Vincent Viguié
email: viguie@centre-cired.fr.

Stéphane Hallegatte

Trade-Offs and Synergies in Urban Climate Policies

Cities are at the forefront of climate policies. 1-6 However, urban climate policies are not implemented in a vacuum; they interact with other policy goals, such as economic competitiveness or social issues. These interactions can lead to trade-offs and implementation obstacles, or to synergies. 7,8 Little analysis investigating these interactions exists, in part because it requires a broad interdisciplinary approach. Using a novel integrated city model, we provide a first quantification of these trade-offs and synergies, going beyond the qualitative statements that have been published so far. We undertake a multicriteria analysis of three urban policies: a greenbelt policy, a zoning policy to reduce flood risk, and a transportation subsidy. Each of these policies appears to be undesirable because it has negative consequences with respect to at least one policy goal; however, in a policy mix, the consequences of each policy are not simply additive. This nonlinearity permits building policy combinations that are win-win strategies. In particular, flood zoning and greenbelt policies are unlikely to be accepted if they are not combined with transportation policies. Our results show that stand-alone adaptation and mitigation policies are unlikely to be politically acceptable and emphasize the need to mainstream climate policy within urban planning.

 Synergies and conflicts with other policy goals also exist, and environmental policies can result in positive feedback with respect to economic and social issues. A decrease in car congestion increases residents' quality of life, enhances economic competitiveness, reduces accessibility inequalities among neighborhoods, and decreases air pollution and GHG emissions. Conversely, while enlarging parks and introducing more vegetation in cities can be a useful way to adapt cities to higher temperatures and can improve the quality of life, such actions may also reduce population density and lead to increased GHG

2 emissions from transportation. These effects can vary by community or location, for example, impact in the suburbs versus that in the city center, leading to unintended redistributions of wealth or amenities that may or may not be consistent with policy goals.

In this context, a pertinent tool is integrated city models (ICMs). [START_REF] For An Example | Downscaling climate change scenarios in an urban land use change model[END_REF] ICMs are highly simplified representations of reality that describe the most important drivers of city change over time and can assess the consequences of various policy choices. ICMs are not supposed to forecast the future of a city, but they can provide decision makers and stakeholders with useful information and can help them understand the main mechanisms and linkages at work. We utilize a multicriteria analysis to capture the synergies and trade-offs with respect to urban climate policies aimed at mitigation and adaptation using a simple ICM, NEDUM-2D (see Methods). Our analysis focuses on Paris, but its qualitative conclusions are generic and likely to be valid for many cities.

In this analysis, we assess urban policies with respect to five policy goals: climate change mitigation, climate change adaptation and disaster risk reduction, natural area and biodiversity protection, housing affordability, and policy neutrality. These goals can be translated into quantitative indicators in many ways. As an illustration, we suggest five possible and relevant ones that our ICM can measure and model. Indicator choice is a crucial issue that depends on the objectives for a given policy and on decision makers' priorities. Moreover, for all practical purposes, indicators (and their weights in the decision process) should be chosen in collaboration with stakeholders and policy makers. [START_REF] Corfee-Morlot | Cities, climate change and multilevel governance[END_REF] The indicators we utilize do not encompass all possible policy impacts on the five policy goals, but are informative for the policies we will be considering (See Section 1 of Supplementary Information), and each can be directly measured:

• Climate change mitigation: Urban policies can influence GHG emissions resulting from transport, heating, and air conditioning. Here we focus on transportation emissions. Our proposed indicator, the average distance traveled by car for commuting, is a simple proxy for GHG emissions in the absence of comprehensive modeling of urban GHG emissions.

• Climate change adaptation and disaster risk reduction: In Paris, one of the main disaster risks is flooding, and climate change may increase this risk, even though models still disagree. We therefore use the population living in flood-prone areas as an indicator.

• Natural area and biodiversity protection: The transformation of natural areas into urbanized area has many environmental impacts, for example, on biodiversity and water and flood management. For this policy goal we use the total urbanized area as an indicator.

• Housing affordability: Access to housing plays an important role in the quality of life and the competitiveness of a city. Improving housing affordability can therefore be both a social and an economic objective. This is particularly crucial in most major cities and can be measured using either rents or average dwelling size. Here we use average dwelling size in the center of the urban area as an indicator. [START_REF]Housing Policy Debate 19[END_REF] • Policy neutrality: Even if a policy has a positive impact as measured using aggregated indicators, it may have large unintended redistributive effects or particularly large negative effects on one category of residents or on one area of the city. Such redistributive effects often make implementation difficult or require corrective measures. To build a quantitative indicator for policy neutrality, we use the spatial distribution of returns on real estate investments in the city and calculate the spatial Gini index of the profitability of real estate investments. A high value of this indicator means that the evolution of a city leads to large changes in relative land prices.

We consider three policies that aim at different targets, but have consequences on the aforementioned five goals: a greenbelt policy, a public transport subsidy, and a zoning policy to reduce the risk of flooding (see Section 3 of Supplementary Information). Using our NEDUM-2D model, we compare these policies to a do-nothing scenario, whereby urbanization is driven only by market forces and the external drivers: transport and energy costs, population, income etc. (see Section 4 of Supplementary Information). Figure 1 illustrates the do-nothing scenario. The model projects a significant extension of the urbanized area between 2010 and 2030 as a result of increased population and decreasing transportation costs relative to income. The first policy is a greenbelt policy whereby land use regulations prohibit building in areas that are not already densely inhabited. This policy aims at limiting urban sprawl and at protecting natural areas. With this policy, the urbanized area in 2030 is the same as in 2010, even though building and population densities are different. As table 1 shows, this policy also limits the increase in private vehicle usage, increases real estate prices, and reduces dwelling sizes by making land scarcer. This increased land scarcity leads more people to live in floodprone areas, which has been empirically observed. [START_REF] Burby | Urban Containment Policy and Exposure to Natural Hazards: Is There a Connection?[END_REF][START_REF] Lall | Density and Disasters[END_REF] The second policy is a public transport subsidy financed by a lump sum tax. We take the example of the recently proposed replacement of the differentiated public transport tariffwhich increases with distance from the city center-by a single tariff for all destinations in the Paris urban area. Such a policy aims at promoting public transport, as well as decreasing the burden of transport costs on suburban households, which in Paris are, on average, poorer than those living in central Paris. The side effects of such a policy are to increase the incentive to live farther out in the suburbs, leading to an increase in the total urbanized area and to a decrease in real estate pressures in the city center.

The third policy is a zoning policy to reduce the risk of flooding. This policy prohibits new buildings in flood-prone areas. Such a policy reduces the available urban ground surface, thereby increasing land scarcity, and causes an increase in housing prices, leading to smaller dwelling sizes in the city center (as can be seen in Table 1).

Fig. 2 presents the results graphically for the three policies. The impact of each policy on each indicator has been assigned a score and is located along one of the five axes of the figure. The -100 percent score is in the middle of the figure; the +100 percent score is at the extremity of each axis. All scores are measured relative to the do-nothing scenario, which is assigned a 0 percent score. The +100 percent score goes to the preferred outcome among all considered policies. [START_REF]Preferred outcome are a decrease in average distance traveled by car, in population living in flood-prone areas, in total urbanized area, in spatial Gini index[END_REF] Each policy is thus ranked best when the corresponding colored area is biggest. For instance, Fig. 2 shows that a public transport subsidy improves the situation compared with the do-nothing scenario for three policy goals (climate change mitigation, housing affordability, and adaptation and disaster risk reduction), and makes it worse with respect to two policy goals (natural area and biodiversity protection and ease of implementation).

As Fig. 2 shows, each policy causes both positive and negative outcomes with respect to different policy goals when compared with the do-nothing scenario. Each policy thus appears to be undesirable because it has negative consequences with respect to at least one policy goal. This result can explain, for instance, why it is so difficult to implement efficient flood zoning or greenbelt policies at local scale, even when it is required by national law. [START_REF] Burby | Flood insurance and floodplain management: the US experience[END_REF] Indeed, negative side-effects on housing availability and on development opportunities understandably create political resistance. Fig. 2. Consequences of a greenbelt policy, a public transport subsidy, and a zoning policy to reduce the risk of flooding compared with the do-nothing scenario. Axes orientation is such that directions towards the exterior of the radar plot represent positive outcomes.

However, as Fig. 3 shows, a policy mix that includes the three policies can mitigate the adverse consequences of each individual policy. For instance, public transport subsidies decrease the real estate pressures caused by a greenbelt or a flood-zoning policy. Flood zoning also prevents the greenbelt from increasing the population at risk of floods. When all three policies are applied together, the situation is improved as measured along all policy goals compared with the do nothing scenario. In particular, these results suggest that flood zoning and greenbelt policies need to be combined with transportation policies to gain real political momentum and effectiveness. Note that in a policy mix, the consequences of each policy are not simply additive. For instance, when all three policies are implemented, the decrease in population in flood-prone areas is smaller than the sum of the variation caused by each policy taken separately. This nonlinearity and the complexity of policy interactions explain why it is useful to analyze various urban policies together, in a consistent framework.

Our analysis shows that building win-win solutions by combining policies is possible, and leads to more efficient outcomes than a set of policies developed independently. Climate goals can thus be reached more efficiently, and with higher social acceptability, if they are implemented through their taking into account into existing strategic urban planning, rather than by creating new independent climate-specific plans. Such "mainstreaming" of climate objectives with other policy goals is found to help design better policies in our model, confirming previous findings in other domains. [START_REF] Klein | Integrating mitigation and adaptation into climate and development policy: three research questions[END_REF][START_REF] Füssel | Adaptation planning for climate change: concepts, assessment approaches, and key lessons[END_REF][START_REF] Kok | Widening the scope of policies to address climate change: directions for mainstreaming[END_REF] Obviously, it does not mean that win-win strategies are always available. In some cases, trade-offs will remain unavoidable, and urban decision-makers will need to make tough choices. This can be done by associating different weights to our indicators -through a process of stakeholder engagement -and by maximizing the resulting weighted sum of indicators. But our analysis shows that a mainstreamed approach can allow for the design of policies that are robust to differences in the weights of different indicators, since they improve all indicators. Such policies are particularly easy to implement, because they are more likely to appear desirable to all stakeholders, in spite of their different priorities, objectives, and world views.

METHODS

We use the NEDUM-2D model to simulate the evolution of the Paris urban area between 2010 and 2030. This model is an extension of the model described in previous papers, [START_REF] Kok | Widening the scope of policies to address climate change: directions for mainstreaming[END_REF][START_REF] Gusdorf | Behaviors and housing inertia are key factors in determining the consequences of a shock in transportation costs[END_REF] which is based on classical economic theory. [START_REF] Gusdorf | Time and space matter: How urban transitions create inequality[END_REF][START_REF] Alonso | Location and land use: toward a general theory of land rent[END_REF][START_REF] Muth | Cities and Housing; the Spatial Pattern of Urban Residential Land Use[END_REF] This theory explains the spatial distribution of land and real estate values, dwelling sizes, population density, and building height and density.

Our approach aims at bridging the gap between high complexity "land use-transport interaction" models, [START_REF] Mills | An Aggregative Model of Resource Allocation in a Metropolitan Area[END_REF] and theoretical urban-economics models. To do so, we propose a model that is fully based on "microeconomic foundations" describing economic agent behaviors (like theoretical models), but that can be calibrated on realistic transportation networks and include precise land-use regulations and natural land characteristics (e.g., rivers and other natural areas).

Two main mechanisms drive the model. First, households choose where they live and the size of their accommodation by assessing the trade-off between proximity to the city center and housing costs. Living close to the city center reduces transportation costs, but housing costs (per unit of area) are higher there. Theoretical extensions to account for decentralized production have been proposed, but are not included in this analysis. [START_REF] Iacono | Models of transportation and land use change: a guide to the territory[END_REF][START_REF] Brueckner | Urban General Equilibrium Models with Non-central Production[END_REF][START_REF] Anas | General equilibrium models of polycentric urban land use with endogenous congestion and job agglomeration[END_REF] Second, we assume that landowners combine land with capital to produce housing: they choose to build more or less housing (that is, larger or smaller buildings) at a specific location depending on local real estate prices and construction costs. We assume that households and landowners do not take into account flooding risk in their location and construction choices, as reflected by the current building rate in flood-prone areas in France, [START_REF] Giuliano | Land Use Impacts, of Transportation Investments in The geography of urban transportation[END_REF] and as supported by behavioral economics research. [START_REF] Laporte | Croissance du nombre de logements en zones inondables[END_REF] Transportation costs include monetary costs such as the cost of gasoline and the cost of time. We assess them using the spatial structure of the Paris transportation networks (roads and public transport). See Section 3 of Supplementary Information for a full description of the model and its equations.

As described in sections 3.3 to 3.5 of Supplementary Information, a validation of the model over the 1960-2010 period shows that the model reproduces the available data on the city's evolution fairly faithfully and captures its main determinants. It also reproduces the spatial distribution of dwelling size, population density, and rents in the urban area fairly well. These results suggest that this tool can be used to inform policy decisions.

The evolution of the Paris urban area depends on several external factors, including demographic, socioeconomic, cultural, and political changes (See Section 4 of Supplementary Information for a more precise description of the scenarios). Our conclusions are robust to changes in these values, as demonstrated by a sensitivity analysis (Section 5 of Supplementary Information).

The model can be used to test many different assumptions about the future development of transport infrastructure. For simplicity, we assume that it remains unchanged between 2010 and 2030 and that congestion on the roads and public transport remains constant, that is, we assume that future investments in the transportation network maintain the same level of service despite population growth (Section 4 of Supplementary Information).

Fig. 1 .

 1 Fig. 1. Map of the total urbanized area of Paris under the do-nothing scenario, 2010 and 2030.

Fig. 3 .

 3 Fig. 3. Consequences of a policy mix including all three policies. Axes orientation is such that directions towards the exterior of the radar plot represent positive outcomes.

  1. Rosenzweig, C., Solecki, W., Hammer, S.A. & Mehrotra, S. Cities lead the way in climatechange action. Nature 467, 909-911 (2010). 2. Dodman, D. Blaming cities for climate change? An analysis of urban greenhouse gas emissions inventories. Environment and Urbanization 21, 185-201 (2009).

Table 1 :

 1 Multicriteria analysis of urban policies on Paris in 2030 with respect to the five policy goals.

			Public
			transport	Flood risk		Do-nothing
	Indicators	Greenbelt	subsidy	zoning	Policy mix	scenario
	Change in average daily distance driven
	in car (m)	+ 1,570	-440	+ 2,550	-880	+ 2,560
	change in population in flood-prone
	areas (thousands of households)	+39,000	-4,000	-6,000	-8,000	+ 6,000
	Change in total urbanized area (km²)	0	+ 690	+ 470	0	+ 480
	Redistributive impacts (Gini index)	+ 0.093	+ 0.271	+ 0.201	+ 0.146	+ 0.203
	Change in dwelling size in the center of
	Paris (m²)	+ 0.17	+ 1.73	+ 0.79	+ 0.95	+ 0.82

Acknowledgements

This study benefited from funding by the Agence Nationale de la Rercherche through the projects "Vulnérabilité Urbaine aux épisodes Caniculaires et stratégies d'Adaptation" (VURCA) (ANR-08-VULN-013) and "Modélisation Urbaine et Stratégies d'adaptation au Changement climatique pour Anticiper la Demande et la production Energétique" (MUSCADE) (ANR-09-VILL-0003-01) projects. The authors are grateful to Didier Rouchaud, Alain Sauvant, Jean-Luc Salagnac, and Nicolas Coulombel for providing invaluable data. Tony Bigio, Jan Corfee-Morlot, Marianne Fay, Elisabetta Genovese, Louis-Gaetan Giraudet, and Paolo Avner provided helpful comments. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its

Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Author Contributions V.V. carried out the computational analysis. S.H. initiated the study. S.H. and V.V. continued and finalized its design. They both wrote the paper.

Author Information Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests. Readers are welcome to comment on the online version of this article at www.nature.com/nature. Correspondence and requests for materials should be addressed to V.V. (viguie@centrecired.fr).


Guilhem Barruol
email: barruol@upf.pf

Anne Deschamps
email: deschamps@geoazur.unice.fr

Olivier Coutant
email: coutant@ujf-grenoble.fr

Mapping upper mantle anisotropy beneath SE France by SKS splitting indicates Neogene asthenospheric flow induced by Apenninic slab roll-back and deflected by the deep Alpine roots

Keywords: Shear wave splitting, Anisotropy, Asthenosphere, Western Mediterranean, Alpine collision, Massif Central hotspot

The presence of two regional seismic networks in southeastern France provides us high-quality data to investigate upper mantle flow by measuring the splitting of teleseismic shear waves induced by seismic anisotropy. The 10 three-component and broadband stations installed in Corsica, Provence, and western Alps efficiently complete the geographic coverage of anisotropy measurements performed in southern France using temporary experiments deployed on geodynamic targets such as the Pyrenees and the Massif Central. Teleseismic shear waves (mainly SKS and SKKS) are used to determine the splitting parameters: the fast polarization direction and the delay time. Delay times ranging between 1.0 and 1.5 s have been observed at most sites, but some larger delay times, above 2.0 s, have been observed at some stations, such as in northern Alps or Corsica, suggesting the presence of high strain zones in the upper mantle. The azimuths of the fast split shear waves define a simple and smooth pattern, trending homogeneously WNW-ESE in the Nice area and progressively rotating to NW-SE and to NS for stations located further North in the Alps. This pattern is in continuity with the measurements performed in the southern Massif Central and could be related to a large asthenospheric flow induced by the rotation of the Corsica-Sardinia lithospheric block and the retreat of the Apenninic slab. We show that seismic anisotropy nicely maps the route of the slab from the initial rifting phase along the Gulf of Lion (30-22 Ma) to the drifting of the Corsica-Sardinia lithospheric block accompanied by the creation of new oceanic lithosphere in the Liguro-Provenc ¸al basin (22-17 Ma). In the external and internal Alps, the pattern of the azimuth of the fast split waves follows the bend of the alpine arc. We propose that the mantle flow beneath this area could be influenced or perhaps controlled by the Alpine deep penetrative structures and that the Alpine lithospheric roots may have deflected part of the horizontal asthenospheric flow around its southernmost tip.

Introduction

Seismic anisotropy can be used as a proxy for the upper mantle flow since it results from minerals elastic anisotropy (e.g., [START_REF] Mainprice | The seismic anisotropy of the Earth's mantle: from single crystal to polycrystal[END_REF], primarily olivine, which represents the main upper mantle constituent and which is the most anisotropic upper mantle mineral [START_REF] Nicolas | Formation of anisotropy in upper mantle peridotites-a review[END_REF][START_REF] Ismail | An olivine fabric database: an overview of upper mantle fabrics and seismic anisotropy[END_REF] and from their preferred orientations induced by tectonic flow [START_REF] Silver | Seismic anisotropy beneath the continents: probing the depths of geology[END_REF][START_REF] Savage | Seismic anisotropy and mantle deformation: what have we learned from shear wave splitting?[END_REF]. Upper mantle seismic anisotropy is measured from the Earth's surface by using the splitting of teleseismic shear waves: A polarized shear wave crossing an anisotropic medium is split into two perpendicularly polarized waves that propagate at different velocities. Two anisotropy parameters can be retrieved from three-component seismic records: the difference in arrival time (yt) between the two split shear waves, which depends on the thickness and on the intrinsic anisotropy of the medium, and the azimuth / of the fast split wave polarization planes, which is related to the orientation of the penetrative anisotropic structure.

Southeastern France is a key area to map upper mantle flow because it represents a geographic transition between different tectonic domains that have suffered different tectonic histories that may have induced different penetrative fabrics in the upper mantle: the still active Alpine collision zone to the north and the western Mediterranean oceanic domains and the related subduction systems to the south. The Alpine collision between the Eurasian and the Apulian plates began 30 Ma ago and evolved as a continental lithospheric subduction. The Eurasian plate is presently subducting eastward down to 300 km beneath the Adriatic promontory in the western Alps, as imaged by seismic tomography [START_REF] Lippitsch | Upper mantle structure beneath the Alpine orogen from high resolution teleseismic tomography[END_REF][START_REF] Piromallo | How deep can we find the traces of Alpine subduction?[END_REF]. The western Mediterranean subduction system also began about 30 My ago. The oceanic Tethys lithosphere was subducting northwestward beneath the Corsica-Sardinia-Calabria continental lithospheric domains. The eastward roll-back of the Apenninic slab [START_REF] Se ´ranne | The Gulf of Lion continental margin (NW Mediterranean) revisited by IBS: an overview[END_REF]Faccenna et al., 2001a) induced the rotation of the Corsica-Sardinia-Calabria block, the opening of the Ligurian basin 20 My ago [START_REF] Rollet | Back arc extension, tectonic inheritance, and volcanism in the Ligurian Sea, Western Mediterranean[END_REF], together with the Algero-Provenc ¸al and of the Tyrrhenian basins 10 My ago [START_REF] Gueguen | On the post-25 Ma geodynamic evolution of the western Mediterranean[END_REF]Faccenna et al., 2001b). The Apenninic slab is presently visible in tomographic images, lying in the transition zone beneath the Apennines and the Calabrian arc [START_REF] Lucente | Tomographic constraints of the geodynamics evolution of the Italian region[END_REF][START_REF] Piromallo | P wave tomography of the mantle under the Alpine-Mediterranean area[END_REF].

Together with the vicinity of the Alpine belt and the Ligurian oceanic basin, another important structure that may have influenced the upper mantle flow pattern in southern France is the presence of hot mantle material ascending beneath the Massif Central. Regional seismic tomography of the northern Massif Central (Granet et al., 1995a;Granet et al., 1995b) evidenced a low-velocity anomaly down to 300-km depth, interpreted as a mantle plume that fed the Tertiary and Quaternary volcanism [START_REF] Maury | Le volcanisme tertiaire et quaternaire en France[END_REF], spreading from the northern Massif Central to the Mediterranean shore. Teleseismic shear wave splitting measurements performed on temporary seismic stations on the southern flank of the Massif Central characterized a homogeneous upper mantle anisotropy pattern [START_REF] Barruol | A Tertiary asthenospheric flow beneath the southern French Massif Central related to the west Mediterranean extension evidenced by upper mantle seismic anisotropy[END_REF], with a fast axis trending NW-SE in the Massif Central and gradually rotating to WNW-ESE toward the Gulf of Lion. The authors proposed that this seismic anisotropy pattern could have been generated by the effect of the Apenninic slab roll-back, the rotation of the Corsica-Sardinia lithospheric block, the opening of the Algero-Provenc ¸al basin. In such a model, the hot and less viscous mantle beneath the northern Massif Central could have been deflected and aspirated toward the south-east by the sinking slab.

Mapping the eastward continuation of the anisotropy pattern observed in the Pyrenees [START_REF] Barruol | Anisotropy beneath the Pyrenees range from teleseismic shear wave splitting[END_REF][START_REF] Barruol | Lithospheric anisotropy beneath the Pyrenees from shear wave splitting[END_REF] and in the southern Massif Central [START_REF] Barruol | A Tertiary asthenospheric flow beneath the southern French Massif Central related to the west Mediterranean extension evidenced by upper mantle seismic anisotropy[END_REF], characterizing the effects of the Alpine structures and deep lithospheric roots, are therefore the primary aims of this paper. After presenting and analyzing the data and the splitting of teleseismic shear waves recorded at two seismic networks located in south-eastern France, we discuss them in light of the Alpine tectonics and the Cenozoic opening of the western Mediterranean.

Data and Results

The Tre `s Grande Re ´solution Sismique (TGRS) network is composed of six stations managed by the Geoscience-Azur seismology group from the Nice-Sophia-Antipolis University and began its operations in 1997. Data can be retrieved by Automatic Data Request Manager (AutoDRM) at autodrm@geoazur. unice.fr. The Re ´seau d'Observations Sismiques des Alpes (RosAlp) network is managed by the Laboratoire de Ge ´odynamique Interne et Tectonophysique (LGIT) installed in the Grenoble University and is running since 1999. Data are interactively accessible through the web at http://www-lgit.obs.ujf-grenoble. fr/observations/rosalp/rosalp1_4.htm. Table 1 lists the station locations presented Fig. 1. All stations are equipped with broadband sensors and record continuously the seismic activity.

In order to get data of the best possible quality, we selected teleseismic events located at distances in the range 858 to 1208 and of magnitude generally greater than 6.0 (Background Dataset, Table 2) during the period 1999-2002. The event origins and locations (Background Dataset, Table 2) are taken from the U.S. Geological Survey (USGS) Preliminary Determination of Epicenters, and the phase arrivals were computed using the IASP91 Earth reference model [START_REF] Kennett | Seismic traveltime tables[END_REF].

We measured the shear wave splitting using the [START_REF] Silver | Shear wave splitting and subcontinental mantle deformation[END_REF] method which determines the anisotropy parameters, / and yt, that best minimizes energy on the transverse component of the seismogram for a selected time window. We mainly used the SKS phase, but for some events, we used the whole SKS+SKKS wave train. For each event, we report in Table 3 the split phase on which we performed the measurement, the splitting parameters (/, yt) with their 1r uncertainty, determined from the 95% confidence interval, and the backazimuth of the event. We also ascribe a quality factor (good, fair, or poor) to the measurements depending on the signal-to-noise ratio of the initial phase, the rectilinear polarization of the horizontal particle motion after anisotropy correction, and the correlation between the fast and slow split shear waves. We present in Fig. 2 few examples of splitting measurements and some demonstrative evidence of azimuthal dependence of the shear wave splitting parameters observed at STET, SAOF, and SMPL.

The individual shear wave splitting results reported Table 3 are plotted Fig. 3 in polar diagrams. The azimuth of the fast split shear wave together with the The number and quality of individual splitting measurements from which the average values are calculated is tabulated.

delay time is plotted on the left panel whereas the backazimuth for which no splitting was detected are plotted on the right. Black lines represent the bestconstrained results, whereas the gray lines represent measurements of intermediate quality and dashed lines measurements of poor quality. These diagrams show the coherency and the quality of the results: for most stations, except OGGM where less data were available, results are well constrained by several high-quality splitting measurements. In a first approximation, the high-quality measurements (in black in Fig. 3) show little scattering at most stations, suggesting homoge- neous mantle structures beneath the stations. At the TGRS stations, numerous high-quality measurements have been observed at all stations. The azimuth / of the fast split shear waves trend in a first approximation between E-W and about N1008E, except at STET where some events led to a N1408E fast split direction. The E-W trending anisotropy observed at the Corsica station SMPL is similar to the finding of [START_REF] Margheriti | Seismic anisotropy beneath the northern Apennines (Italy) and its tectonic implications[END_REF] at the temporary stations NAP0 and NAP1 installed in northern Corsica and in the Elba Island further East as well as at the Mednet permanent station VSL in Sardinia [START_REF] Margheriti | SKS splitting measurements in the Apenninic-Tyrrhenian domain (Italy) and their relation with lithospheric subduction and mantle convection[END_REF]. At the RosAlp network, the southernmost station OGDI (/ trending N1008E and yt=1.12 s) shows similar results than the surrounding TGRS stations. Results at the northern RosAlp sites are different since / rotates gradually to the NW at OGAG, to the NNW at OGGM, and to the North at OGSI. The diagrams in Fig. 3 show at few stations some variability in the anisotropy parameters that could result from either several layers of anisotropy, from inclined anisotropic structures or from lateral variations in the upper mantle structure. STET is the best example with two groups of parameters, one trending roughly N1008E and with yt slightly above 1.0 s and another trending N1408E and with much larger yt, around 2.0 s (see examples in Fig. 2). In order to better understand the origin of such scattering, we present in Fig. 4 the projection of the individual splitting measurements at 100-km depth along the incoming ray: this representation allows to visualize the lateral sampling of the anisotropy measurements and the regional-scale stability of the anisotropy parameters. It is helpful primarily by the fact that it plots the splitting parameters at a location where it could have been (at least partially) acquired. This is interesting for the cases where the crust and the lithosphere are known to have complex and dipping geometries such as in the Alpine collision and along the border of the Ligurian oceanic basins. Furthermore, in the hypothesis of an anisotropy pattern resulting from past or present asthenospheric flow, the observed pattern should be strongly influenced by the shape of the lithospheric root such as beneath the Alps, and one can therefore expect some lateral variations in the upper mantle anisotropy beneath some particular stations. Considering the ray paths through the structures is therefore of importance since they may not sample laterally the same structures depending on their backazimuths. Since the SKS measurements have little vertical resolution, we plot a final, integrated splitting at an arbitrary depth where splitting was perhaps not fully completed. A depth projection of 100 km is chosen. It is large enough to visually separate the various backazimuthal origins of the events and the regions of sampling of each ray. It likely plots measurements at sublithospheric depth in SE France and shows that the NE incoming events recorded at the station installed in the central Alpine units likely cross the Alpine lithospheric root at this depth.

The map shown in Fig. 4 first shows that the lateral mantle sampling is rather homogeneous at the scale of Fig. 3. For each station are presented the splitting (left) and the backazimuth for which no splitting are observed (right). For the splitting measurements, the trend of each segment represents the azimuth / of the fast split shear wave and its length is proportional to the delay time yt (up to 3.0 s). Black lines correspond to well constrained results, dark gray lines to fair and dashed lines to poorly constrained results (Background Dataset, Table 3). south-eastern France, but alternatively that the backazimuthal coverage at each station is rather sparse, most of the events arriving either from the NE or from the SW. Interestingly, projecting anisotropy results at depth shows that the apparent scattering observed in Fig. 3 is not a random feature that could be related to noisy measurements. Instead, the splitting results define coherent patterns consistent with either lateral variations in the upper mantle structure or with the presence of several anisotropic layers at depth, or with dipping structures. The best examples are visible at SAOF, STET, and SMPL. For these three stations, Fig. 2 illustrates some examples of split events arriving from the two opposite backazimuths. At SAOF, we do not find any strong variation in the delay times, but we observe a small dependence of / on the event backazimuth; events arriving from the NE are characterized by / trending almost E-W (three measurements of good quality give a mean of /=N0918E), whereas events arriving from the SW are characterized by / trending N1098E (from two goodquality measurements). The difference is rather small but based on high-quality measurements. SMPL in Corsica shows a backazimuthal dependence primarily on yt and not on /, most of the high-quality / trending E-W. Events arriving from the NE show smaller yt than events arriving from the SW. The mean yt obtained from the four high-quality events arriving from the NE is 1.27 s, whereas the mean yt obtained from seven high-quality measurements from the SW is 1.76 s. At STET, both / and yt are clearly dependent on the backazimuth; events arriving from the NE are characterized by / trending about N1108E and by delay times ranging between 1.0 and 1.2 s (seven good measurements give mean values of /=N1078E and yt=1.12 s), whereas events arriving Fig. 4. Map of the SKS splitting measurements projected from the stations (black points) along the rays at 100-km depth. As for Fig. 3, the black measurements are the best constrained, and the gray measurements represent measurements of lower quality. Poor-quality measurements are not plotted on this figure. This map also displays projections of SKS splitting measurements from the Pyrenees [START_REF] Barruol | Anisotropy beneath the Pyrenees range from teleseismic shear wave splitting[END_REF][START_REF] Barruol | Lithospheric anisotropy beneath the Pyrenees from shear wave splitting[END_REF] and from the southern Massif Central [START_REF] Barruol | A Tertiary asthenospheric flow beneath the southern French Massif Central related to the west Mediterranean extension evidenced by upper mantle seismic anisotropy[END_REF].

from the SW are characterized by / trending N1308E and by much larger yt. From the four high-quality measurements obtained from SW backazimuths at STET, three display yt above 2.0 s (the four highquality measurements give the mean values of /=N1308E and yt=2.06 s).

Interestingly, the backazimuthal dependence is not an ubiquitous feature. Most of the stations displaying such characteristics are located within the Alpine belt, not only in its internal zone but also in the external domains. Although this feature can be explained by the presence of several layers of anisotropy [START_REF] Silver | The interpretation of shear-wave splitting parameters in the presence of two anisotropic layers[END_REF], or from the presence of dipping structures in the mantle, it may simply result from lateral variations in the penetrative mantle deformation, i.e., from large-scale heterogeneities at upper mantle depth. Crustal and upper mantle dipping structures are already described in the western Alps by vertical seismic reflection [START_REF] Bayer | Gravity modelling along the ECORS-CROP vertical seismic reflection profile through the western Alps[END_REF][START_REF] Nicolas | ECORS-CROP traverse and the deep structure of the western Alps: a synthesis[END_REF] or regional seismic tomography [START_REF] Paul | A three-dimensional crustal velocity model of the south-western Alps from local earthquake tomography[END_REF]. Although such dipping structures can generate backazimuthal dependence of the anisotropy parameters if they are intrinsically anisotropic [START_REF] Plomerova | Teleseismic P-residual study in the Italian region; inferences on large scale anisotropic structure of the subcrustal lithosphere[END_REF], resistive structures, such as the Alpine lithospheric roots, may laterally deflect the asthenospheric flow [START_REF] Bormann | Upper mantle anisotropy underneath central Europe: effect of absolute plate motion and lithosphere-asthenosphere boundary topography?[END_REF] around it and therefore may introduce lateral variations in the upper mantle strain and anisotropy that may explain our observations; depending on the event backazimuth, the ray may indeed sample either the lithospheric root or the asthenospheric flow, resulting in backazimuthal dependence of the splitting parameters.

Origin of the anisotropy

The vertical location of anisotropy in the mantle is a key point to discuss SKS splitting measurements. Unfortunately, SKS splitting has a poor vertical resolution because the splitting of a teleseismic shear wave observed at the Earth's surface may be acquired anywhere along the ray between the station and the core-mantle boundary. It is, however, broadly accepted from seismological [START_REF] Fischer | The depth distribution of mantle anisotropy beneath the Tonga subduction zone[END_REF][START_REF] Savage | Seismic anisotropy and mantle deformation: what have we learned from shear wave splitting?[END_REF] and petrophysical arguments (e.g., [START_REF] Mainprice | The seismic anisotropy of the Earth's mantle: from single crystal to polycrystal[END_REF] that most of the anisotropy that affects the vertically propagating shear waves lies within the uppermost 400 km of the Earth. It is also broadly accepted from local earthquake or Mohoconverted S-phases analyses [START_REF] Savage | Seismic anisotropy and mantle deformation: what have we learned from shear wave splitting?[END_REF] and from laboratory measurements [START_REF] Godfrey | Anisotropy of schists: contribution of crustal anisotropy to active source seismic experiments and shear wave splitting observations[END_REF] or petrophysical modeling [START_REF] Barruol | A quantitative evaluation of the contribution of crustal rocks to the shear wave splitting of teleseismic SKS waves[END_REF] that the crust may contribute to the total observed delay times only to a few tenth of seconds, requiring most of the SKS splitting to be explained by subcrustal active or frozen mantle deformation.

Although the Hercynian deep and penetrative structures are poorly known in southeastern France since most of the area is covered by Mesozoic and Cenozoic sedimentary basins, there are some arguments favoring a sublithospheric origin of the anisotropy for the SE France stations. Hercynian terranes outcrop in Corsica, in the Maures Massif and in the basement of several Alpine massifs. Interestingly, the Maures massif is characterized by strong vertical, NS-trending, penetrative structures [START_REF] Vauchez | Charriage crustal, anatexie et de ´crochement ductile dans les Maures orientales (Var, France) au cours de l'oroge `ne Varisque[END_REF][START_REF] Morillon | Diachronous cooling on both sides of a major strike slip fault in the Variscan Maures Massif (SE France), as deduced from a detailed Ar/Ar study[END_REF] likely resulting from Hercynian strike-slip faulting. If some upper mantle deformation related to this structure was present at lithospheric depth, one should expect a NStrending anisotropy [START_REF] Tommasi | Upper mantle tectonics: three-dimensional deformation, olivine crystallographic fabrics and seismic properties[END_REF], which is not observed. There is no obvious correlation between the Hercynian structure and the observed anisotropy pattern, as observed for instance for the Sillon Houiller in the northern Massif Central [START_REF] Babuska | Seismic anisotropy of the French Massif Central and predisposition of Cenozoic rifting and volcanism by Variscan suture hidden in the mantle lithosphere[END_REF]. The second argument that does not favor the Hercynian, lithospheric fabric as a primary source of our shear wave splitting observations is the homogeneity of the anisotropy pattern compared to the heterogeneity of the Hercynian structures [START_REF] Matte | Tectonics and plate tectonics model for the Variscan belt of Europe[END_REF], mainly formed by South-verging crustal nappes in the Massif Central. This discussion was already developed by [START_REF] Barruol | A Tertiary asthenospheric flow beneath the southern French Massif Central related to the west Mediterranean extension evidenced by upper mantle seismic anisotropy[END_REF] for the southern Massif Central and is a fortiori valid for a larger zone where a homogeneous anisotropy pattern is observed. Third, the absence of clear correlation between the Pn fast anisotropic directions and the direction of the polarization of the fast split SKS waves in southeastern France and Corsica [START_REF] Mele | Compressional velocity structure and anisotropy in the uppermost mantle beneath Italy and surrounding regions[END_REF][START_REF] Judenherc | Two-dimensionnal anisotropic tomography of lithosphere beneath France using regional arrival times[END_REF] suggests that the main source of the SKS splitting is deeper than the mantle sampled by Pn waves. Assuming Pn waves are affected by structures within the 10 uppermost km of the lithospheric mantle, the absence of correlation between Pn and SKS fast directions implies either a deeper source of SKS splitting within the lithosphere (requiring the presence of two layers of independent and penetrative strain within the lithosphere), or, as we propose, that a large part of the recorded shear wave splitting in SE France originates at sublithospheric depth. These arguments are primarily valid for the stations installed from the Massif Central to the external parts of the Alps. For the stations sitting in the internal zones of the belt, Alpine, penetrative lithospheric structures are likely to be present at depth, and therefore, the observed shear wave splitting at these stations may also reflect the upper mantle deformation related to the Alpine collision.

Cenozoic asthenospheric flow and the Alpine lithospheric root

The Neogene plate reconstruction in the western Mediterranean area is characterized by a complex geometry and history with simultaneous compression in the Alps (the westward collision of the Apulian plate with the Eurasian plate) and extension few hundreds of kilometers South in the Liguro-Provenc ¸al basin (e.g., [START_REF] Gueguen | On the post-25 Ma geodynamic evolution of the western Mediterranean[END_REF]. Interestingly, the area covered by the TGRS network corresponds to the boundary between both regions. The upper mantle beneath this area has likely suffered strong differential motions able to develop strong and coherent anisotropy. We wish to show that this complex Cenozoic plate reorganization may have induced a regional asthenospheric flow that may be preserved since that time and that could explain the present-day observed anisotropy pattern.

From upper Cretaceous to the end of Eocene times, the general tectonic regime of the western Mediterranean is controlled by the northward motion of Africa inducing the continuous closure of the Tethys Ocean by its subduction beneath the Eurasian active margin. At Oligocene times, the collision of the Adriatic promontory with Eurasia generated important changes in the geodynamic evolution of the western Mediterranean. Between 30 to 22 Ma (Fig. 5a), the southern France suffered the rifting of the continental lithosphere located between the Languedoc and the Corsica-Sardinia block (Se ´ranne, 1999). The extension directions are oriented NW-SE in the southern Massif Central and rotate slightly to E-W in SE France (Se ´ranne, 1999). This regional Oligocene extension is interpreted as back-arc spreading induced by the early stages of the eastward roll-back of the Apenninic slab subducting toward the northwest beneath the Corsica-Sardinia lithospheric block. Fig. 5. Schematic map of the northwestern part of the Mediterranean domain, illustrating the main features of the Neogene tectonic evolution and the proposed model of related asthenospheric flow. Are located the main subduction zones, the assumed oceanic lithosphere (in light gray), the Massif Central hotspot (circles), the extension and compression directions and the direction of the Apenninic slab retreat. The dark gray areas correspond to regions where stiff lithospheres were likely present at 150-to 200-km depth and that could have either induced (like the Apenninic slab retreat) or deflected the asthenospheric flow (like the Alpine lithospheric roots). At the end of Oligocene (a), the southern France is under extension but the Corsica (co)-Sardinia (sa)-Calabrian (ca) lithospheric blocks are still in their original places. Their rotation induced by the retreat of the Apenninic slab began at about 22 Ma and ended around 17 Ma (b), inducing the opening of the Liguro-Provenc ¸al oceanic domain (li-pro) and a NW-SE flow at asthenospheric depth. From 17 to 10 Ma occurred the rifting of the Corsica-Sardinia block (c), followed by the drifting of the Calabrian block and the subsequent opening of the Tyrrhenian basin. We propose that the present-day pattern of seismic anisotropy schematized by the thin dashed lines (d) is the frozen upper mantle flow resulting from this tectonic evolution.

Between 22 and 17 Ma (Fig. 5b), the counterclockwise rotation of this lithospheric block caused by the sinking of the Apenninic slab in the upper mantle induced a strong lithospheric thinning between southeastern France and Corsica and the subsequent creation of new oceanic crust and lithosphere in the Liguro-Provenc ¸al basin (Faccenna et al., 2001a;[START_REF] Rollet | Back arc extension, tectonic inheritance, and volcanism in the Ligurian Sea, Western Mediterranean[END_REF]. During the same time, the Apulian promontory collides further North in the Alps and the Eurasian plate subducts eastward, as seen from the present-day images of the deep crustal structures in the Alps imaged, for instance, by the ECORS seismic reflection profiles [START_REF] Nicolas | ECORS-CROP traverse and the deep structure of the western Alps: a synthesis[END_REF], by compiling recent seismic data [START_REF] Waldhauser | Three dimensionnal interface modelling with two-dimensional seismic data: the Alpine crust-mantle boundary[END_REF], or by local earthquakes seismic tomography [START_REF] Paul | A three-dimensional crustal velocity model of the south-western Alps from local earthquake tomography[END_REF]. At the lithospheric scale, regional seismic tomography [START_REF] Piromallo | P wave tomography of the mantle under the Alpine-Mediterranean area[END_REF] and Pwave residuals [START_REF] Babuska | The deep lithosphere in the Alps: a model inferred from P residuals[END_REF]) define a deep root beneath the western Alps down to about 200 km beneath the internal parts of the belt and thinning toward the South. Gravimetric map of the Alps [START_REF] Masson | Une nouvelle carte gravime ´trique des Alpes occidentales et ses conse ´quences structurales et tectoniques[END_REF]) also points out the eastward dipping of the Eurasian crust and lithosphere. The contemporaneous westward collision of the Apulian promontory in the North and the eastward motion of the slab in the South implies that the southeastern France has been located during the lower Miocene above a zone of strong vertical shearing in the upper mantle, induced by the roughly E-W relative plate displacements. At 10 Ma (Fig. 5c), the Corsica-Sardinia block is in its present-day orientation but begins to be subjected to a rifting episode that is followed few Ma later by the SE drift of the Calabrian block, the creation of the new Tyrrhenian oceanic lithosphere, and the eastward jump of the Apenninic subduction (Faccenna et al., 2001a).

In a previous paper dealing with the southern Massif Central upper mantle anisotropy, [START_REF] Barruol | A Tertiary asthenospheric flow beneath the southern French Massif Central related to the west Mediterranean extension evidenced by upper mantle seismic anisotropy[END_REF] proposed that the sinking of the Apenninic slab East of the Corsica-Sardinia block and the related opening of the Liguro-Provenc ¸al oceanic basin may have induced a NW-SE pressure gradient within the asthenosphere that could have generated the observed mantle flow beneath the southern Massif Central. The authors pointed out two important facts from this model: first, the presence at that time of the ascending hot and low viscous mantle plume beneath the Northern Massif Central (Granet et al., 1995a) could explain why pulling the mantle from the northwest could have been mechanically easier than pulling it from laterally or from below the sinking slab. Second, the maximum intensity in the Massif Central volcanism [START_REF] Maury | Le volcanisme tertiaire et quaternaire en France[END_REF]) that occurred about 10 Ma ago is roughly synchronous with the end of the Corsica rotation, i.e., with the end of the slab suction, allowing the mantle plume to freely continue its upward motion and to generate the peak in the volcanic activity. The new anisotropy measurements performed at 10 supplementary broadband seismic stations in SE France and in the western Alps are still compatible with these ideas and indicate the possible deflection of the asthenospheric flow by the deep Alpine lithospheric roots.

The continuity of the anisotropy pattern from the Massif Central to the southern Alps and Corsica and its good correlation with the Tertiary extension directions (Se ´ranne, 1999) and to the relative plate motions described above are strong arguments to relate the upper mantle anisotropy to this Cenozoic extensive episode. Several factors may explain why this mantle flow and its related anisotropy have been preserved and are still clearly visible: first, there has been no subsequent tectonic nor thermal episode after this Neogene event. Therefore, the corresponding upper mantle fabric could have likely been preserved [START_REF] Vauchez | Comment on bSKS splitting beneath rift zonesQ[END_REF]. Second, the slow absolute velocity of the Eurasian plate [less than 10 mm/year in Nice area, deduced from the HS3-nuvel1 plate velocity models [START_REF] Gripp | Young tracks of hotspots and current plate velocities[END_REF]] may not be sufficient to generate a strong shearing in the upper mantle able to erase the preexisting fabric.

Our anisotropy measurements could be also discussed in light of a model of parabolic, asthenospheric flow related to the passive spreading of the ascending Massif Central plume material beneath the moving Eurasian lithosphere, as proposed for the Eifel plume by K. Walker (personal communication, 2003). We, however, believe that the conditions for a simple parabolic spreading of the plume material beneath the lithosphere are not fulfilled in the case of the Massif Central hotspot. First, because the lithosphere thickness shows much stronger variations in southern France [START_REF] Babuska | Seismic anisotropy of the French Massif Central and predisposition of Cenozoic rifting and volcanism by Variscan suture hidden in the mantle lithosphere[END_REF] than beneath Germany (lithosphere thinning beneath the Massif Central and toward the Mediterranean oceanic basins, lithospheric roots beneath the Alps), that would perturb any mantle spreading. Second, because the slab roll-back in the western Mediterranean, by forcing a deflection of the plume upwelling toward the SE, has likely controlled and channeled the regional upper mantle flow. Finally, we only observe a partial anisotropy pattern around the Massif Central: most of the measurements are located on the southern side of the hotspot.

The parallelism of the fast split directions with the bending of the Alpine structures, particularly for the southern stations located on the external parts of the belt, suggests that the asthenospheric flow arriving from the northwest could have been deflected by the bottom of the eastward-dipping Eurasian lithosphere (Fig. 5c). Interestingly, the southern termination of the Alpine lithospheric root in the Nice area corresponds to the E-W trending / (Fig. 5d). We propose that the southern tip of the Alpine belt may have deflected and concentrated this asthenospheric flow and may have induced lateral variation in the anisotropy magnitude. This may explain at least two characteristics in our measurements: (i) delay times are, overall, stronger in SE France where mantle strain within the asthenosphere could have been more concentrated than further West, beneath the southern Massif Central, where the flow may have been more diffuse, and (ii) the backazimuthal dependence observed at STET and SAOF may be explained by the fact that the seismic rays arriving from NE primarily cross the east-dipping Alpine lithospheric slab, as suggested by the tomographic models [START_REF] Piromallo | How deep can we find the traces of Alpine subduction?[END_REF], whereas the SWincoming rays primarily cross the asthenospheric flow of stronger intrinsic anisotropy, generating the largest yt. The observed delay time variations may therefore reveal different penetrative deformations within the Alpine root and within the asthenosphere beneath the external part of the belt. Considering the amplitudes of shear wave anisotropy determined from petrophysical analyses of upper mantle rocks (e.g., [START_REF] Ismail | An olivine fabric database: an overview of upper mantle fabrics and seismic anisotropy[END_REF][START_REF] Ismail | The Kaapvaal craton seismic anisotropy: petrophysical analyses of upper mantle kimberlite nodules[END_REF], the large yt of about 2.0 s measured from SW backazimuths can be explained by 4% of anisotropy on a 220-km-long path, which is consistent with a rather strong asthenospheric flow beneath this area. The yt of about 1.0 s obtained from NE incoming events at STET and SAOF can be explained by 3% of anisotropy on a 150-km-long path. Interestingly, such backazimuthal variations of the delay times disappear further west such as at RUSF or CALF. This may be explained by the fact that both the NE and SW incoming rays do not cross the Eurasian slab plunging beneath the Alps and could be primarily affected by the sublithospheric anisotropy.

The interpretation of the backazimuthal dependence of the delay times observed at SMPL in Corsica cannot be related to similar origin since there is likely no more Alpine lithospheric root beneath Corsica. On the contrary, there are evidences that the eastern, Alpine, Corsican lithosphere is thinner (40 km) than the western, Hercynian, Corsican lithosphere (70 km) [START_REF] Be ´thoux | The deep structure of Corsica (Mediterranean Sea) as inferred from broad band seismological profile[END_REF]. The observed backazimuthal dependence could therefore suggest either an anisotropy primarily lying within the lithosphere or the presence of several anisotropic layers beneath the island. A similar observation was held at the Mednet station VSL further South in Sardinia, where E-W trending / are observed, together with high yt [START_REF] Margheriti | SKS splitting measurements in the Apenninic-Tyrrhenian domain (Italy) and their relation with lithospheric subduction and mantle convection[END_REF].

In the present state of knowledge, there is no argument to interpret the splitting observed at the two northernmost stations of the RosAlp network (OGSI and OGGM) in terms of sublithospheric mantle flow. Except that they form a continuous anisotropy pattern with the other Alpine stations, the anisotropy at these stations may likely reflect deep Alpine pervasive deformation rather than asthenospheric flow. Much more measurements across the belt would be needed to better constrain the interpretation of upper mantle penetrative structures beneath the Alps.

Conclusions

Mapping the upper mantle flow in southeastern France displays a smooth pattern, in clear continuity with the pattern previously obtained in the southern Massif Central. The absence of correlation between the Pn and SKS fast anisotropic directions, together with the absence of correlation between the trend of the fast split shear waves with the few outcropping Hercynian structures, do not favor Hercynian, lithospheric fabric as a primary source of anisotropy. Instead, the trend we observe in SE France is compatible with a horizontal asthenospheric flow induced by the sinking of the Apenninic slab that began about 20 Ma ago, accompanied by the rotation of the Corsica-Sardinia lithospheric block and the opening of the Ligurian oceanic basin. These new anisotropy measurements seem therefore to confirm that the sinking of the Apenninic slab has had a dramatic effect on the upper mantle structures: if it is broadly accepted that it generated the counterclockwise rotation of the Corsica-Sardinia lithospheric block and the subsequent opening of the Liguro-Provenc ¸al basin, we show that it may have also induced a regional mantle flow at asthenospheric depth that filled the gap left behind it. Part of the mantle upwelling related to the Massif Central hotspot could have been pulled toward the southeast by the retreating slab. We also propose that the Alpine lithospheric root may have deflected and concentrated the mantle flow around its southern tip. This could explain the good correlation between our SKS fast split directions and the trend of the Alpine belt in SE France as well as the increase in the observed delay times at the stations in the Nice area.

Fig. 1 .

 1 Fig. 1. Map of the station locations. TGRS stations are indicated by diamonds whereas RosAlp stations by circles.

Acknowledgments

Many thanks to C. Maron who manages the TGRS network and the data availability. We are grateful to P. Silver for his splitting analysis program. This paper benefited from constructive comments of P. Matte and from fruitful reviews of L. Margheriti and V. Babuska.

Appendix A. Supplementary Data

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.tecto. 2004.08.002.


Ricardo J Rabelo
email: ricardo.rabelo@ufsc.br

Scheila N Costa

David Romero
email: david.romero.diaz@gmail.com

A Governance Reference Model for Virtual Enterprises

Keywords: Collaborative Networked Organizations, Virtual Enterprises, Governance, Reference Model, Instantiation Approach

During its entire lifecycle the Virtual Enterprise (VE) partners should share a sort of assets and sensible information as well as execute intra-and interorganizational business processes in a coordinated and secure way, mostly supported via computer networks. VE partners are however independent enterprises and have their own business strategies. Therefore, it is relevant to properly govern a VE in way to minimize conflicts among its partners and hence the risks for achieving the VE goals. This paper presents a VE governance reference model allowing the instantiation of more concrete governance models for given VEs. An important contribution of this research is the consideration of the economic dimension of governance, not covered in related works.

Introduction

With the increase competition in the global market, enterprises have been open to participate much more actively in strategic alliances. In this context, Collaborative Networked Organizations (CNOs) have arisen as a paradigm to support a number of competitive advantages for all involved organizations, including the exploitation of new market segments and opportunities, costs reduction and risks mitigation [START_REF] Afsarmanesh | VBE Refernce Framework[END_REF].

There are many types of CNOs manifestations. This work focuses on the Virtual Enterprise (VE) type. Generally, a VE can be defined as a temporary alliance formed by autonomous, heterogeneous and geographically dispersed enterprises that join their complementary core competences and resources to better attend to a given demand, dismantling itself after finishing all its legal obligations [START_REF] Afsarmanesh | VBE Refernce Framework[END_REF]. VEs are mostly originated from long-term strategic alliances, namely Virtual organization Breeding Environments (VBEs). A VBE formally groups organizations in order to provide enough pre-conditions and basic operating rules for collaboration among its members aiming at creating VEs with the most adequate partners in a more agile and trustful way [START_REF] Afsarmanesh | VBE Refernce Framework[END_REF].

During its entire lifecycle VE partners should share a sort of assets and sensible information as well as execute intra-and inter-organizational business processes. VE partners are however independent enterprises and have their own business strategies, which creates a complex and intrinsic conflicting VE operation scenario. Therefore, it is of extreme relevance to properly govern a VE in way to minimize conflicts among its members and involved external and hence the risks for achieving VE goals. Some related works on VBE and VE governances (e.g. [START_REF] Romero | Towards Governance Rules and Bylaws for Virtual Breeding Environments[END_REF], [START_REF] Romero | VO Breeding Environments Value Systems, Business Models and Governance Rules[END_REF] and [START_REF] Romero | The Virtual Enterprise from a Governance Perspective[END_REF]) assume that a given VE should generally inherit (partially) the governance model from the VBE whose partners belong to. This seems correct as a VBE somehow imposes to its members a set of common principles and operating rules. In spite of that, this paper goes one step forward. It facilitates the instantiation and definition of particular VE governance models, but keeping them aligned to the VBE governance model [START_REF] Romero | Towards Governance Rules and Bylaws for Virtual Breeding Environments[END_REF] [3] in order to preserve the VBE values and bylaws [START_REF] Romero | The Virtual Enterprise from a Governance Perspective[END_REF].

This assumption is grounded both in empirical observations from some real VBEs implementations (e.g. as described in [START_REF]Special Panel Sessions on Real Collaborative Networkd Organisations[END_REF]) as well as in literature review (e.g. [START_REF] Romero | Special Issue on Collaborative Networks as Modern Industrial Organizations: Real Case Studies[END_REF]). Basically, it has been realized that a VE is mostly unique. Even though the good to be produced is similar to someone previously manufactured, VE partners' composition can be totally different. This may happen due to many reasons, such as the eventual unavailability, non-interest or low historical performance of some previous partners in the related past VEs. Besides that, collaborative business opportunity's requirements, customer requests and commercial rules deeply affect many aspects in the way a VE should behave and hence be managed, like as the required legal framework, logistics itineraries and type of logistics partners, the setting-up of the decision model (between partners) and its structure, and the influence of the customer along the general production process. Therefore, an additional and complementary coordination instrument should be created, which is represented by the VE governance model.

Very few works in the literature have tackled the VE governance from that more comprehensive view. It was also observed that the works on networked governance are very abstract (e.g. [2] [7]), creating difficulties for SMEs to deploy them.

As a contribution in this direction and from a more business processes-oriented perspective, this paper presents a proposal of a VE governance reference model. It allows the derivation of concrete governance models for given VEs, defining the actors, relations among them and with the VBE governance model, rules and mechanisms to be used along each phase of the VE lifecycle (creation, operation/ evolution, dissolution) regarding VE partners' rights and duties, and taking the given business demand's characteristics into account.

This paper is organized in five sections. The first one has introduced the problem and the context of the research work. Second section describes the basic concepts of governance in networked enterprises. The third section presents the proposed VE governance reference model. Section fourth illustrates an instantiation of the governance reference model. Section five summarizes some conclusions of the work.

Governance in Networked Enterprises

Governance in networked enterprises can be defined as "the specification of rules, criteria for decision-making, responsibilities, and boundaries of actions and autonomy for the involved actors. It is created by the own set of organizations to regulate itself. The fundamental role of governance is not managing; but to delimitate/guide the management instead. Actors can use their knowledge within the defined governance framework in way to help organizations to best reaching their common goals [START_REF] Roth | Differences and Inter-Relations of Governance Concepts and Horizontal Networked Enterprises Management[END_REF]".

Networked enterprises governance have to consider two complementary dimensions: one related to the coordination of the economic activities, and another one to the network structure and coordination of its activities [START_REF] Roth | Differences and Inter-Relations of Governance Concepts and Horizontal Networked Enterprises Management[END_REF]. The essential rationale is that the market and power influence directly the way a network should execute and manage its processes and all related information, and hence on how it should be internally organized to correctly and efficiently respond to that.

There are a number of approaches about networked enterprises governance in the literature regarding the economic dimension, providing different perspectives and classifications in terms of governance strategies. However, almost all of them are in practice devoted to "classical" networks, as VBE-like or more static ones.

Under this dimension and in the context of this research, five works were taken as the theoretical foundation basis to identify the required elements for VE governance and to propose a reference model. They are basically explained below, in a sequence, which corresponds to how they have also evolved along the time.

Williamson [START_REF] Williamson | The Mechanisms of Governance[END_REF], for instance, was one of the first ones who identified the relevance of networks, pointing out that the power could no longer be governed by a single enterprise. Storper et al. [START_REF] Storper | Flexibility, Hierarchy and Regional Development: The Changing Structure of Industrial Production Systems and their Forms of Governance in the 1990s[END_REF] depicted the power itself among enterprises using two concepts: core (main enterprise) and ring (suppliers). By means of the combination of these concepts they identified four types of governance in terms of power concentration or distribution: all-ring, no-core; core-ring with coordination firm; core-ring with lead firm; and all-core, no-ring. Gereffi [START_REF] Gereffi | Shifting Governance Structures in Global Commodity Chains, with Special Reference to the Internet[END_REF] has seen the network from the value chain point of view, identifying when the network was fundamentally producer-driven, buyerdriven or information-driven (e-commerce related). In another work, Gereffi [START_REF] Gereffi | The Governance of Global Value Chains[END_REF] complemented this work seeing the network also from the point of view of power relation among buyers and producers as a consequence of the required network's production structure for a given demand. For that, they proposed five other categories of governance types: market, modular value chain, relational value chain, captive value chain and hierarchical. In all these approaches authors assumed a tight connection and a-priori knowledge between the involved enterprises. Provan et al. [START_REF] Provan | Modes of Network Governance: Structure, Management, and Effectiveness[END_REF] was one of the first ones who addressed the problem considering the enterprises as a set of totally autonomous and decoupled organizations but that should also work for a common goal. They have identified three basic governance types: shared governance (when the power is more or less equivalent among the members), leader organization governance (when the power is clearly more concentrated on a given single organization), and network management organization governance (when the network delegates the power to an external organization).

Very few works were found out in the literature proposing more concrete means for a VE governance model from the network structure and coordination dimension point of view. Albers [START_REF] Albers | Configurations of Alliance Governance Systems[END_REF] has identified two sub-dimensions for that, called structural dimension and instrumental dimension. Structural dimension basically copes with the network structure and which tasks partners should do. Instrumental dimension basically refers to the networked coordination and incentive mechanisms to sustain the collaboration. Albers [START_REF] Albers | Configurations of Alliance Governance Systems[END_REF] model is however too abstract, it does not consider anyhow the 'economic dimension', and does not provide any concrete guidelines on how those dimensions should be instantiated to support the network operation. In spite of the importance of this contribution, the author considered a classical network, with fixed partners. Dekkers et al. [START_REF] Dekkers | Industrial Networks: Capturing changeability?[END_REF] recognizes the influence of the market and external contexts in the way a network is organized, coordinated and managed. However, they do not propose a model for that.

In terms of governance models, Romero et al. [START_REF] Romero | VO Breeding Environments Value Systems, Business Models and Governance Rules[END_REF] tackled governance explicitly from the CNOs point of view, but with a focus on VBE-like networks. This first work has generally identified the structural governance elements that a VBE should have: principles, bylaws and rules. Rules in turn can be of functional (e.g. operational procedures to manage the VBE) and behavioral (e.g. ethical code) natures. In another work, Romero et al. [START_REF] Romero | Towards Governance Rules and Bylaws for Virtual Breeding Environments[END_REF] have extended this general model to VEs. Actually, it corresponds to an instantiation from the VBE model and with a focus only in the VE creation phase. That model is however a bit abstract, does not consider the economic dimension, and processes are described at a general level, which creates some difficulties for SMEs to understand how to use and deploy it.

A substantial part consumed in the VE creation process refers to the governance model setting-up [START_REF] Romero | The Virtual Enterprise from a Governance Perspective[END_REF]. Within this context, the underlying value proposition of this work is to provide more systemized, concrete and transparent means to govern VEs considering those two main dimensions simultaneously. This gives better conditions for faster VE creations as well as for more confidence and trust among partners along the VE lifecycle as long as all roles and rules are clearly defined and agreed.

A Virtual Enterprise Governance Reference Model

VE Governance Model Elements

Four key aspects are behind the rationale of the proposed VE governance reference model. The first one refers to the consideration of the two fundamental dimensions of governance: economic and structural. The second one refers to considering governance at its essential, i.e. that it does not manage itself, but rather restrains the limits of management. The third one refers to see that the VE governance is influenced by the VBE governance model. The fourth one refers to considering the requirements of VEs, which are different than the other not dynamic networks.

Camarinha et al. [START_REF] Camarinha-Matos | Collaboraive Networks: A New Scientific Discipline[END_REF] points out the following VE main characteristics that then should be supported (requirements) by any VE-related model: i) VE partners come from another network: a VBE; ii) VE partners are autonomous; iii) VE partners are heterogeneous at several levels; iv) VE members do not know to each other a priori when they become VE partners; v) Due to the fact VE partners come from a VBE, a sort of common principles are agreed and hence the trust building problem is mitigated; vi) a VE (and the way partners should behave) can be totally different from another one created in the past to respond to the equivalent business; vii) VE partners have different roles and hence different rights and duties along the VE lifecycle; viii) a VE should be kept alive until all of its legal obligations are ceased.

This last requirement demands for an extension in the classical VE lifecycle [START_REF] Camarinha-Matos | Collaboraive Networks: A New Scientific Discipline[END_REF], with the addition of the "after sale" phase (e.g. maintenance, warranty, devolution and new extra services). This means that a governance model should also embrace a set of concrete actions that VE partners should carry out after the "product" (in a broad sense) has been delivered (dissolution phase), assuming that the VE has accomplished the business requirements successfully [START_REF] Elhabib | Enginnering Oriented Collaborative Network[END_REF].

Considering those four key aspects above mentioned; Figure 1 shows the proposed VE governance reference model, highlighting the wider framework it is inserted in: as a model that is influenced by the VBE governance model and that behaves according to external business conditions. These conditions are actually affected by the nature of the given collaboration business opportunity, customers, regulations and all external issues that can influence the network from the economic and power perspectives.

Inspired in the work of Romero et al. [START_REF] Romero | Towards Governance Rules and Bylaws for Virtual Breeding Environments[END_REF] and Albers [START_REF] Albers | Configurations of Alliance Governance Systems[END_REF], the proposed VE governance reference model is composed of four fundamental constructs: Actors, Rules, Mechanisms and Principles.

The basic logic of the proposed model can be understood as: actors will be organized and act along different phases of the VE lifecycle making use of rules and mechanisms, and all such actions should respect the VE and VBE principles. The different actors have roles, rights and duties respected to each VE phase in way to guarantee its correct and good functioning, concerning the business requirements and the economic and power constraints.

Actors represent the involved participants in a VE. Considering the different level of responsibilities actors can have, they can be inter-organizational [START_REF] Dekkers | Industrial Networks: Capturing changeability?[END_REF] (e.g. VE manager, VE broker, and VE coordinator) and intra-organizational (e.g. the company manager, an engineer, and a technician).

Fig. 1. VE Governance Framework and Reference Model

Principles represent the underlying values (e.g. honesty, commitment and mutual respect) that companies and people must follow. They usually come from the VBE and can also be complemented with other principles at VE level, depending on the given collaboration business opportunity's requirements. These principles should be somehow reflected in the governance rules. For example, commitment can be "deployed" as rules related to certain type of actor(s) to "send up-to-date information about tasks to the other actors for follow-up purposes" at the VE operation phase.

Rules represent concrete actions that given actors should execute at given VE phase(s) by means of mechanisms respecting predefined principles. Rules are associated to the roles and hence to the rights and duties that VE partners have at the different phases of the VE lifecycle. This means that a given actor may have more than one single role in a given VE. A role is represented by "unitary" actions that given actors can perform (e.g. inform clients about production execution). Depending on how the other governance elements have been decomposed, this exemplified role can be of responsibility of actors VE coordinator and VE manager.

Rules can be of two main categories: functional and behavioral, which in turn are subdivided into operational, control and supervision; and cultural and ethical, respectively. In essence, while functional rules are devoted to help framing the daily operational routine along the VE life (and where control rules are hierarchically above the other two ones), behavioral rules are devoted to people. For example, "supervising the product delivery" is seen as a functional-supervision rule; "sending the information about any delay and the responsible sector as soon as the problem is detected" is seen as a behavioral-cultural rule.

In resume, rules should be handled at a given VE phase by a given actor who has a given role that is settled as his duty, and this only exists because there is another actor(s) who has some rights related to that.

Mechanisms are basically the available or necessary means required to help actors in the rules execution. They can be formed by techniques (e.g. project management methods), software (e.g. groupware systems), devices (e.g. data collectors) and infrastructures (e.g. larger broad-band Internet for some specific situations).

In those hypothetical examples, this would be only possible and correct because (from the economic dimension perspective point of view) the business would have required (regarding the current VBE's members profile) a production structure and governance mode of type relational value chain (when there is a tight connection between the client and producers along the entire production). It would be buyer-driven as the client would have a strong influence all over the process. As the company which got the business (assuming the 'VE coordinator' role, for example) would be clearly the main producer (i.e. core-ring with lead firm), it would be allowed to have the power to ask for qualified information from any VE partner (this would come from a VBE governance model's rule) and then the whole network has to run under the leader organization governance mode.

VE Governance Rules Formalization

An instance of a given VE governance model can have plenty of rules. Having in mind that the most important goal of a governance model is to be indeed followed by the involved actors, it is of extreme importance that its rules should be documented. In fact, rules are the element to which all the economic and structural elements converge to and are reflected in.

There are different ways to express and to formalize such kind of rules (which is not the same than modeling business processes). Regarding the reality of SMEs, the formalism should be simple even though less rich. Writing rules textually is difficult but as some rules' details can be easily forgotten. Rules should be easy to understand by typical SME people, to document, to maintain, and to be quickly consulted and checked. In this sense, this work has opted to model rules using the very known and simple 5W2H technique. By means of a set of "questions", rules can be comprehensively and formally expressed, as showed in Figure 2.

Question Description Element

What?

It defines the concrete action that has to be done.

Functional or Behavioral rule Who?

It defines the actor who has the role to do the "what".

Actors and roles

When?

It defines when (the VE lifecycle phase) that the "what" has to be done by the "who".

VE lifecycle phase

Where?

It defines where (general or specific place) the "who" has to perform the "what" at the phase "when".

Physical place

Why?

It explains in details the purpose of the action "what". Aim

How?

It indicates the way (methods, procedures, protocols, etc.) that the "what" has to be done by the "who" as well as eventual related performance metrics.

Mechanisms

Instantiation of the VE Governance Model

This section presents examples of the instantiation of the proposed VE reference governance model. Actually, this corresponds to a real scenario, based on a case of a Brazilian network of mould-makers called NuFerJ, to which the governance model was applied, tested, and validated. NuFerJ has been found 19 years ago and its members are SMEs, completely independent to each other, although some of its members used to always work with some members in some cases. Since 2010 NuFerJ has started an initiative to (also) work under the VE strategy aiming at enlarging business possibilities (via larger production capacity) and maximizing resources utilization. NuFerJ uses to receive a "package" of moulds. VE partners can then be responsible for an entire mould, part of it, or for some specific operations of it. This VE notion is also communicated to the customers before contracting, i.e. they know the companies that will participate in a given VE. NuFerJ customers are mainly automotive, electro-electronics and home appliances sectors, from a number of different countries, although Brazilian (large) companies are the ones which mostly generate demands. Therefore, NuFerJ -and so VEs that are generated to attend such demands -has to deal with a variable economic environment.

Taking into consideration the governance approaches described in the section 2, NuFerJ "fits" some of them, depending on the collaboration business opportunity, customer, and other general requirements. In order to illustrate a given instance of a derived governance model for a given VE and due to size restrictions of the paper, the example below will take only one "business scenario" and only two rules will be showed. Actually, the current version of NuFerJ VE governance "reference" model is composed of 54 rules that cover important situations over the whole VE lifecycle.

From the governance structural dimension perspective point of view, besides the bylaw, etc., principles of NuFerJ network (so at the VBE level) include honesty (in the sense of always sending trustful information and do not lie during conversations), commitment (partners will indeed put all efforts to keep the business requirements), and collaboration (willingness to help members in the case of problems). should be prepared, configured and set up "some time" in advance (depending on the existing conditions) of the VE creation or when it is going to be created.

The 54 used rules can be taken as templates for other derivations as they follow the reference processes and activities typically executed in a VE along its lifecycle [START_REF] Romero | VO Breeding Environments & Virtual Organizations Integral Business Process Management Framework[END_REF].

Actually, deploying a VE governance model is far from being trivial. This is even more critical regarding that a typical VBE is mostly composed of SMEs. In order to mitigate the deployment work, the proposed governance framework also provides a deployment guide (not presented here due to paper length restrictions). Roughly, along five macro steps, it leads the person(s) in charge of that to go through the model and create an instance of the VE governance reference model for given VEs. To be noted that such person(s) is actually an actor, who is linked to a given role, and that is linked to the VBE and/or VE governance model.

Conclusions

This paper has presented a proposal for a VE governance reference model, integrating two referential perspectives: structural and economic. Dealing with VE governance from those two main dimensions simultaneously and providing concrete means to deploy a model in real cases is, however, complex and challenging. The proposed model represents a contribution towards filling up an existing gap in the literature.

The developed reference model is generic and can be instantiated for different VEs for different business scenarios. The value proposition of this model is concentrated in some perspectives, like faster VE deployment and confidence among VE partners and customers about more formal procedures to minimize VE risks in the accomplishment of its goals.

From the scientific perspective, its main contribution refers to the integration of the economics governance dimension and that the model is very concrete, more formally expressed, and indicates how the model's elements can be instantiated.

Deploying a governance model for given VEs is however not trivial. The analysis of every economic and structural detail of the collaboration business opportunity and deployed VBE demands much experience from the managers. Yet, the agreement about some rules is far from being easy and quick to reach a consensus among the involved actors, requiring many discussions. On the other hand, once reached, the governance model trends to achieve its essential goal: to be followed by all actors, with a more robust commitment, and more customer confidence.

Both VE governance reference model and instances-of it are not completely static once set up. As in any organization, several factors can contribute to change the rules as long as VBE governance model and businesses environments evolve.

The main limitation of the identified rules and view upon the economic dimension is that all information is handled fundamentally from the engineering point of view. Legal, social, management and accounting supporting foundations are not ready "transformed" into rules and will require additional guidelines in the model. Besides that, the model was only evaluated in one network. Therefore, larger evaluations are necessary towards a still more comprehensive reference model. These two issues are the main ones planned to be tackled in the short-term of this research. Another research action refers to evaluate richer modeling formalisms to better capture and express the network dynamics and the governance rules as 5W2H is relatively poor. Finally, a deeper research is needed to better identify the conceptual borders between governance and VE coordination tasks in a more global VE management framework.

Acknowledgements

This work has been partially supported by CNPq Brazilian research funding agency.

In this example, the general governance "framework" would be classified as buyerdriven, relational value chain and core-ring with coordinating firm.

The two rules below show the VE governance model instantiated in two situations. Figure 3 shows a rule to be used in the VE creation phase when a given partner decides (meaning that it has this degree of autonomy in accordance to the governance 'framework' and expressed in the contract) to subcontract another company to make a specific operation which any of the other members are capable to.

What

Hire an outside company. Rule: Right -Functional -Operational.

Who

Inter-organizational Actor: VE manager, VE broker, VE customer. Intra-organizational Actor: Member manager.

Why

In order to cope with very specific product's technical requirements.

When VE creation phase / partners' search and selection sub-phase:

In the case of any VE partner is no longer capable to fulfill the needed requirements.

Where

Not applicable.

How

Following the specific contract clauses. Mechanisms: Partners' Search and Selection software system

How much

Costs cannot be added to the whole contract and are of responsibility of the VE partner contractor to handle this.

Fig. 3. Example 1 of Governance model's rule

Figure 4 shows another situation, of a rule to be used in the VE evolution phase, when the VE manager observes that, after some attempts to solve the problem close to a problematic company that is not working as expected, he is allowed to withdraw the assigned given mould (entirely or part of it) from it.

What

Withdraw a task, part or entire mould from a given partner. Rule: Right -Functional -Operational.

Who

Inter-organizational Actor: VE manager. Intra-organizational Actor: Member manager.

Why

In order to keep product delivery date.

When

Evolution phase. When it is realized that a given VE partner is no longer able to keep producing what it was contracted considering the contract specifications.

Where

NuFerJ office

How

Following the specific contract clauses. Mechanisms: groupware and PMBOK project management

How much

Costs and penalties expressed in the contract clauses.

Fig. 4. Example 2 of Governance model's rule

The process of defining the rules is however "manual" and has some degree of subjectivity (although all rules must be agreed among partners before the VE start). This rational process is reasonably complex to make and involved managers (and even the VBE staff in some cases) are the ones who should analyze the given business scenario and its requirements (from the economic perspective) as well as configure a proper and feasible structure for the VE governance model regarding the VBE governance model (principles, bylaws, etc.) and members' profile. In other words, such manager(s) should know the VBE governance model to "guarantee" that the VE governance model inherits the essentials of that one, and hence that it is aligned with it. The VE governance reference model should then be derived for the given VE and its constructs be instantiated accordingly. Some basic governance model's constructs