Three-dimensional modelling of crustal motions caused by subduction and continental convergence in the central Mediterranean

Transcription

1 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 Bianco 2 and Manel Fernandez 3 1 Dipartimento di Scienze della Terra, Universita di Milano, Via L. Cicognara, 7, Milano, Italy. anna@sabadini.geo sica.unimi.it 2 Centro di Geodesia Spaziale, Agenzia Spaziale Italiana, Localita Terlecchia, C.P. Aperta, Matera, Italy 3 Institute of Earth Sciences `J. Almera'öCSIC, Lluis Solë i Sabar ss/n08028, Barcelona, Spain Accepted 1998 August 25. Received 1998 August 25; in original form 1997 November 12 INTRODUCTION 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, Madrid, Spain. SUMMARY 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. 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 ß1999RAS 261

2 262 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 15 0 NE 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 17 0^37 0 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. MODEL DESCRIPTION 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 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). ß1999RAS,GJI 136, 261^274

3 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 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 ß 1999 RAS, GJI 136, 261^274

4 264 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 southerntyrrhenian (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 Pa s for the crust and harzburgite layer, Pa s for the lower lithosphere, Pa s for the asthenosphere and transition layer, and 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). Thedipoftheslabis70 0 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 30 0 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 10 5^10 6 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 ß1999RAS,GJI 136, 261^274

5 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. MODELLING RESULTS 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 East North absolute relative absolute relative Matera {1:4 (1:0) 23:8 (0:2) 3:4 18:3 (0:3) 4:9 Medicina {2:7 (0:8) 23:2 (0:2) 2:8 15:7 (0:2) 2:3 Noto 0:4 (1:0) 21:9 (0:2) 1:5 18:7 (0:3) 5:3 Wettzell 0:0 20:4 0:0 13:4 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 10 5^10 6 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. V c is the velocity applied to the southern limit of the models to simulate the convergence between Africa and Eurasia. Model V c (N=S) V c (E=W) Features : free 4 6:4 free 5 6:4 free V c applied to both plates 6 6:4 0 locked fault ß 1999 RAS, GJI 136, 261^274

6 266 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; 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. 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 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 ß1999RAS,GJI 136, 261^274

7 Crustal motion modelling, central Mediterranean 267 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 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 6. Velocity vectors corresponding to the GPS results with respect to a xed Europe (from Tonti 1997). ß 1999 RAS, GJI 136, 261^274

8 268 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 mmyr {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. ß1999RAS,GJI 136, 261^274

9 Crustal motion modelling, central Mediterranean 269 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. 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. 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 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. ß 1999 RAS, GJI 136, 261^274

10 270 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 ß1999RAS,GJI 136, 261^274

11 Crustal motion modelling, central Mediterranean 271 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 10 5 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. DISCUSSION OF 3-D MODELLING 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 10 5 yr. Models carrying solely a subducted plate without convergence (models 1 and 3) produce insigni cant roll-back 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 MODELLING OF THE GEOLOGICAL PAST 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 10 7^108 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 ß 1999 RAS, GJI 136, 261^274

12 272 A. M. Negredo et al. 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 (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). CONCLUDING REMARKS 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. ACKNOWLEDGMENTS This work is nancially supported by the EU grant `Geodynamic modelling of the Western Mediterranean' no. CHRX-CT and by the contract no. ARS of ß1999RAS,GJI 136, 261^274