mantle
parts of these plates or, finally, by spreading of
anomalous mantle and “ridge push” (Forsyth and
Uyeda, 1975; Cloetingh and Wortel, 1985; Seki-
guchi, 1985). The forces driving the upper-crustal
layer are determined by their coupling with the
plates of the lower level; they also may be con-
nected with inhomogeneities of crustal thickness
and density. One other special aspect of the two-
level model is that plate interactions at the crustal
level play a greater role in the geodynamics of
crustal blocks and microplates than the corre-
sponding plate interactions at the lower level.
Mechanical aspects of the two-level plate-tectonic
model
To analyse the mechanical problems which arise
in two-level tectonic processes, we first consider
briefly some aspects of the rheological behaviour
of the continental lithosphere under various con-
ditions and strain regimes. The ductile flow law
derived experimentally for crustal and upper-man-
tle rocks at high temperature is:
t=Ar”exp[-Q/R(T+273)]
(1)
where P is the strain rate, 7 = u1 - a3 is twice the
shear stress, T is the temperature in *C; and A, n
and Q are material constants depending upon the
composition, structure and water content of the
rocks (Kirby, 1983).
In Figs. 3a and b are presented (a) the modified
curves of generalized strength (limiting stress) for
different temperature regimes and (b) the non-ho-
mogeneous strain-rate dist~bution in sublayers of
viscous flow that correspond to real tectonic regi-
mes; for instance, to the slip of a lithospheric
subcrusml layer during intr~ntinental subduc-
tion. This difference from the idealized curves
(solid lines, Figs. 1 and 3) should be taken into
account when analysing each particular geody-
namic situation qu~titatively.
Strmgth
I 60
%
4
80
.
”
b
st rain rote
Fig. 3. Model strength profiles of continental lithosphere with
a 15 km thick granitic upper crust and a 25 km thick mafic
lower crust: (a) for different temperature regimes correspond-
ing to g-therms with heat flows of 45 mW/m’ (solid line) and
60 mW/m* (dashed line); (b) for ho~~~us (solid line) and
non-homogeneous (dashed line) strain-rate distribution in the
lithosphere (dotted line).
We now consider some mathemati~l models in
which the main role is played by ductile flow of
the material in the lower crust due to changes in
its thickness.
Consider a two-dimensional mathematical
model in which the x axis is oriented along the
dominantly horizontal motion and the z axis is
oriented vertically upwards (Fig, 4). We assume
that there is a viscous deformable asthenolayer
(II) of the lower crust, with varying thickness,
which is overlain by an elastic-brittle upper crust
(I) and underlain by a horizontally moving
quasi-rigid plate (III’) of the lower level. For
simplicity, we ignore the bending rigidity of the
upper layer (I) and assume it to be non-deforma-
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350
L.I. LOBKOVSKY
AND V.I. KERCHMAN
Fig. 4. Main layers interacting with each other within the
framework of the two-level plate-tectonic concept (see text for
explanation). I = upper brittle crust; 2 = lower ductile crust;
3 = subcrustal quasi-rigid lithosphere.
ble in a horizontal direction. If we assume a
Newtonian viscosity of layer (II) and local iso-
static compensation of the crust (due to a rather
rapid response of the subcrustal lithosphere), the
equation for the evolution of the lower-crustal
thickness h is (Lobkovsky, 1988a):
- ; (Uh)
where K = (pM -
&~cg/lh.m; P,,., ad pc are
the densities of the mantle and crust, respectively,
g is the acceleration due to gravity, q, is an
effective mean viscosity of the crustal lower layer,
and U is the horizontal velocity of the subcrustal
part of the lithosphere relative to the upper-crustal
layer. We consider this in greater detail in the
Appendix.
When the behaviour of the lower crust follows
a more realistic rheological law (1) with index
n = 3, the equation of the evolution of the layer in
an isothermic approximation for a fixed sub-
crustal basement is (see Appendix):
Here:
/3=bB
Pc(Ph4 - Pc)g
3
PM
1
(3)
(4)
where
B = I
exp[ - Q/R(T + 273)] and
b
is a
normalizing factor that depends on the behaviour
of the upper crust: when this layer is horizontally
rigid (flow “under a cap”), b = l/80; when the
upper layer is fractured and blocks of the upper
crust can move freely in a hotintal direction,
b = l/S (Kerchman, 1990).
In the following sections we shall consider
mathematical models of particular geodynamic
processes, using eqns. (2) and (3).
A two-layer collision model at an intrawutiuental
subduction zone
According to orthodox plate-tectonic theory,
the mountain fold belts of the Earth are formed
by the collision of large continental plates and by
the accretion of smaller crustal blocks (terranes) in
zones of lithospheric convergence (Dewey and
Bird, 1970; Ben-Avraham et al., 1981; Zonenshain,
1986). Various mechanisms for crustal thickening
and uplift of mountain areas have been proposed:
namely, frontal compression, shortening and
warping of the crust and lithosphere (Dewey et al.,
1988); partial subhorizontal subduction of one
continental plate under another to cause a
mechanical doubling of the crust (Powell and
Conaghan, 1973); penetration of rigid continental
“indentors” (Adria, Arabia and Hindustan) into
the elastoplastic (Molnar and Tapponnier, 1978)
or viscoplastic (England and McKenzie, 1982;
England and Houseman, 1986) body of an ad-
jacent plate (Eurasian lithcsphere); and various
types of piling up and delamination of the crust
(Oxburgh, 1972; Bird, 1978; Hsti, 1979).
Although the above-mentioned models each
have their own merits and may accurately describe
certain aspects of collision belts, they do not ex-
plain some important special features of their
structure and evolution. For example, they do not
explain the data on thickening of the continental
crust due to accretion of its lower layer (Giese,
1980; Choukroune and Garrido, 1989), the high
geothermal gradient of collision belts (Artyush-
kov, 1979; Morgan and Sass, 1984), post-collision
granitic magmatism (Debon et al., 1986), or the
lower convergence rate of continental blocks in
the collision zone in comparison with that of the
lithosphere plates which carry them (collision of
Hindustan with Eurasia; Trifonov, 1987). As yet,
there is no explanation for phenomena such as the
absence of mid- and deep-focal earthquakes in the
greater part of the Alpine-Himalayas collision
belt, although the entire geological history of the
Tethys closure (Sborschikov, 1988; Kazmin et al.,
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A TWO-LEVEL CONCEFT OF PLATE TECTONICS
351
1986 and the recent data from seismic tomogra-
phy (Spakrnan, 1986) provide evidence for sub-
duction of the lithosphere under Eurasia.
A new model of continental collision was
worked out by Lobkovsky (1988a,b). It arises from
the assumption of two-level plate tectonics, by
which the above aspects of the structure and
evolution of collision belts are explained (Fig 2).
The traditional analysis of the plate-tectonic
evolution of the Alpine-Himalayas belt is based
on the assumption of a mosaic pattern of litho-
spheric microplates (- 100-200 km thick) and on
the standard kinematic models (McKenzie, 1972,
Zonenshain and Savostin, 1979). In contrast to
this approach, the two-level plate-tectonic model
(Fig. 2) supposes that the microplates that we
observe at the surface are of crustal origin and
may move relative to the mantle part of the litho-
sphere, undergoing large rotations and non-elastic
deformations. Palaeomagnetic data actually give
evidence of remarkable rotations of microplates
and blocks in the process of collision (Klootwijk
et al., 1986).
In accordance with this new approach (Bird,
1978; Lobkovsky, 1988a,b), at an early stage in
the collision between continental plates (preceded
by subduction of the oceanic part of the plate,
which carries a “climbing” continent; Hindustan,
for instance), a sharp reduction in the convergence
velocity of the upper brittle layer of the crust
occurs. The mantle part of the lithosphere con-
tinues to move and to subduct under the forces of
convective “dragging” and “pulling” of the sink-
ing edge of the plate (Figs. 2 and 5).
At the same time, an intensive shear flow
evolves in the lower plastic layer of the crust. This
Fig. 5. Two-lewl model of mountain formation in the wmsse of
continental collision (after Lobkovsky, 1988a; see text for
explanation).
flow embraces one area after another (squeezed
between the upper crust and mantle part of the
lithosphere) as the front of deceleration of the
upper crust advances toward the inner parts of the
overriding subcontinent. This propagation of the
deformation front in the crust can be described by
Elsasser’s equation (Lobkovsky, 1988a). Non-elas-
tic compression of the upper crust in the vicinity
of a suture zone is manifested as a system of
thrusts that form the front of the developing
orogen. The principal agent of crustal thickening
and regional uplift is the pumping of the plastic
material of the lower crustal layer into the vicinity
of the subduction zone by the movement of the
underlying mantle part of the lithosphere (Figs. 2
and 5). A similar model of the detachment of
subducted lithosphere from the crust in a colli-
sional orogen, but with a different crustal thicken-
ing mechanism, is considered in papers by Mat-
tauer (1986) and Dewey et al. (1988).
Consider a quantitative analysis of this ap-
proach (Lobkovsky,
1988a; Kerchman and
Lobkovsky, 1990b). Changes in thickness h of the
lower-crustal layer in the approximation of New-
ton quasi-isomers rheology are described by
eqn. (2). The co-ordinate system moves with the
conventional non-deformed upper crust of the col-
liding continent (India, for instance) (Figs. 2 and
5). The slip rate U =
U, of the subcrustal litho-
sphere relative to the upper crust increases from
zero, starting from the moment of detachment
after the first collision phase (which is manifested
by frontal compression thrusts and a slight thick-
ening of the crust), as shown in Fig. 6b.
The following parameter values were assumed
in order to solve eqn. (2) numerically: pc = 2.8-2.9
g/cm3 (for the lower crust), PM = 3.3-3.35 g/cm3
and nc = (0.3-1.5)
X
lo*’ Pa s; therefore K =
(0.5-3) X lo-’ km-’ yr-‘. Time variations in the
rate of slip have been adopted to correspond with
the conditions of the intracontinental subduction
of the lower layer of the Indian plate (Fig. 6b).
In Fig. 6a are shown calculated curves for the
subsequent thickening of the lower-crustal layer
from the moment when the shear flow started.
Thus, the total crustal thickness (its brittle upper
layer is 18-25 km thick) increases to about 70 km
after a time of 40 Ma in the collision zone, which
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352
L I LOBKOVSKY AND V I KERCHMAN
IO
20
30 40
t , Ma
time
Fig. 6. (a) The curves of succe.ssivehickeningof the lower ductile crust in the wurse of continentaJcolIisionobtained by numerical
simulation; values near the curves denote post-collision time in Ma. (b) Time dependence of subduction velocity of subcrustal
litbosphere elative o the upper crust since the beginningof the collision. See text for explanation.)
agrees well with data on the crustal thickness in
the Himalayas. The typical lateral dimension of
such an area with thickened crust (formation of
the Himalayas and Tibet “roots”) is 600-700 km,
corresponding well with the actual area of isostatic
uplift of the territory.
The calculated asymmetry of relief about the
suture zone, which implies a steeper topography of
the frontal erogenic area, a considerably more
gradual slope at its rear, and the existence of a
collisional plateau, is more pronounced in the
calculations when the non-linear viscous rheologi-
cal model of eqn. (1) and the evolutionary equa-
tion (3) are used. In Fig. 7 is shown the evolution
of a collisional plateau due to the northward prop-
agation of the material “pumped” under the orog-
eny.
We should mention that the model described
above is based on the principle of local isostasy
bending rigidity of the lithospheric lower layer
(III’) should be included in estimates of the
isostatic subsidence of the subcrustal part of the
lithosphere under the load of a thick crust (Karner
h.
km
L
L
I
1W 200 300 400 ml
600
X.km
dlstonce from orogen ax,s
Fig. 7. Succe&on of the cakzuiated urves showiiq the evolu-
tion of a collision rdateaa values near the curves denotina
(see eqn. (Al) in the Appendix). In reality, the
post-colliSionime n Ma.
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A TWO-LEVEL CONCEPT OF PL4TE TECTONICS
Fig. 8. Thermal scheme of a three-layered lithosphere witbin an
intracontinental subduction zone, based on the model of con-
tinental collision (see text for explanation). 1 = Granite upper
crust; 2 = “basalt” lower crust, 3 = olivine subcrusti litho-
sphere; 4 = direction of subduction; 5 = horizontal velocity
distribution in the layered lithosphere; 6 = frontal thrusts.
and Watts, 1983; Lyon-Caen and Mohmr, 1985).
Therefore, the above dynamic model of a colli-
sional orogeny should be generalized to include
quasi-elastic bending of the hthospheric lower
layer (III’) under the influence of a thickening
crust. With such a model it would be possible to
study the dynamics of the formation of foredeep
basins, and to have a more realistic view of the
theoretical history of uplift.
We shah now analyse the thermal regime of the
crust and subcrustal lithospheric layer in the zone
of a continental collision, using the above geody-
namic model and considering the additional factor
of dissipative heating of the media. Assuming that
all displacements are horizontal, we consider a
tw~~~ion~ thermal model of a three-layered
lithosphere that includes a “granite” upper layer
of the crust (I), 0 G z B h,(x), a “basalt” lower
crustal layer (II), kl (x)gz G k2(x), and an
olivine subcrustal part of the lithosphere (Fii. 8;
Taylor and McLennan, 1985). Taking into account
the motion of the lower layers (the upper layer of
the crust is assumed to be locked and therefore
stable), dissipation in the ductile layer of the lower
crust and radioactive heat generation in the crust
lead to the following non-stations
heat conduction:
aT
2
a+fi
37 =‘I ax2
(
ar2
1
+Q,=P -z/M
wP)1
O
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354
lL.l. LOBKOVSKY AND V.I. KERCHMAN
km further beneath the Himalayas and Tibet; Fig.
8). The thickness of the “granite” layer was as-
sumed to increase from 12.5 km in the south to 20
km in the north.
The rheological parameters of the rocks com-
posing the deformable “basalt” crustal layer were
taken from experimental data on diabase (Kirby
and Kronenberg, 1987): n = 3.4; A = 3 x lo6
GPa-” s-’ and Q = 260 kJ/mol in the tempera-
ture range from 400 to 800°C and at strain rates
from 10-‘4-10-‘3 s-i.
The temperature distribution in a “normal”
continental lithosphere (Morgan and Sass, 1984;
Taylor and McLennan, 1985) was taken as the
initial state. These temperatures were held con-
stant for the entire period of the modelling process
at the boundary of the study area. Numerical
estimates were made using an explicit finite-dif-
ference scheme with steps of Ax = 6 km; AZ = 2.5
km, At = 0.05 Ma. The numerical analysis de-
scribed here used the following parameter values:
X, = 2.5 W/mK,
(pc,,), = 3 x lo6 J/m3K,
X, = 2 W/mK,
(PC,), = 3 x lo6 J/m3K,
X, = 3.5 W/mK, (PC,), = 4 x lo6 J/m3K,
Q,=2X10e6 W/m3;
qb = 0.5
x
1O-6 W/m3.
In Fig. 9 is shown the evolution of the calcu-
lated geotherms (for 30 Ma) of the plastic flow
developed in the lower crust, with the relative
velocity of the subcrustal lithosphere given by Fig.
6b. It can be seen that the temperature in the
lower-crustal layer increases to 680-700 o C as a
result of dissipative heating. The mantle heat flow
is screened by the anomalously hot lower crust,
leading to temperature increases in the mantle: in
the adjacent 10 km thick layer of the subcrustal
lithosphere, for t = 15-20 Ma, the increase is 80-
150’ C (up to 700-750” C) and, below that, it is
40-80” C (up to 750-800” C). Thus, the litho-
sphere subducted under the Himalayas is already
heated to 700-800” C in its upper part, and so
brittle rupture does not occur in the zone of high
shear strain (Molnar and Chen, 1983; Jackson,
1987). This may explain the aseismic behaviour of
this entire intracontinental subduction zone. Mid-
c
km
Fig. 9. Calculated lithosphere gmtherrns for different times
since the beginning of the collision. I = Initial geotherm; 2 =
geotherm for 10 Ma; 3 = geotherm for 20 Ma; 4 = geotherm
for 35 Ma.
depth and deep-focal seismicity may occur in some
regions of a subducted lithosphere due to some
local underheating (for instance, because of the
sensitivity of the dissipation process to rheological
properties of the media, or because of the ex-
istence of more brittle lithosphere as a result of
water release during deserpentinization of the sub-
siding parts of the oceanic crust (Lobkovsky et al.,
1986).
The estimated dissipative heating of the lower
crust is sufficient to generate collisional and post-
collisional magmatism, since the melt temperature
for damp (hydrous) granites at depths of 15-25
km is 650-700°C (S&mid and Wood, 1976;
Dobretsov, 1980; Reverdatto and Kalinin, 1980;
Taylor and McLerqmn, 1985).
We note that for a period typical of a continen-
tal collision, i.e. 30-50 Ma, the thermal dis-
turbance in the lower crust has only a slight effect
on the surface heat flow. Nevertheless, the high
mean heat flow of Hinchrstan (especiaRy in the
north; &I&, 1985) may he a result of dieraipative
heating of the media; local variations caused by
various types of radiogenic heat release in the
surface crystal layer and by other factors are not
considered in this paper.
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A TWO-LEVEL CONCEPT OF PLATE TECTONICS
Geodynaniics
,of
passive tlwghw taking
into
account te49onic flow of the lower crust and sub-
lithosphere
3nombm mantle
The general features of the genesis of passive
margins have been explained within the frame-
work of the classical theory of plate tectonics (Le
Pichon et al., 1973; Burke and Drake, 1974). How-
ever, certain details of their structure and evolu-
tion cannot, as yet, be explained sufficiently well.
In particular, these phenomena are (1) the forma-
tion of elongated uplifts on the continents, parallel
to passive margins (Ollier, 1985); (2) the existence
and evolution of a system of rift zones at the rear
of passive margins (Milanovsky, 1976; Ziegler,
1982); (3) the process of tearing away of crustal
blocks (such as microcontinents and terranes) from
large continental massifs - a process which, in
fact, is the opposite of accretion tectonics (Sengor,
1984; Vink et al., 1984; Kazmin, 1989); and (4)
the occurrence of a belt of crystalline basement
(100-200 km wide) with an anomalous P-wave
velocity of about 7 km/s between the ~ntinent~
slope and normal oceanic crust (Emery and
Uchupi, 1984).
The two-level geodynamic model of the evolu-
tion of passive continental margins proposed by
Lobkovsky (1989) and Lobkovsky and Khain
(1989) explains the features listed above qualita-
tively. We shall consider this model briefly and
then describe the evolution of passive margins
within its framework quantitatively. To a first
appro~mation, the spreading of the ~thosphere
subsequent to the process of continental rifting
leads to the formation of passive margins. This
spreading is determined by the interaction of the
four main layers of the crust and upper mantle,
namely (I + II’), (II), (111’) and (M), which
were described in the Introduction (Fig. la;
Lobkovsky, 1989).
An accumulation of anomalous mantle first
occurs under the pre-rift uplift during the exten-
sion of the ~thosph~e. This accusation results
in the breaking through of a portion of partially
melted mantle into the crustal level of the geody-
namic system. Thus, a typical continental rift
structure develops that includes upper subcrustal
(IV) and lower sub~~osphe~c (V) lenses of
mf @2 @j-j@ m4 loo;;lS /36 B7
Fig. 10. Successive stages of rifting and spreading processes:
(a) continental rifting; (b) initial stage of ocean spreading; (c)
mature stage of ocean spreading (after Lobkovsky, 1989).
I = Upper brittle crust; 2 = lower ductile crust; 3 = subcrusti
lithosphere; 4 = anomalous mantle; 5 = normal mantle; 6 =
owau crust; 7 = sediments (see text for explanation).
anomalous mantle (Fig. lOa). The size of the
former lens is several tens or hundreds of kilo-
metres, whereas that of the latter is, at first, several
hundreds of kilometres; later, in the stage of ac-
tive spreading, becoming thousands of kilometres.
The appearances of a subcrustal diapir of anoma-
lous mantle and related additional local extension
and heating of the crust lead to thinning of the
lower plastic layer of the crust due to the outflow
of its material off the rift axis, resulting in an
&static near-axial subsidence. The development
of extensional fissures and normal faults in the
brittle upper layer of the crust that forms the
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356
L.I. LOBKOVSKY AND V.I. KERCHMAN
structure of the rift graben can be observed (the
lower crust and anomalous mantle propagating
under the peripheral zones of the rift lift their
“shoulders” simultaneously (Fig. 10a). Thus, the
dynamics of the crustal layer governs this system’s
interaction with the subcrustal mantle lens: the
sublithospheric anomalous mantle causes an uplift
of the terrane and acts as a feeding chamber for
the upper subcrustal lens.
Continental rifting is completed by extreme
thinning of the lower crust and rupturing of the
upper brittle layer, which is also considerably
thinned by that time. A final stage of developed
spreading follows this one. In the final stage, the
separated parts of a continental plate move away
from each other and undergo further evolution
(Figs. lob and c).
The previously cited theoretical papers devoted
to the evolution of the continental passive margins
are mainly concerned with the problem of vertical
subsidence due, first, to the cooling and densifica-
tion of anomalous mantle preserved under the
crust (Artyushkov, 1979; Meissner and Kopnick,
1988) and, second, to accretion of a “heavy”
oceanic lithosphere “brazed” onto the continental
lithosphere along the line of the prime rupture
(Sorokhtin, 1979). Note that the subsidence of the
basement of the passive margin is enhanced by the
additional loading of a rapidly accumulating sedi-
mentary cover (Cloetingh et al., 1984), whereas rift
expansion and subsidence of a continental edge is
accompanied by the development of listric faults
(Le Pichon and Sibuet, 1981, Kazmin, 1987).
In addition to the phenomena described above,
within the passive transitional zones from conti-
nents to oceans, new processes arise that are in-
duced by horizontal motions in various directions
of the media in the upper and lower levels of the
heterogenous system illustrated in Figs. lob and c.
The main process at the lower level is the propa-
gation of a large lens of sublithospheric mantle
away from the axis of a mid-oceanic ridge, which
is usually accompanied by “dragging” through
convection. The formation of wide swells along
passive margins seems to be connected with this
process. It occurs about 30-100 Ma after the
onset of relative spreading (Lobkovsky and
Khain,
1989).
We now consider a quantitative model of this
phenomenon (Figs. lob and c). The equation de-
scribing the evolution of a rheologically homoge-
neous layer of anomalous mantle with variable
thickness h and viscosity na (which is consider-
ably less than that of the over- and underlying
media) reduces to eqn. (2) in view of the observed
isostatic condition (Artyushkov, 1979; Lobkovsky,
1988a).
The coefficient of eqn. (2), K = pM -
Pa)Pag/12Plvrnla, where pM and p, are the densi-
ties of the normal and anomalous sublithospheric
mantle, respectively. Typical values of the parame-
ters are as follows: plLl= 3.4 g/cm3, pM -
Pa =
0.1-0.5 g/cm3; and the viscosity qa of anomalous
mantle is - lo’* Pa s. For the coefficient
K we
thus have an estimate K = (l-5) X lo-’ km-’
yr-‘.
First consider the simplest model problem,
which ignores the convective motion of the sub-
lithospheric mantle (this motion seems to be im-
portant only in a narrow belt, several hundreds of
kilometres wide, along the margin). In this case, if
the axis x is oriented horizontally towards the
motion of the anomalous mantle and the reference
point x = 0 is located under the crest of the coastal
slope of the margin, eqn. (2) is valid only if x >, 0.
Using the equation:
-=KK-
(6)
we solve the problem of the propagation of the
anomalous mantle lens beneath the continent, sub
ject to the boundary condition that its thickness is
constant at x = 0.
hl,_,,=H, hl,=,=O
(7)
We choose an initial condition that represents the
early stage of the under-flow of a localized massif
of anomalous mantle, its width being I, = 100-200
km:
(usually H =
50-80 km,
the dimension of a study
area S being 2500-5000 km; see Fig. 1Oc).
The solution of eqn. (6) with such initial condi-
tions is characterized by a finite rate of propa-
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ATWO-LEVELCONCEI'TOFPLATETECTONICS
I 1
I
/
I
I
Q
I‘? A4
d6 A8 mc
Fig. 11. Graph of the function f(t) for a self-similar asymp-
totic law of anomalous mantle lens propagation.
gation of the frontal boundary of the disturbed
area X(t) (Barenblatt, 1980). The boundary con-
ditions (7) permit self-similar “intermediate”
asymptotics, such as:
h=f fW, E= -
Substituting (8) into eqn. (6) we obtain an
ordinary differential equation for the function
f 5):
the conditions being:
fl
+,=l
and
f
It_co=O
(10)
Here to = lim, _ f0
X(t)/dKH3tl
so that f I ,to
= 0; the function d f 4/dc should be continuous at
the point t = &, to satisfy the flw-continuity con-
dition of anomalous mantle.
A plot of the numerical solution
of this
boundary-value problem is presented in
Fig. 11.
To estimate the time of propagation
for the
351
anomalous mantle front at a distance L, from the
edge of the continental margin, we use the
asymptotic law of propagation of the front:
t=o %Li/~H~
(11)
When
H =
70 km (which agrees with an isostatic
uplift of S = 2 km) and uplift width L, = 1200
km, we have (for K = 0.15 km-’ Ma-‘) I* = 30
Ma.
The general solution for the full eqn. (2) has
been obtained by an explicit finite-difference
scheme. This method permits us to consider a
non-stationary boundary condition at the left-hand
edge of the study area, reflecting, for instance, a
local thinning of an anomalous mantle lens due to
the subsidence of an oceanic plate margin under
the increasing load of accumulating sediments.
The initial form of the protruding massif of
anomalous mantle under the continental margin is
assumed to be:
ho(x)=
i
Hew[-0.2(x/H)2], O~XGI,,
0, l,
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L.I LOBKOVSKY AND V.I. KERCHMAN
The evolution of the anomalous asthenospheric
layer beneath the continent is presented in Fig. 12.
The self-similar law (11) is a good description of
the propagation of the lens for a time t > 10 Ma.
Thus, the flow of anomalous mantle in the
lower level of the system uplifts the edges of
continental passive margins, and lags considerably
behind the primary rifting (Lobkovsky and Khain,
1989; Kerchman and Lobkovsky, 1990a). As flow
beneath the continental passive margin reaches
maturity (Fig. lOc), the margin undergoes various
vertical motions: (1) gradual uplift as a wide
marginal swell is formed as a result of the flow of
asthenospheric matter under the continent
(another competing uplift mechanism may be con-
nected with thermal erosion of the lithosphere
basement, its thinning and isostatic uplift); and
(2) very sharp, large-amplitude, subsidence which
occurs in a much narrower belt, caused mainly by
the cooling and compaction of the upper lens of
anomalous mantle, probably accompanied by
phase transitions of the basalt-eclogite type
(Artyushkov, 1979).
The two main mechanisms presented cannot
completely explain the evolution of continental
passive margins within which, in accordance with
a two-level model of plate tectonics (Lobkovsky,
1989; Lobkovsky and Khain, 1989), one more
geodynamic process affecting the development of
its structure should occur. This is the flow in the
lower ductile layer of the crust within a continen-
tal margin at the spreading stage (Bott, 1972)
(Figs. lob and c). Such a flow, from the continent
towards the ocean, starts when the continental
crust splits. By that time, as was mentioned earlier,
both layers of the continental crust in the rift zone
are already considerably thinned. When the conti-
nents begin to move apart, the ductile lower crust
at the edge of the continental margin tends to be
squeezed out towards the ocean, as it is subjected
to an uncompensated horizontal loading. Taking
into account isostasy on the mantle surface, the
outflow of the non-linear viscous material of the
lower crust towards the ocean can be described by
the evolution equation (3) of the “Mechanical
aspects” section, derived in the Appendix.
Let us consider the problem of a self-squeezed,
semi-infinite layer of the lower crust when it is
I
I
I
I
I
I I
-\
,
-42 -60
-48 -46 -44
-42 a 42
44 E
Fig. 13. Oceanward and continent-ward propagation of a lower
crust thickness inhomogeneity on a continental passive margin.
(a) Numerical solution (values near the curves are time in Ma).
(b) Asymptotic self-similar solution: I, for unfractured upper
crust “cap”; 2, for dissected upper-crust cover of the “tongue”.
(See text for explanation.)
able to propagate horizontally after the continents
start to move apart; that is, under conditions such
as:
H, xx> -1, (hl,i,
h(,=,=O, hl,,_,=H
A numerical solution of the problem of the
flow for H = 18 km, /I = 10e9 kmP3 yr-’ and a
small initial wedge or “ tongue” (I, = 5 km, I, = 10
km) is shown in Fig. 13a. For longer times (t 2 20
Ma), the propagation of the “tongue” towards the
ocean and the depression front towards the conti-
nent are well described by the asymptotic self-sim-
ilar solution (Kerchman and Lobkovsky, 1990a):
h=Hf(E),
E= “-“‘:,a
(BH7f)
where function f satisfies the equation:
4;r;i
fS
3 3++-J
[ i
)I
(15)
in the domain &, f 5) = 0 and for t < t2,
f(E) = 1 (corresponding to an undisturbed state of
the media into which the depression wave propa-
gates at a finite rate). Moving towards the con-
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A TWO-LEVEL CONCEPT OF PLATE TECTONICS
59
tinental interior, such a front captures new por-
tions of the lower crust in accordance with the law
’
,=W t)
‘/4, from which it is seen that the
expansion of the flow of the lower crust decel-
erates sharply with time. The function f(t) is
given in Fig. 13b. Its construction is described in
Kerchman (1990).
The above analysis of ductile flow in the lower
layer of the crust predicts the appearance of ten-
sional stresses in the more brittle layers of the
overlying “granite” crust and underlying rigid
lithosphere. These tensional-stress maxima de-
velop in the vicinity of the disturbed wavefront as
it propagates towards the continental interior. The
maximum tensional stress in the upper brittle layer
of the crust is estimated as:
1
I
x2
e=-
d
rdx
x1
I Pch - P&( If2 -q
%.&
,
h1= Wx,) 07)
where d is the thickness of the upper, mechani-
cally strong layer of the brittle crust; X, is the
section separating the non-fractured part of the
brittle crust from the frontal, oceanward “frac-
tured” area, including the zone of listric faults
(Figs. 14a and b); and x2 is the continent-ward
km
b
Fig. 14. Structure and presumable evolution of continental passive margin: (a) North Atlantic passive margin, Flemish Cap bank
(after Emery and Uchupi, 1984); (b) model pattern of passive-margin dynamics (after Lobkovsky, 1989) (see text for explanation).
I = Synrift sediments; 2 = post-rift sediments; 3 - upper “granitic” crust; 4 = lower “mafic” crust; 5 = subcrustal lithosphere;
6 - anomalous mantle fens; 7 = normal mantle (asthenosphere.); 8 = fractured zone in subcrustal lithosphere; 9 = lower-crustal flow;
10 = filtration in partially melted astbenosphere. (Values on the upper figure denote P-wave velocities in different layers.)
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MO
L 1 LOBKOVSKY AND V 1. KERC’HMAN
front of the flow propagation in the lower crust.
For
d =
8-10 km, H = 15-20 km and h, = 5-10
km, the mean tensional stress in the upper crust
reaches u = 20-40 MPa. A long-term tension of
this size seems sufficient to cause brittle rupture of
the upper weaker part of the crust (Sawyer, 1985)
rifting, and the formation of faults and effective
“removal” of the blocks of the upper crust ocean-
ward (Fig. 14).
The proposed rifting mechanism operates
through the lateral inhomogeneity and rheological
stratification of the crust within the transition
zone. It seems natural to attribute to it the ob-
served evolution of rift structures that are sub-
parallel to continental passive margins - near the
continental slope, in the early stages of ocean
opening, and at the rear of the transition zone in
the later evolutionary stages (Fig. 14b). The same
mechanism acts throughout the geological history
of a passive margin, causing the splitting and
subsequent break-off of continental blocks from
the margins of large continents (Vink et al., 1984;
Lobkovsky and Khain, 1989).
An obvious result of the creep-propagation
model of the lower-crustal “tongue” is the ap-
pearance of a layer of anomalous basement rocks
with a P-wave velocity of about 7.0 km/s (typical
of the lowermost continental crust) in the transi-
tion zone between the continental slope and nor-
mal oceanic crust (Lobkovsky and Khain, 1989).
It is clear from seismic cross-sections of the con-
tinental passive margins that such an anomalous
rock layer does, in fact, underly sediments in the
transition zone, occupying a belt about 100-200
km wide (Emery and Uchupi, 1984). Geochemical
data also exist which provide evidence for the
continental origin of the lower crust in the transi-
tion zone of passive margins, even in cases where
the upper-crustal layers are composed of basalts
(Morton and Taylor, 1987). The model presented
also explains the quiet magnetic field in this tran-
sition zone (Boillot, 1983).
Once local fracturing and the formation of a
fault structure have occurred in the upper crust,
the boundary conditions on the top of the ductile
lower layer change. In particular, it shifts to the
regime of a quasi-free horizontal displacement of
the top boundary, leading to changes in the effec-
tive coefficient in equations of the type (2) or (3).
The coefficient ratio becomes /?,//? - 10 for the
fractured, oceanward-moving tongue (see the Ap-
pendix). This, in turn, causes an approximately
double acceleration of the flow under the newly
fractured part of the brittle crust, and the effective
transport of the corresponding block toward the
ocean, as well as substantial thinning of the dis-
sected crust at the rear of the block and the
consequent formation of a sedimentary basin there
(Figs. 14a and b). The scheme described thus
causes a discrete sequence of events: when the
previous oceanward block of the upper continen-
tal crust is faulted off, a new cycle of preparation
for the subsequent rifting stage starts within its
continent-ward part. According to the above anal-
ysis, the first stages of marginal rifting (at an early
stage in the ocean opening) often break off “small”
blocks such as the Blake plateau, the Flemish Cup
bank, the Rockall plateau, the Vijring plateau, the
San Paulo plateau, the Exmouth plateau and
others. When the “squeezing-out” of the lower-
crustal layer decelerates (due to the cooling and
blocking of the front of the tongue), the flow wave
propagating toward the continent behind decel-
erates. As the pressure gradients on the roof of the
lower crust decrease, a strain sufficient for rifting
accumulates at considerably greater distances from
the continental edge and over the considerably
greater time of hundreds of millions of years. This
time can, for instance, even exceed the duration of
one Wilson cycle in the Atlantic. The graben
systems of China and the Rhine, the Labrador rift
zone and others may be due to this process of
rifting at large distances from the ocean. Very
often, such distant rift zones are located in ancient
weak sections of the subcrustal lithosphere (or of
the crust), especially along suture zones (Vink et
al., 1984; Dunbar and Sawyer, 1988). The ad-
ditional tension of a quasi-rigid subcrustal litho-
spheric core, caused by the flow of the lower crust,
might reactivate the lower-level plate boundaries
(in particular, transform and suture boundaries
might change to divergent).
This might cause complete splitting up of the
lithosphere through formation of a divergent litho-
spheric boundary in the lower level. This may
occur long before the rupturing of the crust. The
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A TWO LEVEL CONCEPi OF PLATE TECTONICS
361
possibility of the complete disintegration of the
continental lithosphere and a jump of an oceanic
spreading axis to a new position at the continental
margin arises when the above rifting rn~h~srn is
superimposed on the general (“background”) ten-
sion of the lithosphere. Such a background tension
may be created by horizontal flow in the astheno-
sphere and/or by a pull due to a subduction zone
on the opposite edge of the oceanic part of the
plate (Bott, 1982). This situation may have oc-
curred during the structural evolution (destruc-
tion) of Gondwanaland, when a powerful horizon-
tal mantle flow (from the south to the north) and
the “pulling” of a subducted oceanic part of the
plate under Laurasia, together with the continu-
ously acting mechanism of the marginal continen-
tal rifting, caused the onset of new rift zones at
the northern boundary of the Gondw~a super-
continent. This mechanism may even have caused
the subsequent break-off of blocks of microconti-
nents, lithosphere terranes and corresponding
jumps of the spreading axes to a new southward
position (Sengiir, 1984; Kazmin, 1989; Lobkovsky
and Khain, 1989).
We note that the problem of the structure and
evolution of passive continental margins has been
studied extensively in the past decade. Various
models for passive margins have been developed,
particularly: models of different types of crustal
and lithospheric extension (McKenzie, 1978; Le
Pichon and Sibuet, 1981; Beaumont et al., 1982;
Wernicke, 1985; Lister et al., 1986); models incor-
porating a different rheology of the upper and
lower parts of the continental crust during the
extension (Bott, 1971, 1982; Meissner, 1985);
“ volcanic” models of the continental margins
(Royden et al., 1980; Mutter et al., 1988; Meissner
and Kiipnick, 1988); models of isostasy of passive
margins (Karner and Watts, 1982); thermomecha-
nical models of the evolution of passive margins,
taking sedimentation into account (Cloetingh et
al., 1984) and others. All of these models consider
various aspects of the structure and evolution of
passive margins, many aspects of which may also
be interpreted within the framework of the pro-
posed two-level scheme.
Modei fur ~~ q~-sy~ extension
of
the continental lithosphereand some featuresof
rifting
We now consider several aspects of continental
rifting from the viewpoint of the two-level plate-
tectonic model. A great deal of attention has re-
cently been devoted to the problem of the out-
crops of ultramafic mantle rocks on the Earth’s
surface (oceanic bottom) as a result of the com-
plete tectonic denudation of the continental crust
during rifting. In fact, the data show the existence
of anomalous ophiolitic sequences in which the
basalt layer and dyke complex are completely
missing, where oceanic sediments directly overlie
serpentinized peridotites which are sometimes as-
sociated with gabbro. Such incomplete ophiolitic
sequences are typical of the Ligurian segment of
the Mesozoic Tethys and occur, for instance, in
the Alps, Apennines and Corsica (Lemoine et al.,
1987). A similar anomalous structure of the oc-
eanic crust has been seen in a few places on recent
continental passive margins; particularly, on the
Galicia Bank and in the North Atlantin (Boillot et
al., 1987) on Zabargad island in the Red Sea
(Bonatti et al., 1986), and on the Sardinia passive
margin in the Tyrrhenian Sea (Lemoine et al.,
1987), where serpentinites or peridotites have been
found beneath sediments by deep-sea drilling.
These data suggested to some geologists that, at
least in the early stages of ocean opening, a special
geodynamic regime exposed the ultramafic base-
ment between diverging blocks of the continental
lithosphere (Boillot et al., 1987; Lemoine et al.,
1987). A model of the splitting and asymmetrical
divergence of continental lithosphere along a gen-
tle, through-going fault has been proposed to ex-
plain the formation of rather extended segments
of oceanic bottom (now composed of se~ent~iz~
peridotites) at divergent plate boundaries. This
model was first introduced by Wernicke (1981) in
an analysis of the tectonic situation in the Basin
and Range Province in the western U.S.A., and it
has subsequently been widely used for various
schemes of rifting (Wemicke, 1985; Lister et al.,
1986).
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362
From the standpoint of mechanics, one cannot
ignore the fact that in the Wemicke scheme the
postulated complete fracture of the lithosphere
along the single, gently dipping fault contradicts
the entire sum of our knowledge of the rheological
stratification of the crust and lithosphere. It seems
more realistic to suppose that the fracture and
deformation of the various layers of the crust and
lithosphere in the course of the rifting occur
according to the particular flow laws acting in
each layer.
Another purely mechanical objection to the
Wernicke scheme arises from the fact that the
lithosphere cannot bend sharply without sec-
ondary faulting during the normal slip of the
adjacent walls of the fixed inclined fault. As early
as 1958, Heiskanen and Vening-Meinesz, in their
L..l LOBKDVSKY AND V.I. KkKCHMAN
fundamental work, showed that during crustal ex-
tension, for instance, a second fault appears due
to the elastic bending of the crustal layer and
results in the formation of a graben structure. It
follows from this argument that even if we assume
an initial fracture of the lithosphere in accordance
with the Wemicke model - a single, gently dip-
ping fault - the further development of extension
would follow another course (see below) and would
be determined mainly by the appearance of an
additional fault in the lithosphere and by the
motion of a lithospheric block cut off by it (Us-
sami et al., 1986).
We now describe a new model of the develop-
ment of continental rifting, proposed by Lobkov-
sky (1989). This scheme is guided by the estab-
lished rheological and tectonic stratification of the
b
d
Fig. 15. Two-level model of continental rifting: successive stages (after Lobkovsky, 1989).
1 =
Upper brittle crust; 2 = lower ductile
crust; 3 = subcrustd lithosphere; 4 = asthenosphere; 5 = volcanics. (See text for explanation.)
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A ‘IWO-LEVEL CONCEPT OF PLATE TECTONICS
lithosphere. Derived from general mechanical con-
siderations and from the results of physical mod-
elling of the extension of an elastic-plastic litho-
sphere floating on a liquid basement (Shemenda,
1984) this model postulates that the loss of stabil-
ity and strain localization in the quasi-rigid mantle
core of the lithosphere would cause the formation
of two conjugate inclined shear planes. These shear
planes bound a central subcrustal lithospheric
block of a wedge-like or of a trapeziform geome-
try, which would rise under the influence of the
applied system of forces and squeeze the viscous
material of the lower-crustal layer away the axis
(Lobkovsky, 1989) (Figs. 15a and b). This, in turn,
would cause thinning of the crust (neck-forma-
tion), as well as additional extension and isostatic
subsidence of the upper brittle layer. It is im-
portant to stress that in this scheme the material
flow that leads to the thinning of the lower ductile
layer of the crust is induced not so much by the
external tensional force applied to the crust but by
the squeezing effect of the rising mantle block
(Fig. 15b).
Unlike the majority of the proposed schemes
(McKenzie, 1978; Le Pichon and Sibuet, 1981), in
this theory the crust is thus not subject to uniform
363
extension during continental rifting. This permits
us to explain the observed discrepancy between
the degree of extension of the crust, determined
from the system of faults, and the estimates of the
extension of the crustal layer derived from its
thinning and the isostatic subsidence of the surface
(Artyushkov, 1988). In fact, the analysis of the
structure of recent and ancient large depressions
within continents shows that in the majority of
cases crustal rifting involves extensions of only
several percent, whereas the thinning of a con-
solidated crust determined from seismic data is
50-lOO’%, i.e. approximately one order of magni-
tude greater.
Let us consider the above-described model in
detail, highlighting the principal stages of rifting
(Lobkovsky, 1989). These stages, which are char-
acterized by the occurrence of two inclined fault
planes, dipping from the axis of the future rift,
and formed in the mantle part of the lithosphere
during its extension, are illustrated in Figs. 15a-c.
As extension increases, a trapeziform block of
subcrustal lithosphere, bounded by fault planes,
begins to move upward under the influence of the
non-u~fo~y applied stresses (Fig. 16). This
movement was verified by physical modelling ex-
b
II..*....
. . . . . .
* - . . . . , . s .
. . . . . . . .
Fig. 16. Rift scheme for cakulation of (a} balanceof forces and (b) uplift amplitudeof the axial sub~~phe~ block {see text for
explanation). I = Weight of the axial block 1rl; 2 = upper brittle crust; 3 = lower ductile crust; 4 = subcrustal lithosphere;
S = asthenosphere.
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364
I..1 LOBKOVSKY AND V.I. KFKCHMAIU
perimems, taking similarity criteria into account
(Shemenda, 1984).
The qualitative explanation of this phenome-
non is as follows. When the ~thosphere blocks Z
and ZZ move away from the central block ZZZ see
Fig. 16a), the average pressure on its inclined
planes AB and CD drops and, as a result of the
buoyancy force applied to the base of block ZZZ, t
becomes unbalanced. A subsequent drop in the
pressure, transmitted from the overhanging parts
of blocks I and ZZ, as they move away, occurs due
to their own elasticity.
Let us consider the uplift of block ZZZquantita-
tively and estimate its ultimate amplitude. We
assume that block ZZZ protrudes into the plastic
layer of the lower crust by an amount Ah. Then
the total hydrostatic pressure on the base of the
block equals:
where ZZ, and H, are the thicknesses of the crust
and of the mechanically strong subcrustal part of
the lithosphere, respectively; p, and p, are their
densities; 1 is the width of the upper surface of the
uplifted block; and a is the inclination of the side
planes of the block (Fig. 16a). The weight of block
ZZZ per unit of length in the plane, perpendicular
to the figure) is p&Z 4 H, cot cu)ZZ,; the pres-
sure on its upper plane is p,g(ZZ, - Ah)Z. The
vertical component of the pressure of the over-
hanging lithospheric blocks Z and ZZ on the side
planes of block ZZZcan be calculated as:
[2p,H,H, - pc(Ahj2 -t P&Z,,, - Ah)‘] g cot a
i-2
J
Hm-Ah(r - Ao cot a) dt
0
where the first term of this expression contains the
pure hydrostatic part of the forces, whereas the
second term reflects the deviation from the hydro-
statics on the side planes of block ZZZ n the lower
quasi-rigid lithospheric layer due to (a) the drop
Au of pressure transmitted from the overhanging
regions; and (b) the friction r along the inclined
faults. From the balance of forces applied to block
ZZZ and its weight, it is seen that at Ah = 0 (the
initial state after the inclined faults are formed;
see (Fig. 16a) the net force affecting block ZZZ is
negative (oriented upward), if the following condi-
tion is satisfied:
Aa > 7 tan cy
It should be noted that the magnitude ha is
proportional to the geomaterial strength up to its
fracture, whereas r has the meaning of a residual
shear strength; then from eqn. (19) it follows that
the uplift of the block may start when the angle a
is not very large, i.e. approximately 0 2 60 ‘.
On the other hand, angle LT annot be too small
(as is assumed in the Wemicke model; Wemicke,
1981); hence, if angles (Y are small, bending of
relatively extended near-fault parts of blocks Z
and ZZof a quasi-rigid lithosphere begins to play a
main role, and this would cause the secondary
faulting of the lithosphere. Such secondary faults
are proposed in the paper by Ussami et al. (1986).
Let us estimate the ultimate amplitude of the
uplift of mantle block ZZZ. First we note that, as
the block uplifts, friction 7 in the faults would
decrease due to the frictional heating of the media
and other factors. Ignoring friction 7 at the ma-
ture uplift stage of the block and assuming the
magnitude of Aa being approximately equal to the
mean strength a, of a quasi-rigid subcrustal litho-
sphere, we would write the condition of the force
balance as:
2u,( ZZ, - Ah) cot IY=
Apg[iAh + (Ah)2 cot CY]
(20)
where Ap = pm - pc.
For typical values of the parameters which are
used in eqn. (20) (Ap 5=0.4 g/cm3, g = lo3 cm/s*,
I = 20-30 km, a* = 100-300 MPa, ZZ,,,= 30-50
km), we have the uplift amplitude of block Ah -
lo-25 km. This means that, in the course of
rifting, a mantle block may be uplifted to the base
of the upper brittle layer of the crust. When a
quasi-rigid mantle block is uplifted, it squeezes
aside plastic matter of the lower crust, the flow of
which - in turn - causes additional extension of
the upper brittle crustal layer (Fig. 15b). Thus,
non-uniform extension of the crust occurs and its
lower ductile layer undergoes almost complete de-
nudation, whereas the upper brittle layer is ex-
tended and becomes thinner, although only by
several percent (Lobkovsky, 1989).
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A TWO-LEVEL CONCEPT OF PLATE TECTONICS
365
If the lithospheric extension ceases at
this stage,
a structure typical of a continental depression of
rift origin is formed, which has a sharply thinned
consolidated crust and a slight extension on its
surface. Some large aulacogens within continents
seem to have been formed according to this model.
Another situation is possible when much more
extension of the upper brittle layer of the crust
leads to its complete splitting. This may lead to an
exposure of mantle rocks directly on the bottom
surface of the opening oceanic basin (Fig. 1%).
Thus the proposed model may explain the ex-
istence of mantle rocks on some parts of the
oceanic bottom which correspond to the initial
stages of the ocean’s formation (in particular, on
passive continental margins). From this stand-
point, the Ligurian ophiolites seem to be attri-
buted to a rather narrow oceanic basin of the type
described.
An important consequence of the described
non-magmatic model of continental rifting is as
follows. Since the uplift amplitude of the mantle
block is proportional to the thickness of the
quasi-rigid core of a subcrustal lithosphere H,,
thinning of this strong core may hinder a rather
considerable uplift of the central block. In such a
case, a further divergence of lithospheric blocks I
and II cannot be compensated by the uplift of
block 111, and their adjacent sides would move
apart. The asthenospheric matter would flow into
the gaps formed as a consequence of this diver-
gence (Fig. 15d). As a result, two large channels
would be formed at the lateral sides of central
block 117, which would provide for the uplift of
the as~enosphe~c matter to the base of the crust
and further onto the Earth’s surface as alkaline
basalt outflows (Lobkovsky, 1989) (Fig. 15d).
It should be noted that the existence of mag-
matic channels along the margins of central block
111 may explain a very curious feature of rift
volcanism: the majority of large volcanoes are
usually attributed not to the central, but to the
peripheral parts of the rift zone. Powerful perip