1 SGI 12/ Boll.Soc.Geol.It. (Ital.J.Geosci.), Vol. 128, No. 1 (2009), pp , 12 figs., 1 tab. Queste bozze, corrette e accompagnate dall allegato preventivo firmato e dal buono d ordine, debbono essere restituite immediatamente alla Segreteria della Società Geologica Italiana c/o Dipartimento di Scienze della Terra Piazzale Aldo Moro, ROMA Propagation of an inherited strike-slip fault through a foreland-chain system: quantitative aspects from analogue modeling and applications GIOVANNI TOSCANI (*), DANIELA DI BUCCI (**), ANTONIO RAVAGLIA (*), (***), SILVIO SENO (*), UMBERTO FRACASSI (****) & GIANLUCA VALENSISE (****) ABSTRACT We investigated quantitatively the propagation of a reactivated strike-slip fault through a sedimentary cover. To this end we prepared five simplified analogue models that reproduce a chain with its frontal allochtonous wedge overrunning the foreland. The foreland/chain deformation follows the reactivation of an inherited strike-slip fault cutting the foreland domain. The observation and quantification of the effects of this reactivation, in particular on the orogenic wedge front, provide new insight on the evolution of this type of tectonic setting. We placed special emphasis on quantifying the structural features observed in the models to (1) interpret the kinematics of the reactivated shear zone, and (2) put forward hypotheses on areas indirectly affected by the reactivated fault. The interpretation of the models was based on an integrated analysis of surface and subsurface data. The results show that the geological setting is strongly influenced by the presence of a reactivated preexisting lineament, that ultimately controls the development and pattern of newly-formed faults. Finally, we present and discuss two natural examples (in Italy Molise-Gondola shear zone, Southern Apennines, and Scicli-Ragusa line, Sicily) in view of the modeling results. KEY WORDS: Fault reactivation, foreland, orogenic wedge, sandbox models, quantitative analysis. RIASSUNTO Propagazione di una faglia trascorrente ereditata attraverso un sistema avampaese/catena: aspetti quantitativi e applicazioni sulla base di modelli analogici. Nel presente lavoro è stata investigata quantitativamente la propagazione di una zona di taglio regionale, trascorrente, ereditata che, riattivandosi, fa risentire i propri effetti su una copertura sedimentaria. Tale copertura è data dalla parte frontale di una catena caratterizzata da unità alloctone (cuneo orogenico), marcatamente sovrascorse sul relativo avampaese in cui è presente la zona di taglio stessa. Per questo motivo, sono stati realizzati cinque modelli analogici che riproducono in modo semplificato le deformazioni a carico di un sistema costituito da avampaese-cuneo orogenico-catena, conseguenti alla riattivazione di una faglia trascorrente ereditata sita all interno dell avampaese e ortogonale al fronte della catena. Le osservazioni e le analisi quantitative degli (*) Dipartimento di Scienze della Terra, Università di Pavia, Via Ferrata, Pavia, Italy. Tel Fax (**) Dipartimento della Protezione Civile, Via Vitorchiano, Roma, Italy. (***) PetroSA, 151 Franns Conradie Drive, Parow 7500, Republic of South Africa. (****) Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata, Roma, Italy. effetti della riattivazione sul cuneo orogenico e sulla catena, possibili grazie alla grande quantità di dati facilmente ricavabili dai modelli, forniscono in particolare ulteriori e nuovi spunti sulla conoscenza della possibile evoluzione di questi sistemi e contesti strutturali. Particolare attenzione è stata dedicata agli aspetti quantitativi di elementi strutturali osservati nei modelli per (1) interpretare correttamente la cinematica del lineamento riattivato e (2) formulare osservazioni e ipotesi sui domini che non ospitano direttamente il lineamento riattivato (cuneo orogenico e catena). L interpretazione dei modelli si è basata sull osservazione e l analisi congiunta dei dati raccolti in superficie e in profondità (superficie del modello e sezioni del modello stesso). I risultati mostrano che il contesto geologico è fortemente influenzato dalla presenza di un lineamento preesistente che si riattiva e che controlla lo sviluppo delle faglie di nuova formazione. Al termine del lavoro, vengono proposti e discussi due esempi di casi naturali in Italia (Molise- Gondola shear zone, Appennino Meridionale e linea Scicli-Ragusa, Sicilia) alla luce dei risultati dei modelli analogici qui presentati. TERMINI CHIAVE: Riattivazione, avampaese, cuneo orogenico, modelli analogici, analisi quantitativa. 1. INTRODUCTION This paper follows and integrates a previous study (DI BUCCI et alii, 2006) where a set of analogue models was studied to clarify the seismotectonic setting of a portion of the Southern Apennines chain and related foreland. In the previous paper, we thoroughly analysed the seismotectonic implications of this set of models. However, a quantitative structural investigation and a detailed analysis of the propagation of the deformation through the models (i.e. through different structural domains) were still missing. For this reason, we carried out the quantitative study here presented, that has to be considered as a complement of the previous work. The paper is organised in three parts. The first one is a short description of the analogue models presented by DI BUCCI et alii (2006) and resumes the main results obtained by these investigators (paragraphs 1, 2 and 3). The second part is completely new, and is focussed on the quantitative analysis of the models and of their kinematics and evolution through time (paragraphs 4, 5, 6 and 7). At the end of the paper, the third part corresponds to an appendix devoted to two real geological cases, showing similar structural conditions, whose interpretation could benefit from insights provided by the analogue models described. A reactivated strike-slip fault may occur in various tectonic settings including foredeeep basins, volcanic
2 2 G. TOSCANI ET ALII Fig. 1 - Block-diagram showing the modes of crack propagation at the tip lines of a right-lateral strike-slip fault of the foreland through the chain. Blocco-diagramma che mostra la propagazione della deformazione ai limiti di una faglia trascorrente destra dell avampaese attraverso la catena. Fig. 2 - Experimental set-up. Two fixed sidewalls confine the sand, parallel to the strike-slip motion, whereas the model is open on the other two sides. The three regional-scale structural domains discussed in the text are indicated as A, B, C. Set-up dei modelli. Due pareti laterali, parallele al movimento della faglia, confinano la sabbia, mentre sugli altri due lati il modello non è confinato. I tre domini strutturali di cui si tratta nel testo sono indicati con A, B, C. domains and chains (a chain is here intended as a stack of thrust sheets with its allochtonous frontal wedge, a few kilometers thick, unaffected by regional vertical strikeslip faults coinciding with those existing underneath, in the buried foreland). Positively identifying a buried fault through the structural analysis of the overlying chain is especially important in active tectonics, as it may allow blind or simply unidentified seismogenic structures to be detected and taken into account in seismic hazard and scenario studies. For this reason, we developed and analyzed a set of sandbox models, aimed at (i) investigating how strike-slip motion along a pre-existing zone of weakness, exposed or buried, propagates toward the surface and affects the cover belonging to a chain-foreland system; and (ii) characterizing the propagation of deformation from this inherited structure as a function of displacement. When propagating through a chain and its «allochtonous» frontal wedge, a buried, reactivated, large strikeslip fault is expected to exhibit the same behavior as a new fault growing in a brittle environment (fig. 1). The propagation is preceded by pervasive brittle damage of the host rock. Due to the perturbation of the stress field at the tips of the fault, strain accumulates in these regions as the fault grows (MANDL, 2000; and references therein). Strain at the tips of a fault has been traditionally described in terms of modes of crack propagation (SCHOLZ, 1990; and references therein), where Mode-I is the tensile or opening mode (crack wall displacements normal to the crack), and Mode-II (displacements in the plane of the crack and normal to the crack edge) and -III (displacements in the plane of the crack and parallel to the edge) are the shear modes. For instance, in case of a vertical strike-slip fault, the Mode-II is expected at the vertical tips of the fault, the Mode-III at the horizontal tips, and a combination of them along the oblique tips (KIM et alii, 2004; KIM & SANDERSON, 2006; fig. 1). 2. EXPERIMENTAL SET-UP We carried out a set of models, deformed in a natural gravity field, aimed at reproducing the crustal volume formed by a foreland hosting an inherited discontinuity, namely a sub-vertical strike-slip fault, and a chain with its frontal wedge overrunning the faulted foreland (fig. 2). All models were scaled 1:200,000 (0.5 cm = 1 km in nature). In scaling the model setup, we took into account geometric, kinematic and dynamic similarity relationships (HUB- BERT, 1937; RAMBERG, 1981). The relation C p /r p = C m /r m links natural and experimental conditions. C is the cohesion, r is the density in nature (subscript p) and models (subscript m), respectively. Knowing that r m is 1500 kgm -3 and r p is 2800 kgm -3, the cohesion in the model (~10 Pa) corresponds to ~100MPa in nature. The frictional properties of granular materials used for the models have been measured using a Casagrande shear box (CASAGRANDE, 1932). The cohesion has been derived indirectly by extrapolating the value from several Casagrande shear box tests. We used two different granular materials: dry sand and glass microbeads. The angles of internal friction (f) are equal both in the models and in nature as the angles measured on the analogue materials (the angle of a stable cone of sand/microbeads) are comparable to those determined experimentally for upper crustal rocks (BYERLEE, 1978). The sand has f = 33 and grain size in the range mm. Glass microbeads have f = 24 and grain size in the range mm. Their low internal friction is due to high sphericity and rounding (SCHELLART, 2000) so that glass microbeads enable low basal friction detachment and inter-strata slip (SASSI et alii, 1993; TURRINI et alii, 2001). The basal detachment has f = 32. For the quantitative description of experimental apparatus and all materials from a rheological point of view we adopted the values described by SCHREURS et alii (2006). The apparatus was provided with a baseplate fault, which extended for the whole length of the models and accommodated a simple right-lateral shear. The basal displacement varied for each model from 0.5 cm to 8.0 cm. We prepared five independent models. The first (SS02; fig. 3) reproduces a typical wrench zone as widely described in literature (among many others: WILCOX et alii, 1973; CHRISTIE-BLICK & BIDDLE, 1985; HARDING, 1985; NAYLOR et alii, 1986; SYLVESTER, 1988; RICHARD & COBBOLD, 1990; RICHARD et alii, 1995; MANDL, 2000; NIEUWLAND & NIJMAN, 2001; LE GUERROUÉ & COBBOLD,
3 PROPAGATION OF AN INHERITED STRIKE-SLIP FAULT THROUGH A FORELAND-CHAIN SYSTEM 3 Fig. 3 - Interpreted plan-views of the final step of reference model SS02 (top) and model SS03 (bottom). Reference vertical lines are spaced ca. 5.5 cm. The horizontal hatched line is the baseplate fault. Final displacement was D = 8.0 cm for both models. Interpretazione della visione in mappa della fase deformativa finale dei modelli SS02 (in alto) e del modello SS03 (in basso). Le linee verticali di riferimento sono spaziate di circa 5.5 cm. La linea orizzontale tratteggiata rappresenta ed indica la faglia di base. Per entrambi i modelli il rigetto finale è pari a 8 cm. 2006). It has a constant thickness of 10 cm, its sand volume has constant physical and rheological characteristics (neither layers of glass microbeads, nor cuts), and the total displacement applied to its baseplate fault is 8.0 cm. This model was used as a reference for four additional models (SS03 to SS06, shown in map view in fig. 4), all specifically designed to reproduce the foreland-orogenic wedgechain system. We added to these models a layer of glass microbeads at the interface between the buried foreland and the orogenic wedge, aimed at simulating the highly tectonized zone in correspondence of the basal thrust separating the chain from its foreland (fig. 2). The chain-side of the model is slightly thicker (11 cm) than the forelandside (10 cm) to account for topography. The models SS03- SS06 were subjected to progressively smaller displacements: 8.0, 5.5, 3.0 and 0.5 cm, respectively. Within the entire foreland domain (both the exposed region and the portion lying below the wedge) a 5 mmthick layer of glass microbeads simulates the presence of a thick layer (~1,000 m) of Triassic anhydrite-dolomite rocks at the bottom of the Apulia platform. The foreland domain is intersected by a vertical discontinuity perpendicular to the wedge front, obtained through a cut that reorganizes the grain distribution (SASSI et alii, 1993; VIOLA et alii, 2004) and creates a preferential slip surface. This discontinuity starts from the baseplate fault and has a vertical attitude. Conversely, no discontinuities were introduced in the chain-side portion of the model and in the wedge itself. The model set-up aims at reproducing the three main regional-scale domains which together describe the tectonic setting we intended to study: domain A - the foreland; domain B - the frontal wedge (including the foredeep deposits); domain C - the chain. In the following these domains will be referred to simply as A, B, C. Fig. 4 - Plan-view of the SS06, SS05, SS04 and SS03 models (from top to bottom) at the end of the deformation. The black line indicates the front of the orogenic-wedge; the hatched white line is the projection of its bottom-end on the model surface. Mappa dei modelli SS06, SS05, SS04 e SS03 (dall alto in basso) al termine della deformazione. La linea nera indica il fronte del cuneo orogenico; la linea bianca tratteggiata è la proiezione sulla superficie della sua terminazione alla base dell esperimento.
4 4 G. TOSCANI ET ALII Fig. 5 - Interpreted line drawing of fig. 4. Different structural domains are represented from left to right with different grey colours (A=foreland=heavy grey; B=wedge=medium grey; C=chain=light grey). Line-drawing di quanto mostrato in fig. 4. I differenti domini strutturali sono rappresentati da sinistra verso destra con differenti gradazioni di grigio (A=foreland=grigio scuro; B=cuneo orogenico=grigio intermedio; C=catena=grigio chiaro). 3. COMPARISON WITH PREVIOUS SIMILAR EXPERIMENTS (STRIKE-SLIP, REACTIVATION) AND LIMITATIONS OF THE MODELS Many workers investigated strike-slip mechanisms and fault reactivation in different geological settings using analogue models and demonstrated how pre-existing lineaments influence the pattern of strike-slip faults in the overlying deposits (NAYLOR et alii, 1986; MANDL, 1988; RICHARD et alii, 1995). The «novelty» of our experiments is that we modeled and analyzed together three different structural domains that interact during the deformation. This allowed us to bridge the gap between a number of natural examples and large part of the existing literature, which is generally focused on single structural domains. Modeling shear zones at different scales has shown that the rheological properties of the materials used and their thickness have the greatest impact on the final width of the shear zone and the length of the associated faults (TCHALENKO, 1970). Different stratigraphies have been tested (brittle and brittle-viscous) to study the geometrical pattern of faults, both in map and in cross section (RICHARD et alii, 1989; RICHARD & COBBOLD, 1990; RICHARD & KRANTZ, 1991). All these studies confirmed that the fault geometry and kinematics are strongly influenced by rheology and that flower structures or palm tree faults may develop even in the absence of transpressive deformation. Fault dip within the flower structure decreases even further whenever a compressional stress component is introduced. The width and complexity of the shear zones vary as displacement increases. As in any modeling technique, sandbox analogue models have several limitations that must be taken into account while reproducing geological settings and analyzing results. In some cases, the scale of the model is a limitation itself; the presence of natural thin viscous layers cannot be simulated, as their modeled thickness would be too small to be reproduced in a sand-box apparatus. For example, in our models the rheological structure of the natural thrust wedge and of the chain is reproduced by a system composed only of brittle rocks. The presence of internal layers, faults, fractures, zones of weakness, etc., all features that occur everywhere in natural cases, is hence neglected, so that these parts of the models are isotropic. In addition, faulting in the upper crust responds to variables like pore-fluid pressure, heat flow, presence of overpressured shales, and flexural and isostatic effects that are difficult to simulate in a sand-box model. Extreme folding is also impossible to reproduce with sand and microbeads only. Finally, an undesired effect that often occurs in sand-box models is dilation, that may cause a volume increase (up to 5% and beyond) depending on grain size, sphericity, rounding and initial gathering conditions of the material (SCHOPFER & STREYER, 2001). Nevertheless, since our work aims at simulating and studying the overall behavior of the complex system composed by the aforementioned tectonic domains, we are confident that these limitations do not prevent large-scale quantitative analyses as those presented in the following paragraphs. This is suggested and supported by the good geometric similarities between the analogue models and the natural cases that we will discuss at the end of the paper for a comparison.
5 PROPAGATION OF AN INHERITED STRIKE-SLIP FAULT THROUGH A FORELAND-CHAIN SYSTEM MODEL EVOLUTION 2. EXPERIMENTAL RESULTS Surface structures can be observed simply by looking at the experiments as they evolve (fig. 5). On the contrary, internal structures can be analyzed only by cutting (that is to say, destroying) the models, unless non-invasive means of analysis (e.g., X-Ray tomography) are available. A detailed analysis of the model evolution can be found in DI BUCCI et alii (2006) where the reference model and the SS03 model are compared step by step and where all faults are distinguished on the base of their activity; for this reason, in this paragraph, we skip this description and analysis in order to focus the attention on the maps of the four models, representing the «bench marks» for the quantitative analysis here presented. Nevertheless, a continuous analysis of the model evolution has been carried out (as the measurements have been taken at every 0.5 cm of deformation), even if it is not shown using every step of the models but only the maps of the main four models. As mentioned earlier, we prepared a model without topographic variations and discontinuities (no pre-cut, no layers of glass microbeads) as a «reference» to which to compare the other models of this study. fig. 3 shows the fault pattern at the surface of the reference model SS02 (top) and of model SS03 (bottom); for both these experiments the displacement of the baseplate fault was 8.0 cm. In SS03 new faults form only in domains B and C. In domain A, the pre-existing fault acts as a preferential slip surface accommodating almost all the displacement; in fact, no newly formed faults will ever show up in domain A. The model sequence from SS06 to SS03 documents the progressive deformation of the same shear zone. As the basal displacement increases from 0.5 cm up to 3.0 cm (models SS06 and SS05, respectively) a number of structures form near the front of the orogenic wedge (domain B) and in particular in the northern (i.e. receding) block exclusively (fig. 5). At 3.0 cm of displacement, the model (SS05, figs. 4 and 5) exhibits a certain concentration of active faults in its central part and an increasing development of faults deviating from the E-W strike. In foreland domain A, the only active fault is the preexisting one, whereas in the orogenic wedge domain B faults are still present only in its northern portion. At 4.5 cm of basal displacement, active faults are detectable over the entire length of the models. These faults strike quite close to the strike of the baseplate fault and tend to be located in a central limited band, parallel to the shear direction. The final steps corresponding to 5.5 cm and 8.0 cm of displacement (models SS04 and SS03) show the evolution of the experiment when a «steady state» is reached and overrun, i.e. when the northern and southern blocks are completely separated by faults and move independently. In these last steps of deformation, the only active faults are the central ones. We do not observe any new active faults between 5.5 and 8.0 cm of basal displacement, but only an increase of displacement on already existing faults that are suitably oriented with respect to the shear direction. The kinematics of the models shows how the initial set-up influences the development of brittle structures. In all models the presence of a pre-existing cut prevents the formation of new faults in domain A. In domain B (orogenic wedge) all the brittle structures develop asymmetrically turning northward from the E-W strike. Finally, structural features of domain C are similar to those seen in models reproducing purely strike-slip displacement (see SS02, fig. 3) FINAL MODEL GEOMETRIES The deformation seen at the surface of model SS03 (no newly-formed faults in foreland domain A, asymmetric fault distribution in wedge domain B, widespread faulting in chain domain C; figs. 3, 4 and 5) has its counterpart in the vertical sections of all the models, as exemplified by model SS05 (figs. 6 and 7). The sections used to create the 3D view are perpendicular to the baseplate fault and typify the three domains A, B and C of the experiments. In domain A (S 66; figs 6 and 7), we observe the complete absence of new faults, confirming that the inherited fault takes up the entire imposed displacement. In domain B (S 54), incipient faulting is evident since the very early steps of deformation (model SS06; 0.5 cm of displacement, fig. 5). As deformation increases, these new faults also grow in number and displacement. For 0.5 cm of basal displacement, the only existing fault hardly reaches the topographic surface with almost no apparent vertical throw. On the contrary, faults of the Fig. 6 - Sketched 3D reconstruction of the central part of the model SS05 (D=3.0 cm), see fig. 5, obtained using sections perpendicular to the baseplate fault. Black lines on sections represent interpreted faults. Ricostruzione schematica 3D della parte centrale del modello SS05 (D=3.0 cm), vedi fig. 5, ottenuta utilizzando sezioni perpendicolari alla faglia di base. Le linee nere sulle sezioni rappresentano le faglie interpretate.
6 6 G. TOSCANI ET ALII Fig. 7 - Sketched 3D interpretation of the central part of the model SS05 (D=3.0 cm). The curved planes of newly-formed faults are shown in light grey, whereas the cut in the foreland both exposed and buried below the wedge is shown in dark grey. Interpretazione 3D schematica della parte centrale del modello SS05 (D=3.0 cm). I piani curvi delle faglie neo-formate sono rappresentati in grigio chiaro, mentre il taglio nell avampaese, sia affiorante sia sepolto sotto il cuneo, è mostrato in grigio scuro. same domain B cause a detectable topographic effect (partially visible in fig. 6, S 42) in the other models (SS05, SS04 and SS03). This implies a dip-slip component of motion on the strike-slip faults. This component is either normal or reverse, and sometimes a transition from reverse to normal is seen along strike of the same fault plane. Vertical sections of domains A and B also show both the layer of glass microbeads that separates the orogenic wedge from the underlying foreland (frontal thrust) and that in the foreland stratigraphic sequence. These layers had no effects on the inception and development of the faults, regardless of the amount of displacement. This is due to the set-up of the models (existence of the pre-cut in domain A, pure strike-slip movement of the two blocks), for which the layers of glass microbeads did not undergo compression but only strike-slip deformation. Moreover, no faults propagate through the layers of microbeads in our models; therefore, the differences in rheology they induce do not affect the shape of the newlyformed faults. Instead, all newly-formed faults originate from the pre-existing vertical fault that exists in the buried foreland and affects the eastern portion of the model (the northern block in map-view). Finally, in domain C (S 34 and S 26; figs. 6 and 7) faults splay up from the baseplate fault and affect quite symmetrically the overburden. They are mainly strike-slip but sometimes exhibit a reverse component producing a vertical throw that varies from model to model. Topographic relief is largest in this domain. Both the reverse component of slip and the topographic relief have been recently interpreted by LE GUERROUÉ & COBBOLD (2006) as due to rock dilation, which simulates transpressive features in spite of the simple shear applied. 5. QUANTITATIVE ANALYSIS We carried out a quantitative analysis by measuring systematically the actual displacements seen along the different faults of models SS03 to SS06 and comparing them with the displacement applied to the baseplate fault. fig. 8 summarizes the results of this analysis, that also shows the line-drawings of the final step of all the experiments (fig. 8, row 1). Notice that the drawings are focused on the central part of the sandboxes, unaffected by edge effects. A related sequence of diagrams is shown below each of the line-drawings. All values reported in the diagrams of rows 2 and 3 were measured on pictures taken at different deformation stages (every 0.5 cm of basal displacement). Finally, values reported in the diagrams of row 4 were measured at the surface of the analogue models at the end of the experiments. All displacement measurements have been based on the «reference lines» traced on the surface of all the models (named by capital letters; fig. 8, row 1) MAXIMUM DISPLACEMENT ALONG THE FAULTS (fig. 8, row 2). These diagrams show the displacement on each fault surface measured at different steps of deformation. The measurements were taken along the fault trace and monitor the increase of displacement every 0.5 cm of baseplate fault slip. The total displacement imposed on the baseplate fault is indicated on the x-axis, whereas the corresponding displacement measured on every single fault is reported on the y-axis. These diagrams allow tracing the entire evolution of the faults in the models: inception, progressive development, deactivation EVOLUTION OF THE SURFACE DEFORMATION (fig. 8, row 3). These diagrams show the cumulative horizontal displacement of all faults (y-axis) measured at each reference line (x-axis) for each step of deformation (different lines). The measurements were taken parallel to the direction of the baseplate fault, regardless of the strike of the faults displacing the reference lines. These diagrams allow quantification of how much of the imposed basal displacement is transferred to the model surface where the pre-existing cut affects the entire thickness of the models (right side of each diagram) or where it affects only part of them, tapering to zero below the orogenic wedge (left side of each diagram) CONTRIBUTION OF EACH FAULT TO THE TOTAL DIS- PLACEMENT (fig. 8, row 4). These diagrams refer to the final step of the models (due to the extremely limited number of measurements we did not diagram model SS06) and show the number of
7 PROPAGATION OF AN INHERITED STRIKE-SLIP FAULT THROUGH A FORELAND-CHAIN SYSTEM 7 faults and the contribution of each fault to the total displacement, measured using the reference lines. The vertical bars reproduce the path of the uppermost curve in the diagrams of row 3. Numbers inside the bars refer to the fault numbers in the maps of the models shown in row DISCUSSION 6.1. GENERAL FEATURES IN 3D An overview of the three domains shows that newlyformed faults occur only in domains B and C, as only the inherited discontinuity exists and is active in domain A. Whatever their geometry and displacement, all these faults splay from a pre-existing lineament (the cut in domain B, the baseplate fault in domain C). The threedimensional sketch of model SS05, shown in figs. 6 and 7, provides an integrated view of what is seen both at the surface and in the cross sections. Significant features are: (i) the general arrangement of the faults, mainly in the northern block; (ii) the lack of new faults where the preexisting fault involves the entire thickness of the model, i.e. in domain A; (iii) the presence of faults only within the wedge where it overlies the foreland, i.e. in domain B; and (iv) faults splaying directly from the baseplate fault where no other lineaments or heterogeneities exist, that is to say, in domain C. The main faults cutting the model (in light grey in fig. 7) are connected with the baseplate fault in domain C and with the cut in domain B. Toward the surface, they depart from the vertical projection of these pre-existing discontinuities; the undulate shape of the fault planes is outlined by their arched traces, both in map view and in cross section. Toward domain B, slip on the pre-existing cut propagated only in the receding block, producing distortion of the grid lines, precursor to the development of faults. This behavior is easy to understand qualitatively, since the material is compressed on the advancing side of the fault and stretched on the receding side (MANDL, 2000). Conversely, grid lines remain almost undeformed to the south of fault P (figs. 5 and 6). From east to west, the influence of the pre-existing cut diminishes as the thickness of the overburden (i.e., of the chain) increases. Accordingly, the width of the shear zone measured at the surface increases toward the west. In domain C, that has no pre-existing discontinuity, the baseplate fault controls completely the structural style of the overburden, and the shear zone attains its maximum width where the overlying sand pack is thickest. Similar observations were reported also by TCHALENKO (1970) and SCHÖPFER & STEYRER (2001). Moreover, grid lines begin to be significantly deformed long before faults reach the surface. 6.2 QUANTITATIVE ANALYSIS In the following we discuss the finer details of the quantitative analysis, always referring to the different rows of fig Maximum displacement along faults (fig. 8, row 2). In all models, the number of simultaneously active faults becomes larger as the amount of basal displacement increases. Only two faults are active in addition to fault P (the pre-existing cut in domain A) when the imposed displacement is less than cm. Recall that fault P is always active in all the models and shows displacement values very close to those of the baseplate fault. This indicates that deformation in domain A is entirely transferred to the model surface only by this fault. Conversely, an increase in the number of active faults is seen in all the models for basal displacement >1.5 cm. These faults remain active for a significant interval of time/basal-displacement: up to ~6 cm of basal displacement in model SS03, and up to the end of the experiments in models SS04 and SS05. In models SS03 and SS04, at ~5.5 cm of basal displacement the surface faults striking close to the baseplate fault join one another forming a single larger fault. This is directly linked with the baseplate fault, extends for the total length of the models and divides them into two separate halves. The central lineament is the only one that remains active for displacements larger than 5.5 cm. Hence the threshold of basal displacement beyond which any increase in displacement occurs essentially on the main fault can be set between 5.0 and 6.0 cm, whereas changes in the surface structures are negligible Surface deformation evolution (fig. 8, row 3). All diagrams show similar paths. The reference lines of domain A (from O to S) exhibit displacement values that are very close to the corresponding baseplate fault displacement. This is due to the reactivation of the preexisting discontinuity, which accommodates the entire deformation thus preventing the development of new faults. Conversely, in domain B and, even more, in domain C, the measured horizontal surface displacements differ from those of the corresponding baseplate fault; in particular, they decrease abruptly starting from the reference line at the boundary between domains A and B (fig. 8, row 3, reference line O). This difference can be explained only by the occurrence of distributed deformation (layer-parallel shortening, large-wavelength folding, fault propagation folding, brittle deformation not resolvable at the model scale, etc.) and of a minor reverse component of motion on mainly strike-slip faults. The partitioning of deformation cannot be quantified based on the analysis of the surface reference lines, but can be inferred from the analysis of the sections perpendicular to the baseplate fault, that show positive variations in the topography of the models. Indeed, topographic variations have been detected in several natural and experimental environments (SYLVESTER, 1988; LE GUERROUÉ & COB- BOLD, 2006). In particular, the development of Riedel fault systems or the formation of flower structures are usually associated with bulging confined within narrow portions of the models or of real shear zones, the San Andreas Fault in the Carrizo Plain being the most striking and widely known example (U.S.G.S., 1990). In the models analyzed in this paper, such topographic bulge characterizes mainly domain C, as shown by the sections in fig. 6 (domain C, S 34 and S 26). The examination of the entire set of available sections (not shown in figure) suggests that bulging of domain C corresponds to the maximum width of the shear zones for all models. The portion of basal displacement that is partitioned as described above, and ultimately not transferred to the models surface, is quantified by the diagrams of fig. 8, row 3. No brittle deformation is seen at the surface of
8 8 G. TOSCANI ET ALII A Fig. 8a - Diagrams referring to models SS03 (D=8.0 cm, first column) and SS04 (D=5.0 cm, second column). Row 1: linedrawing of the final stage of the models. Row 2: maximum displacement along the faults. Row 3: evolution of surface deformation. Row 4: contribution of each fault to the total displacement. Numbers and letters in the diagrams of row 4 refer to the line-drawings of row 1. See text for details about measurements. Diagrammi relativi ai modelli SS03 (D=8.0 cm, prima colonna) e SS04 (D=5.0 cm, seconda colonna). Riga 1: line-drawing della fase finale del modello. Riga 2: massimo rigetto lungo le faglie. Riga 3: evoluzione della deformazione superficiale. Riga 4: contributo delle singole faglie al rigetto totale. I numeri e le lettere nei diagrammi nella riga 4 si riferiscono al line-drawing della riga 1. Per maggiori dettagli si veda il testo.
9 PROPAGATION OF AN INHERITED STRIKE-SLIP FAULT THROUGH A FORELAND-CHAIN SYSTEM 9 B Fig. 8b - Diagrams referring to models SS05 (D=3.0 cm, first column) and SS06 (D=0.5 cm; second column). Row 1: linedrawing of the final stage of the models. Row 2: maximum displacement along the faults. Row 3: evolution of surface deformation. Row 4: contribution of each fault to the total displacement. Numbers and letters in the diagrams of row 4 refer to the line-drawings of row 1. See text for details about measurements. Diagrammi realtivi ai modelli SS05 (D=3.0 cm, prima colonna) e SS06 (D=0.5 cm, seconda colonna). Riga 1: line-drawing della fase finale del modello. Riga 2: massimo rigetto lungo le faglie. Riga 3: evoluzione della deformazione superficiale. Riga 4: contributo delle singole faglie al rigetto totale. I numeri e le lettere nei diagrammi nella riga 4 si riferiscono al line-drawing della riga 1. Per maggiori dettagli si veda il testo.
10 10 G. TOSCANI ET ALII Fig. 9 - Surface evolution of the reference model SS02 and measured amount of displacement on the different reference lines taken at six different steps of deformation (from 3 to 8 cm of basal displacement). Evoluzione superficiale del modello di riferimento SS02 ed entità dei rigetti misurata sulle linee di riferimento a sei differenti step di deformazione (da 3 a 8 cm di rigetto basale). domain C (reference lines from C to G) for basal displacement less than ~2.0 cm. On the contrary, surface faults are clearly seen in domain B at the same deformation stage. As stated earlier, in domain A the surface and basal displacements are very similar. Conversely, during the early deformation stages (basal displacement <4.0 cm) the surface displacement accommodated by faults in domains B and C is consistently smaller than the corresponding steps of basal displacement. For instance, in model SS03 (fig. 8, row 3, first diagram) the lines corresponding to 3.0 and 4.0 cm of basal displacement are clearly less than 1.0 cm apart in domain C (reference lines E, F and G), while they are spaced exactly 1.0 cm in domain A. For displacements larger than 6.0 cm, the difference between the lines is consistently the same (1.0 cm) over all diagrams and for all domains. This is due the fact that for any displacement >5.5 cm all faults join and the model deformation reaches a sort of «steady-state». Since that moment, a single active main fault separates completely the overburden up to the surface into two blocks corresponding with the two baseplate halves. Conversely, for displacement <5.5 cm diffuse deformation still occurs in domains B and C and accommodates a fraction of the baseplate fault displacement roughly corresponding to the difference between the imposed and measured displacements. Model SS03, that was run with a basal displacement of 8.0 cm, is particularly suitable for these measurements as it clearly reached such steady-state. The maximum difference between imposed and measured displacement is 2.5 cm and can be observed at lines G-H, that separate domains B and C (fig. 8, row 3, first diagram). A difference between imposed and measured displacements can be observed also for the other models, when basal displacement grows beyond 2.5 cm (SS04 and
11 PROPAGATION OF AN INHERITED STRIKE-SLIP FAULT THROUGH A FORELAND-CHAIN SYSTEM 11 SS05; fig. 8, row 3, second and third diagrams) which corresponds to the minimum displacement needed to allow faulting to affect the surface of all domains. Moving to the westernmost portion of the models (domain C), the measured displacement increases again, for instance at reference lines E, D and C. This increase is concomitant with the progressive decrease of the width of the shear zone (fig. 8, row 1). Moreover, sections of the same portion of the models show a progressive reduction of the topographic relief, indicating that part of the distributed or non-detectable deformation is also decreasing and the difference between basal and surface displacement diminishes. In model SS03, near the boundary between domains B and C the reduction of measured surface displacement is more significant (2.5 cm). As the imposed displacement is constant, deformation in this portion of the model does not concentrate along fault planes but appears rather spread out. Displacement increases again as one moves westward from the wedge boundary. Therefore, the concomitant presence of the overlying wedge and the pre-existing fault in the buried foreland seem to play a role in reducing the development of faults and partitioning the deformation in the frontal part of domain B. A detailed analysis of this deformation style could be the object of future studies. The same measurements have been carried out for the reference model SS02 (fig. 9). The lack of discontinuities is the essential reason for the obvious differences in the fault pattern. These differences are also highlighted by the measurements in the diagram at the bottom of the figure, showing that the distribution of faults and the strain partitioning are quite constant for the whole duration of deformation and all along the model Contribution of each fault to the total displacement. The diagrams of fig. 8, row 4, illustrate the predominant contribution of the pre-existing fault in accommodating the displacement in domain A and in the eastern part of domain B (near the orogenic front, where the wedge is thinner). Conversely, a larger number of faults is seen also for a smaller cumulated displacement away from the foreland, where the wedge is thicker, and in the chain domain C. In all models, faults take up a larger displacement when their strike is more similar to that of the baseplate fault (e.g. fault 5a in SS03 model; fig. 8, row 4, first diagram) and viceversa (e.g. faults 1 and 2 in models SS03 and SS04; fig. 8, row 4, first and second diagrams). Notice that faults stemming directly from the pre-existing cut increase their displacement abruptly from zero to large values, probably as a result of displacement being transferred from the main onto these newly-formed faults. Notice also that the maximum displacement accommodated by each newly-formed fault does not exceed ~3.5 cm, which indeed gives an indication of how efficient is the reactivation of the pre-existing discontinuity. Based on the observations and quantitative estimates discussed above, we can now re-consider the sandbox models in terms of modes of crack propagation (fig. 1). The boundary between domains A and B (in correspondence with the pre-existing strike-slip fault) is the tip damage zone (sensu KIM et alii, 2006), so that Mode-II is prevalent. As previously stated, the effects of the inherited lineament are almost unobserved in domain C. Mode-III is dominant in this part of the models, as suggested also by the symmetrical arrangement of the newly-formed faults. The shift from one mode to the other approximately occurs in domain B (the wedge) where the effects of the pre-existing lineament decrease going toward domain C. 7. CONCLUSIONS Qualitative and quantitative analyses performed on sandbox models allowed us to verify that the reactivation of a pre-existing lineament strongly controls the development and arrangement of newly-formed faults in an undeformed cover, in our case the frontal part of an orogenic wedge overlying its buried foreland. In particular we found that: in the foreland domain A, the pre-existing fault acts as a preferential slip surface accommodating almost all the displacement so that no new faults are formed. In fig. 8, row 2, the line representing fault P (pre-existing) is the diagonal of the chart, as the basal and surface displacements are equal. The same is seen in fig. 8, row 4; the bar height corresponds to the basal displacement in the foreland zone (domain A), and the bars refer always to a single fault (P). in the wedge domain B, near the front of the orogenic wedge, faults are asymmetrically distributed and exclusively located in the receding block; the effect of the reactivated pre-existing lineament on surface displacement decreases moving away from the foreland-wedge boundary. Fig. 8, row 3 shows that the surface displacement measured in this domain (reference lines N, M, L, I) is the smallest of the entire model. This feature is seen for each step of model development and for all models. in the chain domain C, faults are widespread and exhibit features that are similar to those widely described in literature. As shown by the evolution diagrams of the four analyzed models (fig. 8, row 1), faults cutting this domain are the last to develop. In summary, newly-formed faults take place only in two domains: in domain B, where all the newly-formed faults originate from the pre-existing vertical fault that exists in the foreland buried under the wedge; in domain C, where the faults splay up from the baseplate fault. New faults forms only within the undeformed cover. Conversely, no new faults take place where the pre-existing lineament involves the entire thickness of the model up to the surface (domain A). In this case, the pre-existing fault accommodates the entire basal displacement since the very early stages of deformation. Surface faulting shows different characteristics in the three domains. Domain A is the first one where progressive displacement appears at the surface; then, for increasing basal displacement domains B and C are also affected by faults. Slip at the surface always corresponds to the basal displacement in domain A, whereas in the other two domains the horizontal slip measured at surface slip is only part of the corresponding basal displacement. This is due to the occurrence of diffuse deformation and minor reverse components of motion on strike-slip faults. For displacements >5.5 cm, all faults in the central part of the models join and deformation reaches a «steady-state».
12 12 G. TOSCANI ET ALII Fig Simplified sketch of the Central-Southern Apennines chain (light grey) and related foreland (dark grey), centered on the Mattinata- Gondola shear zone (MGsz). Focal mechanisms of earthquakes with M > 5 that occurred along the MGsz are also shown (after GASPARINI et alii, 1985, DI LUCCIO et alii, 2005). Schema semplificato della catena Appenninica Centro-Meridionale (grigio chiaro) e del relativo avampaese (grigio scuro), focalizzata sulla Mattinata-Gondola shear zone (MGsz). Vengono mostrati i meccanismi focali dei terremoti con M>5 lungo la MGsz (da GASPARINI et alii, 1985, DI LUCCIO et alii, 2005). From this stage onwards, a single active main fault separates the entire overburden into two separate blocks. The three domains also differ for the number of faults: only the pre-existing fault in domain A, few faults in domain B, more faults in domain C. Finally, faults having strike comparable to the baseplate fault take up a larger displacement and remain active for a longer time, whereas more oblique faults with remain active for a shorter time and their displacement measured along strike of the main fault is smaller. APPENDIX Comparison with geological cases In this appendix, we compare our results with two natural examples in Italy: the Molise-Gondola (hereinafter MGsz) and Scicli-Ragusa shear zones (figs. 10 and 11). The first case study is a reminder about an E-W striking deformation belt that cuts the Adriatic foreland (DI BUCCI et alii, 2006; 2007; fig. 10), and it is aimed at comparing the structural setting of the models with the seismotectonic setting of the considered area. The central-eastern portion of the MGsz is exposed at the surface, whereas its western portion is buried below the Apennine foredeep and the outer front of the Southern Apennines. Evidence for MGsz activity dates back to the Cretaceous, but this structure is still active as a right-lateral shear zone, as demonstrated by the frequent and sometimes destructive associated seismicity. Notice that the Southern Apennines thrust sheets and the related foredeep deposits buried the westernmost part of the MGsz in Middle Pleistocene, when motion at the front of the chain ceased (PATACCA & SCANDONE, 2004b). Any subsequent motion along the MGsz must have propagated through the overlying cover as described earlier. Our second case study is from Southeastern Sicily (fig. 11). Here the Hyblean foreland, affected by a long-lived shear zone known as Scicli-Ragusa fault system, plunges beneath the foredeep and the front of the Gela nappe thrust sheets. Also this case fits with the general framework of our models. Both our case studies comprise very active areas that are not fully understood from the seismotectonic point of view. The quantification and the minute description of the structural features observed in the models and the results presented in this paper can be used both to interpret different geological settings, and to shed light on different geological settings and put forward hypotheses on the tectonic setting of areas where field studies are still at an early stage and need to be properly oriented. In particular, the integration of the results of this work with existing field geology studies allowed us: (i) to provide an interpretative key for specific characteristics of the MGsz; (ii) to attempt to use our models for the seismotectonic interpretation of a comparable pre-existing foreland shear zone in Southeastern Sicily. INTERPRETING SPECIFIC CHARACTERISTICS OF THE MGSZ The MGsz has been described as a system that can be identified over a distance of at least 180 km running at the latitude N approximately. Overall the MGsz appears as a ~15 km-wide corridor from the Adriatic fore-
13 PROPAGATION OF AN INHERITED STRIKE-SLIP FAULT THROUGH A FORELAND-CHAIN SYSTEM 13 Fig a) Schematic structural setting of southeastern Sicily. Data simplified and redrawn after LENTINI ed. (1984), BIANCHI et alii, (1987), BIGI et alii, (1992), D AGOSTINO & SELVAGGI (2004). b) The three main structural domains have been colored as in the sandbox models. a) Schema strutturale semplificato della Sicilia Sud-orientale. Dati presi e rielaborati da LENTINI ed. (1984), BIANCHI et alii (1987), BIGI et alii (1992), D AGOSTINO & SELVAGGI (2004). b) I tre principali domini strutturali sono stati colorati coerentemente con quanto fatto per i modelli analogici. land off-shore to the core of the Apennines fold-andthrust belt (fig. 10). Its off-shore portion is known as Gondola line (DE DOMINICIS & MAZZOLDI, 1987; COLANTONI et alii, 1990; DE ALTERIIS, 1995; MORELLI, 2002; RIDENTE et alii, 2008; fig. 10), whereas its onshore portion includes the Mattinata fault (FINETTI, 1982; ORTOLANI & PAGLIUCA, 1987; FUNICIELLO et alii, 1988; PICCARDI, 1998; WINTER & TAPPONIER, 1991; BILLI & SALVINI, 2000; CHILOVI et alii, 2000; BILLI, 2003; BORRE et alii, 2003; PICCARDI, 2005; TONDI et alii, 2005; BILLI et alii, 2007) and the source regions of the 30 July 1627 Gargano earthquake sequence (M w 6.7: Gruppo di Lavoro CPTI; 2004; PATACCA & SCANDONE, 2004a) and of the 31 October-1 November 2002 Molise earthquakes (both having M w 5.7: DI LUCCIO et alii, 2005; VALLÉE & DI LUCCIO, 2005; fig. 10). Our analogue models confirm that the eastern portion of the MGsz, coincident with the Gondola and Mattinata fault systems, has a good chance to be fully reactivated up to the surface (as proposed by PICCARDI, 1998; BORRE et alii, 2003; PICCARDI, 2005; TONDI et alii, 2005; RIDENTE & TRINCARDI, 2006, among others) also for extremely small displacement values.
14 14 G. TOSCANI ET ALII To the west of the Mattinata fault, the Apricena fault (the causative fault of the 1627 earthquakes according to PATACCA & SCANDONE, 2004a) has been interpreted by DI BUCCI et alii (2006) as one of the splay faults developing at the front of the orogenic wedge from the deeper, preexisting discontinuity in domain B of our models. Recall that these splays strike N288 and dip to the SSW, exhibit a normal component of slip and form even for relatively low displacements. The sources of the 31 October-1 November 2002 Molise earthquakes are steeply dipping, blind right-lateral strike-slip faults having a cumulative length of about 15 km and extending between 6 and 20 km depth (VALLÉE & DI LUCCIO, 2005; DISS Working Group, 2007). Despite the limited size of the events, GPS data revealed coseismic deformation consistent with dextral kinematics (GIU- LIANI et alii, 2007). The drainage pattern of the region overlying the 2002 seismogenic faults displays anomalous river sections; some of them trend E-W, violating the general SW-NE trend of drainage (VALENSISE et alii, 2004). Accordingly, our experiments show that in the portion of domain B that corresponds to the structural setting of the 2002 earthquakes, the pre-existing strike-slip fault does not reach the model surface until displacement exceeds ~5.5 cm, corresponding to ~10 km in nature. Nevertheless, the model surface is affected by a region of diffuse strain, showing both horizontal and vertical components of motion, even for very limited displacements. In a more general perspective, the comparison between our models and the structural setting of the MGsz further highlights that the complex structural pattern generated by large fault displacements does not have an obvious equivalent in the modeled part of the Apennines. This observation favors the hypothesis that the most recent activity of the MGsz has not yet accumulated a significant displacement. Finally, we can use our results and reasoning to speculate on the style of potentially active faults west of the source area of the 2002 Molise earthquakes. To do that, we move further toward the interior of the Apennines, i.e. toward the western edge of the models. Here the right-lateral, deep vertical fault is accompanied by moderately- to steeply-dipping oblique faults that may or may not reach the surface depending on the horizontal offset; for instance, no surface faulting is predicted for displacement values such as those discussed above (~1 km in nature). The structural setting of potential active structures west of the 2002 Molise earthquakes should hence be characterized by deep faulting and diffuse surface deformation, without primary surface faulting. This conclusion agrees with the reported lack of surface active faults in this area (CIARANFI et alii, 1983; GALADINI et alii, 2000; MICHETTI et alii, 2000; DISS Working Group, 2007). INTERPRETING THE SCICLI-RAGUSA SHEAR ZONE (SOUTH- EASTERN SICILY) The satisfactory match between the outcomes of our modeling and the setting of the MGsz suggests that the results of our work could be applied to other long-lived strike-slip zones having a geological setting comparable to the one that inspired our models but not fully understood from the neotectonic point of view. This is the case of the southeastern Sicily (fig. 11), where a portion of the foreland exposed in the Hyblean Mts. plunges northward TABLE 1 List of the experiments described in this study and of their geometrical parameters. Lista degli esperimenti descritti in questo studio e dei loro parametri geometrici. Pre-existing Experiment cut Layer of glass Presence microbeads Thickness Displacement of the wedge in the foreland SS02 No No No 10 cm 8.0 cm SS03 Yes Yes Yes cm 8.0 cm SS04 Yes Yes Yes cm 5.5 cm SS05 Yes Yes Yes cm 3.0 cm SS06 Yes Yes Yes cm 0.5 cm beneath the Gela foredeep and the external front of the Gela nappe. This front runs from the Gela foredeep to the Catania Plain and Mt. Etna (LENTINI ed., 1984; BIANCHI et alii, 1987; CARBONE et alii, 1987; BIGI et alii, 1992; fig. 11). The Hyblean Mts. are cut by a regional shear zone known as Scicli-Ragusa fault system, a large structural feature that developed in Meso-Cenozoic times with a predominant right-lateral component of motion (e.g., GHISETTI & VEZZANI, 1980; CARBONE et alii, 1987, with references). The current stress field, however, is characterized by NNW-SSE contraction related to the Eurasia- Nubia convergence (D AGOSTINO & SELVAGGI, 2004; MONTONE et alii, 2004; SERPELLONI et alii, 2007; fig. 11). Evidence for NNW-oriented contraction is supplied also by recent structural observations (CATALANO et alii, 2006; LAVECCHIA et alii, 2007); hence, similarly to the MGsz, the Scicli-Ragusa fault system is favorably oriented for reactivation with an opposite sense of motion, i.e. as a left-lateral shear zone (CATALANO et alii, 2008), a circumstance supported also by focal mechanism data (MUSUMECI et alii, 2005). Our models suggest that evidence of recent motion for this fault system should be found not only where it is exposed, but also where it is buried under the Gela foredeep and the Gela nappe. Here we should see deeper seismicity concentrated along the northern extension of the Scicli-Ragusa fault system, whereas near or at the surface we might expect transtensional faults turning anticlockwise from the surface trace of the line. Current catalogues (Gruppo di Lavoro CPTI, 2004) show a concentration of historical earthquakes along the northward prolongation of the Scicli-Ragusa fault system, but accurate surface structural data (field surveys, mesostructural analyses, absolute dates; a preliminary set of fresh observations is supplied by CATALANO et alii, 2006; 2008) are still strongly needed. New data would highlight the presence or the absence of structural features like those described in this paper, hopefully supporting our work hypotheses and possibly supplying valuable insight into the seismotectonics of Sicily and the dynamics of Mt. Etna. Acknowledgments This work was supported by the University of Pavia, the Istituto Nazionale di Geofisica e Vulcanologia and the Italian Dipartimento della Protezione Civile. The authors are grateful to Luca Visconti and Claudio Antoniazzi, who provided part of the measurements on the models. Quantitative analysis were performed using the software «MOVE» by Midland Valley Exploration Ltd., Glasgow, UK. The Editor and the referees Fernando Calamita and Giacomo Corti are kindly acknowledged for the thorough review and the constructive criticisms that greatly improved this paper.
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