TECTONICS, VOL. 17, NO. 6,PAGES 938-954, DECEMBER 1998
A new multilayered model for intraplate stress-induced
differential subsidence of faulted lithosphere, applied to rifted
basins
R. T. v a n Balen, Y. Y. ~ o d l a d c h i k o v , 'a n d S . A. P. L. C l o e t i n g h
Tectonics/StructuralGeology Group, Faculteit der Aardwetenschappen,Vrije Universiteit, Amsterdam
Abstract. In-plane horizontal stresses acting on predefomed
lithosphere induce differential flexural vertical motions. A
high-precision rccord of these motions can be found in the
sedimentary record of rifted basins. Originally, it was
proposed that rifted basins experience flank uplift and basin
center subsidence in response to a compressive change of inplane stress, which agrees well with observed differential
motions. Subsequently published models predicted that the
vertical motions may be opposite because of the flexural state
of the lithosphere induced by necking during extension.
However, the total, flexural and permanent, geometry of the
lithospherc underlying the rifted basin is the controlling
parameter for the in-plane stress-caused vertical motions. The
largest part of this preexisting geometry is caused by faulting
in the uppermost brittle part of the crust and ductile
deformation in the underlying pans of the lithosphere. Wc
present a new multilayered model for stress-induced
differential subsidence, taking into account the tectonically
induced preexisting geometry of the lithosphere, including
faults in the upper crust. As continental lithosphere may
exhibit flexural decoupling due to a weak lower crustal layer,
the new multilayer in-plane stress model discriminates the
geometrics of the separate competent layers. At a basin-wide
scale, the new model predicts that a compressive change of
in-plane force results in basin center subsidence and flank
uplift, confirming the original hypothesis. Compared to all
previous models, the new model requires a lower horizontal
stress level change to explain observed differential vertical
motions.
1. Introduction
Thc global stress field, inferred from, for example,
earthquake focal mechanism solutions, insitu stress
measurements, and borehole breakout analyses, has persistent
trends, which are uniform over large areas and can be
correlated to plate motions [Cloetingh and Wortel, 1985;
Zoback et al., 1989; Zoback, 1992; Miiller et al., 1992;
Richardson, 1992; Coblenn and Richardson, 1995; Lindholm
et al., 19951. The intraplate stress field originates largely from
'Now at Department of Earth Sciences, Eidgenossische
Technischc Hochschule, Ziirich, Switzerland.
Copyright 1998 by the American Geophysical Union
Paper number 1998TC900003.
0278-7407/98/1998TC900003$12.00
the integrated result of lithospheric density heterogeneities
and processes operating at plate boundaries, that is, slab pull
and ridge push lWortel et al., 1991; Richardson. 1992;
Coblentz and Richardson, 19951. Paleostress analyses (from
stylolites, fault striations, etc.) demonstrate that intraplate
stress orientations and magnitudes can change on a timescale
of a few million years [Philip, 1987; Letouzey, 1986;
Bergerat, 1987; De Ruig et aL, 1991; Csontos et al., 19911.
Futthermore, folding of oceanic [Cloetingh and Wortel, 1985;
Stein et al., 1989; Beekman et al., 19961 and continental
lithosphere [Stephenson and Cloetingh, 1991; Martinod and
Davy, 1992; W o r t and Agarwal, 19961 points to very large
magnitudes of intraplate stresses of up to several hundred
megapascals [Stephenson and Cloetingh, 1991: Cloetingh and
Burov, 19961.
In rifted sedimentary basins, a changing horizontal
intraplate stress level causes flexural subsidence and uplift, as
long as the stress level is lower than the limit defined by
strength of the lithosphere and its weakness zones (see section
6). The induced relative sea level changes are recorded as
onlap and offlap events in the basin stratigraphy LCloetingh et
al., 19851. Therefore flexural uplift arid subsidence caused by
intraplate stress level changes provide a tectonic mechanism
for sea level changes which interferes with truly eustatic sea
level changes. As a consequence, flexural deformations due to
continuously changing intraplate stress magnitudes and
directions can provide a plausible explanation for relative sea
level changes which apparently occurred during the Mesozoic
[Cloetingh et al., 19891, as inferred from (seismo)
stratigraphic data [see Haq et al., 19871. Thus far, no other
known mechanism (e.g., glaciwustasy) can sdlisPd~lorily
explain the inferred bigb-frequency Mesozoic sea level
changes [Pitman and Golovchenko, 19831, although there is
some evidence for the existence of polar ice [Ziegler, 19901.
Numerical forward modeling of thc Notth Sea basin [Kooi
and Cloetingh, 19891, the Barents Sea basin [Reemst et al.,
19941, the Beaufort-Mackenzie basin [Tang and Lerche,
19921 and the Pannonian basin [Van Balen er al., 19981 has
demonstrated that a changing level of intraplate stress can
explain the observed differential subsidence or relative sea
levt.1 changes. These rifted basins all experienced enhanced
subsidence in the basin's center in response to compression
(or a relative sea level rise) during their postrifl phase,
confnuing the predictions oTCluetingh et al. [19851.
In this paper a new model for stress-induced subsidence
and uplift in rifted basins during their postrift evolution is
yrcsented, based on recent insights inlo the rheology and
flexural behavior of the lithosphere [e.g., Burov and Diament,
VAN BALEN ET AL.: A NEW MODEI. FOR STRESS-INDUCED SUBSIDENCE
19951 and the influence of existing faults on its flexural state
[Kusznir et al., 1991; Spadini a d Podlodchikov, 19961. In
contrast to previous work on this subject, our elastic thinplate model takes into account the permanent deformation of
the lithosphere caused by extension, that is, normal faulting
and ductile deformation. As the presence of weak layers in the
continental lower crust and a more detailed shape of the
deformed lithosphere, including faults, are taken into account,
the proposed new thin-plate model also differs from the finite
element model utilized by Cloetingh et al. [1985]. Our model
is based on the elastic thin-plate approach and does not
incorporate viscoelasticity because, in general, flexural
subsidence profiles for rifted lithosphere predicted by elastic
thin-plate models are in good agreement with observations
[e.g., Wans et al., 19821. Furthermore, the values for the extra
parameters in viscoelastic thin-plate models operating on a
million year timescale are not well constrained [Watts et al.,
19821. However, if required, the approach outlined in this
paper can be applied to extend existing viscoelastic thin-plate
models wlricl~include the effecl of in-plane horizontal s k s s e s
[e.g., Lambeck, 19831.
In the first part of the paper, we outline the major
dirferences between existing models and our new model.
Subsequently, we review lithospheric flexure, with special
emphasis on decoupled flexure of continental lithosphere.
Next, our new thin-plate model for in-plane stress-induced
differential motions is outlined. Particular attention is paid to
the specific response of faulted lithosphere and its effect on
the sedimentary record. This is followed by a comparison of
the elastic thin-plate soliltion and the results of finite element
modeling. In-plane stress-induced differential subsidence
patterns are presented for several fault and basin
configuratinns. Finally, we discuss the relationship between
observed differential subsidence of the Pannonian and Noah
Sea basins and the Norwegian margin and the major fault
systems occurring in their basement.
uplift
uplift
A
A
I
v
subsidence
rn preexisting
shape
differential
subsidence
Figure 1. The effect of an in-plane force on a predeformed
elastic plate. The predeformed geometry can be flexural,
permanent, or a combination of both. Arrows indicate vettical
movements caused by the compressive in-plane force.
prdicled opposile differential ve~ticalmotions for the same
stress change, w e n in the abseuce of a sediment load. This
completely different result was attributed to the lateral
variation in plate thickness by Cloetingh et al. [1985].
However, as will be shown below, the geometry of the elastic
plate is the cause for this response.
According to the thin-plate theory, a horizontal in-plane
force applied to a predeformed plate gives rise to moments,
causing additional flexural hending of the plate (Figure 1)
[Timoshenko and Woinowrky-Krieger, 19591. The momen:
equals the product of the in-plane force and the slope of the
midplane of the elastic plate. The slope of the midplane is
caused by preexisting deformation and by bending due to the
in-plane force itself. The preexisting deformation can be
permanent, flexural, or a combination of both. However,
what is the preexisting deflection of the midplane of a thin
plate representing the lithosphere of a rifted basin? This
difficulty is illustrated by the differences in published elastic
thin-plate models. Karner [I9861 applies the in-plane force
2. Previous Research
change to the preexisting deflections of the sedimentThe effect of horizontal in-plane stress variations on the
basement interface and the Mohorovicic discontinuity and
subsidence of rifted sedimentary basins was first investigated
adds the two resulting deflections to obtain a net deflection of
by Cloetingh et al. [1985], who applied a two-dimensional
the lithosphere. His justification for this procedure is that
elastic finite element model. The behavior of two different
these two surfaces represent density interfaces, which can
model sets was studied. One set of models employed a
potentially be affected by lithospheric in-plane stress.
uniform elastic layer, whose thickness was increased with age
Subsequently published thin-plate models [Cloetingh, 1988;
according to a squarc root function. The sewud set of n~odels Kooi and Cloetingh, 1992; Kamer et aL, 19931 basically all
asume that the preexisting deformation of the midplane is
adopted a laterally variable elastic thickness, representing the
basinward decrease of the effective elastic thickness inferred
caused by the flexural bending of the lithosphere due to
thermal, sediment and necking loads (Figures 2a and 2h).
for passive margins [e.g., Caldwell nnd Turcotte, 1979; Watfs
el aL, 19821. The results for the uniform elastic thickness
Pemanel~ldeformation of the lithosphere due to nor~nal
model showed that an increase of compressional in-plane
faulting in the upper crust and extension-drivcn ductilc flow
in the lower crust and mantle, which also deform the
force (stress times elastic plate thickness) causes uplift of the
midplane, is not included. Therefore, as these models do not
basin flank, contemporanous with subsidence of the basin
center, thus inducing a relative sea level change with different
incorporate all the preexistiug deformation of the lithosphere,
sign and magnitude across the basin system. In this model
the predictions of these models cannot bc correct. For basin
modeling purposes, the models of Kooi and Cloetingh [I9921
result, the magnitude of differential subsidence is controlled
by the thickness of the elastic plate and the distribution and
and Kamer et al. 119931 improve the older kinematic basin
magnitude of the applied sediment load. The finite element
evolution models by taking into account that, because of a
models employing a laterally variable elastic plate thickness
deep level of necking during extension, the lithosphere can be
940
VAN BALEN ET AL.: A NEW MODEL FOR S'IRESS-INDUCED SUBSIDENCE
rifted basin
strenath
Figure 3.
The schematic location of the lithospheric
competent layers underlying a rifted basin. On the right, a
schematic continental yield strength envelope is depicted.
Figure 2.
Predefonned shapes of the elastic thin plate
representing the lithosphere of two models proposed in the
literature and our model. (a) Predeformed shape of the elastic
plate in the first generation of elastic thin-plate models. The
predeformed shape is caused by flexure in response to thermal
and sediment loads. Consequently, the predeformed shape is
downward bend. (b) Predeformed shape of the elastic plate of
basin evolution models taking into account necking of the
lithosphere during extension. In this model, depending on the
depth of the level of necking, additional buyoancy forces
rel;dted to the necking can cause an upward bend pd~efornwd
shatx. (cj Our nreferred mcwlcl The nredeformd %haw(ifthe
elastic plate results from dcf&ation
due to -tectonic
processes and the flexural response to thermal, sediment, and
necking-related loads.
in an upward state of flexure [Weissel and Karner, 1989;
Braun and Beaumont, 1989a; Chkiy et a/., 19921. This leads
to different predictions for lithospheric thinning and heat flow
upon forward modeling of rifted basins. However, the flexural
state of the lithosphere is irrelevant in thin-plate models for
determining the response to changing in-plane forces. The
only relevant parameter is the geometry of the midplane at the
time of in-plane force changes (Figure Zc), and this geometry
is caused by many processes, including the flexural response
to necking of the lithosphere during extension. As will be
shown in section 4, inclusion of a preexisting permanent
deformation of the lithosphere, induced by extension
processes, controls the predicted deflections to a large extent.
Because of its rheological structure, the continental
lithosphere cannot be approximated by a single elastic plate.
Depending on crustal thickness and temperature conditions,
mechanical weak layers residing in the lower crust may cause
flexural decoupling between the upper crustal and subcrustal
competent layers [McNutt et al., 1988; Ranalli, 1994; Burov
and Diament, 1995; Cloeringh and Burov, 19%; Ter Voorde
et al., 19981. As these two competent layers deform
differently during extension (Figure 3), our new model fm
stress-induced deflection includes flexural decoupling. Before
presenting our model, we first briefly review the rheology and
flexural behavior of oceanic and continental lithosphere.
3. Effective Elastic Thickness and Rheology of
Oceanic and Continental Lithosphere
For an elastic thin-plate, fiber stresses resulting from
bending are zero at the plate center and increase linearly in
magnitude outward according to a gradient defined by the
Young's modulus, Poisson's ratio, and the curvature of the
plate (Figure 4a) [Timoshenko and WoinowskyKrieger,
19591. The bending moment in the plate is obtained from the
integral with depth of the fiber stresses with respect to the
midplane of the plate. The flexural rigidity D of an elastic
plate is defined as the ratio of the bending moment and
curvature of the bent plate. For an elastic thin plate, the
flexural rigidity is a function of the plate's thickness T and its
elastic properties [Timoshenko and WoinowskyKrieger,
19591:
E T ~
D=
12(1-v2)
where E is Young's modulus and v is Poisson's ratio.
However, fibcr stresses of a lithospheric plate are lir~iited
by its yield strength [McNutr and Menard, 1982; McNutr er
al., 1988; Ranalli, 1994; Burov and Diament, 19951, which
varies with depth according to Byerlee's law for brittle failure
and ductile creep laws [Kirby, 1983; Carter and Tsenn, 1987;
fiber stress
fiber stress
5
4
l?igure 4. (a) pibcr
in a bent single elastic thin
plate. (h) Fiber stress profile in a multilayer elastic thin platc
according to the decoupling model of McNun et al. [1988].
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
Ranalli, 1987; Zoback et al., 1993; Cloetingh and Burov,
19961. Therefore the bending moment in a lithospheric plate
is much smaller compared to that of an equally thick, purely
elastic plate bent to the same curvature. The observed bending
of a lithospheric plate can, however, still be used to compute
its effective elastic thickness 7,. Furthermore, T, can be
computed from the vertical stress distribution for a specific
part of the lithosphere if its rheological state and curvature are
known [Burov and Diament, 19951. Although u~uallynot
considered when T, is computed, scresses from other sources
than bending contribute to yielding of thc lithosphere (i.e.,
thermal stress, in-plane stress, etc.) thus limiting the
magnitude of the fiber stresses and thereforc rcducing the
value of the T, [Kooi and Cloetingh, 1992; Burov and
Diament, 1995, 1996; Cloetingh and Burov, 19961. On the
basis of observed lithospheric deflections, values for T,have
bccn determined from glacial rebound data, foreland basin
shapes, seamount-induced ocean floor deflections, bending of
subducted slabs, and the shapes of rifted sedimentary basins
[McNun and Menard, 1982; Watts et al., 1982; McNun et al.,
1988; Cloetingh and Burov, 19961; see Burov and Diament
[I9951 for an extensive overview.
For oceanic lithosphere, which is characterized by only one
mechanically strong layer, computation and interpretation of
T, is relatively straightfonvard [McNutt and Menard, 1982;
Burov and Diamnt, 19961. In contrast, for continental
lithosphere, depending on composition, crustal thickness,
temperature, and stress conditions, interpretation and
computation of T, is complicated by the possible presence of
one or more weak layers, splitting it up into several
mechanical strong parts [McNutt et al., 1988; Lobkovsky and
Kerchman, 1991; Ranalli, 1994; Burov and Diament, 1995,
19961. Such weak layers are mainly located in the lower crust
[Kirby, 1983; Carter and Tsenn, 1987; Ranalli, 1987; McNun
rt ul., 1988; Burov and Diament, 1995, 1996; Cloetingh and
Burov, 19961. Therefore the competent layers are residing in
the upper crust and upper p a t of the subcrustal lithosphere
(Figure 3). This system of two competent layers separated by
a weak layer can lead to a decoupled flexural behavior.
In the decoupled elastic thin-plate model for continental
lithosphere, originally proposed by McNutt et al. [I9881 and
extended by Burov and Diament's [I9951 leaf spring model,
the lower crustal weak layers are incapable of sustaining fiber
stresses created by bending (Figure 4b), assuming that such
stresses result in instantanuous flow of lower crust. In this
approximation the shear and horizontal stresses applied to one
of the competent layers will not be transferred to the other
competent layer [Burov and Diament, 19961, and lower
crustal shear allows for flexural slip between the upper crustal
and subcrustal competent layers. Owing to limited lower
crustal flow, the vertical motions of the competent layers are
assumed to be the same, that is, the competent layers behave
as a single flexural system. The total rigidity of the decoupled
system is given by the sum of the separate rigidities of the
competent layers. Therefore the total T, of a decoupled system
is given by LMcNun et al., 1988; Burov andDiament, 19951:
(1)
where h,, h , ..., h, is elastic thicknesses of the n separate
competent layers.
94 1
The rigidity of a decoupled system is much smaller than
the rigidity of a welded system of the same thickness bent to
the same curvature. Therefore the decoupling model can
explain that the T, of the lithosphere is generally larger than
the theoretical T,of the crust alone but is smaller than the sum
of crust and subcrustal T, [Burov and Diament, 1995,19961.
The rheological state of the lithosphere controls whether or
not the crust and the subcmstal lithopshetic mantle are
~nechanicallydecoupled, it depends mainly on the thickness
of the crust and the thcrmal stnte of the lithosphere. For old
(cold) lithosphere, the critical thickness is about 35 km, which
coincides with the average crustal thickness. ' h i s suggests
that most of the continents are in a decoupled mode [Burov
nnll Dinment, 19961. About 75% of observed continental T,
can bc explained by flexural decoupling [Burov and Diament,
1995, 1996: Cloetingh and Burov, 19961.
4. New Stress-Induced Differential Subsidence
Model
The preexisting deformation of an elastic thin plate affects
the response of the plate to a change in the magnitude of the
in-plane force [Timoshenko and Woinowsky-Krieger, 19591.
For a single elastic plate an increase in the amount of the farfield in-plane force amplifies the existing bend w,, whereas a
decrease of force will flatten it. The flexural response is given
by [Timoshenko and Woinowsky-Krieger, 19591
where w is force-induced deflection, F is in-plane force
change, D is rigidity, p, is density of asthenosphere, pa, is
density of material filling in the depression (sediment and
water) and g is gravitational acceleration. In the derivation of
(2), w, repxsents the preexisting shape of the midplane of the
thin platc bcforc the forcc is applied [Timoshenko and
Woinowsky-Krieger, 19591. The preexisting defamation can
be permanent, elastic, or a combination of both. The total
deflection of the midplane is given by ( w + w, ).
In the decoupling model, however, the lithosphere consists
of two or more superimposed elastic thin plates. This can he
accounted for in the flexure equation hy noting that each
elastic plate carries p a t of the total in-plane force applied to
the lithosphere [Cloetingh and Burov, 19961. Each of these
separate forces acts on a deformed midplane, with the shape
of the preexisting deformations differing between the
individual plates forming the composite beam. For example.
the stress-induced deflection for a continental lithosphere
consisting of two elastic plates, one residing in the upper crust
and one residing in the upper subcrustal mantle, is described
by the following equation:
+ w(Pm - Ptill)8 = 0
(3)
where D is rigidity of decoupled elastic plate system, Fc is inplane force change in the crustal layer, Fm is in-plane forcc
change in the lithospheric mantle, w, is preexisting deflection
of crustal midplane, w,,, is preexisting deflection of subcrustal
mantle midplane and w is deflection of the lithosphere caused
942
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
by the in-plane force. Assuming an elastic response and no
stress relaxation in the fibers, Fc and Fm can he related to the
total force F acting on the lithosphere and the thicknesses of
the upper crustal and subcrustal competent layers:
F m h= F A
Fc=- h
h,+ h,
hc+hm
where h, is uppercrustal competent layer thickness and h,, is
subcrustal fiber thickness.
An approximation for the shape of the preexisting
deformation of the crustal elastic plate is given by the
basement topography. However, the basement topography
must be corrected for erosion which is likely to take place
during the synrift and early postrift phase of the basin,
particularly in the area of the rift shoulders. As the midplane
is located about halfway between the upper and lower
boundary of the upper crustal competent layer, it is displaced
downward by half the magnitude of erosion (i.e., the bottom
of the layer is not modified by erosion):
w, = hwement topography + erosion amount / 2
The topography of the Moho discontinuity is probably the
best approximation for the shape of the preexisting
deformation of the subcrustal flexural midplane, as it is
located close to the strongest part of the mantle lithosphere
predicted by rheological modeling using yield-strength
envelopes [e.g., Cloetingh and Burov, 19961. For basin
nrodding purposes, both the Moho and the basement
topography have the advantage that they can be observed and
mapped on deep-seismic profiles.
In the twolayer mudel, the flexural effect of a change in
the magnitude of an in-plane force depends on the curvature
of the midplanes of the lithospheric competent layers. As
outlined above, those parts of the continental lithosphere
contributing to its flexural strength are mainly located in thc
upper crust and the uppermost part of the subcrustal mantle.
During extension processes, these parts are permanently
deformed by extensional brittle faulting and ductile flow. As
demonstrated by the results of deep seismic profiling
[Holliger and Klemperer, 1990: Bois, 1993; Posgay et al.,
19961, dynamic models for lithosphere extension [Zuber and
Parmentier, 1986; Braun and Beawnont, 1989b; Bassi et al.,
19931 and tectonostratigraphic forward modeling [Cloetingh
et al., 19951, the upper crust is generally displaced downward,
and the lithospheric mantle is displaced upward because of
lithospheric extension. Therefore the preexisting shapes of the
upper crustal and subcrustal fibers are opposite, as is the
contribution of these fibers to the total in-plane force-induced
deflection. However, on deep seismic profiles of rifted
sedimentary basins, the Moho is relatively smooth compared
to the basement topography [Holliger and Klemperer, 1990;
Buis, 19931, although subcrustal faults can also occur [Flack
et al., 1990; Posgay et al., 19961. During the posuift phase of
basin subsidence the Moho relief is reducing because of
thermal subsidence. Moreover, lower crustal flow, occuning
on a large timescale, may contribute to flattening of the Moho
during the postrift stage [Kaufman and Royden, 1994; Ter
Voorde et al., 19981. If the Moho topography has a negligible
curvature, then the preexisting shape of the midplane of the
submstal competent layer contrib~~tes
little to the differential
venical motions of the lithosphere upon the buildup of in-
plane force. In contrast, the shape of the sediment-basement
interface is generally highly irregular. This shape is an
approximation for the geometry of the upper crustal
competent layer. Therefore total basinal in-plane forceinduced deflections should be largely determined by the
effects of the geometry of the midplane of the upper crustal
competent layer. As a result, an increase in compressive inplane force will in most rifted basins cause a downward
dcflcction of the center of the rifted sedimentary basin,
because the preexisting upper nustal midplane geometry is
bent downward.
As can be observed on seismic profilcs and in outcrops, the
upper crustal part of the lithosphere is permanently deformed
by discrete faults, causing a rugged hwement topography. In
fact, in rifted basins most of the deformation of the upper
crustal competent layer results h m faulting. Therefnre, at
first sight, the curvature of the upper crustal flexural midplane
locally attains extremely high values, particularly along the
rift margins which are marked by large border faults with
throws of a few kilometers. However, owing to the presence
of faults, the upper crustal midplane is discontinuous, and
therefore the curvature of the midplane is not defined at the
position of faults. A new theory is required in order to resolve
this problem.
4.1. Faulted Lithosphere and Stress-Induced Deflection
A fault in the upper crust causes an offset in the upper
crustal competent layer. For vertical loading, the iaulted
elastic plate behaves like an equally thick continuous plate
[e.g., Kusznir et al., 19911, because the loads are acting
perpendicular to the plate. As faults and fractures are
widespread in the lithosphere, this is a basic assur~rplionfor
all models dealing with lithosphcric flcxure in response to
vcrtical loading. Howcvcr, for horizontal loading the venical
offset causes an additional moment at the fault, because the
in-plane stress is tmnsmitted through the overlap zone of the
two pans of the plate which are separated by the fault. The
overlap zone, located at the fault, is narrower than the plate,
leading to a slight concentration of in-plane stress. The
horizontal in-plane stress profile in the overlap zone is not in
equilibrium with respect to the midplanes of thc two
snbplates, that is, at the overlap zone the integral of in-plane
stress with respect to the midplanes of the subplates is
nonzero. This causes a moment at the fault (Figure 5).
Seismotectonic and deep seismic reflection data suggest
that fundamental basement faults in rifted sedimentary basins
are planar and are restricted to the brittle, cold, topmost pan
of the lithosphere, corresponding to the upper crust [King et
al., 1988; Jackron and White, 1989; Kusznir et aL, 1991;
Roberts and Yielding, 1991; Van Wees et aL, 19961.
Therefore, in the model we constructed a venical fault that is
assumed to cut the entire upper crustal competent layer. The
results of finite element modeling, presented in section 4.2,
demonstrate that the assumption of a vertical fault plane does
not significantly influence the prediction as long as the fault
dip is higher than 63'. Fundamental planar basement faults
must have the largest effect on stress-induced deflections, as
they cause most of the deformation of the upper crustal
competent layer in rifted basins. However, elastic solutions
for Fdulls no1 culling the entire upper crust also exist [Savage
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
force
-- midplane
elasticplate
Figure 5.
The in-plane force-induced moment at a fault
from the
of the faulted thin plate, The
moment results from disauilibrium of the horizontal in-olane
stresses with respect to the'midplanes of the subplates.
A
and Guohua, 19851 and possibly can be extend* to include
variations in in-plane force levels.
by a faulted thin plate is
The hrfield in-p'ane force
constant. Using this balance of horizontal in-plane force and
that the
the geometry of the faulted Plate, it can be
total in-plane force-induced moment at the position of a fault
equals minus the magnitude of in-plane force times fault
offset, -F u [Van Balen and Podladchikov, 19981. Using
gmeral solutions for the thin-plate equation [e.g., Hetdnyi,
19461, ht:flexural profile caused by the in-plane forceinduced moment can bc found unalytically for several
scenarios, including variable rigidity [Van Balen and
Podladchikov, 19981. For a constant rigidity the elastic
flexural profile due to the moment is described by
w=-
Fu
4Dap
sin(xp) e-''la
B=-
(4)
where w is deflection, D is flexural rigidity, F is in-plane
force (positive for compression), u is fault displacement, a
and B are flexural parameters, Ap is density difference
between infilling and compensating material, x is 0
corresponds to the fault position, and g is gravitational
acceleration. The value of u is positive if the downthrown
block is on the left side of the fault; otherwise, it is negative.
Typical profiles predicted by this equation are presented in
section 4.2.
4.2. Finite Element Modeling
In this section, the flexural profile predicted by (4) is
compared to elastic finite element solutions. Two sets of
models are analyzed: the first set employs a 10 km thick
elastic plate, and the second set has a plate thickness of 5 km.
These values for the elastic thickness are warranted by T,
estimates from the shapes of deflections around normal faults
in rift settings [King et al., 1988; Kusznir et al., 1991; Roberts
and Yielding, 19911. Rifting processes occur at the same
timescale as in-plane stress level changes, that is, a few My
943
(in fact, rifting is caused by an in-plane stress magnitude
which exceeds the tensile strength of upper crustal
lithosphere). Furthermore, flexural bending due to normal
faulting occurs at the same spatial scale as fault-moment
bending. Therefore we assume that both normal faulting
during rifting and flexural bending due to fault moments are
controlled by the same T, (see also section 4.4).
All models apply 100 MPa far-field compression and a
fault throw of + I km, which is within the limits defined by the
yield strength of the lithosphere [Kusznir and Park, 1984;
Savage and Guohua, 19851 and values deduced from studies
on folding of oceanic [Cloetingh and Wortel, 1985; Beekman
et al., 19961 and cu~lline~ilal
lithosphere [Lambeck, 1983;
Cloetingh and Burov, 19961. Apart from thc intraplatc strcss,
applied boundary conditions are zero vertical displacement at
the lateral boundaries of the model (Figure 6). An array of
springs at the bottom of the plate simulates the buoyancy
conditions. The upper side of the model is a free surface. In
order to reduce the effect of the lateral boundary conditions,
the models have a total length of 1500 km. For some models,
the plate is not allowed to thicken under the application of
compressive stress thus mimicking the thin-plate assumption
made in the derivation of the general elastic flexure equation
[Timoshenko and Woinow,vb-Krieger, 19591.. The adopted
values for Young's modnlus, Poissonk ratio and the density
contrast between compensating
are the same for the
analytical and finite element models, that is, 7x101Upa,0.25,
and 90(1 kg
respectively. me applied density contrast is
based on the density of fresh, surlicial, hardly compacted
sediments with a density of about 1800 kg m-3 and a lower
crustal density of 2700 kg m ~ 3 ,
For the
km thick model the analytical solution is
to finite element results for models employing 1 km
by 1 km and 2 km by 2 km quadratic finite elements,
respectively (Figure 7a). Both nu&cal models predict the
same result, indicating that the element size is not influencing
the prediction. The difference between the analytical result
and numerical solutions is up to 10% at the maxima of the
flexural nrofile. The finite element model in which the date is
not allowed to thicken predicts a flexural profile which nearly
coincides with the analytical prediction. For the 5 km thick
plate Lhe analytical solution is compared to finite element
models with 1 km by 1 km and 2 km by 1 km elements,
respectively (Figure 7b). Both these models predict the same
deflection, indicating again that the element size docs not
influence the predictions. The maximum difference between
numerical and analytical solutions is now up to 14%. The
finite element model without plate thickening deviates
,,-;
6. Outline of
geometry and boundary conditions
used in the finite element
nefault displacement is
represented by a step in the upper and lower boundaries of the
plate. Vertical springs at the bottom of the plate simulate
buoyancy conditions.
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
944
analvtical solution
o
N
........
2x2kmFE
fixed dy FE
firmre 7. Comparison of analvtical predictions for deflection caused bv a fault moment to results of finite
cl&ncnt modelini employing q;adrat~i elements. The models cmploy a iaull throw of I km and an in-plane
stress ot IW MPa i l ktlobar). (3) K e s u l ~of~ 10 km thtck elastic fin~teelement model, ctn~lovineI X I km and
2x2 km sized elements and.lx1' km elements without vertical thickening compared to inaiytical prediction
employing the same horizontal in-plane stress and elastic parameters. (h) Analytical results compared to
\&ou; tinite element snlutlons for i 5 km thick plate. The numerical models inludf 1x1 km and 2x1 km si7eJ
elemenl.~, I X I km elements w~thnutvenisal thickcntng, and a fault with a dip of 63'. Scc text tior discussion.
slightly (7%) from the analytical solution. We also tested the
influence of fault inclination. As shown by the result, a
numerical model employing a 63" fault angle does no1 differ
significantly from the numerical models employing a vertical
fault plane. As predicted by the analytical solution (equation
(4)). the stress-induced deflection scales linearly with fault
throw u. T%is is confirmed hy numerical modeling: plates
with fault throws of 2 km and 3 km subjected to 100 MPa
stress predict deflections with magnitudes which are 2 and 3
times larger, respectively (in Figure 7b the resulting flexural
displacements are divided by 2 and 3). On the basis of the
numerical modeling results, we conclude that the analytical
elastic thin-plate equation (4) is accurate enough for basin
modeling purposes and that fault dip does not significantly
influence the predicted flexural profile as long as it is larger
than 63O.
4.3. Predicted Flexural Profiles for Multiple Fault
Moments and Varinble Rigidity
In-plane force-induced flexural profiles for fault systems
can be obtained by applying the method of elastic
superposition [HetPnyi, 19461, that is, by adding up the
flexural profiles for the single fault solution (Figure 8a). The
flexural profile for a moment occuning at a single normal
a half graben, was obtained by applyitig a
fault, represe~~ting
5 km.T,,
a Pdult throw of 2 km and an in-plane compression
of 100 MPa carried by the whole plate (resulting in an
in-plane force of 5x10" N m-'). As shown by (4), the
magnitude of the differential subsidet~cecaused by the fault
moment scales linearly with applied in-planc forcc and fault
displacement. Therefore the flexural profiles presented below
can also result h m a combination of larger fault throws with
less in-plane stress and vice versa. The elastic parameters
have the same values as in the previous models. The predicted
flexural profile for the half graben is characterized hy a
maxirnurn uplift of about 75 m at the footwall and an equal
amount of subsidcncc at thc hangingwall (Figurc 8a). I h e two
maxima are separated by 50 km. Therefore the slope of the
differential subsidence profile is at its steepest position equal
to 0.17'. The differential subsidence profile predicted for a
system consisting of two master normal faults dipping in
opposite directions and spaced 50 km apart, delineating a
simple rift, shows almost 150 m subsidence in the graben and
75 rn uplift at the flanks. The larger amount of subsidence in
the maben is caused bv positive interference of the two
flexGal profiles induced by h e fault moments. The maximum
slope in this profile is 0.23". A model involving a set of five
master normal faults spaced 25 km apart and having throws in
the same direction predicts a flexural profile with maxima of
140 m Figure 8c). Finally, a model combining two opposing
sets of five master faults predicts a maximum subsidence in
the graben of about 210 m and a maximum uplift at the flanks
of 170 m (Figure 8d). The maximum slope in this profile is
0.17". The resulting profiles show that closely spaced
multiple-fault systems generate positive interference, causing
enhanced compression-induced subsidence at a scale largcr
than the individual tilted fault block scale, that is, basin-wide.
945
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
I
-100 -50
0
50
,
l
,
I
,
-100 -50
100
I
,
l
0
,
l
50
I
I
100
distance (km)
distance (km)
0 0
7
-
u
-
1
1
1
-100 -50
1
1
1
1
0
50
distance (kin)
1
1
1
1
100
u
-
I
,
I
,
/
-100 -50
,
l
I
I
0
50
distance (km)
I
l
~
l
-
100
Figure 8. In-plane stress-induced differential subsidence profiles (continuous line), or relative sea level
change, for different fault combinations. Faults have tbmws of 2 km. The elastic plate has a thickness of 5 km
and is subjected to a 100 MPa compressive stress. Dashed lines indicate the faulted basement profile (vertical
scale bas to be multiplied by 10). (a) Resulting profile for a single fault. The compression induces 75 m uplift
of the footwall and an equal amount of subsidence of the hanging wall. This profile is used to construct the
predictious for the other scenarios by applying etdslic superposition. @) Simple rift with two master faults
spaced 50 km apart. Predicted footwall uplift (flank) is about 75 m;stress-induced subsidence in ihe graben
center equals 150 m. ( c ) Five faults with displacement in the same direction, spaced 25 km apan. m e
maximum uplift and subsidence are both about 140 m. The resulting differential subsidence pattern shows an
almost linear trend across the faults, with a slope of 0.16". (d) Results for two opposing sets of five faults.
Within a set, faults are spaced 25 km apart and have the same tbmw direction. The two sets are spaced 50 km
apart. The maximum of the predicted subsidence exceeds 210 m, whereas maximum uplift is about 170 m.
m e trends of differential subsidence across the fault sets are almost linear, with slopes of 0.17'.
4.4. Implementation of Fault Moment Solution
Although it is the most important part, the contribution of
fault-related moments to the differential subsidence in a rifted
basin is only part of the total response of the rifted basin to
changing far-field stresses. The shape of the m s t a l midplane
without faults and in some exceptional cases the shape of the
r~laritlemidplale (see below) also contribute. The lotal, basinwide differential subsidence pattern can be obtained by
superposition of the components conmbuting to it. The shape
of the upper crustal elastic layer without the faults is found
when the fault throws are reversed. After the fault offsets are
946
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
restored, the discontinuities in the basement profile are
eliminated and therefore the resulting shape of the upper
crustal elastic plate is differentiable. The flexural subsidence
profile due to a changing in-plane forcc can be found by using
a standard finite difference method.
For oceanic, thick, and hot continental lithospheres, (2)
should be used in combination with the fault solution (4).
because, owing to the rheological state, their flexure can be
effectively described by one elastic plate [Cloetingh and
Burov, 1996). Stress-induced deflection for an average
continental lithosphere should be calculated using (3) in
conjunction with the fault solution (4). Flexure of a thin
continentaL lithosphere underlain by normal or cold mantle is
dominated by the mantle rheology. Therefore, in this
exceptional case, the single elastic plate equation (2) should
be used, and fault moment contributions can be neglected.
The T,controlling the fault moments can be substantially
less than the T, of (decoupled) lithosphere. Values of T,
estimates from the shapes of deflections resulting from
normal faulting are about 5-10 km [King et al., 1988: Kusznir
et al., 1991; Roberts and Yielding, 19911. The timescales of
normal faulting (e.g., rifting) and fault moments are the same,
that is a few million years. Additionally, they have also the
same spatial scale. Therefore they should be governed by the
same T,. The T, of large-scale deflected, (decoupled) rifted
continental lithosphere is in the range of 10 - 20 km [Watts er
al., 1982: Burov and Diament, 19951. The low value of T, for
faulting and fault moments can be explained by
a
combination of two effects: a reduction of T, around faults
because of relaxation of fiber strcss [Kusznir et al., 19911, and
the effect of the scale of the deflection or, equivalently, by
the difference in load distribution [Ter Voorde et al., 19981:
Sediment, thermal and necking loads typically have a basinwide distribution. This causes a relatively minor pressure
gradient on the lower crustal low-viscosity channel, inducing
negligible lower crustal flow on a 10-100 My timescale.
Normal faulting and fault moments, however, produce more
localized loads and therefore cause higher pressure gradients
in the lower crust. Therefore local lower crustal flow may
provide flexural compensation for normal faulting and fault
moments. The T, for faulting and fault-moments is thus
controlled by the effective elastic thickness of the upper crust
alune. Additionally, the relaxation of fiber stress in the
vicinity of faults may cause a reduction of T, compared to the
upper crustal value [Kusmir er al., 19911.
Moho uplift (Figure 9b). The models with a flat Moho
represent a basin orginating from a deep level of necking
during extension. The models with a Moho uplift represent a
hasin which developed with an interrncdiatc depth of necking,
located in the lower crust. Each model set contains three
configurations for the total T, distribution. As the T, results
from decoupling, it can be located mainly in the upper crust
or mainly in the subcrustal mantle, or it can be about equally
distributed between the mechanically strong layers, resulting
in the same total T, according to (1). In the models,
combinations of upper crustal and subcrustal competent layer
thicknesses of 5 km and 14.8 km, 11.9 km and 11.9 km, and
14.8 and 5 km are applied.
The result for the models adopting a flat Moho show 100 to
200 m flank uplift and 180 to 240 m basin center subsidence
(Figure 9a). The model with the largest upper crustal
competent layer thickness (14.8 km) predicts the largest
amplitude of deflection.The models adopting a slight Moho
uplift predict 150 to 200 m flank uplift and 150 to 190 m
basin center subsidence, also depending on ihe competent
layer thickness distribution (Figure 9b).
For the model adopting thicknesses of 5 and 14.8 km for
the upper crustal and subcrustal competent layers,
rcspwtivcly, the separatc contributions from thc faults, the
geometry of upper crust without the faults, and the deformed
shape of the mantle to the total stress-induced deflection is
shown in Figure 9c. In this model, upon compression, the
subcrustal competent layer causes most of the flank uplift,
whereas the faults induce the basin center subsidence.
The results demonstrate that with increasingly deeper
levels of lithospheric necking during rifting the stress-induced
differential subsidence amplitude increases. Furthermore, the
total amount of stress-induced subsidence and uplift depends
on the thickness of the upper crustal competent layer, because
the total in-plane force acting in this layer is the product of inplane stress and the thickness of the layer. Finally, the models
representing a basin orginating from an intermediate level of
necking during extension predict flank uplift which is greater
than the basin center subsidence, leading to a considerable
narrowing of the basin. The flank uplift is mainly caused by
stress-induced deflection of the subcrustal upper mantle.
4.5. Predictions for Total Stress-Induced Deflection
Applying the numerical procedure outlined in section 4.3,
we have computed stress-induced differential subsidence and
uplift of a decoupled continental lithosphere for different
rifted basin scenarios. In all examples, the total T, of the
decoupled lithosphere is 15 km, and the T, for the fault
moments is 5 km. The adopted in-plane stress level change is
100 MPa compression. Elastic parameters have the same
values as in previous examples. The dcnsity difference for
lower crustal compensation is taken as 700 kg I"",
asthenospheric compenstaion is calculated adopting a dcnsity
diffcrcncc of 1300 kg m-'. Two opposing sets of five faults
are located in the upper crust; each fault has a throw of 2 km.
Two types of models are analyzed, one set has a flat Moho
discontinuity (Figure 9a), while the other set adopts a slight
5.1. Southern North Sea Basin
5. Examples of Stress-Induced Subsidence and
Uplift in Rifted Basins Related to Faults
During the Tertiary, the overall development of the North
Sea basin is characterized by subsidence rates in accordance
with the poshift development following Triassic to Early
Cretaceous rifring events [Ziegler, 1990; Kooi et al., 19911.
During late Pliocene-Quaternary times unusually rapid
subsidence and sedimentation occurred in the southern pan of
the North Sea basin, leading to a Quaternary sediment
thickness of up to 1 km (Figure 10). Since most sediments
were deposited in a shallow-water environment, this part of
the Noah Sea basin must have experienced an extremely high
tectonic subsidence rute during the Quuternay [Kooi et al.,
19911.
Emhquake focal mechanism solutions and borehole
breakout data indicate that the present-day stress field in the
-
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDIJCED SUBSIDENCE
c
I
uplift
#
+ZN
m o o
G=o
.
$ S T :subsidence
-0
rE z
t
o
5 R -r
Moho
p
-
/
-5114.8
f
0
I
100
200
1
I
I
300
400
500
1
I
distance (km)
I
I
I
!subsidence
-
5114.8
11.9111.9
14.815
100
b) O
E?N
m o o
F O
200
300
400
500
distance (km)
-
---- --.- -
-
L _
-
'
7-
I
:uplift
\
- 1
I
I
,
-
top of crust
/
-
-
/
-7
S E -r
-crust
subcrust
faults
~ o h o
-
0
100
200
300
-
__/----
$=? :subsidence
C)
-
5
:
c
-
I
C
.-O - N r- uplift
Zg?
o
-
11.9111.9:
14.815
-
-
a)
-. .
---
-
400
-
:
-
500
distance (km)
Fimve 9. Predicted differential subsidence for rifted basin eeomebies orieinatine from deeo and shallow
lcL.ls of lithospheric necking during extension. For e ~ c hg c o ~ ~ c t rthc
y , towi?; of i 5 km i\ distrihutd oier
the unner crustal and subcrucwl a)mnctcnt l ~ v e nas ~,t~rnhinations
of 5 km and 14.8 km. 11.9 km and 11.9
km, a i d 14.8 and 5 km. The applied'in-plan~suess is 100 MPa. (a) The results for the models representing
deen neckine show 100 to 200 m flank uolift and 180 to 240 basin center subsidence. The model with the
Irrrge\t u p p crustal competent l q e r thicknes5 predicts the lugest amplirudc of strcss-induced deflection. (b)
The rndels adtnuinu a slight Moho uol~h.reoresentinr an intermediate level of neckine. nredict I50 to 200m
flank uplift and 155 to i90 m bash center subsidence, depending on the thickne; of the upper crustal
compctcnt layer. (c) The sepnrate contributions of upper crustal faults, geometry of upper crust without faults,
and shape of the subcrustal lithosphere to the total deflection for the model adopting a slight Moho uplift and
thicknesses for the npper crustal and subcrustal competent layers of 5 and 14.8 km, respectively. The faults
contibute most to the predicted subsidence in the basin center, whereas the subcrustal suess-induced
deflection causes the largest put of thc basin flank uplift. See text for further discussion.
-
948
VAN BALEN ET AL.: A NEW MODELFOR STRESS-INDUCED SUBSIDENCE
Figure 10.- (a) Contour map of the Quatemary thickness distribution in the southern part of the North Sea
basin [Kooi et al., 1991; Van den Berg, 1994). Axial labels are in hundreds of mctm. Thc maximum
thickness locally exceeds 1 km. (b) Main Mesozoic fault zones and rift systems in the southem North Sea
basin [Ziegler, 1990; Kooi et al., 1991; Van den Berg, 19941. Abbreviations are as follows: MF, Morray
Firth: VG, Viking Graben; CG, Central Graben; DCG, Dutch Central Graben; SP, Sole Pit basin; BF, Broad
Fourteens basin; HG, Horn Graben. A good correlation exists between the N-S orientated faults and the local
maxima (plus sign) and minima (minus sign) of Quaternary subsidence. Hanging walls correspond to
maxima; footwalls correspond to minima. See text for discussion.
southem part of the Nonh Sea basin is characterized by a
maximum compressive stress orientated NW-SE [Ahorner,
1975: Illies, 1975: Miiller er al., 1992; Lindhulrn et ul., 19951.
The NW-SE compression is caused by a combination of
Alpine collisional forces and North Atlantic ridge push. The
effea uf the stress field on Quatemary subsidence was
investigated by Kooi et al. [1991]. Their results indicate that
the anomalous subsidence can be partly explained by a
combination of a 300 MPa far field compressive stress and a
decrease of T, from 20 km at the rims of the basin to about 1 2 km below the Quaternary centers of maximum deposition
(giving rise to an unrealistic local in-plane stress of about
3000 MPa). The fit was improved by adopting a decrease of
paleowater depth during the Quaternary. However, their
model requires a high amount of far-field stress and a
paleohathymetry which is not in accordance with
observations. Therefore Kooi et al. [I9911 favor a model
based on hypothetical focal extension below the Quaternary
centers of maximum deposition because of pull-apart
tectonics related to strike-slip faulting, for which no evidence
exists. A three-dimensional forward model of Quaternary
stress-induced subsidence by Van Wees and Cloetingh [1996],
also excluding the permanent deformation of the lithosphere,
utilizes a lower far-field in-plane stress level (150 MPa)
compared to the twedimensional flexural model of Kooi et
al. [1991]. The 3-D flexure model can explain up to 70% of
Lhe Local Quatemary thickness in the DuLch Central Graben
(Figure 10) but fails to predict the remaining patterns of
Quaternaty deposition. Furthermore, their model also requires
a substantial decrease of T, in the Dulch CenLrdl Graben area
(from 15 km at the flanks to lcss than 5 kin in the center).
Therefore Van Wees and Cloetingh 119961 also suggest that
other tectonic mechanisms, like pull-apart extension, have
played a significant role in Quaternary subsidence of the
southern North Sea basin. There is, however, no evidence for
major, large-scale Quaternary faulting, and the relationship
between the NW-SE directed maximum compressive stress
directions and the geometry of the fault system requires that
the N-S orientated centers of maximum deposition are
transpressed by the proposed strike-slip motions and not
pulled avart.
The thickness distributinn of Quatemary sediments is
characterized by a saucer shaped long-wavelength component
and local elongated thickness maxima and minima (Figure
10a). The largest Quaternary centers of deposition in the
southem North Sea basin, located in the Dutch Central
Graben area, are on the downthrown sides of N-S striking
Mesozoic normal faults (Figure lob) [Kooi and Cloetingh,
1989; Van den Berg, 19941. Local minima of Quaternary
thickness are on the footwalls of these faults. The strike of the
N-S normal faults bas an angle of 45' to the maximum
compressive stress direction. The NW-SE orientated faults,
parallel to the maximum compressive stress direction, are not
associated with Qualm~ary cmlers or deposition and
949
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCEO SUBSIDENCE
thickness minima. Furthermore, in the Central Graben and
Egersund Basin of the northern North Sea basin liltle or no
increase in subsidence has occurred [Hall and White, 19941;
these basins strike parallel to the maximum compressive
stress direction. The N-S striking faults have a component of
the maximum compressive stress acting on them. Therefore
we suggest that the Quaternary centers of maximum
deposition and thickness minima can be explained by
compressive stress-induced suhsidence related to moments
acting at the position of the Mesozoic faults. Faults with
throws of several kilometers (up to 7 km) are common in this
par1 o l the Nonh Sea basin [Ziegler, 1990; Holliger and
Klemperer, 19901. As the differential subsidence caused by
the moments scales linearly with the Caul1 displacement and
in-plane force, the results in Figure 8 can be used to cstimate
thecontribution of the moments to the differential subsidence
(a T, of about 5 km for the faulted upper crust of the Nolth
Sca basin is inferrcd by Roberts and Yielding [1991]). In the
centers of maximu deposition, the thickness of Quaternary
sediments is about 400 m more than the regional longwavelength trend. This can, for example, he explained by a
combination of fault throws of 5 km and a far-field stress of
100 MPa. The total Quaternaty thickness distribution is then
the sum of
small-wavelength fault-related differential
subsidence and the long-wavelength Quaternary distribution.
The latter can be explained by the compressive stress
response of the downflexed lithosphere caused by necking,
sediment, and thermal loading
5.2. Pannonian Basin
The Pannonian basin is a Neogene intramontane basin
system hounded in the west by the Alps, in the north, east,
and southeast by the Carpathians, and in the southwest by the
Dinarides. 'The Pannonian basin orginates &om
contemporanous tectonic escape in the Alps, asthenospheric
upwelling, and subduction rollback along the Carpathian kont
[Ratschbacher et al., 1991: Horvdth, 19931. Because of
changes in platc motions, the stress field in the Pannonian
basin changed to compression during late Pliocene [Csontos
et al., 1991; Muller et al., 19921. The maximum horizontal
stress direction in the southern part of the basin is roughly
SW-NE oriented and in the northern pan coincides with the
European NW-SE trend [Muller er al., 19921. During late
Pliocene-Quaternary times, lhe wnlral pan of the basin
system experienced an acceleration of subsidence, whereas
the external parts were uplifted, with the exception of the
local subhasin ccnters in the southwestern and northwestern
parts of the basin system (Figure I la). Dilferenlial subsidence
took place without major fault reactivation [Horvdth and
Cloetingh, 19961, indicating a flexural mechanism. Uplift in
excess of 300 rn occurred in the Trans-Danubian central
range, whereas about 1500 m of sediment accumulated in the
Mako Trough and Bikks Basin during the same time interval.
Using the previously published thin-plate model [i.e., Kooi
and Cloetingh, 19921, the differential subsidence pattern can
be explained by the buildup of the contemporanous
compressive stress field. adopting a 300 MPa in-plane stress,
in combination with ongoing thermal subsidence in the center
of the basin system [Horvdth and Cloetingh, 1996; Van
Balen et al., 19981. A comparison of the differential
suhsidence pattern with the fault system in the basin shows a
clear relatiouship (Figure llb), evidencing that the faults
exett a first-order control on the stress-induced differential
subsidence. The subsidence and uplift in the Sava and Drava
Troughs in the southwest and the Little Hungarian Plain
(LHP) in the northwest are perfectly fault bounded. The faults
bounding the Mako Trough and Bekes Basin are overstepped
by late Pliocene-Quaternary sediments, indicating a flexural
rigidity which is less for the hanging walls compared to the
footwalls [Van Balen and Podiadchikov, 19981. This can be
explained by the high heat flow in the Mako Trough and
B6k6a Basin [Pusgay er al., 19x1, causing weakening of the
lithosphere.
5.3. Norwegian Margin
The morphology of Norway, in combination with the
almost complete absence of post-Paleozoic sediments,
evidences large-scale Tertiary uplift of western Fennoscandia.
Two domal uplifts in southern and noahem Norway are
inferred from the present position of preserved planation
surfaces [Riis and Fjelhkaar, 1992; Riis, 19961 and results
from fission-track thermochronology [e.g., Rohrman et al.,
1995; Riis, 19961. These uplifts are spatially separated by a
low-lying region. The onshore domes correspond to narrow
ullshure shelves, whereas the low-lying saddle in between
thcm is associated with the broad shelf of the mid-Norwegian
mnrein
and Eldholm.19961.
The domes
.
. .. are
- lStuevold
.
.
elongated and roughlv ~arallelto the Atlantic coastline. Their
maximum elevation is about 2 km. The flexural nature of the
domal uplifts is evidenced by their shape and the absence of
major fault activity associated with their development. The
observed asymmetry of the domes, consisting of a steep
westward face and a more gentle slope eastward, is explained
by amplified weathering on their seaward flank [Sruevold and
Eldholm, 19961.
The domal uplift in southem Norway is hounded in the
south and west by the North Sea basin and in the noahwest by
the M0re Basin and the mid-Norwegian margin (Vering
Basin) (Figure 12). These basins were formed in response to
Permo-Triassic to Early Cretaceous rifting. A final Paleocene
~xtensionphase in the Mere Basin and the mid-Norwegian
margin caused the opening of the North Atlantic Ocean. The
structural, basinward dip of strata and deposition of large
clastic wedges in the Norwegian offshore sedimenrary basins
record substantial Tertiary uplift and erosion of the mainland
and subsidence in the basins [Sluevold er a/., 1992; Stuevold
and Eldholm.1996; Riis, 19961.
The flexural uplift and subsidence of the Norwegian
mainland and the surrounding basins is separated in time from
the opening of the North Atlantic. Several mechanisms havc
been proposed, including convectivekhermal processes,
innaplate compression, rift shoulder uplift, glacial erosion,
mantle plumes, and phase changes. However, uone of these
can satisfactorily explain the uplift and associated subsidence
(for an overview see Stuevold and Eldholm [19961). In
addition, the exact timing of uplift is controversial: a late
Oligocene to early Miocene time is suggested by Rohrmn et
al. [I9951 and Stuevold and Eldholm [1996]. Recently, using
morphological evidence and offshore seismic reflection data,
Riis [I9961 proposed that the Tertiary uplift and subsidence
-
- ..
. -
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
a)
b)
Figure 11. (a) Late Pliocene-Quaternary subsidence and uplift pattern in the Pannonian Basin [Horvdtk and
Cloefingk, 1996; Van Balen et al., 19981. In general, the flanks of the basin system are uplifted and the central
part subsides. Noticeable exceptions are the centers of the Drava and Sava Troughs and the Little Hungarian
Plane (see Figure 1lb). Dotted areas indicate the foredeep, flysch belt, volcanic, and metamorphic units of the
Alpine-Carpathian-Dinaide belt. (b) Nwgene basement fault pattem and subbasins of the Pannonian Basin
system [Horvath, 19931. Abbreviations are as follows: DT, Drava Trough; ST, Sava Trough; LHP, Little
Hungarian Plain; MT, Mako Trough; BB, BCk6s Basin; and TDCR, Trans-Danubian central range. The major
fault-boundcd subbasins show subsidence or enhanced suhsideuce, whereas their flanks are uplifted,
indicating that the faults exert a first-order control on the subsidence and uplift pattern. The faults bounding
the Mako Trough and Rikis Basin are overstepped by thc late Pliocene-Quaternary sediments, indicating a
flexural rigidity which is less for the hanging walls compared to the footwalls. This can he explained by a
higher heat flow in the Mako Trough and BCkCs Basin.
took place in two phases: a Palcogene phase and a P l i e
Pleistocene phase, each with about an equal amount of uplift.
Tlle hinge liues o l the duma1 uplifts, separating uplifted from
downwarped areas, coincide almost everywhere with major
basement faults. Along the North Sea coast, the hinge liue
coincides with the 0ygarden Fault Zonc (Figurc 12) [Riis,
19961, which consists of two major faults, each with a throw
of more than 5 km toward the basin [Gabrielsen et al., 19901.
Northward, the hinge line is located at the position of the
M0reTmndelag Fault Zone. On the mid-Norwegian margin,
the hinge line coincides with the Bremstein and Revfallet
fault complexes [Stuevold and Eldkolm, 19961. This
cornlation pattern continues farther northward [Riis, 19961.
Therefore it seems that the major fault zones exerted a firstorder control on the distribution of uplift and subsidence. The
stress system of the Norwegain mainland and adjacent basins
is comparable to that of the North Sea area [Bungum et al.,
1991; Miilkr et al., 1992; Lindholm et al., 19951. Furthemore,
if mantle upwelling has contributed to the domal uplift of the
Norwegian mainland, it can explain part of the compressive
stress distribution 1e.g.. Poliakov et al., 19931, and the total
uplift may be the result of a stress-induced amplification of
the mantle-caused uplift.
6. Discussion
In a recent paper, Kurner et al. [I9931 slated that the
developmenl of global or regional unconfotmities by in-plane
force variations is difficult to accept for the following
reasons: (1) localized fault reactivation dominates the
response of the lithosphere lo applied Corces, (2) thc
orientation and sign of the present-day stress field changes
markedly across the same plate, (3) the magnitude of the inplane force required to modify the stratigraphy of an evolving
basin is extremely large, and (4) the flexural deformation is
governed by factors that will give very dilferent responses of
thc lithosphcrc f a thc samc in-plane force. However, not
every in-plane force change leads to active faulting: as long as
the prevailing in-plane force is at a level lower than the
integrated strength of the lithosphere underlying the basin
(including weakness zones due to preexisting faults), flexural
deformation of the basin dominates. For example, the latest
Cretaceous inversion of the mid-Polish Trough is preceded by
a flexural acceleration of subsidence. Possible analogues are
the rapid Paleocene-early Eocene phase of tectonic
subsidence of the Sverdmp Basin in arctic Canada [Dadlez et
al., 1995; Stephemon, 19961 and the acceleration of
subsidence during the Paleocene in the central Nonh Sea
[Ziegler et al., 19951. These examples show that prior to fault
reactivation, flexural subsidence in response to the buildup of
compressional stresses occurs in the basin center. Only if the
in-plane force reaches a threshold defined by the strength of
lithosphere [Kusmir and Park, 19841, will fault reactivation
take place. Therefore, if the in-plane force does not reach this
threshhold, the lithosphere will respond to changing in-plane
forces by flexure. The in-plane force of 5xlO"N m.'adopted
in the models in this paper is within the limits defined by the
yield strength of the lithosphere [Kusznir and Park, 1984;
Savage and Guohua, 19851, and values deduced from studies
on folding of oceanic [Cloetingh and Worrel, 1985; Beekn~an
et al., 19961 and continental lithosphere [Lambeck, 1983;
Cloetingh and Burov, 19961
VAN RALEN ET Al,.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
8
4
4
8
uplifted area
El ~ p i i f>t 1500 m
Figure 1 2 Generalized Mesozoic-Paleocene fault map of
southern Nonvay and the mid-Norwegian margin [Gabrielsen
er al,, 1990; Blysrad et al,, 1995: Riss, 19961, Abbreviations
are
as~
follows:
~ ..~~-.
~7nne:
~ MTFZ
M~~~
-. .
-.--.
-~ @FZ.
,- - -, fivgarden
-,-.--.
~- .-..
- -l- - - t, Tmndelag Fault Zone; BFC, Bremstein Fault Complex; m,
Revfallet Fault Complex; NSB, North Sea basin; MB, M0re
basin; VB, V0ring basin; and VMH, V@ring marginal high.
Ruled areas indicate the extent of the late 01';goce&-~lioc&e
uplift [Riis, 1996; Stuevold and Eldholm, 19961. The hinge
line of the uplift coincides with major fault zones.
.
As shown by numerous studies, the orientation and sign of
the intraplate stress field strongly correlates to plate motions,
and the stress field has persistent trends over large areas
[Cloetirigh and Wortel, 1985; Zoback et al., 1989; Zoback,
1992; Miiller et al., 1992; Richardson,l992; Coblentz and
Richardson, 1995; Lindholm er al., 19951.
Indeed, the amount of in-plane force in previously
published models is large (up to 300 MPa); the new model
presented in this paper requires lower stress levels (100 MPa).
In addition, the inferred discrepancy between estimated
average stress levels arising from plate boundary forces and
isostatically compensated loads (less than 100 MPa) and
951
measured and calculated stresses (up to 300 MPa) can be
explained by the ductile nature of the lower part of the crust
which causes a redistribution of stresses applied to the whole
lithosphere and their amplification in the more brittle parts of
the lithosphere [Kusznir and Park, 1984: Savage and Guohua,
19851. Furthermore, the thickness over which the in-plane
force is distributed should be taken into account. For example.
a ridge push force of 2 . 4 ~ 1 0N
' ~ m-l applied to 80 km thick
lithosphere may produce 30 MPa, whereas the same force
applied to 160 thick lithosphere gives only 15 MPa [Kusznir
and Park, 19841. If the same in-plane force is applied to a 15
km thick strong p m of the lithosphere, a stress of 160 MPa
results.
The flexural response of rifted lithosphere to an in-plane
force change is dominated by the faulted shape of the upper
crustal competent layer and, in exceptional cases, also the
subcrustal mantle fiber. In rifted basins, the large-scale shape
of the faulted upper crustal flexural midplane is always
downward bend. Therefore the response of rifted basins to an
in-plane force change should always be the same: basin center
subsidence and flank uplift. This confirms the original results
of Cloetingh et al. [1985]. The elastic thin-plate models
including necking of the lithosphere during extension [Kooi
and Cloetingh, 1992; Karner et al., 19931 concluded that the
deeper the level of necking is during extension the less stressinduced differential vertical motion there is during the postrift
phase. Also, if the level of necking during rifting was deer,
enough, the flexural response to in-plane stress changes
during the postrift stage would be reversed compared to a
situation with a shallow level of necking during extension.
However, a deeper level of h e lithospheric necking causes an
incrcascd dcformed geometry of the uppcr crustal competent
layer. As a result, the postrift stress-induced vertical motions
increase when the synrift lithospheric necking level is deeper.
Using the argument that stress-induced lithospheric
deflections cause simificant tiltine of sedimentarv strata.
Karner er al. [I9931 argued that parillel seismic reflectors are
indicative for eustatic sea level changes. O w results
demonstrate that the angle of tilting is so extremely low (less
than 1") that such tilting is hardly observable on seismic
sections. Therefore parallelism of seismic reflectors is not
necessarily an indication of a eustatic control on onlap and
offlar, configurations.
After reversing the sign of the horizontal intraplate stress,
our model predicts tlexural uplift in the center of a rift basin
in response to tension. The upward bending of the plate
causes additional tensile fiber stresses in the center of the rifi.
These additional Lensile stresses augment the far-field tensile
stress and therefore will facilitate further extensional faulting
in the rift. As a consequence, our model predicts tbat rifting
will localize in preexisting rift grabens.
For the elastic stress-induced differential subsidence
model, a decrease in tensional slress has the samc cffcct as an
increase in compressiorral stress. As shown by our results, an
increase in compressional stress leads to uplift of a basin
flank. Therefore the release of tensional stress when rifting
ceases is a mechanism for flank uplift. Evidence from various
passive margins demonstrates that erosion of a rift shoulder
causcs uplift of the nearby sedimentary basin, inducing
stratigraphic offlap during the early phases of the postrift
VAN BALEN ET AL.: A NEW MODEL FOR STRESS-INDUCED SUBSIDENCE
evolution of a rifted basin [Van Balen et al., 19951. This can
he explained by flexural compensation for erosion on a flank
uplift [Van Balen et al., 19951, which amplifies the stressinduced uplift and the resulting relative sea level change.
Fmally, application of the presenled equation for fault
moments is not restricted to faulted elastic plates. In fact, this
cquation can be used to study the effects of any steep lateral
change of the geometry of a competent layer on in-plane
stress-induced deflections. Such steep morphology may, for
example, exist at ocean-continent boundaries.
7. Conclusions
Our new model for intraplate stress-induced subsidence
takes into account flexure of a multilayered continental
lithosphere and its structural configuration prior to the change
in the in-plane stress regime. The preexisting deformation
influences the response of a thin plate to a change in in-plane
force (stress times plate thickness) considerably [Timoshenko
and Woinowsb-Krieger, 19591. Because the preexisting
deformation of a rifted sedimentary basin has a concave
geometry, the response of a basin to compression is
subsidence in the basin center and upbft of the tlanks.The
preexisting gwmehy is not properly taken into account in
published thin-plate models. The largest part of the
preexisting deformation in rifted sedimentary basins is caused
by faults in the upper crustal competent layer. The offset of
the midplane of the upper crustal competent layer due to a
fault causes an additional moment at the position of the fault.
This moment causes suhbidence on the downthrown sidr of
the fault and uplift of the footwall. The amount of differential
uplift depends on the vertical throw of the fault, the
magnitude of the in-plane stress, the thickness of the upper
crustal competent layer. and the degree of flexural coupling
between the upper crustal and upper mantle competent layers.
As shown in section 4, uplift and subsidence of several
hundred meters are predicted for conservative values of these
parameters in a basinal setting with multiple faults. Therefore
the total stress-induced deflection, or relative sea level
changes, of rifted basins can be of the order of 1 km in the
case of a l u g e in-plane stress level change (up to 300 MPa),
large fault throws (several kilometers), and a strong upper
crust in combination with a relatively weak subcrustal layer.
In-plane stress level changes caused by, for instance,
lithospheric plate reorganizations [e.g., Cloetingh et al., 19891
can therefore have a substantial impact on relative sea level
change in a rifted basin. As the lithospheric plates form an
interlocking system, plate boundary reorganizations may
cause a global change in in-plane stress level, and this may
induce worldwide onlap and offlap events, interpreted as
custatic sca level changes [e.g., Haq et al., 19871.
Examples frnm the southern North Sea basin, Pannonian
basin, and the Norwegian margin demonstrate that faults do,
indeed, play a key role in the pattern of observed stressinduced differential subsidence of rifted sedimentary basins
during their postrift evolution. The results of our new model
confirm the original hypothesis of Cloetingh et al. [1985]: an
increase in the level of compressive far-field in-plane stress
causes flank uplift and basin center subsidence.
Acknowledgments. T h e authors want to thank Fred Beekman,
Ritske Huismans, Henk Kwi, Tore Skar, and Marlies ter V w r d e for
helpful discussions. Ronald van Balen was sponsored by Norsk
Hydro as. and Yuri Podladchikov was sponsored by the,"Universitair
Stimulerings Fonds" of the Vrije Uniuersiteit. Sergei Medvedev,
Fritz Schlunegger, and P.A. Ziegler have provided useful comments.
This is Netherlands Research Schwl of Sedimentary Geology
publication 980301.
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