Hoang-Hai Tran
email: tranhoang.hai@inria.fr

Bruno Tuffin
email: bruno.tuffin@inria.fr

A distributed auction-based algorithm to allocate bandwidth over paths

In the literature, Vickrey-Clark-Groves (VCG) double-sided auctions have been applied to inter-domain traffic exchange because they provide incentives to be truthful and lead to an efficient use of the network, among relevant properties of mechanism design. Unfortunately, the resulting resource allocation scheme is neither budget-balanced nor solvable in a decentralized way, two important properties. We present a different but more realistic auction-based algorithm for allocating bandwidth over paths to end users or ISPs, leading to a new budget-balanced pricing scheme for which allocations and charges can be computed in a decentralized way.

I. INTRODUCTION

In communication networks, there are several mechanism design-based approaches to allocate network bandwidth over time [START_REF] Altman | A survey on networking games in telecommunications[END_REF]. Pricing-based mechanisms have especially been considered as a relevant way to provide incentives to agents involved in networking games to act "properly". Several papers have been devoted to the study of such situations [START_REF] Wang | Truthful multicast routing in selfish wireless networks[END_REF], [START_REF] Crowcroft | Providing incentives in providerless networks[END_REF], [START_REF] Feigenbaum | A BGPbased mechanism for lowest-cost routing[END_REF], [START_REF] Su | Auction in multi-path multi-hop routing[END_REF], [START_REF] Jain | An efficient Nash-implementation mechanism for network resource allocation[END_REF]. We consider here inter-domain resource allocation problem where the network is made of Autonomous Systems (AS)es trying to deliver their traffic by routes going through independent ASes which have to be "rewarded". Inter-domain allocation problem was first introduced in the context of mechanism design in [START_REF] Nisan | Algorithmic mechanism design[END_REF], [START_REF] Feigenbaum | A BGPbased mechanism for lowest-cost routing[END_REF]. The authors formulated incentive inter-domain routing as a mechanism design problem using Vickrey-Clarke-Groves (VCG) auctions. Most works on pricing and resource allocation have followed up their proposition [START_REF] Feigenbaum | Incentivecompatible Interdomain routing[END_REF], [START_REF] Eidenbenz | COMMIT: a sender-centric truthful and energy-efficient routing protocol for ad hoc networks with selfish nodes[END_REF], [START_REF] Anderegg | Ad hoc-VCG: a truthful and costefficient routing protocol for mobile ad hoc networks with selfish agents[END_REF], [START_REF] Jain | An efficient Nash-implementation mechanism for network resource allocation[END_REF], [START_REF] Yang | VCG-kelly mechanisms for allocation of divisible goods: Adapting vcg mechanisms to one-dimensional signals[END_REF], [START_REF] Hershberger | Vickrey pricing in network routing: Fast payment computation[END_REF] since VCG is the only mechanism [START_REF] Moulin | Strategyproof sharing of submodular access costs: Budget balance versus efficiency[END_REF] which provides a general way of constructing a dominantstrategy, incentive-compatible, individually rational, and efficient mechanism. However, it is often neglected in those works that VCG auction mechanisms for multiple heterogenous items may not be computationally tractable and budget-balanced [START_REF] Maille | Why VCG auctions can hardly be applied to the pricing of inter-domain and ad hoc networks[END_REF], [START_REF] Tran | Inter-domain pricing: Challenges and possible approaches[END_REF]. Combinatorial double-sided auctions on the other hand have been studied by R. Jain and J. Walrand [START_REF] Jain | An efficient Nash-implementation mechanism for network resource allocation[END_REF], [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF] but in centralized control. Our pricing mechanism is inspired by those works but is different in several significant aspects.

In our paper, we formulate the inter-domain allocation problem in which the players are both buyers and sellers at the same time. Our main contribution is though to propose a new pricing rule such that all allocations and prices can be computed in a decentralized way, a key criterion for large networks often neglected in the literature. We look for an algorithm that is BGP-compatible such that each AS negotiates only with its neighbors. We then illustrate numerically the impact of this scheme on the inter-domain pricing game and compare it with the previous propositions.

This paper is organized as follows. Sections II presents a combinatorial double-sided auctions mathematical model applied to inter-domain. In Section III, we describe a forward and backward induction algorithm to find the globally optimal solution while allowing each agent to execute our algorithm asynchronously. Section IV illustrates the power of our algorithm thanks to simulations, as well as the convergence of the pricing game to an ǫ-Nash equilibrium. The comparison of efficiency (in terms of social welfare) and incentive compatibility obtained with VCG auctions and combinatorial doublesided auctions is also provided. Finally, Section V concludes the paper with a brief discussion of future work.

II. INTER-DOMAIN RESOURCE ALLOCATION PROBLEM

MODELING

The communication network is modeled as a graph G = (V, L). There are n nodes in V , corresponding to the n agents, and links in L are the links between ASes. We assume that there is no capacity constraint. There is a set R of routes. Each route r ∈ R is defined as an ordered list of nodes, each node appearing only once, and such that for two successive nodes in the list there exists a link ℓ ∈ L between those two nodes. Define also for node v ∈ V , R S (v) the subset of routes starting at v and R D (v) the subset of routes ending at v. Each provider v places buy-bids on a set of routes R v (note that routes are here initiated from v, but this can be extended without difficulty). For each route r ∈ R v , the bid is made of the maximum per unit price ĉI v (r) AS v is willing to pay and the maximum amount ŷr he is willing to get. He additionally places sell-bids (ĉ T v (r), xT v (r)) for routes r AS v is on, where ĉT v (r) is the minimum unit price he wants to sell resource and xT v (r) the maximum amount he agrees to sell. Define R i v this set of route going through v but not initiated from v, that is the routes where v has to transfer traffic.

The auctioneer designer seeks to determine allocations y r on routes r as the solution of the following linear optimization problem

max y v r∈Rv ĉI v (r)y r - v r∈R i v ĉT v (r)x T v (r) (1)
such that

0 ≤ y r ≤ ŷr , ∀r (2) y r ≤ xT v (r) ∀v, ∀r ∈ R i v (3) x T = Ay ≤ xT , (4)
where

A = (A vr ) v,r with A vr = 1 of v ∈ r, 0 otherwise y = (y r ) r x T = r x T v (r) v .
The first constraint [START_REF] Wang | Truthful multicast routing in selfish wireless networks[END_REF] says that the allocation flow should be matched with buyer's maximum demand ŷr and only nonnegative allocations are allowed. The second constraint (3) means that at each node v the incoming traffic flow on each route r should not exceed the amount of traffic v is willing to sell. The third constraint says that total flow allocation x T v to seller v should equal the sum of flows on the routes through v.

Our new mechanism comes for the remark that (1) can hardly be solved in a decentralized way [START_REF] Tran | Inter-domain pricing: Challenges and possible approaches[END_REF]. For this reason, we alternatively apply a modified double-sided auction. We consider routes r independently (thanks to the assumption about no capacity constraint, a relevant assumption in core networks) , and therefore a single buyer with multiple sellers corresponding to intermediate nodes on the route. We will say that an allocation r * is efficient for a source provider if it is a solution of the optimization problem arg max

r∈R S i ,yr≥0 ĉI i (r)y r - ∀r∈R S i j =i ĉT j (r)x T j (r) (5)
such that

0 ≤ y r ≤ ŷr (6) x T j (r) ≤ xT j (r) ∀j ∈ r (7)
x T j (r)A jr = y r ∀j, ∀r ∈ R S i .

In Equation ( 5), (ĉ I i (r), ŷr ) denotes the buy-bid from source provider i on route r, (ĉ T j (r), xT j (r)) denotes the sell-bids from intermediate nodes along route r. The allocation y r is chosen in a way that each buyer's bid will be matched up with his maximum demand ŷr and seller's bid will be matched within their maximum supply xT j (r). In this optimization, the allocation is determined for a route or a set of routes for a single source-destination pair. The constraints have similar meaning as in the global optimization in (1) except for the last one saying that the actual flow should be the same on each intermediate nodes along route r.

The settlement price is called the reserved price and is determined at each intermediate node. It is the ask-price of the matched seller which provides the corresponding route r * to destination. Notice that if the solution of the optimization at each intermediate node is a set of routes (r) * from multiple sellers, the reserved price at this stage is the highest ask-price among matched sellers and the declared cost of an intermediate node will be made of its own declared cost plus the reserved price from himself to destination in the backward induction process, see Equation [START_REF] Anderegg | Ad hoc-VCG: a truthful and costefficient routing protocol for mobile ad hoc networks with selfish agents[END_REF] later on. The source provider's payment is finally determined as the total reserved prices at each backward stage, which is included in the cost of the matched neighbors of the source node, being

ρr * = max(ĉ T j (r * )), ∀j ∈ N D i . (9)
Using surplus maximization in each allocation stage, the individual buyer can satisfy its demand with the lowest cost while pricing mechanism remains incentive-compatible for all sellers (recalling that they are neighbors of the buyer) but the matched seller with the highest ask-price. The theoretical and numerical analysis on the incentive-compatible property will be given in the sections III and IV. The difference between our proposed payment scheme and [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF] is that our payment rule determined step-by-step at each stage of the backward induction. The source provider's payment is the cost of its matched neighbors, and it includes all reserved cost of the remaining nodes. In [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF], the payment rule is determined at the end of the allocation process: the source provider pays each intermediate node the highest ask-price among matched sellers. As a result, the settlement price in [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF] is always more than or equal to the settlement price at each allocation stage, leading to the higher revenues for the sellers than our proposed pricing scheme. For this reason, the social welfare1 in our proposed pricing scheme is relaxed as compare to the social welfare in centralized combinatorial double-sided auction in [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF]. The simulation results in the next section will show the social welfare comparison of different pricing schemes.

III. FORWARD AND BACKWARD INDUCTION ALGORITHMS

We now propose a distributed algorithm to find the solution of (5). The algorithm is made of sequential stages between neighbor nodes in order to exchange bidding information. The ASes send messages to each of their neighbors; the source node initiates the allocation process and then other neighbor nodes relay the message according to the following steps. The forward induction is described in Algorithm 1, where the goal is to determine a set of possible paths (R S src ) to destination. More precisely:

• The source node initiates the request messages including its maximum demand ŷr for the route r, and sends to its neighbor nodes. During the allocation process, each node indeed communicates only to its neighbor nodes, i.e N D i the set of neighbor nodes of node i. • If a neighbor node j agrees to forward ŷr and the request message has not previously been received, indicated by visited(j) = f alse, it also initiates a request message including its own maximum demand ŷr (r) to relay traffic on route r, ŷr (j) 2 and propagates this request to its neighbor nodes. Otherwise, it sends a reject message to previous hop. The procedure is repeated until all request messages reach the leaf nodes, which are nodes one-hop away from the destination.

Algorithm 1 Building all possible paths to destination node repeat for all j ∈ N D i do sending request (r, ŷr ) if visited(j) = f alse then Add its maximum demand ŷr (j) to request messages Forward request messages to its neighbors Set visited(j) = true else Send reject message to previous hop end if end for until j := destination When this algorithm stops, we proceed backward on the route started from leaf nodes, each leaf node k declares its bid, (ĉ T k , xT k ), including it in ACK packets and sends it back to previous hop. The second step of Algorithm 2 is to find a flow (or maybe a set of flows) with minimal cost from neighbor bids at each intermediate buyer j (i.e. arg min(ĉ

T k xT k ), ∀k ∈ N D j )
. Each node announces its bid up on the tree. The price an intermediate node announces is the price at which it was reserved from its neighbor including its own transit price. If rational, an intermediate node should propose a price at least its reserved price as a transit price in order to have positive payoff, i.e.,

ĉT k = cT k + ρk , ( 10
)
where ρk is its reserved price for its neighbors and cT k (r) is its transit price. Backward induction process is then repeated until it reaches back the source node. Figure 1 illustrates how the message passes through intermediate nodes. In our proposed algorithm, each node plays both the seller and the buyer role at the same time.

Proposition 1: The backward induction process yields the minimal cost among possible routes at each intermediate node.

Proof: For each intermediate node j on route r ∈ R S j , the chosen routes are based on local surplus maximization (5) which we recall (r) * = arg max

r∈R S i ,yr≥0 ĉI j (r)y r - k =j ĉT k (r)x T k (r) (11)
This problem is similar to minimizing the cost from preceding neighbor nodes on the built tree

(r) * = arg min k∈N D j ĉT k x T k (r) (12)
s.t k∈(r) *

x T k ≥ ŷr (j).

Algorithm 2 Finding the corresponding routes to destination backward on each intermediate node repeat for all j ∈ T i do if j is next hop to destination then Attach its bid,(ĉ T j , xT j ), to ACK Send ACK back to previous hop of j else Find (r) * = arg min(ĉ

T k xT k ), ∀k ∈ N D j Subject to k∈N D j xT k ≥ ŷr (j)
Attach its bid,(ĉ T j , xT j ), to update messages of BGP protocol Send ACK back to previous hop of j end if end for until j := i; Proof: With (r) * as the set of solution routes of the optimization following (5):

arg max r∈R S i ,yr≥0s ĉI i (r)y r - ∀r∈(r) * ∀j∈r ĉT j (r)x T j (r). ( 13
)
In algorithm 2, the source node chooses a route with minimal cost or a set of such routes if demand is not fully met. Moreover, in Proposition 1, we have proved that each feedback route is formed by the route with minimal cost. As a result, we have r * = arg min ∀r ∀j∈r

ĉT j (r)x T j (r) (14)
is the minimal aggregated valuation cost on intermediate nodes, providing the maximal value in [START_REF] Su | Auction in multi-path multi-hop routing[END_REF].

Remark that this maximization property is in terms of the declared costs. Though, as we will see, since players' best interest is not to bid truthfully, efficiency property will not be satisfied at the equilibrium point of the game on declared costs. Proposition 3: The allocation outcome satisfies individual rationality.

Proof: The reserved price at each stage of an intermediate node is the highest ask-price among its matched sellers, which is ρi = max(ĉ T j ), ∀i ∈ r * , ∀j ∈ N D i . Each intermediate node should pay the highest ask-price from its preceding neighbor and then receives a payment from its succeeding neighbors. Thus, the matched sellers never receive a payment less than their declared cost, leading to a non-negative payoff. The unmatched sellers get nothing, thus our algorithm verifies individual rationality.

Proposition 4: The mechanism is incentive-compatible except for the highest matched seller at each stage of backward algorithm in allocation process, assuming that each player has no information about others and is risk-averse.

Proof: At each stage of the allocation process, an unmatched seller has no incentive to bid lower than his reservation cost because it leads to a negative utility. If he bids higher, he cannot change its settlement price but may end up getting unmatched. Thus, the best interest for them is to bid truthfully. The matched seller has no incentive to bid higher than its reservation cost because his action may end up getting unmatched (by increasing its valuation cost in optimization) due to the lack of information about competitors, which is not approved by the risk-averseness assumption. Thus, at each stage of allocation process when a intermediate node negotiates with its neighbors, it is incentive-compatible for all sellers except for the matched seller with the highest ask-price. The mechanism remains fairly incentive compatible which means the pricing mechanism are not fully satisfied truthful bidding to all agents involved in the game, similarly to the centralized algorithm provided in [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF]. The further analysis on the incentive compatibility property which is described as the degree of manipulation (the amount of deviation from truthful bidding) compared to VCG auctions will be given later.

IV. ALGORITHM ANALYSIS

In this section, we first illustrate numerically our resource allocation algorithm for a random, single pair of nodes. We then investigate the behavior of nodes reacting to our allocation and pricing scheme when they can change their strategies periodically.

A. Numerical illustration

We consider the simple topology with the real cost of transit traffic under each node described in Figure 2. We assume that the source node starts the forward induction process by sending out its maximum demand, ŷr = 5 to its neighbor ASes 1 & 2. An intermediate node receives the request message and forwards it to its own neighbors including the maximum demand from source node. The bidding information can be sent thanks to update messages in the BGP protocol. When the request messages are forwarded to leaf nodes, which are ASes 3, 4, and 5, it ends the forward induction process because leaf nodes could transfer directly traffic flow to destination node. The result is a set of possible routes R S src to destination node which is simply illustrated in Figure 3. During the backward induction process, leaf nodes submit their sell bids backward along the path as depicted in Figure 4 including the maximal prices per unit they are willing to sell and their maximal bandwidth supplies. After deciding the corresponding route to destination, each intermediate node declares its own bid backward to the source node which is described as follows:

• Node 1 receives one bid from leaf node 5, (x T 5 , ĉT 5 ) = (5, 2), and the corresponding route to destination node through AS 5 has a total cost of 10, being the amount times price per unit traffic. The highest ask-price for matched sellers is 2 per unit traffic because there is only one matched seller at this stage. In order to have a positive net payoff, we assume that it submits its own bid (x T 1 , ĉT 1 ) = (5, 3) which includes the price ρ1 reserved for its neighbor AS-5 plus its own transit price cT 1 , and then sends it back to the source node.

• Node 2 receives two bids from its neighbors which are (x T 4 , ĉT 4 ) = (3, 2) and (x T 3 , ĉT 3 ) = (2, 3). Thus, it should allocate corresponding routes from both ASes 3 and 4 due to their limited bandwidth supplies. The matched sellers are both ASes 3 and 4 with the highest ask-price of 3 per unit traffic leading to the total route cost of 15. Similarly, it submits its bid (x T 2 , ĉT 2 ) = (5, 4) and then sends it back to the source node.

• Source node receives two bids from ASes 1 and 2, which are (x T 1 , ĉT 1 ) = (5, 4) and (x T 2 , ĉT 2 ) = (5, 3) respectively. The shortest cost route is the one from AS 1 having total cost of 15 and the highest ask-price from this matched seller is 3 per unit traffic. As a result, the route r * is allocated through ASes 1 and 5. The payment imposed on source node by AS 1 is 3 per unit traffic and afterwards AS 1 should pay 2 per unit traffic to AS 5. It ends our algorithm. Remark that our mechanism is strongly budget-balanced. Also the chosen route on each intermediate node is the one providing the minimal cost from feedback information of its neighbors. If AS 1 increases its own transit cost to 5 per traffic unit, the allocated routes would change to AS 2 because we In comparison with the centralized version in [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF], the allocated routes are the same than with our algorithm but the settlement price imposed on source node is the highest ask-price from matched sellers which is 2 per traffic unit for both ASes 1 and 5, i.e., a different value. In case of a single allocated route from source to destination, an intermediate node receives as a payment exactly what he has bid.

B. Game on declared costs

We wish now to investigate numerically how ASes can play with their declared costs when they can change their bids over time instead of having a one-shot game, in order to improve their revenue. We consider the same network topology than in Section IV-A where the true reservation costs of nodes are randomly taken from a uniform distribution over the integer set {2, . . . , 8}, while the initial declared cost are also randomly chosen, by adding a random cost uniformly chosen in {0, 1, 2} to their true cost. Assuming the bid process is played round by round, the nodes restart the allocation process after each round and update their declared transit cost (always taken larger than or equal to their true cost to ensure a non-negative revenue) based on previous history. To summarize the behavior, the matched sellers increase by a small amount their current declared cost to try to increase their revenue during next round, while the unmatched sellers decrease their current declared cost, if possible, to try to get matched by the mechanism during next round. The amount added or subtracted at each round is randomly and uniformly taken within the set [0, 0.5]. The results illustrate a convergence to a periodic behavior. This oscillatory behavior is due to the fact that, starting from round 6 in the allocation process illustrated in Figure 5, the matched sellers get unmatched next round if they increase by a small amount their declared cost. For the unmatched sellers, their best strategies are to bid close to their true reservation cost to become selected, and whenever they try to increase their utilities, they get unmatched next round again. In order to avoid such oscillations, the network manager can impose a bid fee ǫ > 0 for changing costs after a given number of rounds, bid sufficiently high that no one has an interest in deviating from its current bid. Another option is to fix the number of rounds to a finite value unknown from the ASes, so that they cannot play strategically in terms of it. For example, if we chose a bid fee ǫ defined as the maximal gain of nodes from previous oscillation ǫ = max(uosc)-min(uosc) yr 3 since round 10 of allocation process, we have found a so-called ǫ-Nash equilibrium which is illustrated in Figure 7, where an ǫ-Nash equilibrium is a bid profile such that no player can improve his utility by more than ǫ. We can remark in this game that ASes declare costs larger than the true cost. It illustrates the difference with VCG auctions described in [START_REF] Feigenbaum | A BGPbased mechanism for lowest-cost routing[END_REF], [START_REF] Feigenbaum | Incentivecompatible Interdomain routing[END_REF], where it is a dominant strategy for nodes to bid truthfully. We illustrate in Figure 8 the impact of untruthful bidding by displaying the cumulative distribution of social welfare for our proposed pricing scheme, VCG auctions and the combinatorial double-sided auctions [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF], given the random true cost choices. The social welfare is also taken with our proposed pricing algorithm at the ǫ-Nash equilibrium. It shows that even at ǫ-Nash equilibrium, the efficiency is relaxed too, as compared with the combinatorial double-sided auction and VCG auctions, but not to a large extent. V. CONCLUSION In this paper, we have proposed a BGP-compatible, decentralized resource allocation algorithm based on double-sided auction. To have a decentralized and strongly budget-balanced allocation pricing scheme, two key properties, we have relaxed efficiency and incentive compatibility properties as compared to VCG auctions [START_REF] Feigenbaum | A BGPbased mechanism for lowest-cost routing[END_REF], [START_REF] Feigenbaum | Incentivecompatible Interdomain routing[END_REF] and combinatorial double-sided auctions [START_REF] Jain | Efficient market mechanisms for network resource allocation[END_REF]. We give some simulation results and illustrate that the system outcome reaches an ǫ-Nash equilibrium in a finite number of rounds if we charge a bid fee ǫ for any change of declared cost. This outcome is illustrated to be a good trade-off between complexity and efficiency.

VI. ACKNOWLEDGMENT

This work was done in the framework of the INRIA and Alcatel-Lucent Bell Labs Joint Research Lab on Self Organized Networks.

Fig. 1 .

 1 Fig. 1. Forward & backward induction illustration

Fig. 2 .

 2 Fig. 2. A simple topology

Fig. 3 . 2 ĉT 2 < xT 1 ĉT 1 .

 32211 Fig. 3. Forward induction

Fig. 5 .Fig. 6 .

 56 Fig. 5. Payoff of nodes over allocation process through a single route

Fig. 7 .

 7 Fig. 7. ǫ-Nash equilibrium

Fig. 8 .

 8 Fig. 8. Empirical cumulative distribution of the social welfare.

Aggregated utilities of the sellers

ŷr(j) may be different from ŷr of the source node, depending on its own demand traffic to destination on route r and its own maximum supplies.

A bid fee ǫ is chosen as the maximal gain of nodes from previous oscillation, where uosc is the net pay-off during oscillation.


Marga Garcia
email: garcia@gmail.com

Agnès Maillard

Daniel Aslanian

Marina Rabineau

Belén Alonso

Christian Gorini

Ferran Estrada

Marga García

The Catalan margin during the Messinian Salinity Crisis: Physiography, morphology and sedimentary record

Keywords: Valencia Basin, Catalan Margin, Messinian Salinity Crisis, Sea level, Drainage systems

Introduction

The Messinian Salinity Crisis (MSC) has concentrated the interest of many researches since the drilling of evaporites and salt in the Mediterranean basins in the 70's (Hsü et al., 1973a,b;[START_REF] Ryan | Initial Reports of the Deep Sea Drilling Project[END_REF]. Nevertheless, the bulk of investigations has focused on the marginal or deep evaporite basins, while only few works have dealt with the record of the MSC on the continental margins, which should be considered as key areas to link marginal to deep basins and to elaborate a global MSC scenario. In the Northwestern Mediterranean, the Gulf of Lions shelf-slope-deep basin transition has been studied thanks to a solid database [START_REF] Guennoc | Histoire géologique du Golfe du Lion et cartographie du rift oligo-Aquitanien et de la surface Messinienne[END_REF][START_REF] Lofi | Erosional processes and paleo-environmental changes in the Western Gulf of Lions (SW France) during the Messinian Salinity Crisis[END_REF][START_REF] Gorini | The Late Messinian salinity crisis and Late Miocene tectonism: Interaction and consequences on the physiography and post-rift evolution of the Gulf of Lions Margin[END_REF][START_REF] Bache | Evolution Oligo Miocène des Marges du Micro Océan Liguro-Provençal[END_REF]among others). Recent studies have also dealt with the transition from margins to deep basin on other Northwestern Mediterranean areas [START_REF] Sage | Seismic evidence for Messinian detrital deposits at the western Sardinia margin, northwestern Mediterranean[END_REF][START_REF] Cornée | Onshore to offshore reconstruction of the Messinian erosion surface in western Sardinia, Italy: MSC implications[END_REF]Obone Zue Obame et al., 2010) and in the Eastern Mediterranean area (Bertoni andCartwright, 2006, 2007). More recently, a new multi-site study has allowed a synthetic approach to the study of the MSC on the Western and Eastern Mediterranean and Black Sea [START_REF] Lofi | Atlas of the Messinian seismic markers in the Mediterranean and Black Seas[END_REF]. The Catalan continental margin is a key area for studying the correlation between the well-studied Gulf of Lions and the Valencia Basin (Fig. 1). This continental margin is particularly important because it is located at the transition of an oceanic basin margin (Gulf of Lions/Provençal Basin) and an aborted rift (Valencia Basin) represented by the North-Balearic Fracture Zone [START_REF] Maillard | Crustal structure and riftogenesis of the Valencia Trough (North-Western Mediterranean Sea)[END_REF]. In this complex context the local structural effects can be expected to have an important effect on the record of the Messinian events, in particular on the erosion surfaces and the resulting deposits. On the basis of these premises, this paper intends to improve the understanding of the Messinian event on the Catalan continental margin by studying the physiography and morphology of erosional and depositional features. We focus on establishing the major factors that controlled the record of the MSC event on the Catalan margin and on analyzing different interpretations for the Messinian sea level changes in the region.

Geological setting

The Catalan Continental Margin

The Catalan continental margin is located at the NW of the Valencia Basin in the Western Mediterranean. It is limited by the Cap de Creus to the north, by the Ebro delta to the south, and opens to the deep Provençal Basin (Fig. 1a). The Valencia Basin has developed in a complex tectonic setting. A first compressional episode occurred during the Paleogene, when the fault-related tectonic uplift on the Catalan Coastal ranges was compensated by erosion and isostatic subsidence [START_REF] Gaspar-Escribano | Cenozoic vertical motions of the Catalan Coastal Ranges (NE Spain): the role of tectonics, isostasy, and surface transport[END_REF]. At the end of the Oligocene to Early Miocene, subsequent extension, involving back-arc processes in relation to the African-European convergence started in the Gulf of Lions and propagated southwestwards to the Valencia Basin [START_REF] Olivet | La cinématique de la Plaque Ibérique[END_REF][START_REF] Jolivet | Lithosphericscale geodynamic context of the Messinian salinity crisis[END_REF][START_REF] Bache | Evolution of rifted continental margins: the case of the Gulf of Lions (Western Mediterranean Basin)[END_REF]. The extensional processes were not homogeneous along the basins separated by the North-Balearic Fracture Zone, as accretion occurred in the Provençal Basin while the Valencia Basin ended as an aborted rift [START_REF] Maillard | Crustal structure and riftogenesis of the Valencia Trough (North-Western Mediterranean Sea)[END_REF]Fig. 2). The extensional episode included a syn-rift stage (Upper Oligocene-Lower Burdigalian), responsible for the present-day half-graben structure and sediment deposition in the troughs, and a post-rift stage (Late Langhian-Present) of attenuated tectonic activity [START_REF] Le Pichon | La Mediterranée Occidentale depuis l'Oligocene schema d'evolution[END_REF][START_REF] Bartrina | Evolution of the central Catalan margin of the Valencia trough (western Mediterranean)[END_REF][START_REF] Roca | The Neogene structure of the eastern Iberian margin: structural contraints on the crustal evolution of the Valencia trough (Western Mediterranean)[END_REF][START_REF] Torres | Initiation and evolution of the Valencia trough (Western Mediterranean): constraints from deep seismic profiling and subsidence analysis[END_REF]Roca et al., 1999b).

The pre-Cenozoic basement of the offshore Catalan continental margin shows NW-SE to NNW-SSE structures offshore the Gulf of Rosas, including the Riumors-Roses Basin, which forms a NW-SE-oriented trough, delimited by the Pals high and the Cap de Creus (Roca et al., 1999b). To the south, the basement presents NE-SW trending faults offshore Barcelona and Palamós, delimiting the Barcelona, Calella and Sant-Feliu half-grabens (Fig. 2). The basement shallows towards the proximal areas of the margin and forms two relatively flat platforms, the Malgrat high off Mataró and the Roses high seawards of the Sant Feliu half-grabens (Roca et al., 1999b;Fig. 2). Basinwards, a prominent E-W-oriented high has been identified on the basement [START_REF] Maillard | Crustal structure and riftogenesis of the Valencia Trough (North-Western Mediterranean Sea)[END_REF]Fig. 2). On the deep basin the presence of numerous morphological highs is the result of rifting-related volcanism [START_REF] Marti | Cenozoic magmatism of the Valencia Trough (Western Mediterranean): relation between structural evolution and petrogenesis[END_REF][START_REF] Maillard | Structure et volcanisme dans la fosse de Valence (Méditerranée Nord-Occidentale)[END_REF]Fig. 3). Both basement highs and volcanoes are not totally buried by the Miocene sediments but still outcrop in the Margin Erosion Surface and in the Top Erosion Surface (MES/TES) and partially in the present-day seafloor.

The pre-Messinian sedimentary record in the Catalan margin includes Lower to Upper Oligocene sediments deposited in piggyback basins during the pre-extensional episode, Lower Miocene sediments deposited in the graben troughs during the syn-rift episode and late Langhian to Messinian sequences that show a gradual transition to the post-rift stage (Roca et al., 1999b).

The Catalan continental margin has been defined as an essentially closed sedimentary system where onshore sediment sources converge to the Valencia Channel and feed the Valencia deep sea Fan [START_REF] Dañobeitia | Geological framework of the Ebro continental margin and surrounding areas[END_REF][START_REF] Amblas | Morphogenetic mesoscale analysis of the northeastern Iberian margin, NW Mediterranean Basin[END_REF]Fig. 1). The sediment transport is controlled by submarine valleys that include two types of features, major and minor canyons. The major Palamós and Blanes canyons run from short distance (few km) from the coast to the deep basin and are directly connected to minor rivers (Ter and Tordera rivers respectively, Fig. 1; [START_REF] Canals | The role of canyons in strata formation[END_REF]. The role of these canyons as major sediment transport pathways from the continental margin to the deep basin is enhanced during storm events and cascading processes [START_REF] Palanques | Sedimentology and evolution of the Valencia Valley and Fan (Northwestern Mediterranean)[END_REF][START_REF] O'connell | Morphology and downslope sediment displacement in a deep-sea valley, the Valencia Valley (Northwestern Mediterranean)[END_REF][START_REF] Alonso | Seavalleys and related depositional systems in the Catalan Sea (Northwestern Mediterranean Sea)[END_REF][START_REF] Alonso | A deep-sea channel in the Northwestern Mediterranean Sea: morphology and seismic structure of the Valencia Channel and its surroundings[END_REF][START_REF] Palanques | General patterns of circulation, sediment fluxes and ecology of the Palamós (La Fonera) submarine canyon, Northwestern Mediterranean[END_REF][START_REF] Martin | Composition and variability of downward particulate matter fluxes in the Palamós submarine canyon (NW Mediterranean)[END_REF][START_REF] Zúñiga | Particle fluxes dynamics in Blanes submarine canyon (Northwestern Mediterranean)[END_REF]. The minor canyons (Arenys, Besos, La Berenguera, Foix) incise the continental slope break in the southwestern part of the Catalan continental margin (Fig. 1). They are short linear downslope-trending canyons, generally without tributaries, and are apparently disconnected from fluvial sources [START_REF] Canals | The role of canyons in strata formation[END_REF]. Most of these canyons connect directly to the 400 km long Valencia Channel [START_REF] Amblas | Morphogenetic mesoscale analysis of the northeastern Iberian margin, NW Mediterranean Basin[END_REF], which runs along the axis of the Valencia Basin, maintained by mass-transport processes and associated retrogressive slumps [START_REF] Alonso | A deep-sea channel in the Northwestern Mediterranean Sea: morphology and seismic structure of the Valencia Channel and its surroundings[END_REF]2000;Fig. 1). This channel acts as the main collector of the Valencia Basin drainage network [START_REF] Alonso | Late Quaternary sedimentation patterns of the Ebro turbidite systems (Northwestern Mediterranean): two styles of deep-sea deposition[END_REF]Farran and Maldonaldo, 1990;[START_REF] Field | Pliocene-Pleistocene growth of the Rio Ebro margin, northeastern Spain: a prograding-slope model[END_REF][START_REF] Nelson | Factors controlling late Cenozoic continental margin growth from the Ebro Delta to the western Mediterranean deep sea[END_REF][START_REF] Escutia | Palaeogeographic implications of the Messinian surface in the Valencia Trough, northwestern Mediterranean Sea[END_REF][START_REF] Palanques | El sistema turbidítico de Valencia: características morfo-sedimentarias durante el Plio-Cuaternario[END_REF]. This network included the Ebro drainage system since at least the end of the Messinian event [START_REF] Babault | Did the Ebro basin connect to the Mediterranean before the Messinian salinity crisis?[END_REF].

The MSC context

The Messinian Salinity Crisis (MSC) was an extreme event that affected the entire Mediterranean area during a relatively short period , when the Mediterranean-Atlantic connection progressively closed, leading to the evaporative concentration of a highly saline brine (Hsü et al., 1973a,b;[START_REF] Krijgsman | Chronology, causes and progression of the Messinian salinity crisis[END_REF][START_REF] Ryan | Decoding the Mediterranean Salinity Crisis[END_REF]among others). The subsequent sea level fall exposed the margins to subaerial erosion while a thick evaporite sequence was deposited in the basin (Hsü et al., 1973a,b;[START_REF] Montadert | Messinian event: seismic evidence[END_REF][START_REF] Rouchy | The Messinian Salinity Crisis in the Mediterranean basin: a reassessment of the data and an integrated scenario[END_REF][START_REF] Ryan | Decoding the Mediterranean Salinity Crisis[END_REF]. Following the new synthetic nomenclature [START_REF] Ciesm | The Messinian Salinity Crisis from mega-deposits to microbiology -A consensus report[END_REF][START_REF] Lofi | Atlas of the Messinian seismic markers in the Mediterranean and Black Seas[END_REF], the evaporite sequence includes: the Lower Unit (LU), the Mobile Unit (MU), and the Upper Unit (UU). The material eroded from the margins was deposited downslope in the form of seaward prograding sets and/or fan-shaped deposits showing chaotic seismic facies [START_REF] Clauzon | The Messinian Var Canyon (Provence, southern France) -Paleogeographic implications[END_REF][START_REF] Barber | Messinian subaerial erosion of the proto-Nile Delta[END_REF][START_REF] Stampfli | Messinian palaeorelief from 3-D seismic survey in the Tarraco concession area (Spanish Mediterranean Sea)[END_REF][START_REF] Guennoc | Histoire géologique du Golfe du Lion et cartographie du rift oligo-Aquitanien et de la surface Messinienne[END_REF][START_REF] Lofi | Plio-Quaternary prograding clinoform wedges of the western Gulf of Lion continental margin (NW Mediterranean) after the Messinian Salinity Crisis[END_REF]Lofi et al., , 2005;;Maillard et al., 2006;[START_REF] Ottes | The Messinian Salinity Crisis in the Nile Delta: chasing shallow marine reservoirs in a deep-water basin[END_REF][START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF][START_REF] Ryan | Decoding the Mediterranean Salinity Crisis[END_REF][START_REF] Lofi | Atlas of the Messinian seismic markers in the Mediterranean and Black Seas[END_REF].

The Zanclean flood sealed the end of the MSC at 5.33 Ma [START_REF] Hilgen | A critical re-evaluation of the Miocene-Pliocene boundary as defined in Mediterranean[END_REF][START_REF] Lourens | The Neogene Period[END_REF]. This event at 5.33 Ma has received several interpretations, from a catastrophic water flow lasting a few years [START_REF] Blanc | The opening of the Plio-Quaternary Gibraltar Strait: assessing the size of a cataclysm[END_REF][START_REF] García-Castellanos | Catastrophic flood of the Mediterranean after the Messinian salinity crisis[END_REF] to a progressive flooding occurring in two different phases of rising sea level [START_REF] Bache | Evolution Oligo Miocène des Marges du Micro Océan Liguro-Provençal[END_REF][START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF]. After the MSC, the presence of the salt induced salt tectonism, with the development of listric faults affecting the Pliocene-Quaternary deep sea sedimentation [START_REF] Gaullier | Diapirisme liguro-provençal: les effets d'une topographie résiduelle sous le sel messinien. Apports de la modélisation analogique[END_REF][START_REF] Reis | Salt tectonics, a controlling factor on the development of the Marseilles and Grand-Rhone sedimentary ridges, Gulf of Lions, Western Mediterranean Sea[END_REF], 2005).

The MSC in the Valencia Basin

The Valencia margin is characterized by the polygenic Margin Erosion Surface (MES) related to a succession of erosional events upslope, and by the existence of detrital bodies (Fig. 3). Towards the Valencia basin, the Messinian depositional units are bracketed by a Basal Erosion Surface (BES) and a Top Erosion Surface (TES), which marks the last Messinian erosional event (Maillard et al., 2006). Numerous submarine valleys eroded the Catalan continental margin. They formed a convergent network of tributaries that flew down into the deep Valencia paleo-channel, which cut the TES in the basin [START_REF] Escutia | Palaeogeographic implications of the Messinian surface in the Valencia Trough, northwestern Mediterranean Sea[END_REF]Fig. 3). Only some of these MSC canyons are active today (Foix, Blanes, Palamós; Fig. 1), while many others cannot be identified in the present-day bathymetry (Figures 1 and 3;[START_REF] Escutia | Seismic stratigraphic and sedimentologic studies of the depositional environments, margin architecture and growth patterns in the Valencia Trough continental margins (Northwestern Mediterranean Sea), since the Messinian[END_REF][START_REF] Escutia | Palaeogeographic implications of the Messinian surface in the Valencia Trough, northwestern Mediterranean Sea[END_REF][START_REF] Tassone | Evolución del sector septentrional del margen continental catalán durante el Cenozoico[END_REF]. Onshore, the Messinian event has also been identified, in the form of Messinian canyons along or close to the present-day Llobregat and Besos rivers (Vicente i Castell, 1986;[START_REF] Ventanyol | El plioce marí del Pla de Barcelona i del delta del Besos[END_REF][START_REF] Parcerisa | Estratigrafía y petrología del subsuelo precuaternario del sector SW de la depresión de Barcelona (Cadenas costeras catalanas, NE de Iberia)[END_REF], and a Messinian NW-SE-oriented trough that connected to the Riumors-Roses marine basin on the Alt Emporda area [START_REF] Escuer | Evolucion de los sistemas sedimentarios neogenos de la Cuenca del Alt Emporda (Gerona). I Congreso del Grupo Español del Terciario[END_REF]. After the Zanclean reflooding the Valencia Basin registered an important sedimentation in the form of canyon infilling, hemipelagic deposition and prograding units [START_REF] Dañobeitia | Geological framework of the Ebro continental margin and surrounding areas[END_REF][START_REF] Escutia | Palaeogeographic implications of the Messinian surface in the Valencia Trough, northwestern Mediterranean Sea[END_REF][START_REF] Bartrina | Evolution of the central Catalan margin of the Valencia trough (western Mediterranean)[END_REF]. The Pliocene sequence is represented by a terrigenous shelf and a prograding slope infilling the Messinian valleys and depressions, and was controlled by the basinward tilting of the continental shelf [START_REF] Tassone | Evolución del sector septentrional del margen continental catalán durante el Cenozoico[END_REF]. The Quaternary sequence presents a similar configuration, although the major glacioeustatic variations have substituted tectonics as the major controlling factor [START_REF] Ercilla | Pleistocene progradational growth pattern of the northern Catalonia continental shelf (northwestern Mediterranean)[END_REF][START_REF] Tassone | Evolución del sector septentrional del margen continental catalán durante el Cenozoico[END_REF] as also observed in the Gulf of Lions [START_REF] Rabineau | Paleo sea levels reconsidered from direct observation of paleoshoreline position during Glacial Maxima (for the last 500,000 yr)[END_REF].

Methodology and dataset

This study is based on a seismic database that includes seismic profiles obtained during several scientific cruises and oil industry seismic profiles obtained from the SIGEOF database of the Instituto Geologico y Minero de España (IGME, www.igme.es) (Fig. 4a). This database has provided to the public a wide amount of seismic profiles in the form of TIFF files (scanned profiles) and the associated navigation files. The conversion of the TIFF files into SEGY files was performed with the Image2SEGY software [START_REF] Farran | IMAGE2SEGY: Una aplicación informática para la conversión de imágenes de perfiles sísmicos a ficheros en formato SEG Y[END_REF]http://www.icm.csic.es). This software converts the pixels of the TIFF image into values of amplitude, and associates these values to the navigation, producing high-quality SEGY files. For this study we have used the Kingdom Suite software to construct and interpret the seismic database.

This study of the MSC is focused on the identification of the MES/TES surface that marks the end of the Messinian event, and constitutes the base of the Pliocene. This surface corresponds to the former unique M surface defined by [START_REF] Ryan | Initial Reports of the Deep Sea Drilling Project[END_REF], and is defined today as the MES on the continental margins (no MSC deposits) and as the TES on the basins, on top of the basin MSC deposits. The information from several drilling sites, both from the oil industry and scientific drillings, has been used to establish the chronostratigraphy of the seismic profiles and to identify the MES/TES. Besides the predominant erosive character of the surface, marked by the truncation of the underlying reflections, other seismic criteria taken into account are (Fig. 4b): 1) variation in the frequency of seismic reflections, between the Miocene and the Pliocene megasequences; 2) changes in the tectonic imprint, generally from a more-tectonised pre-MSC unit to a less-disturbed Pliocene-Quaternary unit [START_REF] Gorini | The Late Messinian salinity crisis and Late Miocene tectonism: Interaction and consequences on the physiography and post-rift evolution of the Gulf of Lions Margin[END_REF]; 3) Prograding clinoforms overlying the MES/TES; and 4) double high-amplitude reflection in the basin [START_REF] Escutia | Palaeogeographic implications of the Messinian surface in the Valencia Trough, northwestern Mediterranean Sea[END_REF]. For the calculation of gradients on the MES/TES, a two-layer velocity model has been applied, assuming a value of 1500 ms -1 for the speed of sound in seawater and 2290 ms -1 as an average value for the Pliocene-Quaternary sediments (Maillard et al., 2006).

Results

Physiography and morphology of the MES/TES

The Catalan Messinian continental shelf was 3-25 km wide, with minimum widths toward the northern sector (off Cap de Creus and Cap de Begur) (Fig. 5), The width and depth increases towards the south, where the shelf forms two relatively flat platforms (from 0 to 0.5 s TWTT; inclined seaward at present day) limited by two prominent valleys that correspond to the present-day Palamós and Blanes canyons. Two small flat platforms also occur off Cap de Begur (5-15 km wide and from 0 to 0.5-0.7 s deep) and off Barcelona (10 km wide, from 0 to 1-1.1 s deep). The continental slope is 25-45 km wide and runs from 0.3-0.5 to 2-2.5 s TWTT depth. The continental rise is 25-50 km wide (increasing its width towards the south) and occupies depths of 3.2-3.5 s, where it connects to the deep basin (Fig. 5).

On the continental slope, the MES/TES shows a sharp transition from a proximal rough, badland-type character with many valleys and incisions to a distal smooth surface gently dipping basinwards (Figures 5 and10). This updip transition occurs at consistent depths on the seismic profiles throughout the entire study area, ranging between 1.4 and 1.7 s TWTT, except for the area around the Palamós paleo-drainage system, where it occurs at depths of up to 1.9 s TWTT.

In addition, the MES/TES on the Catalan margin was characterized by the presence of a variety of paleo-drainage systems. The Palamos and Blanes canyons were present in the MES/TES, as the first-order conduits of two well-developed paleo-drainage systems. Two other drainage systems have been identified in the MES/TES, but do not exist today: the Cap de Creus paleo-drainage system (Gulf of Rosas), also consisting of a relatively complex and hierarchic network of valleys, and the Barcelona paleodrainage system, consisting of a single valley. The domains and the paleo-drainage systems will be described in detail in the next sections.

On the base of the morphology of the MES/TES and its relationship with the structural features, the Catalan continental margin can be subdivided into three well-differentiated domains (Fig. 5). From north to south: the Creus domain extends between the Cap de Creus and the Palamós Canyon; the Girona domain is limited by the Palamós and the Blanes canyons; and the Barcelona domain extends from the Blanes canyon to the southern limit of the study area.

The Creus domain

The morphology of the MES/TES on the Creus domain is strongly affected by the basement, and globally coalesces with it (Figs. 5 and6). The basement outcrops in the proximal coastal areas along the entire domain and forms numerous morphological highs (Fig. 6). The basement forms a NW-SE-oriented elongated outcrop off the Begur Cape, named Pals high (Fig. 2; Roca et al., 1999b). Numerous morphological scarps can be identified in the proximal areas at the borders of the basement outcrops, but also at deeper areas, where they seem to be related to NNW-SSE to NW-SE-trending faults (Roca et al., 1999b). Two major paleo-drainage systems have been identified in this domain: the Cap de Creus paleo-drainage system, which is located off the Gulf of Rosas, and the northern part of the paleo-Palamós drainage system, at the south of the domain (Figs. 5 and6).

The Girona domain

In the Girona domain the MES/TES is affected by few isolated basement outcrops. The most important structural features are two prominent W-E-oriented ridges located at the foot of the continental slope (Fig. 5). The southernmost ridge forms a 50 km long morphological high with a relief of up to 1.6 ms TWTT and gradients of up to 8° on its southern side, where it outcrops in the present day seafloor. The northernmost ridge is about 30 km long and has a less pronounced relief, up to 1 s TWTT, with gradients of 5° where it outcrops.

On the continental shelf, the MES/TES shows a relatively shallow MSC platform (Fig. 7), limited to the NE and SW by the rims of the paleo-Palamós and paleo-Blanes drainage systems respectively (Figs. 5 and7). This platform, with a maximum width of 25 km, is characterized by a relatively smooth surface, with rare truncated reflections. On the flanks of this platform, as well as on the deeper areas of the continental slope, the MES/TES has an irregular and more erosive character indicated by the truncation of reflections. Its outer limit to the SE coincides with the limit of the Rosas High (Fig. 2; Roca et al., 1999b).

Barcelona Domain

In the Barcelona domain, the basement half-graben morphology controlled both the MSC platform that occupies most of the continental shelf and the slope platform located off Barcelona (Figs. 5 and8). The MSC platform, 20 km wide and 0.4-0.6 s deep, is bounded by scarps and is oriented in a coast-parallel direction. It coincides with the Malgrat basement high (Fig. 3), which is delimited by normal SE-dipping faults (Roca et al., 1999b). The MES/TES has a smooth character on the platform, while it is irregular and clearly erosive on the rest of the domain. An ENE-WSW-oriented valley is incised at the western part of the platform (the Barcelona paleo-drainage system), while the eastern part is affected by the Blanes paleo-drainage system (Figs. 5 and8). The major part of the continental slope at the western part of this domain presents numerous downslope-trending parallel valleys spaced 8 to 10 km, with widths of 5-10 km and incision depths of 0.5-1.1 s (Fig. 5).

Paleo-drainage systems

The Cap de Creus paleo-drainage system is located in the Creus domain, at about 30km southwestward of the present-day Creus Canyon (Fig. 5). It consists of a major NW-SE oriented valley and its tributaries. The main valley is about 30 km long and its head is incised few kilometers from the present-day coastline. The valley location coincides with the Riumors-Roses Basin at the northern side of the Pals basement high (Figs. 2 and5). The MES/TES shows that the transversal profile of the valley is asymmetrical and V-shaped, with 10-12 km wide and up to 0.9 s deep incisions at the proximal part. On the middle part, the profile is relatively symmetrical and U-shaped, and the valley size becomes smaller, about 5.5 km wide and up to 0.6 s deep. On the distal part, the transversal profile is also asymmetrical and U-shaped, and the valley increases its size to widths of up to 12 km and depths of up to 1 s. Tributary valleys occur on the upper slope and connect with the main valley, mostly at its northern side, off Cap de Creus. They are 1-2 km wide and up to 0.6 s deep, are spaced few kilometers and design mesa-like reliefs with flat tops at depths of about 0.5 s (Fig. 6).

The Palamós paleo-drainage system consists of a major valley (the Palamós paleocanyon) at the same location than the present-day Palamós Canyon, and a dendritic network of tributary valleys (Figs. 5 and9). The paleo-canyon is WNW-ESE-oriented. It is about 30 km long, 15-20 km wide and shows a V-shaped, asymmetrical profile with a steeper southwestern flank (Fig. 9). The main tributary is about 22 km long, has a NNW-SSE direction, and receives the input of some smaller-scale tributaries. It has widths of up to 5 km and incision depths of 0.5-0.6 s. This valley coincides with the NE part of the Begur Basin, which forms a narrow (2-5 km wide) trough limited by faults, at the SW side of the Pals high. On the western side, several smaller-scale tributaries have been identified, with a general WSW-ENE to SSW-NNE direction, lengths of 15-25 km and incision depths of up to 0.58 ms. Those tributaries are limited by the scarps at the eastern side of the Girona domain platform and are incised in the Sant Feliu graben (Figs. 2 and5).

The Blanes paleo-drainage system consists of a major valley (the Blanes paleocanyon), at the same location than the present-day Blanes Canyon, that limits the Girona from the Barcelona domains, and a convergent, dendritic network of tributary valleys (Fig. 5). The paleo-canyon is oriented NNE-SSW to N-S. Its head is located at less than 5 km from the present-day coastline and it can be followed for about 60 km. The proximal part is narrow (up to 15 km wide) and shows symmetrical transversal profiles, with incision depths of up to 0.5 s. The distal part the paleo-canyon widens to 30 km, and presents an irregular transversal profile, mostly U-shaped and asymmetrical, with a steeper and narrower western flank (Fig. 5). The distal part cannot be precisely determined with the available data, but no relief can be identified at depths deeper than 3 s. This valley receives tributary valleys from both the northern and southern sides. A major 15 km long tributary valley, 3-5 km wide and 0.25-0.45 s deep mouths into the upper paleo-canyon from the NE side. This valley also receives the input of some smaller-scale tributaries, and this secondary system is excavated into the Girona domain platform, coinciding with the Sant Feliu graben (Figs. 2 and5). Several tributaries mouth into the main valley at its middle and distal course, both from the eastern and western sides. These tributaries have variable trends, lengths of up to 30 km and widths of up to 14 km and reach depths of 0.45 s (Figs. 2 and5).

The Barcelona paleo-drainage system is incised into the eastern side of the Barcelona domain (Fig. 5). It consists of a unique, 30 km long valley oriented NE-SW, parallel to the present-day coastline. It is limited by well-marked scarps and is incised in the Barcelona half-graben (Figs 2 and5). The transversal profile is irregular and U-shaped, and the incision depth reaches 0.65 s. Width increases from about 8 km at the proximal areas to more than 10 km at the distal reaches. The valley orientation changes to a downslope direction at its distal part (Figures 5 and8).

MSC depositional units

The limit of the MSC depositional units (detrital and evaporite deposits) has been defined by completing the initial work of Maillard et al. (2006) using all new available seismic information. The upslope limits of the detrital deposits, the Upper Unit (UU) and the Mobile Unit (MU) in the Catalan continental margin and basin are shown in Figure 10. The detrital deposits are identified on the seismic profiles as wedge-shaped units characterized by chaotic to transparent seismic facies (Fig. 10). They are generally located downslope at the transition between the MSC deposits domain and the MES domain. Basinwards they are bracketed by the BES and the TES, being therefore coeval to the MSC deposits. The depth of the upslope limit of the detrital deposits varies along the continental margin. In the Creus and Girona domains this limit occurs at depths around 3 s TWTT, and it generally shallows southwards and locally at the mouth of the valleys. Indeed, the distribution pattern of the detrital deposits shows a preferential deposition off the major paleo-drainage systems. In the Barcelona domain, the detrital deposits reach depths of 1.8 s TWTT and clear indentations exist in the Palamós and Blanes valleys and also between the E-W-oriented ridges at the foot of the Girona domain slope (Fig. 10). On the basin, UU and MU represent the Messinian deposition.

Plio-Quaternary sedimentary record

As a general trend, the thickness of Plio-Quaternary sediment increases basinwards. There are practically no deposits at the coastal areas, on MES platforms, basement highs and in the axis of the Palamós and Blanes canyons. The maximum values occur (0.5 to 1 s) at the present-day shelf-edge (Fig. 11). Relatively thick deposits (up to 0.7 s) occur on the Creus and Barcelona paleo-drainage systems, as well as on the tributaries of the major paleo-valleys. The thickness of Plio-Quaternary deposits decreases slightly on the present-day continental slope and presents relatively constant values in the basin (~0.5 s). Nevertheless, the Plio-Quaternary deposits distribution is irregular along the three domains identified in the Catalan continental margin. The Creus domain (Fig. 11), presents thin deposits (<0.35 s thick) at the coastal areas and the Pals basement high while thickness increases abruptly in a downslope direction. The main depocenter of the entire study area (1.5 s) occurs on the present-day outer shelf off the Gulf of Rosas. Secondary depocenters occur on the shelf-edge south of the basement high. Plio-Quaternary deposits fill the NW tributary of the Palamós paleo-drainage system (0.7 s thick depocenter) and the Creus drainage system (up to 0.6 s), whose relief cannot be identified in the present-day bathymetry. The infilling deposits consist of thick sediment wedges prograding in a SW to S direction.

The Girona domain presents thin Plio-Quaternary deposits on the MSC platform (<0.25 s). The thickness increases abruptly on the present-day shelf-edge (up to 1 s) (Fig. 11). The tributaries of the Palamós and Blanes paleo-drainage systems were also totally infilled during the Plio-Quaternary, contrasting with those at the SE side of the Blanes paleo-drainage system, which are identifiable on the present-day bathymetry. Two major depocenters (1 s thick) occur at both sides of the two E-W-oriented basement ridges at the foot of the slope.

The Barcelona domain presents the minimum thickness of Plio-Quaternary deposits (less than 0.25 s) on the platform, while the major depocenters locate on the presentday shelf-edge and upper slope (0.7 s), infilling the tributaries of the Blanes paleodrainage system (Fig. 11). The Barcelona paleo-drainage system and some of the valleys on the present-day continental slope are also completely filled by these deposits.

Discussion

Geological significance of the MES/TES in the Catalan continental margin

The physiography of the MES/TES shows a narrow continental shelf (3-25 km), especially on the Cap de Creus domain, where the paleo-shelf-edge, represented by the limit of the MSC platforms, is located more than 20 km landwards from its presentday position (Fig. 5). The most important morphologic features characterizing the MES/TES are the complex drainage systems that eroded the entire continental margin during the Messinian crisis. Drainage systems show consistent differences from the present-day ones in several aspects, including their location, their morphological parameters and their connection to the onshore and distal drainage system.

Regarding their location, only some of the Messinian paleo-valleys can be identified on the present-day seafloor (Figs. 1 and5). This is the case of the major Palamós and Blanes canyons and of some minor downslope-trending valleys located at the southern part of the study area (Arenys and Besos canyons). They respectively correspond to the major and minor present-day submarine canyons of the Catalan continental margin. In contrast, the Creus and Barcelona paleo-drainage systems as well as most of the tributaries have been totally infilled by Plio-Quaternary deposits (Figs. 1 and5).

A comparison between the morphological parameters (e.g. width, depth and transversal profile) of the paleo-and present day-valleys can be made for the Palamós Canyon (Fig. 9). The paleo-canyon was wider and shallower (up to 27 km wide and 1.1 s deep) than the present-day canyon, which is less than 18 km wide and 2.1 s deep. Both paired and impaired terraces occur on the paleo-canyon walls. They are 3-4 km wide and are identified at depths of 1 s TWTT. (Fig. 9b). Regarding the connection to onshore drainage areas, it is only documented for the Cap de Creus and the Blanes paleo-drainage systems. The Cap de Creus paleo-drainage system could be connected to the Messinian NW-SE-oriented valley in the Alt Emporda area (Fig. 2; [START_REF] Escuer | Evolucion de los sistemas sedimentarios neogenos de la Cuenca del Alt Emporda (Gerona). I Congreso del Grupo Español del Terciario[END_REF][START_REF] Tassone | Evolución del sector septentrional del margen continental catalán durante el Cenozoico[END_REF]. The downslope-trending valleys at the south of the Barcelona domain could have been connected to the valleys identified along the Besos and Llobregat rivers (Fig. 2; Vicente i Castell, 1986; [START_REF] Ventanyol | El plioce marí del Pla de Barcelona i del delta del Besos[END_REF]. For the rest of the continental margin, the connection to onshore drainage areas seems to be hindered by the Catalan Coastal Ranges (Fig. 2), which formed a morphological barrier that limited the connections to the Mediterranean Sea. Regarding the distal continuation of the paleo-drainage systems, most of them seem to lose their relief as they reach the lower continental slope. With the available data, the Palamós and Blanes paleo-canyons cannot be identified at depths greater than 2.5 s TWTT and the downslope-trending valleys of the Barcelona domain show no relief at depths greater than 2 s TWTT.

Subaerial origin of the paleo-drainage systems

The morphology of the paleo-drainage systems, including the dendritic pattern of the drainage network and the rough character of the erosive surface with the presence of mesa-like relief at the inter-valley areas (Figs. 6 to 8), suggests an origin related to subaerial erosion as the result of the Messinian sea level drop [START_REF] Barber | Messinian subaerial erosion of the proto-Nile Delta[END_REF][START_REF] Lofi | Erosional processes and paleo-environmental changes in the Western Gulf of Lions (SW France) during the Messinian Salinity Crisis[END_REF]. Rapid retrogressive erosion, in which tributaries form a dendritic pattern draining the area between the major valleys, is suggested by the morphology of the paleo-drainage systems [START_REF] Glock | The development of drainage systems: a synoptic view[END_REF]. Terraces and badlands topography have also been observed westward in the Ebro shelf and related to subaerial erosion (Stampfli and Hocker, 1989;[START_REF] Frey Martinez | 3D seismic interpretation of the Messinian unconformity in the Valencia Basin, Spain[END_REF][START_REF] Urgeles | New constraints on the Messinian sealevel drawdown from 3D seismic data of the Ebro Margin, western Mediterranean[END_REF].

Subaerial margin erosion has also been documented by several studies all around the Mediterranean, such as the Gulf of Lions [START_REF] Clauzon | Le Canyon de la Durance (Provence, France): une preuve paléogéographique du bassin profond de dessication[END_REF][START_REF] Clauzon | Le canyon Messinien du Rhône: une preuve décisive du 'dessicated deep-basin model' (Hsü, Cita and Ryan[END_REF][START_REF] Guennoc | Histoire géologique du Golfe du Lion et cartographie du rift oligo-Aquitanien et de la surface Messinienne[END_REF][START_REF] Lofi | Plio-Quaternary prograding clinoform wedges of the western Gulf of Lion continental margin (NW Mediterranean) after the Messinian Salinity Crisis[END_REF][START_REF] Lofi | Erosional processes and paleo-environmental changes in the Western Gulf of Lions (SW France) during the Messinian Salinity Crisis[END_REF][START_REF] Loget | Mesoscale fluvial erosion parameters deduced from modelling the Mediterranean sea level drop during the Messinian (late Miocene)[END_REF][START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF], Italy [START_REF] Rizzini | Erosional surface of Messinian age in the subsurface of the Lombardian Plain (Italy)[END_REF], the Nile margin (Rizzini et al., 1978;[START_REF] Barber | Messinian subaerial erosion of the proto-Nile Delta[END_REF][START_REF] Ottes | The Messinian Salinity Crisis in the Nile Delta: chasing shallow marine reservoirs in a deep-water basin[END_REF] and the Ebro continental margin and Valencia Basin [START_REF] Stampfli | Messinian palaeorelief from 3-D seismic survey in the Tarraco concession area (Spanish Mediterranean Sea)[END_REF][START_REF] Escutia | Palaeogeographic implications of the Messinian surface in the Valencia Trough, northwestern Mediterranean Sea[END_REF][START_REF] Frey Martinez | 3D seismic interpretation of the Messinian unconformity in the Valencia Basin, Spain[END_REF]Maillard et al., 2006). In particular, the badland Messinian surface identified on the Gulf of Lions, that presents the same character as the MES/TES on the Catalan continental margin, is interpreted to have developed subaerially in less than 0.3 Ma [START_REF] Lofi | Erosional processes and paleo-environmental changes in the Western Gulf of Lions (SW France) during the Messinian Salinity Crisis[END_REF] as the result of a retrogressive cutting of gullies, mass wasting and avalanches, in a climate dominated by intense, short rain storms [START_REF] Chamley | La sédimentation argileuse au Tertiaire supérieur dans la domaine méditerranéen[END_REF][START_REF] Lofi | Erosional processes and paleo-environmental changes in the Western Gulf of Lions (SW France) during the Messinian Salinity Crisis[END_REF].

The Messinian detrital deposits: relationship with the MES/TES and evaporite deposits

In the Catalan continental margin the most proximal Messinian deposits correspond to the detrital deposits, formed by sediment eroded from the shallow areas and transported by the paleo-drainage systems (Fig. 10). The varying depth of the detrital wedges (2-3 s TWTT) could be explained by a combination of different factors, including variations on the nature of the sediment supply, the occurrence of slope instability processes and local tectonic effects. Sediment eroded from different source areas in the Catalan continental margin, from the basement on the northern part of the margin to the Miocene-Oligocene sediment in the southern areas (Roca et al., 1999a,b), should be expected to undergo processes (i.e. erosion, transport, deposit) with a different degree of efficiency, leading to variable localizations of final sedimentary products. Slope instability processes favored by the deposition of evaporites and slope tilting [START_REF] Govers | Regional isostatic response to Messinian Salinity Crisis events[END_REF][START_REF] Ryan | Decoding the Mediterranean Salinity Crisis[END_REF] may also be responsible for part of the detrital bodies, whereas the effect of tectonically-controlled mass movements should not be neglected. In any case, the post-depositional effect of differential subsidence must be taken into account as it changes the geometries after deposition.

Detritals are therefore proposed to come from fluvial drainage and/or slope instability. Basinwards, their precise relationship with the basin MSC deposits (LU, MU, UU) is generally complex and controversial [START_REF] Lofi | Evidence for pre-Messinian submarine canyons on the Gulf of Lions slope (Western Mediterranean)[END_REF][START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF][START_REF] Lofi | Atlas of the Messinian seismic markers in the Mediterranean and Black Seas[END_REF]. In the Valencia Basin, it seems that most detritals are onlapped by the UU, which would confirm that most of the erosion and deposition would have occurred during an early stage of the MSC (Maillard and Mauffret, 2006;[START_REF] Bache | Evolution Oligo Miocène des Marges du Micro Océan Liguro-Provençal[END_REF][START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF].

Significance of the "rough-smooth boundary"

The boundary between the rough and smooth MES/TES (Fig. 10) is considered as the equivalent to that identified by [START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF] in the Gulf of Lions. Following their interpretation, the smooth surface would correspond to a first stage of slow sea level rise which progressively levels the Messinian subaerial erosion by wave ravinement abrasion, while the rough surface would be the result of the subaerial erosion preserved by a second stage of very rapid sea level rise at the end of the MSC. In the Catalan continental margin, this limit is identified at 1.4-1.7 s TWTT, approximately the same depth than in the Gulf of Lions (1.6 s TWTT). The high gradients of the MES and probably the lithology of the ridge would prevent the development of an abrasion surface around the eastern part of the E-W-oriented ridges at the Girona domain slope (Fig. 5), which explains the absence of the rough-smooth boundary in this area. At the area around the Palamós paleo-drainage system the rough-smooth boundary locates at a slightly deeper position (up to 1.9 s TWTT). Differential vertical movements after the MSC should be related to this fact, since the sea level variations should have affected the entire study area in a similar way.

The smooth surface could be alternatively interpreted as the result of erosion during periods of sea level stagnation along the general Messinian drawdown (as suggested by [START_REF] Bertoni | Major erosion at the end of the Messinian Salinity Crisis: evidence from the Levant Basin, Eastern Mediterranean[END_REF], and the morphological arguments to differentiate between erosion during sealevel regression or transgression are not evident [START_REF] Just | Erosion of continental margins in the Western Mediterranean due to sea-level stagnancy during the Messinian Salinity Crisis[END_REF]. However, the subaerial erosion following a stagnation period during the regression would have further eroded the margin and transformed the smooth surface to a continuous rough surface, therefore not preserving the smooth surface. The position of the smooth surface landward (updip) of the detritals is another piece of argument. In the Catalan margin, while erosion during regression must definitely have happened, the preservation of the smooth surface suggests that a final erosion by wave abrasion occurred during the early Zanclean flood, when sea level rise was probably slower.

Factors controlling the MSC imprint on the Catalan margin

The MES/TES on the Catalan margin confirms the subaerial exposure of the margin due to the drastic sea level fall during the Messinian event and the development of the MES on the margin [START_REF] Escutia | Palaeogeographic implications of the Messinian surface in the Valencia Trough, northwestern Mediterranean Sea[END_REF][START_REF] Frey Martinez | 3D seismic interpretation of the Messinian unconformity in the Valencia Basin, Spain[END_REF]Maillard et al., 2006;[START_REF] Urgeles | New constraints on the Messinian sealevel drawdown from 3D seismic data of the Ebro Margin, western Mediterranean[END_REF]. Therefore, the sea level fall can be considered as the major factor controlling the margin evolution during the MSC, since it was a unique event affecting the entire region. This major factor was however modulated by the structural framework, explaining the variations of the characteristics and features of the MES/TES along the margin.

The Messinian sea level changes as the major regional factor

The MSC sea level fall has been estimated to be of around 1500 m [START_REF] Ryan | The nature and distribution of Messinian erosional surfaces -Indicators of a several-kilometer-deep Mediterranean in the Miocene[END_REF][START_REF] Clauzon | Le Canyon de la Durance (Provence, France): une preuve paléogéographique du bassin profond de dessication[END_REF][START_REF] Clauzon | Le canyon Messinien du Rhône: une preuve décisive du 'dessicated deep-basin model' (Hsü, Cita and Ryan[END_REF], and 1500-2000 m in the Valencia Basin [START_REF] Stampfli | Messinian palaeorelief from 3-D seismic survey in the Tarraco concession area (Spanish Mediterranean Sea)[END_REF]Maillard et al., 2006). The fact that Messinian valleys cannot be identified on the distal margin (>2000 m) agrees with these maximum estimations, however they should be corrected from post-depositional vertical movements. Figure 12 shows a schematic diagram of the sea level changes during the MSC and the resultant erosion surfaces and deposits. During the MSC drawdown, subaerial erosion on the margin and deposition of detrital wedges and/or evaporates occurred on the slope. Relatively short events of drastic sea level drop could have punctuated the general regressive tendency during the MSC, as suggested by the mesa-like relief delimiting the interfluves areas in the Cap de Creus domain (Fig. 6; [START_REF] Barber | Messinian subaerial erosion of the proto-Nile Delta[END_REF]. The sea level drop must have induced the over-excavation of the paleo-drainage systems including the present-day onshore domain, as in the case of the Cap de Creus and Blanes paleo-drainage systems and the downslope-trending valleys at the south of the Barcelona domain. In addition, terraces identified on the paleo-canyons walls may indicate single or multiple sea level stagnancies that could be related to periods when the inflowing waters from the Atlantic kept the Western Mediterranean sea level constant at the depth of the Sicily Sill and the starting water spilling to the Eastern Mediterranean Basin (Just et al. 2010).

The Zanclean flooding would have occurred in at least two phases (Fig. 12), as suggested by the smooth/rough erosive surfaces [START_REF] Bache | Evolution Oligo Miocène des Marges du Micro Océan Liguro-Provençal[END_REF][START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF]. The first phase was characterized by a slow sea level rise responsible for the abrasion surface at depths of 1.4-1.7 s TWTT. This major erosive event could also be responsible for the erosion of the distal parts of the drainage systems, whose distal connection to the basinal drainage network cannot be identified. Alternatively, the absence of drainage features on the distal continental margin may be explained by a change on the sediment transport processes at the foot of the slope, from a channelized transport that developed complex drainage networks to a non-channelized transport that would spread the sediment charge on the basin. Assuming the 1500-2000 m of sea level drop [START_REF] Stampfli | Messinian palaeorelief from 3-D seismic survey in the Tarraco concession area (Spanish Mediterranean Sea)[END_REF]Maillard et al., 2006), the channelized system would have consisted of subaerial rivers that would have deposited their sediment charge in the form of shallow-water deposits (in deeper areas). A second phase of rapid sea level rise allowed the preservation of the subaerial rough MES (Fig. 12;[START_REF] Bache | Evolution Oligo Miocène des Marges du Micro Océan Liguro-Provençal[END_REF][START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF].

After the end of the MSC, the rise in base level induced changes in accommodation space and sediment supply that led to the infilling of the Cap de Creus and Barcelona paleo-drainage systems. The first one was fossilized during the Plio-Quaternary by the sediment supply from the N-NE, as indicated by the thick prograding wedges that have induced a seaward progradation of the continental shelf of more than 20 km (Fig. 6). The sediment supply probably came directly from the Gulf of Lions through the Liguro-Provencal current that follows the shelf edge to the west and southwest around Cap Creus both for Surficial and Intermediate, Levantine waters [START_REF] Millot | Circulation in the Western Mediterranean Sea[END_REF]. In the case of the Barcelona system, the origin of the sediment is less clear from the seismic profiles, but the general NE-SW direction of the current along the margin [START_REF] Millot | Circulation in the Western Mediterranean Sea[END_REF] suggests a sediment supply from the NE.

Structural framework as the major local factor

The most important local factor is the structural framework, directly related to the North Balearic fracture zone, which separates the NE-SW-oriented Girona and Barcelona domains from the NW-SE-oriented Creus domain belonging to the Provençal Basin [START_REF] Mauffret | Tectonics and deep structure of the north-western Mediterranean Basin[END_REF]. The Rosas graben and Pals high are located between this fracture zone and the Central fracture zone off Barcelona (Fig. 2; [START_REF] Mauffret | Tectonics and deep structure of the north-western Mediterranean Basin[END_REF][START_REF] Maillard | Crustal structure and riftogenesis of the Valencia Trough (North-Western Mediterranean Sea)[END_REF]. Even if they were not active during the Messinian, and despite the thickness of the Lower Miocene deposits (Roca et al., 1999b), the resulting faults could have acted as inherited steps. The structural framework controlled the erosional and depositional products of the MSC in different ways, determining: (1) the location and preservation of the paleo-drainage systems, both offshore and onshore;

(2) the distribution of Messinian deposits; (3) the character of the erosional surface, specifically with regard to the location of the rough-smouth surface bondary; and (4) the rate of post-deposition subsidence.

Regarding the location of the major Messinian valleys, the major paleo-valleys show a close relationship with the structural features of the basement (Fig. 2). The Cap de Creus paleo-drainage system was controlled by the NNW-SSE-oriented faults that delimit the Riumors-Roses basin, at the NE side of the Pals high (Vázquez et al., 1993;[START_REF] Tassone | Evolución del sector septentrional del margen continental catalán durante el Cenozoico[END_REF]Roca et al., 1999b). The Palamós paleo-canyon was controlled by the structure of the Begur basin, which determines its NW-SE trend (Vázquez et al., 1993;Roca et al., 1999b) and the northern tributary of the Palamós paleo-drainage system was related to the NNE-SSW faults system at the SW side of the Pals high. The Blanes paleo-canyon was also incised on the basement depression between the Malgrat high and the Calella half-graben and could be controlled by the arcuate NNW-SSE-oriented normal fault at the east side of the basement platform and ridge on the Girona domain [START_REF] Maldonado | Mapa Geológico de la Plataforma Continental Española y Zonas Adjacentes[END_REF][START_REF] Maillard | Crustal structure and riftogenesis of the Valencia Trough (North-Western Mediterranean Sea)[END_REF]. The strong structural control may be also responsible for the maintenance of the major Palamós and Blanes canyons through all the Pliocene-Quaternary, probably in relation to the high-energy sediment transport during storms and cascading processes [START_REF] Canals | Flushing submarine canyons[END_REF]. On land, the structural control exerted by the physiography of the Catalan Coastal Ranges would also have determined the onshore extension of the paleodrainage systems, limiting the connections to the Gulf of Rosas and to narrow passages that allowed the incision of the Besos and Llobregat paleo-rivers.

The location of the tributaries of the major paleo-drainage systems, and the entire Barcelona paleo-drainage system may also be interpreted in relation to the structural half-graben framework. In the Girona and Barcelona domains, the differential erodibility between the basement platforms and the sediment infilling (consisting of alluvial and lacustrine successions, marine shelf deposits or fan deltas, Roca et al., 1999a) could have enhanced the effect of the meteoric rain in a graben-parallel direction, that is, parallel to the coastline, with the incision of the Barcelona paleo-drainage system and the tributaries of the Palamós and Blanes paleo-drainage systems.

Regarding the distribution of the Messinian deposits, the E-W-oriented basement ridges in the Girona domain slope seem to have acted as structural traps for the sediment eroded from shallower areas, preventing the evacuation of sediment to the deep basin. After the MSC, these ridges would have continued playing the same role, since they record more than 1 s TWTT thick Plio-Quaternary deposits in between ridges.

Slight differences in the location of the rough-smooth boundary on the Catalan margin may be related to differential vertical movements after the MSC, as the extensional NE-SW fracture playing during the Pliocene [START_REF] Tassone | Evolución del sector septentrional del margen continental catalán durante el Cenozoico[END_REF] and the basinwards tilting of the margin [START_REF] Lofi | Plio-Quaternary prograding clinoform wedges of the western Gulf of Lion continental margin (NW Mediterranean) after the Messinian Salinity Crisis[END_REF][START_REF] Rabineau | Paleo sea levels reconsidered from direct observation of paleoshoreline position during Glacial Maxima (for the last 500,000 yr)[END_REF][START_REF] Ryan | Decoding the Mediterranean Salinity Crisis[END_REF]. The division of the Valencia Basin by transfer fracture zones [START_REF] Maillard | Crustal structure and riftogenesis of the Valencia Trough (North-Western Mediterranean Sea)[END_REF] could determine local different response to these vertical tectonic movements and explain the distribution of Pliocene-Quaternary deposits (Fig. 11).

Summary and conclusions

The study of the MES/TES provides information about the significance of erosive and depositional features, and the role of the Messinian sea level changes and the structural framework as major controlling factors. The results of this study provide the following conclusions:

-Based on the morphological and structural features on the MES/TES surface, three domains have been differentiated: Creus, Girona and Barcelona domains, reflecting the different geological controlling factors. The major morphological features are extensive drainage systems that eroded the entire Catalan margin.

-The Messinian sea level drop produced subaerial erosion of the margin and deposition of detrital wedges on the slope and basin. The subaerial erosion excavated two types of drainage systems: (1) Structurally-controlled valleys that were connected to onshore drainage areas and have been preserved after the MSC. Only the Cap de Creus paleo-drainage system has been later infilled by the high sediment supply from the Gulf of Lions; and (2) Valleys excavated by meteoric rain into basins limited by basement blocks. They have been infilled by the Plio-Quaternary deposition.

-The distribution of the MSC detrital deposits was controlled by the structural framework, that determined both the nature of the sediment supply and the efficiency of the sediment transport, the reworking of deposits and the development of structural traps for the deposition of the eroded sediment.

-This study seems to confirm the Zanclean transgression occurring in two phases [START_REF] Bache | Evolution Oligo Miocène des Marges du Micro Océan Liguro-Provençal[END_REF][START_REF] Bache | Messinian erosional and salinity crises: view from the Provence Basin (Gulf of Lions, Western Mediterranean)[END_REF]. During the first phase, the sea level rose relatively slowly and as a result of wave abrasion a smooth erosive surface developed on the margin. The second phase consisted on a rapid sea level rise that preserved the MSC features.

This work reveals the potential of the available industrial and scientific seismic profiles for the re-interpretation of regional or local geologic topics with the aid of modern software. Nevertheless, new high-resolution seismic data, especially on the slope area, are required in order to better define the precise timing of the MSC events. Regarding the chronology of the drainage systems within the Messinian crisis, two points need to be clarified: the volume of detrital deposits on the Valencia Basin and the volume of sediment eroded both onshore and offshore. This information will allow establishing the age of detrital products and to constrain an exact scenario for the MSC. Another question that should be clarified concerns the distal part of the drainage systems, regarding the connection of the paleo-valleys to the deep sediment transport and the processes involved in their formation.

Figures

Figure 1 .

 1 Figure 1. Study area. a) Location and bathymetry of the Catalan margin, NW Mediterranean. b) Bathymetric chart of the study area, limited to the north by the Cap de Creus, by the Foix Canyon to the south, and opened to the deep Provençal Basin. The major submarine canyons are represented, from North to south: AC: Aude Canyon; CC: Creus Canyon; PC: Palamós Canyon; BC: Blanes Canyon; ArC: Arenys Canyon; BeC: Besos Canyon; LBC: La Berenguera Canyon; FC: Foix Canyon.

  Figure 1. Study area. a) Location and bathymetry of the Catalan margin, NW Mediterranean. b) Bathymetric chart of the study area, limited to the north by the Cap de Creus, by the Foix Canyon to the south, and opened to the deep Provençal Basin. The major submarine canyons are represented, from North to south: AC: Aude Canyon; CC: Creus Canyon; PC: Palamós Canyon; BC: Blanes Canyon; ArC: Arenys Canyon; BeC: Besos Canyon; LBC: La Berenguera Canyon; FC: Foix Canyon.

Figure 2 .

 2 Figure 2. Structural framework of the Catalan margin. The major structural onshore and offshore features, as well as the basement isochrones, are represented. All the features represented in the map have been obtained from a bibliographic review. Legend: HG: Half-Graben; H: High.

Figure 3 .

 3 Figure 3. Synthesis of the MSC record in the Valencia Basin. MES/TES isobaths are in metres. The Messinian event is recorded in the form of erosive (Messinian valleys and erosional surfaces, MES and BES) and depositional (detrital bodies and evaporites) features. Volcanism and salt diapirs are common features in the area. Modified from Maillard et al. (2006) and Bache et al. (2009) for the Gulf of Lions

Figure 4 .

 4 Figure 4. Methodology and dataset. a) Seismic profiles database analysed in this work, including information from the SIGEOF database (IGME) and data from research cruises. b) Examples of seismic profiles showing the criteria for the identification of the MES/TES.

Figure 6 .

 6 Figure6. The Creus domain is the northernmost domain of the study area, limited to the south by the Palamós paleo-drainage system (PDS). a) Bathymetry of the MES/TES and location of the seismic profiles (see legend in Figure5). b) to d) Seismic profiles showing the MES/TES, which coincides in many cases with the basement. White arrows mark the progradation of the Plio-Quaternary sediments on the MES/TES. Figure6dshows the mesa-like reliefs on the Creus PDS.

Figure 7 .

 7 Figure 7. The Girona domain is limited by the Palamós PDS to the north and by the Blanes PDS to the south. a) Bathymetry of the MES/TES and location of the seismic profiles (see legend in Figure 5). b) and c) Seismic profiles showing the MES/TES and e basement. This domain is characterized by a wide and flat MCS platform. th

Figure 12 .

 12 Figure 12. Schematic diagram of the sea level changes during the MSC and the resultin s

Acknowledgements

This study is mainly funded by an Institut Carnot-Ifremer-EDROME grant (for Marga Garcia) and also supported by the GDR and Action-Marges Mediterranée Occidentale (France). It also benefited from the support by the Projects TOPO-MED (CGL2008-03474-E/BTE), CONTOURIBER (CTM2008-06399-C04-04/MAR) and MONTERA (CTM2009-14157-C02), of the Ministry of Education and Science (Spain). The authors would like to thank the effort of the Instituto Geológico y Minero de España (IGME) for making their broad industry seismic data available to the public, and Marcel.li Farran (ICM-CSIC) for his help in the transformation of seismic profiles into digital data. We thank Seismic Micro-Technologies for providing the KingdomSuite software used for the seismic stratigraphy analysis. We are grateful to Eduard Roca (UB), Jean-Loup Rubino (TOTAL), Jean-Pierre Suc (CNRS-Université de Lyon), François Bache (UPMC, CNRS) and Estelle Leroux (Université de Brest, Ifremer) for their help in the elaboration of this paper. We also thank the editors and reviewers (C. Bertoni and an anonymous reviewer) for their comments that greatly improved this paper.