Download Three-dimensional modelling of crustal motions caused by

Geophys. J. Int. (1999) 136, 261^274
Three-dimensional modelling of crustal motions caused by
subduction and continental convergence in the central
Mediterranean
Ana Maria Negredo,1, * Roberto Sabadini,1 Giuseppe Bianco2 and Manel Fernandez3
1
Dipartimento di Scienze della Terra, Universita© di Milano, Via L. Cicognara, 7, 20129 Milano, Italy. E-mail: [email protected]¢sica.unimi.it
Centro di Geodesia Spaziale, Agenzia Spaziale Italiana, Localitä Terlecchia, C.P. Aperta, 75100 Matera, Italy
3
Institute of Earth Sciences `J. Almera'öCSIC, Lluis Solë i Sabar|¨ s s/n 08028, Barcelona, Spain
2
Accepted 1998 August 25. Received 1998 August 25; in original form 1997 November 12
S U M M A RY
Crustal deformation in the central Mediterranean is modelled by means of 3-D ¢nite
element models assuming a viscoelastic rheology. The tectonic mechanisms under
investigation are subduction of the Ionian oceanic lithosphere beneath the Calabrian
arc and continental convergence between the African and Eurasian blocks. Very Long
Baseline Interferometry (VLBI) data at the station Noto in Sicily and the results from
global models of plate motions are taken as representative of the motion of the African
plate with respect to Eurasia, while VLBI solutions at Matera and Medicina, in the
southern and northern parts of the Italian peninsula, are geodetic observations that
must be compared with modelling results. Vertical deformation rates are taken from
geological and tide gauge records. The model that best ¢ts the observations includes the
e¡ects of subduction in the southern Tyrrhenian and convergence between Africa and
Europe.
The overthrusting of the Tyrrhenian domain onto the Adriatic domain results in an
eastward component of the velocity at the eastern border of the Tyrrhenian domain,
in agreement with VLBI data from the Matera and Medicina stations and GPS
data from northeastern Sicily and the Eolian Islands. The highest subsidence rates are
obtained in the southern Tyrrhenian, and are of the order of 1.2^1.4 mm yr{1. Along
the whole Adriatic coast of the Italian peninsula, subsidence in the foredeeps is
of the order of 0.2^0.5 mm yr{1. The Apenninic chain is rising with rates of the order
of 0.2^0.4 mm yr{1. Subduction beneath the Calabrian arc is responsible for a rollback velocity higher than in the northern areas. 2-D models, built for the geological
past, indicate the possibility of roll-back velocities of several centimetres per year. In
particular, active rifting in the Tyrrhenian and softening of the crust in the back-arc
basin result in a trench retreat velocity in agreement with geological estimates. Our
results show that numerical modelling can be used to estimate present-day deformation
rates and the contribution of active tectonics to sea-level changes along coastal areas.
Key words: 3-D modelling, central Mediterranean, convergence, deformation rate,
subduction.
I NT ROD UC T I O N
The Mediterranean region is attracting considerable attention
due to the complexities of its tectonic setting, which is considered a unique natural laboratory for studying the occurrence of extensional tectonics in a framework of continental
convergence.
* Now at: Departamento de Geof|¨ sica, Facultad de Ciencias F|¨ sicas,
Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040
Madrid, Spain.
ß 1999 RAS
In this paper, we will focus on the central Mediterranean, the
Tyrrhenian basin and surrounding mountain belts; this region
is a¡ected by the collision between the African and Eurasian
blocks and by the subduction of the Ionian lithosphere.
Extension started in the Tortonian within a N^S-trending
Alpine orogenic belt west of the Sardinia^Corsica block,
and evolved in a di¡erent way in the northern and southern
parts of the Tyrrhenian basin, with moderate extension in
the north and stronger extension in the south, where lithospheric thinning produced oceanic crust (Kastens et al. 1987).
Extension initiated in the western part of the Tyrrhenian basin
261
262
A. M. Negredo et al.
and migrated southeastwards with time (e.g. Spadini et al.
1995). A plausible scenario for the opening and evolution of
the central Mediterranean has been proposed by Malinverno
& Ryan (1986) based on a mechanism of trench retreat or
roll-back of the subduction hinge (Elsasser 1971) that causes
the opening of a back-arc basin, if the overriding plate does not
move towards the subducting plate to compensate for the
trench retreat. An important corollary in this scenario is that
back-arc basin formation and trench retreat can also occur
within a general context of convergence that occurs roughly at
right angles to the direction of trench retreat. The constraints
on the present-day style of convergence are provided by global
models of plate motion (Argus et al. 1989; DeMets et al. 1990),
by the release of seismic energy in the area (Pondrelli et al.
1995) and by geodetic studies using Very Long Baseline
Interferometry (VLBI) and Satellite Laser Ranging (SLR)
data (Ryan et al. 1992; Ward 1994; Robbins et al. 1992; Smith
et al. 1994). Recent VLBI analyses indicate that convergence
between the African and Eurasian blocks occurs at a rate of
about 6 mm yr{1 in a 150NE direction (Lanotte et al. 1996),
while previous studies based on global plate models and VLBI
measurements gave velocities of 7^8 mm yr{1 and directions
of 170^370 NW (DeMets et al. 1990; Ward 1994).
Subduction in southern Italy is indicated by seismic tomography (Spakman 1990; Selvaggi & Chiarabba 1995), deep
seismicity (McKenzie 1972; Gasparini et al. 1982), petrological
and geochemical studies (Serri et al. 1993) and recent analyses
of the modern stress ¢eld (Rebai et al. 1992). The occurrence
of intermediate seismicity beneath the northern Apennines
down to 90 km provides some indication of subduction in the
northern part of peninsular Italy also, although di¡erent in
style from the Calabrian subduction (Selvaggi & Amato 1992).
The purpose of this work is to model the geodynamics of this
area by means of a fully 3-D analysis based on numerical
methods. We start with the simplest 3-D models, adding
complexities such as realistic geometries at di¡erent stages in
order to understand the e¡ects of the various parameters of
the models. All the models are based on the idea of searching
for the e¡ects of the interplay of subduction and convergence
on vertical and horizontal crustal motions, which can be
compared with geological and geodetic data.
Recent e¡orts have focused on 2-D ¢nite element schemes in
vertical cross-sections at subduction zones (Giunchi et al. 1994;
Giunchi et al. 1996) and in the horizontal plane to simulate the
e¡ects of collision between Africa and Eurasia, where subduction is parametrized by means of trench suction forces
applied at plate boundaries (Bassi & Sabadini 1994; Bassi et al.
1997). In this 3-D study, both convergence and subduction are
taken into account self-consistently; unlike previous 2-D
subduction studies (Giunchi et al. 1996), convergence between
the continental blocks, occurring roughly at right angles to the
Tyrrhenian subduction, is taken into account. At the same
time, in contrast to the thin-plate analyses in the horizontal
plane carried out by Bassi & Sabadini (1994) and Bassi et al.
(1997), slab pull at subduction zones does not need to be
parametrized, being included self-consistently in the ¢nite
element modelling by means of density anomalies within the
subducted plate.
Fig. 1 is a simpli¢ed portrait of the neostructural domains
for peninsular Italy and surrounding regions (Ambrosetti et al.
1987), from which vertical crustal motion can be estimated for
the purpose of testing the modelling results. One of the main
goals of this study is to model the pattern of vertical velocities
characterized, as indicated in this ¢gure, by subsidence in the
foredeeps along the Adriatic and Ionian coasts, an uplifting
zone in the Apennines and Calabrian arc, and broad subsidence in the Tyrrhenian coastal areas. Another salient feature
on which we would like to focus attention is the arcuate shape
of peninsular Italy, which results from a higher roll-back
velocity in the southern area. This idea was ¢rst proposed by
Malinverno & Ryan (1986) and quanti¢ed by Negredo et al.
(1997) by means of a simpli¢ed 3-D model. The pattern of
subsidence and uplift together with the pattern of migration
velocity of the hinge line are the tectonic features that we want
to model in our study using a realistic con¢guration of the
central Mediterranean.
MOD E L D E S C R I P T I O N
We have developed a 3-D model based on a realistic geometry
to study the e¡ects of subduction and convergence on the
deformational pattern of the Italian peninsula and surrounding areas. With respect to our preliminary 3-D analysis
(Negredo et al. 1997), which assumed a simpli¢ed geometry
to study the ¢rst-order variations of roll-back velocity and
vertical motions from north to south, we now add some complexities such as the arcuate shape of the subduction hinge line
in order to permit a more detailed comparison between model
predictions and observations. In addition, we discuss the
e¡ects of the boundary conditions and their implications for
the tectonic mechanisms active in the central Mediterranean.
Fig. 2 shows the geometry and boundary conditions of the
model. The horizontal extension of the modelled area is
2700 km from west to east and 760 km from south to north.
We impose a free-slip condition to the eastern and western
boundaries of the model; this condition accounts for the
¢niteness of the Mediterranean domain and for the presence
of a strong oceanic lithosphere to the west of the Corsica^
Sardinia block and the Dinarides chain to the east of the
Adriatic domain. The northern and southern boundaries of
the domain trend E^W and correspond to the northern
termination of the Apenninic chain and the southernmost
Calabrian arc, respectively. An E^W free-slip condition has
been applied to the lithosphere at the northern boundary, with
zero S^N displacement, since convergence is considered
with respect to a ¢xed North European platform. In order to
investigate the relative importance of subduction and convergence, we have applied di¡erent conditions to the lithosphere at the southern boundary: free E^W slip, and a ¢xed
S^N velocity of convergence. In most models, the convergence
velocity is only applied to the Tyrrhenian block, in agreement
with the style of seismicity from western Sicily to Gibraltar
(Pondrelli et al. 1995). However, since it remains unclear
whether the motion of Africa is transmitted to the Adria
domain or whether this domain should be considered as an
independent microplate (see Faccenna et al. 1996 for further
discussion), we will discuss later the e¡ects of also applying
convergence to the subducting plate. Free motion of the
asthenosphere and lower mantle across the vertical boundaries
is allowed. The bottom of the model is ¢xed in the vertical
direction. The buoyant restoring force is applied at the top of
the model and is assumed to be proportional to the density
contrast at the surface and to the vertical displacement
(Williams & Richardson 1991).
ß 1999 RAS, GJI 136, 261^274
Crustal motion modelling, central Mediterranean
263
Figure 1. Simpli¢ed neotectonic map of Italy showing the main neostructural domains (simpli¢ed from Ambrosetti et al. 1987). The line with white
triangles represents the outermost belt of the Pliocene^Pleistocene thrusts. 1: Pre-Pliocene Alpine chain (uplift); 2: Pliocene foreland and Pliocene^
Quaternary foreland (uplift); 3: Pliocene^Quaternary foredeep (subsidence); 4: Pliocene foredeep (subsidence); 5: Apenninic^Maghrebian chain
(uplift); 6: Apenninic^Maghrebian chain (subsidence); 7: pre-Pliocene chains (uplift); 8: pre-Pliocene chains (subsidence).
We have modelled the dynamics of the central
Mediterranean by means of the ¢nite element MARC. The 3-D
mesh, consisting of 4125 elements, is portrayed in Fig. 2, with
the modelled area superimposed on top. The model includes
the lower and upper mantle, the subducted oceanic lithosphere
beneath the Calabrian arc, and the thinned lithosphere in the
Tyrrhenian domain. The accuracy of the solutions has been
veri¢ed by means of benchmark calculations, changing the
element size of the mesh. The 2-D mesh with eight nodes
per element used by Giunchi et al. (1996) is less sti¡ than the
3-D mesh used in this study. The 3-D counterpart of the 2-D
element with eight nodes could not be used because of the high
storage memory requirement.
The modelled hinge line is indicated by the thick dashed
line in Fig. 3. The most salient features are the two arcs, a
gentle one in the northern Apennines and a narrow one in
the southeast, corresponding to the Calabrian subduction
zone. One of the simplifying assumptions of the model is that
decoupling is limited to a single subduction fault, separating
an area of subsidence related to the sinking of the subducting
plate from an area of uplift at the border of the overriding
ß 1999 RAS, GJI 136, 261^274
plate. Therefore, the modelled hinge line follows not the
outermost belt of the thrusts but the boundary between subsiding and uplifting areas (Fig. 3), except in the northern
Apennines, where the curvature is less than in reality to avoid
numerical di¤culties due to the coarse mesh in this area
(Fig. 2). The gravitational sinking and roll-back of the slab
along the subduction fault is modelled assuming a zero friction
coe¤cient and using the slippery nodes method. The condition
of a locked subduction fault will also be tested in some of the
following calculations.
A key feature of our model is the di¡erent depths of subduction in the southern and northern areas (separated by the
thin solid line in Fig. 3). In the southern part of the model, we
have assumed a N^S extent of the area of deep subduction of
180 km (open triangles in Fig. 3), in agreement with the lateral
extension of the area a¡ected by deep seismicity (Selvaggi &
Chiarabba 1995). In this area, we have adopted the same
geometry, rheology and slab density structure as in Giunchi
et al. (1996). The subducting Ionian lithosphere is modelled
as an oceanic plate, consisting of a crust 10 km thick, a
harzburgite layer 30 km thick and a lower lithosphere 40 km
264
A. M. Negredo et al.
Figure 2. Model geometry, boundary conditions and 3-D ¢nite element mesh used in the calculations. The circles denote a free-slip condition.
The arrow denotes the velocity applied in some calculations to the southern boundary of the Tyrrhenian domain to simulate the motion of the
African plate. The springs represent the buoyant restoring force applied at the surface.
thick. Due to the high heat £ow values measured in the
southern Tyrrhenian (Mongelli et al. 1991), we have considered
a lithospheric thickness of 40 km, whereas a lithospheric
thickness of 80 km has been assumed for the northern areas.
For the sake of simplicity, the other parameters of the model do
not change from south to north and the whole Tyrrhenian
domain is assumed to be a continental plate. We have used a
linear viscoelastic rheology, with viscosities of 1024 Pa s for the
crust and harzburgite layer, 5|1022 Pa s for the lower lithosphere, 1021 Pa s for the asthenosphere and transition layer,
and 3|1022 Pa s for the lower mantle (Whittaker et al. 1992;
Spada et al. 1992). The elastic parameters are calculated using
the PREM reference model (Dziewonski & Anderson 1981).
The dip of the slab is 700 and reaches a depth of 500 km.
Although some authors suggest that the slab may be totally or
partially detached (e.g. Spakman 1990), we have modelled a
continuous slab on the basis of the absence of seismicity gaps
(Anderson & Jackson 1987; Selvaggi & Chiarabba 1995) and
on the results of numerical models (Giunchi et al. 1996), which
show that the stress pattern and present-day surface motions
are better reproduced when assuming a continuous slab. The
density anomalies within the slab, due to the phase transformation of a subducting oceanic plate, are based on the
petrological model of Irifune & Ringwood (1987) and reach a
maximum value of 400 kg m{3 at 400 km.
Further to the north, the interaction between the Tyrrhenian
and the Adriatic domains is a matter of debate. The presence of
subcrustal seismicity down to 90 km (Selvaggi & Amato 1992)
together with petrological and geochemical studies (Serri
et al. 1993) indicate a process of subduction/delamination of
the Adriatic lithosphere. However, the existence of a highvelocity body beneath the northern Apennines, representing a
detached (Spakman 1990) or continuous slab (Amato et al.
1993), is still a matter of debate. Mele et al. (1997) showed that
a region of shear-wave attenuation exists in the uppermost
mantle beneath the northern Apennines. Due to these still
controversial results, we have followed the cautious point of
view by modelling the dynamics of the Apennines for the
Quaternary as a zone of collision between the Tyrrhenian and
Adriatic domains. Comparison with geological observations
justi¢es a posteriori our hypothesis, and shows that it is
not necessary to invoke a process of subduction to explain
subsidence and uplift rates in the Adriatic foredeep and
northern Apennines, respectively. The underthrusting of the
Adriatic lithosphere is assumed to occur via a megathrust
(solid triangles in Fig. 3) dipping about 300 and reaching a
depth of 90 km.
The density contrasts in the slab and the convergence
velocity are activated at time t~0 and maintained constant
thereafter, following the same procedure as Whittaker et al.
(1992). After a time interval of about 250 kyr since loading,
dynamic equilibrium between the buoyant restoring force and
the forces arising from density contrasts and convergence
is attained. By this time, the unrealistic initial stress and
velocity distribution associated with instantaneous loading
have vanished and reached steady-state values; the vertical and
horizontal components of the velocity are then sampled at the
surface. The timescale of validity of the modelling results is
105 ^106 yr, during which the geometric con¢guration does not
change signi¢cantly; for longer integration times, viscoelastic
models overemphasize the sti¡ness of the lithosphere.
The velocity vectors shown in Fig. 3 correspond to the
CGS-VLBI-EUR96 solution, obtained by the Centre of Space
Geodesy of the Italian Space Agency in Matera. Table 1 gives
the velocities in mm yr{1 of the CGS-VLBI-EUR96 solution
for the VLBI stations Noto, Matera and Medicina in the
local topocentric reference frame (Lanotte et al. 1996). In order
to obtain the horizontal components of the velocity with
ß 1999 RAS, GJI 136, 261^274
Crustal motion modelling, central Mediterranean
265
Figure 3. Model boundaries (thick solid lines) superimposed on the simpli¢ed neotectonic map of Italy (for legend see Fig. 1). The modelled hinge
line (dashed line) follows approximately the limit between subsiding and uplifting areas. The thin solid line indicates the limit between the area of deep
subduction in the south and the area of thrusting further to the north. The open triangles indicate deep subduction of the Ionian lithosphere, whereas
the black triangles denote underthrusting of the Adriatic lithosphere to a depth of 90 km. The arrows indicate the directions and relative amplitude
of the velocity from VLBI data.
respect to northern Europe plotted in our ¢gures, the east and
north components of the velocity of Wettzell, taken from the
NUVEL1 model (DeMets et al. 1990), must be subtracted from
the components of the Mediterranean stations.
MOD E L L I NG R E S U LT S
Before presenting the modelling results, we summarize in
Table 2 the main assumptions of the models considered in
this study. In the following ¢gures, the horizontal and vertical
velocities are provided in the horizontal plane, superimposed
on the coastline of the Italian peninsula, in order to allow a
Table 1. CGS-VLBI-EUR96 solution of Lanotte et al. (1996),
obtained by the Centre of Space Geodesy of the Italian Space
Agency in Matera. The absolute velocity components and those
relative to Wettzell, and the standard deviations (in brackets) are given
in mm yr{1 .
Location
Up
Matera
Medicina
Noto
Wettzell
{1:4 (1:0)
{2:7 (0:8)
0:4 (1:0)
0:0
East
absolute relative
North
absolute relative
23:8 (0:2)
23:2 (0:2)
21:9 (0:2)
20:4
18:3 (0:3)
15:7 (0:2)
18:7 (0:3)
13:4
ß 1999 RAS, GJI 136, 261^274
3:4
2:8
1:5
0:0
4:9
2:3
5:3
0:0
direct comparison between modelling results and the pattern
of uplift and subsidence indicated by the neotectonic map
in Fig. 1. Comparisons with observations must be viewed
cautiously for two main reasons. First, viscoelastic models
tend to overestimate the £exural response of the lithosphere.
Second, the modelling results are valid for a timescale of
105 ^106 yr, which is shorter than the timescale of geological
observations. Therefore, we do not try to match exactly
the observed values of vertical motions, which might not
be representative of the large-scale features, but prefer a
qualitative comparison with the general trends shown in the
neotectonic map of Italy (Fig. 1).
Table 2. Summary of the characteristics of the di¡erent models. Vc is
the velocity applied to the southern limit of the models to simulate the
convergence between Africa and Eurasia.
Model Vc (N=S) Vc (E=W)
1
2
3
4
5
6
0
6:4
0
6:4
6:4
6:4
0
0
free
free
free
0
Features
Vc applied to both plates
locked fault
266
A. M. Negredo et al.
Model 1
In this ¢rst model the only active mechanism is slab pull; convergence has not been activated in order to emphasize the
e¡ects of subduction on the deformation pattern. The southern
border of the Tyrrhenian domain has been ¢xed in the E^W
direction.
The horizontal velocity pattern is shown in Fig. 4(a). The
main feature is that the gravitational sinking of the slab in
the southern Tyrrhenian induces horizontal £ow towards the
trench region in both the Tyrrhenian and the Adriatic domains;
this horizontal £ow is not limited to the subduction zone but is
also well developed at large distances from the subduction
zone, especially in the Tyrrhenian domain. It should be noted,
on the other hand, that, due to the ¢xed southern edge of the
Tyrrhenian domain, the amplitude of this £ow is small, at most
0.5 mm yr{1. These 3-D results indicate that the trench suction
force, caused by the gravitational sinking of the slab, also
exerts its in£uence at large distances from the trench region. If
we compare our results with the VLBI velocity at stations
Matera and Medicina, we realize that subduction cannot be the
only tectonic force acting in the central Mediterranean for the
present-day tectonic setting, because velocities for these two
VLBI stations are totally inconsistent with observations, in
both amplitude and direction.
Considering now the pattern of vertical velocity, the most
noticeable feature of Fig. 4(b) is the broad subsidence in the
southern part of the model, a¡ecting the Tyrrhenian and
Ionian domains. If we consider a transect perpendicular to
the hinge line, we recognize the characteristic features of the
vertical motion at subduction zones, which are subsidence
in the back-arc basin and the trench. East of the Calabrian
arc, a broad subsidence reproduces well the Plio-Quaternary
subsidence in the Ionian Sea, as indicated in the neotectonic
map of Fig. 1; it is remarkable that the highest subsidence
rate occurs in the southernmost sector of the Tyrrhenian sea, in
agreement with neotectonics. The values of the subsidence
rates in the back-arc basin and in the trench are respectively 0.6
and 0.2 mm yr{1. The subsidence rate in the back-arc region is
lower than that recorded by the ODP Leg 107 survey, which
was 1^2 mm yr{1 in the Marsili basin (Kastens et al. 1987).
The subsiding region is not localized at the subduction zone
but, although reduced in amplitude, extends to the north for
distances much larger than the lateral dimension of the subduction area. From the analysis of Fig. 4(b), we conclude that
subduction is the mechanism responsible for the subsidence in
the southern Tyrrhenian and Ionian seas. On the other hand,
this model underestimates the subsidence rates in the back-arc
and trench regions and is unable to reproduce the observed
uplift at the Apenninic and Calabrian arcs and the subsidence
in the northern Tyrrhenian and Adriatic foredeep, being thus
discordant with the neotectonic map of Italy. At least for the
present-day tectonic setting, a model in which subduction
beneath the Calabrian arc is the only active mechanism does
not reproduce VLBI data and the Quaternary pattern of
vertical velocities in the central and northern parts of the
Italian peninsula. Subduction is the mechanism that we must
invoke, on the other hand, to explain the style of subsidence in
the southern Tyrrhenian and Ionian seas.
Model 2
Figure 4. Results of model 1, where the only active mechanism is
subduction. E^W motion of the southern boundary of the Tyrrhenian
domain is not permitted. (a) Horizontal velocity distribution; the thick
arrows represent the VLBI velocity vectors (not scaled). (b) Vertical
velocity distribution in mm yr{1 . Positive values denote uplift and
negative values denote subsidence.
In this second model, a N^S convergence rate of 6.4 mm yr{1
is applied to the southern boundary of the overriding plate.
This velocity is an averaged value, both in amplitude and
direction, of the di¡erent estimates of the rate of convergence
between Africa and Europe deduced from global plate models
and geodetic observations at station Noto.
In comparison with Fig. 4(a), the horizontal velocity ¢eld is
drastically modi¢ed by the e¡ects of continental convergence
between the African and Eurasian blocks, which is responsible
for a generally north- to northeast-trending velocity in the
ß 1999 RAS, GJI 136, 261^274
Crustal motion modelling, central Mediterranean
267
allochthon caught between both plates (Fig. 3), it is hard
to distinguish whether it is recording the horizontal motion of
the overriding plate or that of the subducting plate. Strong
evidence in favour of the ¢rst hypothesis comes from recent
GPS results from Tonti (1997), which highlight the continuity
of the velocity vectors along northeastern Sicily, the Eolian
Islands and Matera (Fig. 6). The calculated north-northeast
component of the velocity at the eastern boundary of the
southern Tyrrhenian (Fig. 5a) is in good agreement with
the GPS results shown in Fig. 6. When we move to the north,
the velocity ¢eld in the proximity of the boundary between the
two plates shows a larger eastward component and a reduction
in the northward component. The reduction in the horizontal
component of the velocity is also consistent with VLBI data
from station Medicina. The model-predicted present-day
horizontal velocity pattern is characterized by a northward
component, due to the push of Africa, that is reduced when
moving to the north, and an eastward component due to the
overthrusting of the Tyrrhenian domain onto the Adriatic
domain, made possible by the relative slip of the two plates at
their junction.
The model-predicted velocity ¢eld in the Calabrian arc
shows the same characteristics as stations Noto and Matera, in
agreement with the results of ongoing GPS campaigns in the
area (Zerbini, personal communication, 1998). On the basis
of this model, appropriate for the present-day tectonic con¢guration of the central Mediterranean, the eastward component of the velocity, indicative of the opening of the
southeastern Tyrrhenian, is small, suggesting that the rollback velocity of the Calabrian arc in the short sampling time
window of geodetic data is much lower than the roll-back
velocity inferred from geological records. A detailed discussion
on this issue will be provided later.
If we compare Fig. 5(b) with Fig. 4(b), the most striking
e¡ect of the N^S collision of the African block is the appearance of subsidence along the Adriatic and Tyrrhenian coasts
Figure 5. Results of model 2, where convergence and subduction are
active. Same representation as in Fig. 4, but with the VLBI velocity
vectors scaled to the model results.
whole area (Fig. 5a). The most remarkable feature is the
rotation to the east of the velocity ¢eld in the Tyrrhenian
domain as one goes north, in contrast with the results of
model 1, in which the eastward component increases southwards. This larger eastward component in the north is clearly
due to the unlocked boundary between the two plates, which
allows for the overthrusting of the Tyrrhenian domain onto
the Adriatic domain. Station Medicina can be considered as
belonging to the Tyrrhenian domain as far as the horizontal
motion is concerned. This is consistent with plate tectonic
concepts, in which the allochthon is involved in the motion
of the overthrusting plate. This assumption becomes more
problematic when interpreting the motion measured at station
Matera: owing to its proximity to the outer limit of the
ß 1999 RAS, GJI 136, 261^274
Figure 6. Velocity vectors corresponding to the GPS results with
respect to a ¢xed Europe (from Tonti 1997).
268
A. M. Negredo et al.
of the peninsula, and uplift at the easternmost border of
the Tyrrhenian domain, which coincides with the front of the
Apenninic chain. The uplift of the outermost portion of the
chain agrees well with neotectonics (Fig. 1). The overthrusting
of the chain in the north onto the Adriatic plate is now
responsible for the appearance of a huge amount of subsidence in the Po valley, to the southeast of the Alps. In the
Adriatic and Ionian foredeeps, subsidence is substantially
increased with respect to model 1, while the uplift of the
Calabrian arc is now more pronounced, in agreement with the
elevation of marine terraces, which provide an uplift velocity of
0.9 mm yr{1 (Westaway 1993). The maximum of the modelled
uplift is, however, too far north and the model predicts subsidence in the southern portion of the arc, in contrast with
neotectonics. A possible reason for this mis¢t is that we have
considered an arcuate geometry not only for the hinge line but
also for the slab. Therefore, gravitational sinking produces a
di¡used subsidence in the surface and prevents uplift along the
whole Calabrian arc.
In contrast to Fig. 4(b), subsidence appears along the whole
Adriatic coast, in good agreement with Fig. 1. In the northern
Adriatic sea, backstripping analysis of commercial well
data yields Quaternary subsidence rates up to 0.5 mm yr{1
(Carminati et al. 1998), similar to our results (0.2^0.4 mm yr{1 ).
This comparison must, however, be viewed with caution due
to the local isostasy assumption made in the backstripping
calculations and to the model limitations mentioned.
Uplift of the Apenninic chain ranges from 0.2 to 0.4 mm yr{1 ,
in agreement with geological records (Zerbini et al. 1996). The
unrealistic rapid transition from uplift in the Apennines to
subsidence in the Adriatic foredeep is caused by the simplifying
assumption of accommodating the slip between the two plates
on a unique megafault. The model underestimates the E^W
extent of the portion of the peninsula subject to uplift, due
to the exaggerated £exural behaviour of the model already
pointed out, which has the tendency to create a zone of
subsidence in response to the uplifting chain.
With respect to model 1, subsidence in the southern
Tyrrhenian and Ionian seas is increased by the combined
e¡ects of subduction and overthrusting of the Tyrrhenian
domain onto the Ionian lithosphere. In the Tyrrhenian,
the subsidence velocity increases from 0.4^0.6 mm yr{1 in
Fig. 4(b) to 0.8^1.0 mm yr{1 , in closer agreement with geological records (Kastens et al. 1987). However, modelled
subsidence rates still underestimate the geologically recorded
rates by about the 30 per cent. A possible reason for this mis¢t
is that our modelling only considers the e¡ects of subduction
and convergence, and not extension and spreading in the
southern Tyrrhenian. Crustal thinning related to rifting would
cause additional subsidence due to the replacement of crust by
heavier mantle. Furthermore, our models predict £exural uplift
in the central and western Tyrrhenian Sea, which is a¡ected
by subsidence. Oceanic expansion occurred in this area during
the Pliocene (Trincardi & Zitellini 1987) and it is probably
a¡ected by thermal subsidence associated with cooling of a
thinned lithosphere, which cannot be reproduced by our purely
mechanical analysis.
An important source of information for testing the style
of subsidence along the coastal areas of the peninsula is sealevel records. Zerbini et al. (1996) determined vertical crustal
movements of less than +1:0 mm yr{1 from the tide gauge
records in the Mediterranean region. These values agree well
with the amplitudes of vertical motions along the coastal areas
portrayed in Fig. 5(b).
Model 3
In contrast to models 1 and 2, we now allow for E^W motion
of the southern boundary of the Tyrrhenian domain (Figs 7
and 8); this boundary condition accounts for a relative E^W
transcurrent motion of the Tyrrhenian and African domains,
indicated by the large shear zone north of Sicily (Del Ben
1997).
Fig. 7(a) shows the horizontal velocity pattern when subduction is the only active mechanism. The eastward motion of
the Tyrrhenian domain is increased with respect to Fig. 4(a),
Figure 7. Results of model 3, where only subduction is active and
E^W motion of the southern boundary of the Tyrrhenian domain is
allowed. Same representation as in Fig. 4.
ß 1999 RAS, GJI 136, 261^274
Crustal motion modelling, central Mediterranean
leading to an increase in the roll-back velocity and in the
eastward migration of the Calabrian arc. This result indicates
that the e¡ect of subduction on the retreat of the hinge line is
severely a¡ected by the boundary conditions that we apply at
the southern edge of the model or, when we compare our
modelling with reality, by the plate interaction in the southern
part of the Mediterranean. The vertical velocity pattern of
Fig. 7(b) is less a¡ected by the modi¢cation in the boundary
conditions with respect to Fig. 4(b), except for a slight increase
of the subsidence rates in the southern Tyrrhenian, with
the overall pattern remaining the same, and con¢rming that
subduction is the major controlling factor of the pattern of
subsidence in a region with lateral extent much larger that the
N^S extent of the slab.
269
Model 4
Fig. 8 shows the results obtained when a northward component of the convergence velocity of 6.4 mm yr{1 is applied
to the southern boundary of the modelled Tyrrhenian domain.
With respect to model 2, we now allow for E^W motion of
the southern boundary, thus increasing the eastward component of the velocity (Fig. 8a). When comparison is made
with the VLBI datum of Medicina, we observe that this model
shows a better agreement with the eastward component of the
velocity recorded at this station. With respect to Fig. 5(b),
the pattern of vertical motions is not substantially modi¢ed,
except for a general increase in the subsidence rates in the
southern Tyrrhenian and in the Adriatic and Ionian foredeeps. The reason for this increase is that free E^W motion
of the southern boundary enhances the overthrusting of the
Tyrrhenian block onto the Adria^Ionian domain. The conclusions drawn from Fig. 5(b) on the basis of the comparison
between modelling results and geological observables related
to the uplift rates of the Apennines and tectonic subsidence
inferred from commercial wells are the same as for Fig. 8(b).
Note that the subsidence rates calculated for the Ionian
and southern Tyrrhenian show a better agreement with
observations than those shown in Fig. 5(b).
Model 5
Figure 8. Results of model 4, which di¡ers from model 3 in that
convergence is also active. Same representation as in Fig. 4 with VLBI
velocity vectors scaled to the model results.
ß 1999 RAS, GJI 136, 261^274
In Fig. 9 the push from the African block is also applied
to the eastern plate, corresponding to the Adria^Ionian
domain. With respect to Fig. 8(a), the eastward motion in the
Tyrrhenian domain is reduced, while a westward component
is acquired by the Adriatic domain; this reduction is a consequence of the active underthrusting of the Adriatic plate
beneath the Tyrrhenian domain caused by the active push at
the southern edge of the plate. Due to the reduction in the
E^W component of the horizontal velocity along the border of
the overriding plate, the VLBI datum at Matera is less well
reproduced than in Fig. 8(a). Also, the velocity ¢eld that is
recorded in the Calabrian Arc by the ongoing GPS campaign
should resemble the VLBI datum of Matera. Further to the
north, this model also underestimates the eastward component
of the velocity recorded at the station Medicina. From this
model, we deduce that GPS campaigns in the Adriatic sector of
the Italian peninsula could become important in establishing
whether the African block is actively pushing the Adriatic plate
to the north with the same velocity as is recorded at station
Noto.
The pattern of the vertical velocities shown in Fig. 9(b)
shows some interesting new features compared with Fig. 8(b).
The uplift now follows the whole Apenninic chain, with the
uplift in Calabria uniformly distributed along the whole arc and
not con¢ned to the northern part of Calabria. The maximum
of the subsidence in the southern Tyrrhenian is now displaced
to the north, in agreement with the neotectonic map of Italy.
Subsidence and uplift rates are similar to Fig. 8(b), except
that uplift occurs in the whole Calabrian Arc, parallel to the
Apennines. Another remarkable di¡erence compared with
Fig. 8(b) is the substantial increase in subsidence in the Po
valley, and in the whole northern Adriatic sector. It should
be noted that the £exural response to this subsidence is
responsible for the uplift of the eastern portion of the Adriatic
plate.
270
A. M. Negredo et al.
Figure 9. Results of model 5, which di¡ers from model 4 in that the
convergence velocity is also applied to the southern boundary of the
Adria^Ionian domain. Same representation as in Fig. 4 with VLBI
velocity vectors scaled to the model results.
Model 6
In the set of calculations carried out in the previous models,
we have assumed that the boundary between the two plates is
free to slip, or totally unlocked. We now carry out another
experiment in which the boundary between the two plates
is totally locked. The convergence velocity is applied solely to
the Tyrrhenian sector. The pattern of the horizontal motion
shown in Fig. 10(a) preserves the rotation to the east towards
the Adriatic domain. We notice two major di¡erences from
previous unlocked models. First, the Adriatic domain now
has the same velocity pattern as the Tyrrhenian domain,
although reduced in amplitude. Second, we notice a substantial
reduction in the velocity, which is particularly evident in the
Figure 10. Results of model 6, which di¡ers from model 2 in that the
fault separating the Tyrrhenian and Adria^Ionian domains is totally
locked. Same representation as in Fig. 4 with VLBI velocity vectors
scaled to the model results.
Calabrian Arc, where the predicted amplitude is about a factor
of two lower than in previous calculations. This reduction is
clearly due to the resistance o¡ered by the Adriatic plate to
the northerly motion of the Tyrrhenian domain. These results
suggest that Matera and Medicina could be considered as
carrying the motion of the Adriatic domain only in the case in
which the two plates are coupled, which means that, on the
short timescale of VLBI observations, seismic release of energy
or aseismic creep are not su¤cient to unlock the boundary
between the two plates.
The pattern of the vertical velocities shows that the
maximum subsidence in the Tyrrhenian basin due to subduction is substantially reduced and displaced to the north
with respect to the unlocked models. The maximum subsidence
ß 1999 RAS, GJI 136, 261^274
Crustal motion modelling, central Mediterranean
resembles that of the model without convergence, owing to
the reduced e¡ectiveness of convergence in the locked model.
The subsidence maximum results from contributions from the
negative buoyancy of the subducted slab and from the £exural
response to the exaggerated uplift induced at the southern
edge. We have thus noticed that in general all the models
have the tendency to overestimate the £exural response of the
plates. This is clearly the unavoidable consequence of using
continuous plates, while in the real situation deformation
is accommodated by faults and aseismic creep. In the central
and northern sectors of the peninsula, the uplift disappears,
because the Tyrrhenian domain cannot overthrust onto the
Adriatic plate, and, for the same reason, subsidence in
the Adriatic foredeeps is drastically reduced. It is clear that this
locked model fails completely to reproduce the pattern of
vertical motions in the whole peninsula and surrounding basins
and foredeeps. This is the indication that, at least on the timescale of 105 yr, the two sectors of the peninsula, the Tyrrhenian
and Adriatic sectors, are decoupled. This decoupling occurs via
earthquakes and aseismic creep, as can be seen in the distribution of the earthquakes along the peninsula, which follows
the megafault separating the two plates in our model (Pondrelli
et al. 1995). We can say that the sequence of earthquakes
following the Apenninic chain accommodates the slip on the
megafault in our model on a geological timescale.
D I S C US S I O N OF 3 -D MODE L L I NG
The two cases that we have considered, totally unlocked and
totally locked, are of course two end-members of the real
con¢guration, in which the boundary between the two plates
can be partially locked, with heterogeneities along the whole
Italian peninsula, and with phases of locking and unlocking at
di¡erent times. Of course, there is no possibility at the moment
of modelling such a complex tectonic situation, so, to ¢rst
order, we limit our attention to these two end-members,
assuming the same coe¤cient of friction along the whole
boundary separating the two plates. Ongoing GPS campaigns
will probably provide better constraints on the interaction
between the two plates along the Italian peninsula in the near
future.
The pattern of vertical and horizontal motions of the
surface is reproduced properly by models 2 and 4 (Figs 5 and 8),
which include the e¡ects of subduction under the southern
Tyrrhenian Sea and convergence between Africa and Eurasia.
Discrepancies between model predictions and observations in
the southern Calabrian arc and in the Tyrrhenian Sea are
attributed to model limitations.
Fig. 11 shows in detail the variation of roll-back velocity
along the modelled subduction hinge line for the set of
models using an unlocked fault. This velocity is calculated
as the di¡erence at the hinge line between the horizontal
E^W velocities of the overriding and subducting plates. The
most evident features of this ¢gure are the high variability
of roll-back velocity among the di¡erent models and the
location of the maximum at the southern part of the study
area, corresponding to the subduction zone. The latter result
demonstrates the major role of slab-pull in controlling the
velocity of trench retreat on timescales of 105 yr.
Models carrying solely a subducted plate without convergence (models 1 and 3) produce insigni¢cant roll-back
ß 1999 RAS, GJI 136, 261^274
271
Figure 11. Variation of the roll-back velocity along the modelled
hinge line, obtained for the models (indicated by the labels) with an
unlocked fault.
values. The e¡ects of subduction on roll-back velocity are
enhanced when convergence is activated and E^W motion of
the southern boundary is permitted (models 4 and 5); strong
variations of roll-back velocity occur along the hinge line. At
the subduction zone, roll-back increases from 1 mm yr{1 in
model 3 to 5 mm yr{1 in models 4 and 5, while a substantial
reduction is observed along the hinge line. In the northern
sectors of the peninsula, the presence of the Adriatic plate
counteracts the eastward extrusion of the Apenninic chain,
whereas further to the south, the sinking of the slab permits
the lateral extrusion of the Calabrian Arc. Our results indicate
that slab sinking acting roughly at right angles to continental
collision has the e¡ect of `opening the door' to the escape of
crustal material, favouring faster roll-back velocities at the
subduction zone.
2 -D MOD E L L I NG OF T H E G E OL O G ICA L
PA ST
Geological estimates based on the migration of hinterland
extensional and foreland compressional basins indicate a rate
of trench retreat since the Tortonian of 5^6 cm yr{1 for the
southern Calabrian Arc and 1.5^2 cm yr{1 for the northern
Apennines (Patacca et al. 1990; Cipollari & Cosentino 1994).
Model 4 provides an average roll-back velocity in the southern
area three times higher than in the northern area, in agreement
with the geologically observed trend. However, the precise
values are not comparable, because modelling of the tectonic
evolution since Tortonian times would require modi¢cation of
the geometry of the plates and a softer rheology, appropriate
for timescales of 107 ^108 yr (Gurnis et al. 1996). In general, all
the models shown in the previous ¢gures predict roll-back
velocities lower than those estimated from geological records;
possible causes could be the sti¡ness of the 3-D mesh and the
simpli¢ed rheology and geometry of the models.
We have seen, on the other hand, that roll-back is extremely
sensitive to the geometry and boundary conditions imposed on
the model in the vicinity of the subducted slab, and it could well
be that modelled velocities derived for the present-day tectonic
setting are not representative of the geological past. Since it
is impossible to establish with the necessary precision the
272
A. M. Negredo et al.
(Vigliotti & Langenheim 1995); this event was followed by
rifting in the Tyrrhenian. During this phase, hot uppermantle material replaced the broken continental crust. In our
purely mechanical model, this event is modelled by means of
decreasing the viscosity of the lithosphere to asthenospheric
values, as in the rifted Tyrrhenian model (dashed curve). This
reduction causes an increase in the roll-back velocity of about
50 per cent with respect to the reference model (solid line),
providing a value that, although underestimating the geologically inferred roll-back velocities quoted above, agrees
well with the average velocity of hinge retreat during the
last 20 Myr of 2 cm yr{1 estimated by Malinverno & Ryan
(1986).
Inspection of the lower panel of Fig. 12 indicates that the
pattern of vertical motion rates is less a¡ected by the modi¢cation in the boundary conditions than the horizontal
motions. We notice, however, that the fastest model (dotted
line) predicts vertical velocities in the arc and in the trench two
times higher than those of the reference model (solid line).
CO NC LU D ING R EM A R K S
Figure 12. (a) Horizontal and (b) vertical components of the surface
velocity obtained with three di¡erent 2-D models. The free edge model
assumes free E^W motion of the left edge. The rifted Tyrrhenian model
assumes a reduction of the lithosphere viscosity in the area of the basin
to account for continental break-up.
geometry and conditions for the geological past, we test some
simpli¢ed 2-D models with the same geometry and element
type as Giunchi et al. (1996) in order to study the possible
causes of higher roll-back velocities in the past. The horizontal
and vertical surface velocities are shown in Fig. 12. Positive
and negative values of horizontal velocity denote eastward and
westward motions, respectively. The discontinuity at 1675 km
corresponds to the location of the hinge line. The model
assuming free motion of the left edge of the overriding
plate could be representative of an old tectonic setting, when
large southward and eastward motions in the Mediterranean
allowed the formation of the Balearic and Liguro^Provencal
basins and counterclockwise rotation of the Corsica^Sardinia
block (Auzende et al. 1973). With respect to the ¢xed edge
model (solid line) roll-back is increased by a factor two
to nearly 3 cm yr{1. This value is comparable to the high
velocities of trench retreat for open oceanic environments, such
as in the Paci¢c.
These results indicate that in a closed environment such as
the Mediterranean, roll-back velocities of the Calabrian Arc
are necessarily lower than those found in oceanic environments
such as the Paci¢c, because of the ¢niteness of the domain
that, at least for the present-day tectonic setting, inhibits the
possibility of large displacements of the overriding plate and
£ow in the mantle.
The free left edge boundary condition is not realistic
after the Middle Miocene (about 15 Myr ago), when the
Corsica^Sardinia block stopped its counterclockwise rotation
The generally satisfactory agreement between 3-D modelling
results and the crustal motion pattern inferred from geological
and geodetic observations indicates that, to ¢rst order, the
principal tectonic structures and forces have been correctly
reproduced, at least for the Plio-Quaternary. Discrepancies
between model results and observations in the Tyrrhenian Sea
can be attributed to model limitations, since the model does
not account for subsidence caused by rifting. The present-day
horizontal motion pattern, together with the subsidence in
the back-arc basin and in the foredeeps and the uplift of the
Apennines can only be reproduced when both subduction
in the Calabrian Arc and convergence between Africa and
Europe are included in the models. The model that best ¢ts the
observations, model 4, assumes that the interaction between
the Tyrrhenian and Adria^Ionian domains occurs via an
unlocked fault, and that the southern boundary is free to move
in the E^W direction.
Although slab-pull alone causes a very low hinge retreat
velocity, sinking of the slab strongly enhances the eastward
extrusion of the Calabrian arc when convergence is active.
This study con¢rms that subduction beneath the Calabrian
arc is responsible for a faster hinge retreat velocity in the
southern areas of the model, in agreement with previous
studies (Malinverno & Ryan 1986; Faccenna et al. 1996;
Negredo et al. 1997).
Calculated roll-back velocities along the hinge line are
clearly smaller than those inferred from geological studies. 2-D
models built for the geological past indicate that the roll-back
velocity could have been signi¢cantly higher in the past, either
due to a reduced viscosity in the back-arc basin accounting for
active rifting in the Tyrrhenian Sea or due to E^W motion at
the western boundary.
AC K NOW L E D G ME N T S
This work is ¢nancially supported by the EU grant
`Geodynamic modelling of the Western Mediterranean'
no. CHRX-CT94-0607 and by the contract no. ARS -96-120 of
ß 1999 RAS, GJI 136, 261^274
Crustal motion modelling, central Mediterranean
the Italian Space Agency. Dr H. Zeyen and an anonymous
referee are thanked for very constructive reviews that helped
to improve the contents and structure of this paper. Carlo
Giunchi is thanked for useful discussions. We also thank
Susanna Zerbini for providing us with the GPS data shown in
Fig. 6.
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