Earth and Planetary Science Letters 144 Ž1996. 21–34
Spacing of consecutive normal faulting in the lithosphere:
A dynamic model for rift axis jumping ž Tyrrhenian Sea/
Giacomo Spadini, Yuri Podladchikov
)
Faculty of Earth Sciences, De Boelelaan 1085, Vrije UniÕersiteit, 1081 HV Amsterdam, The Netherlands
Received 2 October 1995; revised 26 July 1996; accepted 15 August 1996
Abstract
We propose that the flexure of a broken elastic plate can determine the spacing of consecutive and localized zones of
shearing on a lithospheric scale. The model provides a dynamic explanation for rift axis migration and, as a consequence, for
a ‘wide rift’ mode of extension. Calculated values for rift axis shifting are consistent with the available observations and
kinematic modelling results in the Tyrrhenian Basin. The quantitative relation obtained between lithospheric fault spacing
and the effective elastic thickness ŽTe . of the lithosphere can be used in an inverse modelling approach, in which paleo Te
values are calculated for a basin where the diachronous and spaced nature of rifting is known.
Keywords: Tyrrhenian Basin; extension tectonics; shear zones; normal faults; rift zones
1. Introduction
It is widely accepted that lithospheric extension is
the major mechanism responsible for passive margin
formation and continental break-up, but the role
played by the dynamics of extension in imposing the
style and kinematics of rifting is still a matter of
debate w1,2x. Narrow and wide rift modes have been
proposed as the two major geometric styles of extension. The wide basin mode occurs when deformation
migrates laterally and new unstretched areas undergo
extension. In order to explain this pattern of evolution, the role of different parameters, such as the
pre-rift geotherm, the thickness of the crust and the
strain rate has been pointed out w3x. Hardening of the
)
Corresponding author. Fax: q31 20 6462457. E-mail:
podl@geo.vu.nl
stretched area associated with both cooling w4x and
thinning of the weak crust w5x can cause the site of
extension to migrate laterally. However, these studies do not provide quantitative predictions of the rift
axis migration in the wide rift mode of extensional
basin formation.
Recent studies have pointed out the existence of
lithospheric scale shear zones that can lead to localized deformation in the upper mantle. An example is
given by Burov et al. w6x, who revealed the existence
of a broken plate beneath the North Baikal rift zone.
Their model was characterized by a competent upper
crust and a competent upper mantle separated by a
weak lower crust; the authors showed that the behaviour of the diverging plates in the North Baikal
rift requires a mechanical discontinuity beneath the
rift axis. In the absence of ductile detachment in the
lower crust, these type of discontinuities can propagate trough the entire lithosphere.
0012-821Xr96r$12.00 Copyright q 1996 Elsevier Science B.V. All rights reserved.
PII S 0 0 1 2 - 8 2 1 X Ž 9 6 . 0 0 1 6 5 - 3
G. Spadini, Y. PodladchikoÕr Earth and Planetary Science Letters 144 (1996) 21–34
of the oceanic model, equal to half the width of the
basaltic domain divided by a greater stretching factor.
fault. The distance to this new fault location Žspacing
of the normal faulting. is:
Ss
4. Model
We employ the popular model of flexure of a thin
elastic plate floating on inviscid substrate ŽFig. 3a.
w17,18x. A lithospheric scale normal fault forms when
the averaged horizontal deviatoric stress reaches a
critical value. After a finite displacement along this
fault, the lithosphere bends and creates an additional
perturbation to the horizontal stress field ŽFig. 3b..
This perturbation can be easily determined by solving the thin elastic plate equation w19x. Taking into
account the continuity of slope, bending moment,
and shear stress, the solution of the flexure equation
requires continuity of the first, second and third
derivatives across the fault. The only solution having
these properties and being discontinuous at fault
location is given in Fig. 3b. This simple solution
accurately approximates vertical displacement and
distribution of horizontal stress for xra ) 0.2 w20x,
where a is the flexural parameter. Following
Heiskanen and Vening Meinesz w19x, we suggest the
area of maximum perturbation of the horizontal stress
as the best candidate for the location of the next
25
pa
4
s
p
4
(
4
ETe3
3 Ž 1 y n 2 . Dr g
Ž 1.
where a is the flexural parameter w17x; Te is the
effective elastic thickness of the lithosphere; Dr is
the difference in density between the viscous substrates above and below the elastic layer; E and n
are the elastic moduli; g is the gravitational acceleration. Eq. Ž1. is equally applicable both to the entire
lithosphere and to the elastic core of the subcrustal
lithosphere in the decoupled state of extension Žsee
discussion below.. Substitution of the typical values
for parameters in Eq. Ž1. ŽE s 1.75 = 10 11 Pa, n s
0.25, g s 9.8 mrs 2 , Dr s 300 kgrm3, for the coupled state of the lithosphere; E s 1.5 = 10 11 Pa,
n s 0.25, g s 9.8 mrs 2 Dr s 500 kgrm3, for the
decoupled state of the lithosphere. yields a relation
between effective elastic thickness, Te , and S:
(
4
S s 8 Te3
Ž 2.
where both S and Te are in kilometres.
Since the horizontal stress perturbation is symmetric along the plate ŽFig. 3b., there are two possible directions for fault migration. In Fig. 3c we
hypothesize about the state of stress in these two
Fig. 4. Schematic strength envelopes for Ža. a decoupled and Žb. a coupled state of the lithosphere during extension. The Te for the coupled
situation ŽTeCo upled . is equal to the thickness of the crust plus the elastic core of the subcrustal lithosphere ŽTeDe coupled .. See Fig. 6 for the
estimate of TeDe coupled .
26
G. Spadini, Y. PodladchikoÕr Earth and Planetary Science Letters 144 (1996) 21–34
locations after a finite displacement along the fault.
Immediately after the formation of the first fault, the
stress distribution in the plate is homogeneous in the
x direction and is equal to a broken yield stress as a
function of depth. After a finite displacement along
the fault, the resulting stress will be the sum of the
broken yield stress profile Žas the initial stress before
the bending. and a perturbation due to the bending
stresses. The horizontal bending stresses Ž sxx . are
linear functions of depth with two maxima at the
upper and lower boundaries of the elastic layer. The
magnitude of the maxima is a function of horizontal
position Ždistance to the fault. and reaches two equal
maxima as a function of x at positions S and yS,
which we suggest as candidates for the new fault
location. To initiate a new fault we need to build up
a critical bending at location S or yS. Therefore, the
new fault location depends on where the critical
bending is lower. If broken and unbroken plates have
different slopes of the brittle yield envelopes Žbecause of reduction in the friction coefficient due to
strain softening., then the plate is likely to break in
the hanging wall first because, at the position of the
maxima of the stress perturbation, there is an additional extension at a shallow level of the hanging
wall and at a lower level of the foot wall. If the
broken yield line is closer to the unbroken one at
shallow levels than at deeper levels, the hanging wall
will break first.
of a ductile lower crust, separating the brittle upper
crust from the brittle portion of the mantle. The
depth of the brittle–ductile transition in the crust is
characterized by the equation:
5. Estimate of the effective elastic thickness
where Z Mo ho and T Moho are the depth and the temperature of the Moho. Fig. 5a shows coupledrdecoupled mode boundaries in Moho depthrMoho temperature space for different strain rates, assuming a
diabase rheology for the lower crust ŽTable 1.. Instantaneous rifting acting on a ‘normal’ continental
crust is likely to occur in a decoupled mode. Post-rift
cooling, finite rate of extension, thinned pre-rift crust
To compare our theoretical prediction for fault
spacing to observations we need an estimate of the
effective elastic thickness ŽTe . of the lithosphere
during rifting w21x. The major control on Te is the
coupledrdecoupled state of the lithosphere ŽFig. 4..
The decoupled state is characterized by the presence
Ž 3.
s b s sd
where s b is the brittle yield strength and sd is the
ductile yield strength.
Assuming Byerlee law for s b in the form w21x:
Ž 4.
s b s 2.2 = 10 4 Z
where s b is the brittle yield strength in Pa and z is
the depth in metres, Eq. Ž3. can be written as:
2.2 = 10 4 Z bd s Ay1 r ne 1r n exp Ž yQr Ž nRT bd . .
where z bd and T bd are the depth and the temperature
of the brittle ductile transition in the crust ŽFig. 4.,
respectively; A is the initial constant in the power
law creep function; e is the strain rate; Q is the
activation energy; n is the power law exponent; and
R is the gas constant. See Table 1 for values adopted.
The shift from a decoupled to a coupled state
takes place when Z bd is equal to the depth of the
Moho ŽFig. 4.. Thus, the transition between the
coupled state from the decoupled state can be defined by:
2.2 = 10 4 Z Mo ho s Ay1 r ne 1r n exp Ž yQr Ž nRTMoho . .
Ž 6.
Table 1
Power law creep parameters
Parameter
A
n
Q
Definition
Initial constant
Power law exponent
Activation energy
Unit
yN
Pa
Felsic granulite
y1
s
J moly1
Ž 5.
y21
2 = 10
3.1
243000
See references in Carter and Tsenn w22x, Wilks and Carter w34x and Ranalli w35x.
Diabase
Mafic granulite
y20
3.16 = 10
3.05
276000
8.83 = 10y22
4.2
445000
30
G. Spadini, Y. PodladchikoÕr Earth and Planetary Science Letters 144 (1996) 21–34
Table 2
Rifting parameters
Parameter
Strain rate Ž10y1 5 , sy1 .
Rift axis jump
Averaged crustal thinning
Time of jump ŽMa.
Moho depth Žkm.
Lithospheric thickness Žkm.
6. Discussion
Rift axis jump number
1
2
3
20
29
1.55
6.5
26
58
30
50Ž75.
1.7Ž2.
4.8
22
42
41
76Ž95.
1.3Ž1.33.
2.2
12
24
Rifting parameters inferred from kinematic modelling w12x and
from paleotectonic and paleogeographic reconstruction w7x.
most realistic estimate for the case study considered,
which has to be used to check the dynamic predictions of Eq. Ž2.. However, this estimate is strongly
affected by the crustal geotherm and rheology, which
are poorly constrained parameters. To minimize the
influence of crustal rheology, we limit ourselves to
the prediction of the coupledrdecoupled state of the
lithosphere ŽFig. 5. and use of the above recipe
ŽFigs. 4 and 6. of the two first estimates to calculate
Te . This simplification again means neglecting rigidity of the crust compared to rigidity of the subcrustal
mantle lithosphere in the decoupled state, which is
usually a good approximation for continental lithosphere. For this strongly simplified way of calculation of the third estimate, the only additional information needed compared to the first two estimates is
the rheology of the lower crust. We use three different dry rheologies, spanning a very wide range of
possible compositions of the lower crust Žfrom silicic
to mafic, via standard diabase., to construct the
coupledrdecoupled mode boundaries in Fig. 5b. Fortunately, despite the strong potential dependence on
the lower crustal rheology, the first and third fault
jumps are relatively well placed within decoupled
and coupled fields, respectively. The "508C uncertainties in the Moho temperatures result in the error
bars for the third estimate of Te in Fig. 7. We do not
show the third estimate Žerror bars. for the second
jump since the uncertainties on lower crustal rheology and Moho temperature result in a scatter of the
Te predictions covering the whole interval between
the coupled and decoupled state.
Considering the number of simplifications made
while constructing the third estimate of Te , Fig. 7a
shows a remarkable fit between ‘dynamic’ and
‘kinematic’ predictions for the first and third fault
jumps. The good fit is encouraging, since we use
common, or ‘conservative’ values for the parameters
involved in the fitting; that is, the crustal rocks at the
Moho depth are dry, subcrustal mantle composed of
dry olivine. The uncertainties in these parameters,
except for the Moho temperature, have a relatively
weak influence on the testing of the model presented
in Fig. 7a. The evolution of the Moho temperature
was estimated based on the four-layer model, resulting in the error bars of "508C. These error bars
have only minor influence on the test results. However, the thermal calculations based on one- or twolayer pure shear models may result in Moho temperatures as much as 2008C higher w12x. Such changes
in the Moho temperature would noticeably disturb
the fit presented in Fig. 7a. Since the four-layer
model is a more precise description for the extension
of the continental lithosphere Že.g. w15,16,21,23x., its
predictions must be used preferably to the predictions of the one- or two-layer models. Moreover, the
uncertainties in the Moho temperature mostly affect
the prediction about the coupledrdecoupled state of
the lithosphere and the third estimate of Te Žthe
narrow error bars for the first and third jumps.. The
first Žthe lower dashed line. and second Žthe upper
dashed line. estimates of Te , which constitute a much
large range of possible values of Te , are relatively
independent of the Moho temperature and other assumptions made while calculating the ‘more precise’
third estimate of Te Ži.e., ignoring the influence of
the crustal contribution in the decoupled state.. The
fact that our theoretical curve for the fault spacing is
in between the dashed lines confirms the model
testing for the Tyrrhenian Basin at the present level
of accuracy. This fact can be considered as a verification of Eq. Ž2., since there are almost no ‘fitting’
or ‘tuning’ parameters involved in plotting the dashed
lines. The model that we propose for rift axis migration has some noteworthy implications.
Buck w1x discussed the possibility of lateral migration of deformation during extension and the creation
of a ‘wide’ rift. Realistic pre-rift conditions of the
32
G. Spadini, Y. PodladchikoÕr Earth and Planetary Science Letters 144 (1996) 21–34
conversely, as a coupled system in the last phase
Žsubcrustal and crustal thinning factors tend to coincide.. For the intermediate phase of deformation
Žsecond jump. the kinematic modelling results do not
allow discrimination between a coupled or a decoupled situation and, thus, the estimate of the effective
elastic thickness, affected by the faulting, varies
between a maximum and a minimum value, respectively.
6.1. The role of subduction
A back-arc model w8,29x can explain the origin of
the extensional processes that the Tyrrhenian area
underwent during the compressional deformation of
the Apennines and the subduction of the Ionian plate
beneath the Calabrian arc ŽFig. 9.. The trench retreat
produces a tensional stress field in the back-arc area
that leads to the formation of a rifted basin. The slab
retreat process could also explain a shifting of the
depocentre at the rear of a migrating arc–trench
system. This mechanism would most probably result
in a time-continuous and spatially gradual process. In
fact, we observe a rifting history that is characterized
by no quiescent periods during extension, but the
spatial distribution of thinning and stretching indicators is clearly discrete. A good example is given by
the stratigraphy of the MM ŽFig. 1.. This area Žalso
called in the literature ‘‘Cornaglia Basin’’. is characterized by up to 1 km of Messinian evaporitic sediments. This unit abruptly decreases in thickness at
the sides of the Cornaglia Basin Ž; 200 m.; for the
same period, in the LM there is evidence of subaerial
environment and erosion w10x. The Cornaglia Basin
constitutes a very well defined paleo-rift axis. The
most compelling argument to consider the Tyrrhenian rifting as constituted by spatially separated rift
axes is the presence of two distinct oceanic domains.
The Vavilov and the Marsili basins ŽFigs. 1 and 2.,
underlined by oceanic crust, have different ages and,
above all, are separated by a block of continental
crust w30x. This is the strongest argument in favour of
a real jump of extension-related processes.
It appears that the elastic core of the extending
plate is more likely to control the observed kinematics of rifting and the subsidence history. Independently from what is the cause of extension, the
broken elastic plate model can simulate a continuous
process of rift axis migration characterized by spatially separated paleo-rift axes. Such kinematics could
alternatively be explained by jumps in the subduction hinge line, which should probably produce
crustal roots in the positions of the abandoned slab.
There are no indications from deep seismic or gravity for crustal roots in the Tyrrhenian. At the present
state of knowledge, the shifting of the subducting
slab below the Tyrrhenian appears to be gradual and
with no jumps. Moreover, if the dynamics of subduction are non-trivial, they would be expected to have a
much larger characteristic timing and spacing.
6.2. The fourth jump?
Extensional tectonics are still active in the southern Tyrrhenian area and are at present affecting the
Calabrian arc ŽFigs. 1 and 9.. Is this the result of a
further shift of extension after the end of drifting in
the MB? We can verify this possibility in the framework of our model. If we take into consideration
that, for the lithospheric sector between the MB and
the Italian peninsula, we have well constrained data
on lithospheric and crustal geometry, heat flow and
deformation rate w7,27,31,32x, we can conclude that
the lithosphere is in a coupled situation ŽFig. 5. and
we can calculate the Te using diagrams of Fig. 6. We
obtain a range of values of 28–33 km for the Te of
this sector of the Tyrrhenian plate. Substituting this
value in Eq. Ž2. we obtain a value for the possible
jump of 100–110 km. It is noteworthy to observe
that crustal and upper mantle seismicity show that
most of the earthquakes, including the largest events
occurring in the Calabrian arc Ž6.5 - 7.1., are located within a narrow normal fault belt located onshore of Calabria w32x approximately 110 km to the
southeast of the MB. This normal fault belt, related
to ESE–WNW extension has been active since the
middle Pleistocene. We do not know if this extensional system will develop in a future rift axis, we do
not have the geological record that we had for the
previous phases of the Tyrrhenian evolution, but the
fit with our model prediction is remarkable. At present, the lithosphere of Tyrrhenian Sea is weak and
is not capable of supporting strong deviations from
the isostasy Ži.e. is not competent in this context.,
but it may result in a few tens of kilometres spacing
of consecutive normal faulting.
G. Spadini, Y. PodladchikoÕr Earth and Planetary Science Letters 144 (1996) 21–34
33
7. Conclusions
References
The main conclusions of the paper are summarized in Fig. 7. We propose a quantitative relation
between the spacing of rifting migration and Te at
the time of jump. Our theoretical function ŽEq. Ž2..
is able to reproduce the rifting migration trend observed in the Tyrrhenian Basin. A dynamic explanation for the direction and the spacing of rift axis
migration is given: the elastic core of the lithosphere
ŽFig. 3a. governs the direction and the spacing of a
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Acknowledgements
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project Žcontract number JOU-CT 92-0110. by the
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