Tarek Moulahi

Salem Nasri

Hervé Guyennet

Broadcasting Based on Dominated Connecting Sets with MPR in a Realistic Environment for WSNs & AD-HOC

Keywords: Wireless Sensor Networks, Broadcasting, Connected Dominating Sets, MultiPoint Relay, Lognormal model

Broadcasting in wireless sensor networks (WSNs) is the dissemination of packets from one node to all nodes in the network. This flooding causes redundant data and broadcast storm problems. To counteract this effect, many methods have been introduced to minimize the redundancy, such as MPR (MultiPoint Relay) or DS-MPR (Connected Dominating Sets with MPR). These methods stipulate that a packet is correctly received if the receiver node is in the transmission radius of the sender node. But this fact is not always true, due to many factors like signal attenuation, noise and existence of obstacles. This paper focuses on DS-MPR. Firstly, we test it in a realistic environment to show its limit in terms of reachability. Secondly, we introduce a modification of DS-MPR to be applicable with a realistic physical layer. Our heuristic method is called RDS-MPR (Realistic DS-MPR). This heuristic has improved DS-MPR in reachability, which may exceed more than 94%. Finally, we introduce an extension of RDS-MPR, called eRDS-MPR (extended RDS-MPR) which provides a reachability up to more than 97%.

Introduction

Recent advances in wireless communication technologies and the fabrication of low-cost wireless devices have led to the appearance of wireless sensor networks (WSNs). Due to the multi-functionality of sensors, WSNs have been utilized for a variety of applications such as environment monitoring, surveillance, and military. Moreover, WSNs can provide a good observation of nature and a high capacity of collecting information. However, the most important disadvantage of WSNs is their limit in energy. As a result, many methods, algorithms and protocols were introduced and developed to take into consideration this constraint. Since WSNs are considered ad-hoc networks with other characteristics, many algorithms and methods of ad-hoc networks [START_REF] Abdou | Using an Evolutionary Algorithm to Optimize the Broadcasting Methods in Mobile Ad hoc Networks[END_REF][START_REF] Akbari | A link stability-based multicast routing protocol for wireless mobile ad hoc networks[END_REF] could be reused and reconfigured according to the WSNs' specificity. In this paper, we focus our interest on broadcasting algorithms in WSNs and ad-hoc. Firstly, broadcasting means the packet distribution from a source sensor to all other destination sensors in the network. Many research projects have been developed discussing solutions to broadcast information in these kinds of networks and taking into account the minimization of energy consumption. Since the communication process consumes more energy compared to the others processes (i.e., sensing, communicating and processing), many methods and algorithms have focused on reducing the number of relay nodes in order to minimize the number of communication packets. This also minimizes the consumed energy and broadcast storm problems. By studying currently broadcasting method, we find that the most of them are conceived in an ideal environment (i.e., they stipulate that a message send from a node is certainly received by another node if the receiver is in the sender covering area). This fact has negative consequences on communication and clearly decreases the accessibility of the broadcasting method used, because in a real environment there are signal attenuation, obstacles and nature factors. In this manuscript, an overview of DS-MPR is given. Thus, a modification of DS-MPR to be applicable with a realistic environment is proposed, aiming to increase the accessibility. This paper is organized as follows: Section 2 outlines the most well-known methods of broadcasting and provides the problem definition of our topic. In Section 3, we perform a study of DS-MPR, and we show that this method is not a valid method of broadcasting because its reachability is less than 80% in the best cases. Section 4 presents RDS-MPR, which is an improvement of DS-MPR to be applicable with a realistic physical layer using the lognormal shadowing model (LNM). In LNM, a node correctly receives a packet from another node with a probability p. This probability is defined as a function of transmission radius, power attenuation factor and distance between nodes. In Section 5, an extension of RDS-MPR is proposed. This new method, called eRDS-MPR, greatly improves DS-MPR in reachability. Finally, in Section 6, a performance study of the proposed methods compared to DS-MPR is given.

Preliminaries

Related work

To perform the task of broadcasting, pure flooding is used first. This method increases the number of redundant packets, broadcast storm problems and energy consumption. Subsequently, many research projects have focused on minimizing these problems. In literature, there is several methods and protocols for broadcasting in WSNs. Most of them are conceived in an ideal environment [START_REF] Hsu | Efficient Broadcasting Protocols for Regular Wireless Sensor Networks[END_REF][START_REF] Chien-Chun | A Power-Preserving Broadcast Protocol for WSNs With DoS Resistance: Proceedings of International[END_REF][START_REF] Williams | Comparison of Broadcasting Techniques for Mobile Ad Hoc Networks[END_REF][START_REF] Orecchia | Localized Techniques for Broadcasting in Wireless Sensor Networks[END_REF][START_REF] Deng Yubo | Modeling of Broadcasting based on Distance Scheme for WSN: International Joint Conference on INC[END_REF], also called unit disk model (UDM). In UDM, a receiver node can correctly get a packet of data if it is in the emission radius of the sender node. In a real environment, this assumption is not always true, due to many factors like signal attenuation and presence of obstacles. In what follows, we list the most known broadcasting methods according to their environment assumption.

UDM-based broadcasting

• MPR [START_REF] Qayyum | Multipoint Relaying for Flooding Broadcast Messages in Mobile Wireless Networks[END_REF]: First proposed by Qayyum and al., this method treats broadcasting from the sink node to all nodes in a network and it is based on levels (i.e., the sink's neighbors are considered as level one nodes, the level one nodes' neighbors are considered as level two nodes). So, the broadcasting is performed by levels and the method choose each time the best nodes to relay. These nodes are a subset of a unique level nodes. The selection of relaying nodes is performed according to many factors. The aim of the MPR method is to minimize the redundant packets and the cost of communication, but it suffers from some problems because it is conceived in an ideal environment which means that a packet of data is correctly sent from a node A to a node B if the distance between A and B doesn't exceed the emission radius of A. Since its apparition, this method has been widely studied. In [START_REF] Ou Liang | Gateway multipoint relays an-MPR-based broadcast algorithm for ad hoc networks[END_REF], the authors propose Getaway MPR, which is an improvement of MPR. In [START_REF] Busson | An analysis of the Multi-Point Relays selection in OLSR: RR-5468[END_REF], MPR is used to conceive a routing protocol.

• DS-MPR [START_REF] Adjih | Computing Connected Dominated Sets with Multipoint Relays: International Journal Ad Hoc & Sensor Wireless Networks[END_REF][START_REF] Chen | Reducing Connected Dominating Set Size with Multipoint Relays in Ad Hoc Wireless Networks[END_REF]: This method is an improvement of MPR, in which the broadcasting process is based on the connected dominating set which contains the nodes that have the greatest weight in the network. This weight is computed for every node in the network as a function of node degree and node remaining energy. Therefore, using DS-MPR in broadcasting can increase the lifetime of the network. This was improved in [START_REF] Wu | Extended Multipoint Relays to Determine Connected Dominating Sets in MANETs[END_REF] by defending an extension of MPR [START_REF] Montolio-Arandaa | Improved flooding of broadcast messages using extended multipoint relaying[END_REF] to compute the dominating set. In [START_REF] Shang | Algorithms for minimum m-connected k-tuple dominating set problem[END_REF], the authors propose an algorithm to minimize m-connected k-tuple dominating sets which help to realize a fault tolerant broadcasting.

• In [START_REF] Sivaraman | Dynamic Cluster Broadcasting for Mobile Ad Hoc Networks[END_REF][START_REF] Cheng | Scalable and Energy-Efficient Broadcasting in Multi-hop Cluster-Based Wireless Sensor Networks[END_REF][START_REF] Wei Chen | Novel Broadcast/Multicast Protocols for Dynamic Sensor Networks[END_REF] the authors propose broadcasting algorithms in structured WSNs (i.e., WSNs which are organized in clusters). In such a network, clustering has been used to induce a hierarchical structure over a flat WSN which minimizes communication overhead. However, all these method stipulate the environment as ideal.

LNM-based broadcasting

• MPR with LNM: In [START_REF] Lehsaini | MPRbased broadcasting in ad hoc and wireless sensors networks with a realistic environment[END_REF][START_REF] Ingelrest | Maximizing the Probability of Delivery of Multipoint Relay Broadcast Protocol in Wireless Ad Hoc Networks with a Realistic Physical Layer: Mobile Ad hoc and Sensor Networks[END_REF], there are propositions of MPR in a realistic environment. The given methods improve the reachability of the original heuristics. Thus, it provide a logic and realistic performance.

In the proposed heuristics, the MPR algorithm is modified in order to maximize its performance.

• GHA: Greedy Heuristic Algorithm : In [START_REF] Gary | Efficient broadcasting in multi-hop wireless networks with a realistic physical layer: Ad Hoc Networks[END_REF], the authors provide a broadcasting method using a realistic physical layer by adopting a probability of reception between nodes. The use of LNM induces a broadcasting method with acceptable reachability.

• DS-MPR with LNM: In [START_REF] Moulahi | An Energy Aware MPR-based Broadcasting Algorithms for Wireless Sensor Networks: International Conference on Selected Topics in Mobile and Wireless Networking[END_REF], there is a simple proposition of DS-MPR in a realistic environment, aiming to increase its reachability in such an environment.

Summary

The use of LNM provide a realistic behavior to the methods conceived in UDM. According to the best of our knowledge, there is no proposition of DS-MPR with a realistic physical layer except in [START_REF] Moulahi | An Energy Aware MPR-based Broadcasting Algorithms for Wireless Sensor Networks: International Conference on Selected Topics in Mobile and Wireless Networking[END_REF]. Therefore, we try to provide a new model to compute node weight in this paper. This model takes into account communication factors in a realistic environment.

Notations and problem definition

WSNs or ad-hoc network can be considered as a graph G(V, E), where the nodes constitute the set of vertex V and E the set of edges. An edge Symbol Signification G(V, E) Graph connectivity where V is the set of vertex and E is the set of edges. u Initial sender node N 1(u) The set of neighbors of a node u (order 1 neighbors) N 2(u) The set of neighbors of u's neighbors (order 2 neighbors)

N 3(u) order 3 neighbors of u v Element of N 1(u) w Element of N 2(u) or N 1(v) x Element of N 3(u) or N 2(v) or N 1(w) S(u) Subset of N 1(u) chosen to relay S1(u) Subset of N 2(u) not covered yet by nodes in S(u)
exists between the two nodes A and B in this graph if a packet sent from A can be received at B or from B to A. In table 1, we introduce the symbols used in this paper and their definitions.

In figure 1, we suppose the broadcast of a message from u to all other nodes in the networks taking into account:

• The minimization of redundant packets

• The minimization of energy consumption

Resolving this problem by using the relay-based broadcasting method means choosing an optimal subset of N 1(u) taking into consideration the previously mentioned criteria. This subset will resend the packet received from u (not all nodes in N 1(u) resend). Finally, the packet should reach nodes in N 2(u) according to the optimality of the subset chosen. If the network has many levels the same strategy of choosing a subset to relay is executed in every step. In the next section, we make an overview of a solution for this problem [START_REF] Adjih | Computing Connected Dominated Sets with Multipoint Relays: International Journal Ad Hoc & Sensor Wireless Networks[END_REF] (which is DS-MPR), and we show its limitation in a realistic environment.

DS-MPR: An overview

DS-MPR heuristic

As describe above, the DS-MPR broadcasting process is based on a connected dominating set which contains the nodes having the greatest weight

W (u) = α × W Degree (u) + β × W Energy (u) (1)
With:

α + β = 1 (2)
To choose the optimal subset of N 1(u), the algorithm below is applied (we have made a slight moderation to the original algorithm).

Algorithm 1: DS-MPR heuristic 1. Start with an empty set S(u) and S1(u) = N 2(u).

2. First select nodes in S1(u) which have a single parent in N 1(u) then remove them from S1(u) and add their parents to S(u).

3. While there still exist some nodes in S1(u): (a) Compute the weight of all nodes in N 1(u) \ S(u) (b) Add node v to S(u) for which this weight is maximum. If there is more than one node with the same maximum weight choose the one which has the maximum remaining energy. Then remove N 1(v) from S1(u).

This heuristic method is applied in UDM, and in the next subsection, we evaluate it into LNM, and we show the difference of accessibility of DS-MPR in these two models.

Lognormal model

With a realistic physical layer a reception cannot be performed as in a unit disk model due to many factors like signal attenuation, obstacle presence, distance between the sender, and the receiver, or communication time slot

R = 21m R = 20m R = 19m R = 18m R = 17m R = 16m Number of nodes in line = 250 (2 × R)
, we suppose that the distance between nodes is the same 5.95 6.25 (day or night). Therefore, we find the lognormal model (3), which is defined below, as a probability function according to most of these factors [START_REF] Lehsaini | MPRbased broadcasting in ad hoc and wireless sensors networks with a realistic environment[END_REF][START_REF] Gary | Efficient broadcasting in multi-hop wireless networks with a realistic physical layer: Ad Hoc Networks[END_REF].

P (x) =                    1 - ( x Rc ) 2α 2 if 0 ≺ x R c ( 2Rc-x Rc ) 2α 2 if R c ≺ x 2R c 0 otherwise (3)
Below, we describe the symbols used: α: Signal attenuation factor. R c : Sender node transmission radius.

x: Distance between sender and receiver nodes

DS-MPR illustration in a realistic environment

The test was performed using NS2 [START_REF] Aad | NS-2 for the impatient[END_REF]. We worked in a field of 250m × 250m, with nodes that have 25m as transmission radius. The average distance between nodes according to their density is given in figure 2. We chose an average between 21m and 16m, which is real in our opinion. The average distance starts at 21m for 30 nodes and becomes 16m for 64 nodes in the field. In table 2, we try to compute the number of nodes in a field of 250m × 250m according to a transmission radius average between 21m and 16m. In figure 3, we make a comparison between probabilities of reception in UDM and in LNM for a transmission radius Rc = 25. Consequently, we can find a difference due to that in UDM the probability of reception is equal to 1 if the distance between the sender and the receiver is less than 25 and equal to 0 if otherwise. However, in LNM, the probability of reception is computed according to [START_REF] Lehsaini | MPRbased broadcasting in ad hoc and wireless sensors networks with a realistic environment[END_REF].

In figure 4, we make a comparison between the accessibility of DS-MPR in the two models according to figure 2 and figure 3. We can see that in an ideal environment DS-MPR looks as ideal with an accessibility of 100% due to the fact that a packet of data is certainly received when the distance between the sender and a receiver doesn't exceed the transmission radius. However, in a realistic environment, this accessibility started at less than 58% and can reach 80% in the best case. With more than 64 nodes, we can see that the curve of accessibility becomes almost linear. So, this method looks invalid in LNM because its reachabilty cannot exceed 80%. In the next section, we propose a modification of DS-MPR to be applicable with a realistic physical layer.

DS-MPR in a realistic environment

Connected Dominating Sets with multiPoint relay is a method of broadcasting where a weight for each node in the network is computed. This weight is a function of node remaining energy and node degree. Then, a set of nodes to relay packets is chosen. This set consists of nodes that have the greatest weight and should provide good reachability. Furthermore, this method is conceived in an ideal environment and, in what follow, we try to define it with a realistic physical layer.

RDS-MPR heuristic

In this heuristic, we propose a new weight function, called RW (Realistic Weight (4,5)), which is changed from DS-MPR (2) to RDS-MPR, taking into account the reception probability according to the lognormal model (3):

RW (u) = α × RW Degree (u) + β × RW Energy (u) + γ × RW P robability (u) (4) with α + β + γ = 1 (5)
(i) The realistic weight degree of a node v (6) is the number of nodes reachable by v and not reachable yet by another node in S(u) divided by the maximum degree weight of the nodes in N 1(u) \ S(u).

RW Degree (v) = |N 1(v) S1(u)| M ax{|N 1(v i S1(u))|; v i ∈ N 1(u) \ S(u)} (6)
(ii) The realistic weight energy of a node v (7) is the remaining energy in v divided by the maximum weight energy of the nodes in N 1(u) \ S(u).

RW

Energy (v) = E(v) M ax{E(v i ); v i ∈ N 1(u) \ S(u)} (7)
(iii) The realistic weight probability of a node v (8)is a local weight probability q(v) (9) divided by the maximum local weight probability of the nodes in N 1(u) \ S(u).

RW P robability (v) = q(v) M ax{q(v i ); v i ∈ N 1(u) \ S(u)} (8)
(iv) This local probability q(v) (9) computes the v node weight according to the probability of reception from u to v and from v to its neighbors.

q(v) =              p(u, v) × |N 1(v) S1(u)| i=1 p(v, w i ) |N 1(v) S1(u)| if |N 1(v) S1(u)| = 0 0 otherwise (9)
After giving the definition of every weight in the new weight function, we have written our heuristic bellow. We recall that: pt: is a temporary probability in the heuristic and with it, a reception can be performed well. p0: is the minimum probability of a good reception. With less than p0, we consider the data received is wrong or the reception was not performed.

Algorithm 2: RDS-MPR heuristic 1. Start with an empty set S(u) and S1(u) = N 2(u). 2. First select nodes in S1(u) which have a single parent in N 1(u) then remove them from S1(u) and add their parents to S(u). 3. While there still exist some nodes in S1(u): (a) Compute the weight of all nodes in N 1(u) \ S(u) (b) Add node v to S(u) for which this weight is maximum and p(u, v) > pt. If there is more than one node with the same maximum weight choose the one which has the maximum remaining energy. Then remove N 1(v) from S1(u). (c) Compute reachability Re. (d) If Re < 90% and pt > p0 then slightly reduce pt and slightly increase γ Else break.

RDS-MPR illustration

To evaluate our heuristic, we test it with the same density used to test DS-MPR. In figure 5, we can see that RDS-MPR provides a good accessibility with γ =1/3 and p0 = 0.6 This accessibility started near 80% with a density of 30 nodes and becomes more than 90% for a density with 64 nodes. With γ = 1/2 and p0 = 0.5, our heuristic provides a good accessibility that become more than 94% with 64 nodes as density.

Extended DS-MPR in a realistic environment

eRDS-MPR heuristic

In this subsection, we define another broadcasting method which is an extension of RDS-MPR. We try to change the node weight by making it deep. What we mean by deep is changing the node degree weight, the node energy weight and the node probability weight by taking into account N 2(u) and N 3(u) (see figure 6). First, the extended nodes weight EW (10, 11) is defined. With:

EW (u) = α × EW Degree (u) + β × EW Energy (u) + γ × EW P robability (u) (10)
α + β + γ = 1 (11)
Every weight in the function above is defined below:

(i) The extended weight of a node degree v( 12) is the weight of v given in [START_REF] Wu | Extended Multipoint Relays to Determine Connected Dominating Sets in MANETs[END_REF] divided by the maximum of the same weight (13) of nodes in N 1(u) \ S(u).

EW Degree (v) = EW Degree (v) M ax{EW Degree (v i ); v i ∈ N 1(u) \ S(u)} (12)
With:

EW Degree (v) =              |N 1(v) S1(u)| × |N 1(v) S1(u)| i=1 |N 1(w i )| |N 1(v) S1(u)| if |N 1(v) S1(u)| = 0 0 otherwise (13)
The previous weight computes the number of nodes that can be reached by v and not reached yet by node of N 1(u) multiplied by the average of nodes that can be reachable by w i (w i = N 1(v)). Consequently, this weight helps us to choose nodes having the best reachability for the next level (w i nodes), in addition to the level after (x i nodes).

(ii) The extended weight of a node energy v( 14) is the weight of v given in [START_REF] Shang | Algorithms for minimum m-connected k-tuple dominating set problem[END_REF] divided by the maximum of the same weight [START_REF] Shang | Algorithms for minimum m-connected k-tuple dominating set problem[END_REF] of nodes in N 1(u) \ S(u).

EW

Energy (v) = EW Energy (v) M ax{EW Energy (v i ); v i ∈ N 1(u) \ S(u)} (14)
with:

EW Energy (v) =              E(v) × |N 1(v) S1(u)| i=1 E(w i ) |N 1(v) S1(u)| if |N 1(v) S1(u)| = 0 0 otherwise (15)
This weight computes the remaining energy in v multiplied by the average of remaining energy of w i . We choose only nodes which is not reachable yet (i.e., w i in N 1(v) S1(u)). Consequently, this weight helps us to choose nodes having the maximum remaining energy and which can be reached. This weight allows also the selection, in the next level, of nodes having the maximum average remaining energy. As well as increasing the reachability, the proposed weight can increase the lifetime of the network because the node with the maximum remaining energy is used first. (iii) The extended weight of a node probability v( 16) is the weight of v given in [START_REF] Ingelrest | Maximizing the Probability of Delivery of Multipoint Relay Broadcast Protocol in Wireless Ad Hoc Networks with a Realistic Physical Layer: Mobile Ad hoc and Sensor Networks[END_REF] divided by the maximum of the same weight [START_REF] Ingelrest | Maximizing the Probability of Delivery of Multipoint Relay Broadcast Protocol in Wireless Ad Hoc Networks with a Realistic Physical Layer: Mobile Ad hoc and Sensor Networks[END_REF] of nodes in N 1(u) \ S(u).

EW P robability (v) = EW P robability (v) M ax{EW P robability (v i ); v i ∈ N 1(u) \ S(u)} (16)
With:

EW P robability (v) =                            p(u, v) × |N 1(v) S1(u)| i=1 p(v, w i ) × |N 1(w i )| j=1 p(w i , x j ) |N 1(w i )| |N 1(v) S1(u)| if |N 1(v) S1(u)| × |N 1(w i )| = 0 0 otherwise (17)
We define this weight in order to choose the route with the best probability. This route starts from u to v afterward, from v to w and finally, from w to x. Consequently, this weight computes p(u, v) multiplied by the average of probability from v to w i multiplied by the average of probability from w i to x j . By analogy to the RDS-MPR heuristic, below, we introduce our eRDS-MPR heuristic and we recall that: pt: is a temporary probability in the heuristic. With it, a reception can be performed well. p0: is the minimum probability of a good reception. With less than p0, we consider that the data received is wrong or the reception was not performed.

Algorithm 3: eRDS-MPR heuristic 1. Start with an empty set S(u) and S1(u) = N 2(u). 2. First select nodes in S1(u) which have a single parent in N 1(u) and then remove them from S1(u) and add their parents to S(u). 3. While there still exist some nodes in S1(u): (a) Compute the weight of all nodes in N 1(u) \ S(u) (b) Add node v to S(u) for which this weight is maximum and p(u, v) > pt and p(v, w i ) > pt. If there is more than one node with the same maximum weight choose the one which has the maximum remaining energy. Then remove N 1(v) from S1(u). (c) Compute reachability Re. (d) If Re < 90% and pt > p0 then slightly reduce pt and slightly increase γ Else break.

eRDS-MPR illustration

To evaluate our heuristic, we test it with the same density used to test DS-MPR and RDS-MPR. In figure 7, we can see that RDS-MPR provides a good accessibility with γ = 1/3 and p0 = 0.6. This accessibility starts near 80 % with a density of 30 nodes and becomes more than 90% for a density with 64 nodes. With γ = 1/3 and p0 = 0.5, RDS-MPR provides a high accessibility that becomes more than 94% with 64 nodes as density. However, the eRDS-MPR heuristic tested with γ = 1/3 and p0 = 0.6 gives a reachability starts at 87% with 30 nodes and can exceed more than 97% with a density of 60 nodes. We can conclude here that our method is valid and makes an important improvement in the term of reachability if we accept that a broadcasting method is considered valid when it provides more than 90% reachability.

Performance evaluation

In this section a performance comparison between DS-MPR, RDS-MPR and eRDS-MPR is given. This comparison treats the consumed energy, and the use of nodes resources in each method.

Comparison of the consumed energy

In figure 8, a comparison of consumed energy to accomplish the broadcasting task is provided. The simulation is performed on networks with different densities. The packet size used to test is 200b. It is clear that increasing reachability causes more energy consumption. In fact, we have to exchange more messages to appreciate the state of nodes and to reach more sensors. However, In DS-MPR there is a lot of lost energy used to send packets to unreachable nodes. For example, if we consider a network with 64 nodes:

• According to figure 8, RDS-MPR and eRDS-MPR increase the energy consumption of DS-MPR respectively with Thus, we can conclude that the augmentation of reachability is performed with less amount of energy.

Performance comparison

In this subsection, we compare the performance of three approaches in term of exchanged message, communication time and memory used. We introduce the following notations (figure 9):

• d: The average degree of nodes in the graph

• t:
The average time which is necessary to perform a communication between two nodes

• x: the average size to save data concerning a weight in node memory

We assume in our case that all nodes have the same proprieties in term of exchanged messages, communication time and data size. Figure 9(a) describes the average number of necessary messages to be exchanged for collecting data in order to compute weights in each methods, whereas figure 9 (b) describes the average of necessary wait time for collecting data used in the weight formula before computing weights in each methods. Finally, figure 9 (c) describes the average memory size necessary for saving data for each weight. Figure 9 provides a performance comparison in term of messages number to be exchanged, waiting time for necessary data and memory size in which necessary data for computing weights will be saved. The measurements are based on level average in the network. We notice that values in the eRDS-MPR method are doubled compared to RDS-MPR due to the levels number, yet, exchanged messages and waiting time values of RDS-MPR are the same compared to DS-MPR except for the memory size needed, because RDS-MPR have one extra weight. Finally, although eRDS-MPR provides an improvement of RDS-MPR in reachability, this comparison indicates that RDS-MPR is better than eRDS-MPR in term of optimizing the use of node resources in the network.

Conclusion

Many algorithms of broadcasting in WSN and Ad-Hoc networks were focused on solving problems caused by pure flooding (i.e., redundant data, packet collision and important energy consumption). Most of these solutions model communications are in ideal environments, adopting the unit disk model. In this hypothesis, algorithms are not valid. We consider that a method of broadcasting with reachability less than 90% is not enough. Therefore, researchers propose new methods taking care of nature's factor. In this paper, we adapt the DS-MPR broadcast algorithm, to be applied in a more realistic environment, taking into account packet loss and unreliable communication links. Our proposal is RDS-MPR, which improves DS-MPR and provides accessibility at more than 94%. We propose also eRDS-MPR, which can give us a reachability that can exceed 97% in the best case and no less than 87% in the worst case. Finally, we compare the performance of the three approaches in term of consumed energy, exchanged message, communication time and memory used.

Figure 1 :

 1 Figure 1: Example of a network: the initial sender node is black and the relay nodes are gray

Figure 2 :

 2 Figure 2: Average distance between nodes according to the density

Figure 3 :Figure 4 :

 34 Figure 3: Comparison of probability of reception between unit disk model and lognormal model for a transmission radius = 25 m

Figure 5 :

 5 Figure 5: Comparison of the accessibility in lognormal model between DS-MPR and RDS-MPR for γ = 1/3, p0 = 0.6 and for γ = 1/2, p0 = 0.5

Figure 6 :

 6 Figure 6: Example of WSNs: the initial sender node is black and nodes chosen to relay are gray; we also define N 1(u) ,N 2(u) and N 3(u).

Figure 7 : 6 Figure 8 :

 768 Figure 7: Comparison of the accessibility in lognormal model between DS-MPR and RDS-MPR for γ = 1/3, p0 = 0.6 and for γ = 1/2, p0 = 0.5 and eRDS-MPR for γ = 1/3, p0 = 0.6

Figure 9 :

 9 Figure 9: Performance comparison, (a): Exchanged messages, (b): Communication time and (c): Memory size

Table 1 :

 1 Notation and symbols

Table 2 :

 2 Number of nodes according to the transmission radius


Mohamed Ben Chelbi
email: med.benchelbi@gmail.com

Samir Kamel

Salah Harrab

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Tectono-sedimentary evidence in the Tunisian Atlas -Bou Arada Trough: Insights for the geodynamic evolution and Africa-Eurasia plate convergence

Keywords: Bou Arada Trough, Geodynamic evolution, Tunisian Atlas, Transtension, Rifting, Transpression, pull-apart basin, Eurasia-Africa convergence

The Bou Arada Trough (BAT) is an E-W oriented structure located 80 km SW of Tunis, characterizing the central Tunisian Atlas. This trough is filled by a thick Quaternary sand and clay series and is bordered by complex systems of folds generally trending NE-SW. Contacts between the BAT and the neighbouring folds are accommodated by NE-SW and NW-SE oriented faults. Contrary to the other troughs of the Tunisian Atlas, which are related to the Plio-Quaternary orogenic period, the geodynamic evolution of the BAT has been started since began in the Maastrichtian and has continued until the present day. Structural, tectonosedimentary and seismic data analyses are undertaken in the studied area to better understand the evolutionary scenario of this trough. Results obtained show that the BAT is fragmented into three NW-SE oriented sub-basins and records a continuous history of downthrow. Indeed, during extensional to transtensional regimes, this trough has evolved in response to the two networks of perpendicular fractures while during compressive to transpresssive periods, the collapse of the BAT has been induced by a pull-apart mechanism using the same network of faults but with a strike slip movement. The Bou Arada Trough thus preserves a record of the convergence between the European and African plates since the Maastrichtian.

Introduction

The present configuration of the Tunisian margin has resulted from the convergence and collisional movement between the African and European plates including the Tethys geological domain. The central Tunisian Atlas and the Algerian Sahara Atlas mountain ranges contain several troughs filled with Quaternary deposits arranged in a structural band between the Zaghouan and Teboursouk master faults (Fig. 1A). The average trend of these grabens is NW-SE to WNW-ESE, orthogonal to a set of NE-SW trending folds (Fig. 1B). [START_REF] Castany | Les fossés d'effondrements de Tunisie[END_REF] and [START_REF] Glangeaud | Interprétation tectono-physique des caractères structuraux et paléogéographiques de la Méditerranée occidentale[END_REF] deduced that these structures developed during Plio-Quaternary orogenic phases. These hypotheses were reinvestigated by [START_REF] Jauzein | Contribution à l'étude géologique des confins de la dorsale tunisienne[END_REF], [START_REF] Richet | Mise en évidence de quatre phases tectoniques successives en Tunisie[END_REF], [START_REF] Dlala | Evolution tectonique mio-plio-quaternaires du fossé de Kasserine (Tunisie centrale). Implication sur l'évolution géodynamique récente de la Tunisie[END_REF], [START_REF] Philip | Evolution tectonique mioplio-quaternaire du fossé de Kasserine (Tunisie centrale): implications sur l'évolution géodynamique récente de la Tunisie[END_REF] and [START_REF] Chihi | Les fossés de l'extrémité orientale du Maghreb (Tunisie et Algérie orientale) : tectonique mio-plio-quaternaire et implication dans l'évolution géodynamique récente de la Méditerranée occidentale[END_REF]. These authors linked the development of these troughs to slip on the E-W and NE-SW faults, so that the grabens resulted from a compressive tectonic regime related to the convergence between African and European plates [START_REF] Bousquet | Neotectonics of the tyrrenean Arc and Apennines: an example of evolution from Island to collisional stages[END_REF][START_REF] Ricou | Tethys reconstructed: plates, continental fragments and their boundaries since 260Ma from Central America to South Asia[END_REF]. Although Plio-Quaternary tectonic movements are significant, our recent work [START_REF] Ben Chelbi | Analyse tectonique des structures liées à la faille de Tunis-Ellès[END_REF][START_REF] Ben Chelbi | Précision sur l'évolution structurale de l'Atlas septentrional de Tunisie depuis le Crétacé (Bassin de Bir M'Cherga). Echos d'une évolution polyphasée de la marge tunisienne dans son cadre méditerranéen[END_REF], based on structural, tectono-stratigraphic and seismic analyses, shows that the Tunisian troughs have developed since the Maastrichtian.

The ESE-WNW to E-W Bou Arada Trough (BAT), the target of our present study, is located ~ 80km southwest of Tunis (Fig. 1) and, unlike the other Tunisian Atlas troughs, was not studied by our predecessors. The aims of this work are: (1) to analyze the contacts between this trough and the neighbouring structures; (2) to explore the deep geometry of this structure using three seismic lines; (3) to examine the spatial and temporal changes in facies and thickness of the stratigraphic sequences since Campanian time; (4) to define and characterize links between the evolutionary model of the BAT and the rest of the Tunisian margin; and (5) to correlate the evolution of this graben with other examples in neighbouring regions.

Methodology

The study of tectonic contacts between the BAT and neighbouring geological structures is primarily inferred from cross sections and analysis of fault movements. Ten geological cross sections show the current dynamics of the different faults bordering the BAT. In addition, we devote a particular care to the various geometries of these bordering faults. Four seismic sections obtained from the Tunisian Petroleum Company (ETAP), are interpreted in this study to illustrate the main structural geometry of the BAT at depth. The W1 petroleum well is used to show the succession of different stratigraphic sequences characterizing the trough using time-depth conversion of lithological data.

The geodynamic evolution of the BAT is interpreted, first, through the analysis of vertical facies variations and thicknesses of the different series on both sides of the NW-SE oriented faults. Since the Campanian, sedimentation has been controlled by this network of faults in which we note a large variation of facies and thicknesses. Second, palaeostress regimes are obtained by measurement of syn-depositional faults. These fault plane orientations and directions and senses of slips are subsequently analyzed using [START_REF] Angelier | Tectonic analysis of fault slip data sets[END_REF], 1989) Direct Inversion Method (software version 5.42). This combination of surface and sub surface data will contribute to the development of an evolutionary scenario for the BAT.

Geological setting

Stratigraphy

The stratigraphic series outcropping in the study area are essentially of Triassic, Cretaceous and Palaeogene age (Figs 2 and3). Triassic beds crop out in Jebel Ech Chehid and Jebel Bessioud (Fig. 3B), composed of clay, marl, limestone, gypsum, salt, anhydrite and sand. The Germanic facies of Triassic, typical of the Tunisian margin, is evident. The Early Cretaceous is formed by thick series of clay, limestone and rare quartzitic intercalations. This sedimentation characterizes the "Sillon tunisien" [START_REF] Sekatni | Le passage Lias-Dogger de la Dorsale de Tunisie septentrionale Nouveaux apports biostratigraphiques. Âge Toarcien supérieur de la distension téthysienne[END_REF]. The Late Cretaceous is represented by carbonate and argillaceous sedimentation. It begins with alternations of gray marl and limestone (Fig. 3). These alternations characterize the Fahdène and Bahloul Formations, respectively of Albian and Cenomano-Turonian ages [START_REF] Burollet | Contribution à l'étude stratigraphique de la Tunisie centrale[END_REF]. The middle part of the Late Cretaceous corresponds to the argillaceous Aleg Formation, allotted to the Turonian-Coniacian-Santonian-Middle Campanian [START_REF] Burollet | Contribution à l'étude stratigraphique de la Tunisie centrale[END_REF]. The Abiod Formation, Late Campanian to Maastrichtian in age, is composed of two limestone beds interbedded by marl (Fig. 3). The Tertiary is represented by Palaeocene clay (El Haria Formation), Early Eocene limestone (Bou Dabbous Formation), Late Eocene clay (Souar Formation) and Oligocene alternations of sand and clay (Fortuna Formation). These Tertiary sequences mark marine sedimentation during the Palaeocene and Eocene, and continental units of the Oligocene period. These various Palaeogene units are unconformably covered by Mio-Pliocene continental deposits formed essentially of sands and silt (Fig. 3).

Structural evolution

The geodynamic evolution of the Tunisian Atlas Mountains and margin has been part of the Tethys geological domain from the first stages of rifting until the present stage of the collision between Eurasia and Africa (Fig. 4). Evidence of first stages of the Tethyan rifting are dated to the Jurassic [START_REF] Alouani | Les structures en décrochement au Jurassique de la Tunisie de Nord : Témoin d'une marge transformante entre Afrique et Europe[END_REF][START_REF] Soussi | Platform collapse and pelagic seamount facies: Jurassic development of central Tunisia[END_REF][START_REF] Soussi | New Jurassic lithostratigraphic chart for the Tunisian atlas[END_REF][START_REF] Boughdiri | Calpionellid zonation of the Jurassic-Cretaceous transition in North-Atlasic Tunisia. Updated Upper Jurassic stratigraphy of the 'Tunisian trough' and regional correlations[END_REF][START_REF] Sekatni | Le passage Lias-Dogger de la Dorsale de Tunisie septentrionale Nouveaux apports biostratigraphiques. Âge Toarcien supérieur de la distension téthysienne[END_REF]Fig. 4). This Jurassic rifting phase has been inferred from the alkaline composition of the igneous rocks and in the presence of radiolarians in rocks associated with the middle Jurassic series. This rifting resulted from N-S extension and this mechanism of opening continued during the Early Cretaceous [START_REF] Letouzey | Paleo-stress around the Mediterranean since the Mesozoic from microtectonics: comparison with plate tectonics data[END_REF][START_REF] Soyer | La crise aptienne en Tunisie central: approche paléostructurale aux confins de l'Atlas et de l'Axe Nord-Sud[END_REF][START_REF] Morgan | The strucral evolution of the Zaghouan-Ressas structural belt, northern Tunisia[END_REF]. The minimum stress direction was NE-SW until the Aptian [START_REF] Soyer | La crise aptienne en Tunisie central: approche paléostructurale aux confins de l'Atlas et de l'Axe Nord-Sud[END_REF][START_REF] Ben Chelbi | Précision sur l'évolution structurale de l'Atlas septentrional de Tunisie depuis le Crétacé (Bassin de Bir M'Cherga). Echos d'une évolution polyphasée de la marge tunisienne dans son cadre méditerranéen[END_REF][START_REF] Melki | Tectono-sedimentary events and geodynamic evolution of the Mesozoic and Cenozoic basins of the Alpine Margin, Gulf of Tunis, north-easternTunisia offshore[END_REF]Fig. 4). This change in the minimum stress orientation was attested by reactivation of the NW-SE trending faults with normal activity, which created several basins elongated NE-SW [START_REF] Ben Chelbi | Précision sur l'évolution structurale de l'Atlas septentrional de Tunisie depuis le Crétacé (Bassin de Bir M'Cherga). Echos d'une évolution polyphasée de la marge tunisienne dans son cadre méditerranéen[END_REF], and by intense magmatic activity associated with sedimentation.

Contemporaneous to this activity, the Tunisian Atlas records intense halokinetic activity (Fig. 4) forming a large system of diapirs and/or salt glaciers [START_REF] Vila | Découverte en Tunisie au SW du Kef de matériel triasique interstratifié dans l'Albien: extension du domaine à «glacier de sel» sous-marin des confins algéro-tunisiens[END_REF].

During Late Cretaceous the Tunisian margin was controlled by transtensional tectonics [START_REF] Zouari | Tectonique transtensive de la paléomarge tunisienne au cours de l'Aptien-Campanien[END_REF][START_REF] Ben Chelbi | Précision sur l'évolution structurale de l'Atlas septentrional de Tunisie depuis le Crétacé (Bassin de Bir M'Cherga). Echos d'une évolution polyphasée de la marge tunisienne dans son cadre méditerranéen[END_REF], characterized by reactivation of the N-S, E-W and NE-SW trending normal faults with dextral component. The general inversion of the structures was recorded during the Middle Eocene [START_REF] Masrouhi | New tectono-sedimentary evidence constraining the timing of the positive tectonic inversion and the Eocene Atlasic phase in northern Tunisia: Implication for the North African paleo-margin evolution[END_REF][START_REF] Melki | Tectono-sedimentary events and geodynamic evolution of the Mesozoic and Cenozoic basins of the Alpine Margin, Gulf of Tunis, north-easternTunisia offshore[END_REF].

The first period of folding is assigned to the Tortonian [START_REF] Tlig | Tectogenèses alpine et atlasique : deux évènements distincts dans l'histoire géologique de la Tunisie. Corrélation avec les évènements clés de la Méditerranée[END_REF], while the ultimate compression leading to the building of the Tunisian Atlas Mountains began during the Villafranchian and continues to the present-day [START_REF] Bouaziz | Tectonic evolution of the northern African margin in Tunisia from paleostress data and sedimentary record[END_REF]Fig. 2). This long period of compression controlled by NNW-SSE to N-S stress has contributed to the final configuration of the Tunisian Atlas in which NE-SW, NW-SE, E-W and N-S oriented faults were respectively reactivated with sinistral reverse, dextral reverse, reverse and sinistral slip.

The central Tunisian Atlas is characterized by the coexistence of folding and rifting (Fig. 1B).

The anticlines and large syncline basins that developed in this part of the Tunisian Atlas and are generally filled up with by Late Eocene deposits are elongated NE-SW. NW-SE oriented rifts, filled up by Mio-Plio-Quaternary deposits, developed orthogonally to these folds [START_REF] Philip | Evolution tectonique mioplio-quaternaire du fossé de Kasserine (Tunisie centrale): implications sur l'évolution géodynamique récente de la Tunisie[END_REF]. The NE-SW oriented sinistral and NW-SE oriented dextral normal faults ensured the formation of these rifts following a pull-apart model [START_REF] Ben Ayed | Interprétation structural de la Tunisie Atlasique[END_REF].

Evaporite layers, mostly Triassic in age, are present as a deep decollement level [START_REF] Ahmadi | The geomorphological hallmarks of hinges migration in fault related folds. A study case in southern Tunisian atlas[END_REF]. During both extensional and compressional phases this Triassic salt has been remobilized throughout the preexistent system of faults. Some of them are considered as diapirs [START_REF] Gharbi | Manifestations tectono-diapiriques synsédimentaires et polyphasages d'âge Crétacé supérieur-Quaternaire dans la région de Zag Et Tir (Tunisie centre-nord)[END_REF] in which salt occupies the core of the anticlines, others as salt glaciers [START_REF] Ben Chelbi | Mode de mise en place des corps salifères de l'Atlas septentrional. Exemple de l'appareil de Bir Afou[END_REF][START_REF] Ben Slama | Albian extrusion evidences of Triassic salt and the clues of the beginning of the Eocene atlasic phase from the exemple of the Chitana Ed Djebs structure (N. Tunisia): implication in the North African Tethyan margin recorded events, comparisons[END_REF]) in which Triassic evaporites were interstratified within the Aptian clay series. These salt structures started to grow during the Aptian [START_REF] Snoke | Structural evolution of the Jebel Debadib anticline: a clue to the regional tectonic style of the Tunisian Atlas[END_REF][START_REF] Perthuisot | Les corps triasiques des monts du Mellègue (confins algéro-tunisiens) sont-ils des diapirs ou des «Glaciers de sel»?[END_REF] or even earlier [START_REF] Boukadi | L'halocinèse en Tunisie: contexte tectonique et chronologique des évènements[END_REF].

These different tectonic phases that affected the Tunisian margin since the first stage of rifting have affected the structural zoning of Tunisia. The major domains are, respectively, from north to south: the Tell zone; the Atlasic domain, itself subdivided into the northern, central and southern Atlas; the stable Sahara Platform; the Eastern Platform; and the North-South Axis (Fig. 1B).

Field studies of the structural position of the BAT

Detailed structural analysis of Quaternary deposits that cover the plain and neighbouring folded structures reveals that the history of the BAT is intimately associated with the activity and the evolution of a complex fault system. We present here the main structural features that border the BAT depression.

Northern contacts:

The BAT is bounded to the north by Jebel Rihane, Henchire Bou Ftis and Jebel Bessioud (Fig. 2A andB). The contact between these structures and the plain is represented by a complex system of faults having two major NW-SE and NE-SW orientations (Fig. 2B). Indeed, Jebel Sidi Brahim and Aïn Agueb, which consist of Aptian-Albian limestone series, are bordered to the south by NW-SE oriented faults (Fig. 5A).

These contacts include the so-called Bou Jlida fault (Fig. 2B) that separates the southern El Aroussa plain and northern Jebel Rihane. Detailed examination of these generally SW dipping faults reveals three generations of striations, oriented S60°E and with weak pitch to the SE and strong pitch to the NW, indicating three phases of tectonic activity. Near Sidi Dakhli, the contact between Late Eocene claystone and Cenomanian limestone is represented by a NE-SW trending normal fault (Fig. 5B). The latter has a fault plane dipping SE with two generations of striations. The first generation has a pitch towards the SW indicating a dextral movement, while the second one has a pitch towards the NE indicating a sinistral sliding movement. The southern side of the Henchir Bou Ftis structure is truncated by several NW-SE trending en echelon faults (Fig. 2B and5C). All these faults indicate polyphase activity of normal dextral slip with three generations of striations (pitches of 15° to the NW, 45° to the NW and 75° to the SE). In the south-eastern part of the Jebel Bessioud syncline, the Oligocene is missing. Slip on several NW-SE oriented faults has resulted in the submergence of this area below Quaternary alluvial deposits (Fig. 5C). In the east, a NW-SE system of faults delimits the Sabkhet El Korzia depression.

Western Contacts:

The BAT is bordered to the west by the large Triassic diapir of Jebel Ech Chehid (Fig. 2B), which is moulded onto the NE-SW oriented El Alia-Téboursouk fault [START_REF] Perthuisot | L'accident El Alia-Tébessa dans la région de Téboursouk[END_REF][START_REF] Ben Slama | Albian extrusion evidences of Triassic salt and the clues of the beginning of the Eocene atlasic phase from the exemple of the Chitana Ed Djebs structure (N. Tunisia): implication in the North African Tethyan margin recorded events, comparisons[END_REF]). The Campanian limestone layers and related geometry of Draa Sidi Haj Amor shows the sinistral movement of this NE-SW fault (Fig. 2B). This structure constitutes a drag fold formed on the fault which gave rise to the Jebel Ech Chehid diapir. Moreover, at Faïd Ez Zitoun, slip on a SE dipping and NE-SW trending normal fault may explain the subsidence of the El Aroussa plain (Fig. 5D). On the fault plain we measured two generation of striations. The first shows a strong pitch to the SW (60° SW) while the second one has a weak pitch to the SW (20° SW), indicating two phases of tectonic activity.

Southern Contacts:

The contact between the folded structures of Jebel er Remil and Taref Ech Chena, in the south, and the Quaternary plains of El Aroussa, Bou Arada and Sabkhet Taref Ech Chena, in the north, is represented by two NW-SE and NE-SW trending fault systems (Fig. 2B). Indeed, the Mio-Pliocene sand and clay formations covering the Jebel er Remil syncline are truncated by a succession of NW-SE trending normal faults (Fig. 6E).

The slickensides on these faults indicate normal slip with a component of dextral slip. The curvature of Jebel Strassif is truncated by a NE dipping and NW-SE trending normal fault (Fig. 6F). A cross section at this location shows that the last movement recorded on this fault is reverse, given the overlap of the Palaeocene Sidi Ali Ben Ali Formation over Oligocene deposits (Fig. 6G) but without the normal faulting movement recorded during periods of extension. The Campanian dome of Aïn Bou Slama is bordered by a NE-SW oriented normal fault involving the downthrown of the Late Eocene Formation of Jebel er Remil (Fig. 6H).

The northern periclinal termination of the Cretaceous Jebel Taref Ech Chena anticline is truncated by a network of NW-SE and NE-SW oriented faults (Fig. 6Í) with several generations of striations. On both sides of these faults no variation of thicknesses or facies is observed in the Late Cretaceous (pre-Maastrichtian) series. Further east, the downthrown of the northern part of the Taref Ech Chena structure (Fig. 6J) is accommodated by NW-SE oriented faults (Fig. 2B).

Seismic data analysis and graben formation

We have used four seismic profiles P1, P2, P3 and P4, respectively oriented NS, NNE-SSW, E-W and NW-SE across the BAT (Fig. 2B). These seismic profiles are calibrated by the W1 well.

Profile P1 (Fig. 7) shows that the BAT is bordered on the northern and southern areas by two major faults, named F1 and F2, respectively. At Jebel Rihane, fault F1 shows the downthrow of the Late Campanian calcareous series. The cumulative vertical displacement of this limestone layer is estimated as 1700m. At the surface, F1 corresponds to the Sidi Dakhli fault which places the Late Eocene Formation in contact with the Cenomanian marly-limestone (Fig. 5B). In the south, the BAT is separated from the folded structures by north dipping fault F2. According to vertical displacement between the limestone bed of the Abiod Formation in the centre of the trough and its equivalent forming the Aïn Bou Slama dome, the downthrow is estimated to 1300m. In the same locality, the thick clay series of the Souar Formation is in direct contact with Campanian limestone deposits (Fig. 6H). The general configuration represented by this seismic section is of a negative flower structure in which the maximum subsidence is recorded at the centre of the basin.

Profile P2, with a NNE-SSW orientation, is located west of profile P1 and crosses the principal depocentre of the El Aroussa Trough (Fig. 2B). This profile shows that this trough is formed by two major faults constituting another negative flower structure (Fig 7) Profile P3 (Fig. 8) crosses Sabkha Taref Ech Chena and continues through the Triassic diapir of Jebel Ech Chehid (Fig. 2B). It shows that the plain of Bou Arada is compartmentalized, from east to west, into three distinct basins along three NE-SW oriented faults, marked at depth by offset in Triassic units, structure this compartmentalization. These bordering faults of hidden basins have normal slip and show small reverse bends which could be induced by progressive structural inversions.

Profile P4 (Fig. 8) crosses the Bled et Tlili anticline and continues to Jebel Hzem Lessoued (Fig. 2B). It shows that this area of BAT is affected by a NE-SW trending normal fault which is also responsible for the subsidence of the El Aroussa plain. The cumulative vertical displacement recorded on this fault by the reference bed of the Abiod Formation is estimated as 1500m. The depressions revealed by profiles P3 and P4 were filled by Mio-Pliocene sand and clay deposits that cover unconformably the Oligocene series.

Tectono-sedimentary evolution since the Campanian

To determine the structural evolution of the BAT, we measured the orientations of striations on fault planes that affect different formations. Syndepositional fault populations, providing direct dating of tectonic events, have been specially analyzed. We then calculated the orientations of the principal stress axes σ 1, σ 2 and σ 3 and the ratio Ф of principal stress differences [Ф = (σ 2σ 3)/(σ 1σ 3)] using the Angelier Direct Inversion Method software version 5.42 [START_REF] Angelier | Tectonic analysis of fault slip data sets[END_REF][START_REF] Angelier | From orientation to magnitudes in paleostress determinations using fault slip data[END_REF]. Several deformational phases affecting the studied area were thus established (see Table 1; also [START_REF] Ben Chelbi | Analyse tectonique des structures liées à la faille de Tunis-Ellès[END_REF][START_REF] Ben Chelbi | Précision sur l'évolution structurale de l'Atlas septentrional de Tunisie depuis le Crétacé (Bassin de Bir M'Cherga). Echos d'une évolution polyphasée de la marge tunisienne dans son cadre méditerranéen[END_REF].

The first phase of deformation thus recognised involved extension towards N64°W-S64°E on the NW-SE oriented normal faults during the Coniacian-Campanian. These NE-SW faults show a dextral normal movement involving the uplift of Triassic series. The maximum downthrow and sediment thickness during this phase developed at Jebel Rihane and Aïn Bou Slam (Fig. 9A). In addition, the activity recorded by this network of faults delimits a high zone with a thin series of sediments, corresponding to the modern BAT (Fig. 9A). The configuration of the sedimentary floor was thus controlled by a succession of horsts and grabens in which the current site of BAT is the uplifted zone and Jebel Rihan and Aïn Bou Slam correspond to the collapsed areas (Fig. 9A').

In the second phase, the Maastrichtian to the Middle Eocene period was characterized by a transpressive to compressive tectonics with the maximum compressive strain oriented in the direction N41°W-S41°E. This was determined by analysis of syndepositional micro-faults affecting the formations that characterize this period (Fig. 10 A). This tectonic regime reactivated the NE-SW striking faults with reverse slip and the NW-SE to E-W striking faults with dextral normal slip (Fig. 10 B). This structural configuration involved the downthrow of NW-SE to E-W oriented blocks, for example in the BAT (Fig. 9 B and B'). We note the significant thickness (150m) of the limestone series forming the upper member of the Abiod Formation, the argillaceous series of the El Haria Formation and the various limestone layers of the Bou Dabbous Formation. These three formations are missing at Jebel Rihane and much reduced at Jebel Bou Ftis in the north and at Jebel Bou Arada Aïn Bou Slama in the south.

The phase of extension oriented N16°E-S16°W during the Late Eocene-Aquitanian was also deduced by analyzing syndepositional micro-faults (Fig. 11A). At this time the NW-SE to E-W oriented normal faults (Fig. 11 B) accommodated subsidence of BAT and the uplift of its neighbouring areas (Fig. 9). The NE-SW to N-S trending fault system also accommodated normal slip, amplifying the subsidence of the trough (Fig. 11 C andD).

During the Middle Miocene, the micro-faults analysed indicate N25°W-S25°E compression associated with the crustal shortening of the Atlas Mountains (Fig. 12 A). This phase reactivated the NE-SW oriented faults with reverse slip and the NW-SE to WNW-ESE system with normal slip (Fig. 12 B). The structures bounding the BAT were folded, maintaining the downthrown in the interior of the trough (Fig. 12 C andD). The Late Miocene-Pliocene period was marked by continental sedimentation in an extensional tectonic regime associated with a S61°W-N61°E oriented principal strain (Fig. 13 A andB), once again revealed by analysis of micro-faults. The pre-existing faults were reactivated with normal slip that accommodated subsidence in the BAT (Fig. 13 C andD).

From the Early Quaternary to the present, the Atlas Mountains of Tunisia have been subjected to shortening with N-S compressive strain [START_REF] Letouzey | Cenozoic paleo-stress pattern in the Alpine Foreland and structural interpretation in a platform basin[END_REF][START_REF] Tlig | Tectogenèses alpine et atlasique : deux évènements distincts dans l'histoire géologique de la Tunisie. Corrélation avec les évènements clés de la Méditerranée[END_REF][START_REF] Mzali | Caractérisation géométrique et cinématique des structures liées aux phases compressives de l'Éocène au Quaternaire inférieur en Tunisie : exemple de la Tunisie nord-orientale[END_REF][START_REF] Ben Chelbi | Précision sur l'évolution structurale de l'Atlas septentrional de Tunisie depuis le Crétacé (Bassin de Bir M'Cherga). Echos d'une évolution polyphasée de la marge tunisienne dans son cadre méditerranéen[END_REF][START_REF] Melki | Tectono-sedimentary events and geodynamic evolution of the Mesozoic and Cenozoic basins of the Alpine Margin, Gulf of Tunis, north-easternTunisia offshore[END_REF]. In our study area this neotectonic regime has reactivated the NW-SE and E-W oriented faults with reverse slip (Fig. 14A).

Moreover, the NE-SW and N-S fault system has also been reactivated and shows sinistral movements (Fig. 14B).

Discussion

On the basis of our morphostructural, tectono-sedimentary and seismic analyses and interpretations we infer a complex history of development of the BAT since the Maastrichtian. Moreover, this graben presents a particular geometry different from the other troughs of the central Tunisian Atlas. Indeed, this depressed structure, with an ESE-WNW to NW-SE orientation, is fragmented into three sub-basins, each one oriented NW-SE to WNW-ESE. These sub-basins are, from east to west, the Taref Ech Chena, Bou Arada and El Aroussa basins. They are separated by NE-SW trending sinistral faults and are downthrown essentially by the WNW-ESE to NW-SE oriented normal faults (Figs 8 to 14). The evolution of BAT indicates some differences when compared to the other Plio-Quaternary troughs of the central Tunisian Atlas described by [START_REF] Dlala | Evolution tectonique mio-plio-quaternaires du fossé de Kasserine (Tunisie centrale). Implication sur l'évolution géodynamique récente de la Tunisie[END_REF], [START_REF] Philip | Evolution tectonique mioplio-quaternaire du fossé de Kasserine (Tunisie centrale): implications sur l'évolution géodynamique récente de la Tunisie[END_REF] and [START_REF] Chihi | Les fossés de l'extrémité orientale du Maghreb (Tunisie et Algérie orientale) : tectonique mio-plio-quaternaire et implication dans l'évolution géodynamique récente de la Méditerranée occidentale[END_REF]), Haj Sassi et al. (2006) and Belghith et al. (2011). Indeed, an intimate relationship exists since the Campanian between the facies distribution and thicknesses, and movements of the NW-SE oriented faults. The BAT shows Palaeogene units unconformably covered by Mio-Pliocene continental deposits. The facies and thicknesses of these formations are largely controlled by a complex system of faults.

In principle, two possible scenarios can account for the development of the BAT. The first is extension or transtension, accommodated, on the NW-SE to WNW-ESE and NE-SW to ENE-WSW oriented normal faults; the occurrence of this process would lead to the classification of the BAT as an extension or rift basin. Second, the BAT might develop as a pull-apart basin in response to strike-slip movement associated with compression or transpression (Fig. 15).

Our results suggest the following evolutionary model of the BAT (Fig. 10 to 14): (i) -During the Late Maastrichtian to the Middle Eocene, the compressive to transpressive tectonic mode applied a horizontal N319 principal strain and a N220 intermediate extensive strain (Fig. 11A). These strains activate the NE-SW to ENE-WSW oriented faults in reverse to dextral reverse movement (Fig. 10 B). The NW-SE to WNW-ESE oriented faults are reactivated into normal mechanism with considerable dextral component (Fig. 10 B). The interference of sliding movements recorded on these bordering faults coupled with the normal movement of the sub-parallel faults to the maximum stress, involves the subsidence of BAT (Fig. 10 C) due to a pull-apart mechanism of opening (Fig. 10 D and Fig. 15). This syndeposits activity is attested by the total absence of the Maastrichtian, Paleocene and Early to Middle Eocene Formations in Jebel Rihane and Bou Ftis. In parallel, at Jebel Taref Ech Chena, Jebel Bou Arada and Drâa Sidi Haj Amor the equivalent deposits are condensed. At these localities the maximum thicknes of these Formations were lower to 40m (Fig 9). This opening model of BAT is comparable to that proposed for the opening of the Permian basin of Hercynian Morocco described by Saïdia et al. (2002). This considered period is contemporary to the significant convergence between Africa and Eurasia plates [START_REF] Biju Duval | From the Tethys ocean to the Mediterranean Sea: a plate tectonic model of the evolution of the western Alpine system[END_REF][START_REF] Dercourt | Présentation de 9 cartes paléogéographiques au 1/20000000 s'étendant de l'Atlantique au Pamir pour la période du Lias à l'Actuel[END_REF][START_REF] Carminati | The role of slab detachment processes in the opening of the western-central mediterranean basins: some geological and geophysical evidence[END_REF][START_REF] Carminati | Mediterranean Tectonics[END_REF] inducing the obduction of the Maghrebian furrow on the Alboran-Kabylia-Calabria block and the beginning of the thrust-and-fold tectonics that form the Maghreb Atlas Mountains [START_REF] Piqué | Evolution structurale des domaines atlasique du Maghreb au Méso-Cénozoïque; le rôle des structures héritées dans la déformation du domaine atlasique de l'Afrique de Nord[END_REF][START_REF] Frizon De Lamotte | Mesozoic and Cenozoic vertical movements in the Atlas system (Algeria, Morocco, Tunisia): An overview[END_REF].

(ii) -During the Late Eocene-Oligocene-Aquitanian interval, the study area was subjected to extension-transpression tectonic regime implying minimum N16 horizontal strain and N269 intermediate compression strain (Fig. 11 A). In response to this strain distribution, NE-SW to ENE-WSW oriented faults have normal mechanism, while the NW-SE to WNW-ESE oriented faults show normal mechanism with oblique component (Fig. 11 B)). This faulting activity shown by the two conjugate systems also involves the uplift of neighbouring structures in the BAT (Fig. 11 C). This syn-sedimentary normal faulting activity is attested by the strong accumulation of the Late Eocene clays and the Oligocene-Aquitanian sands and clays within the graben, and their reduction or absence at Jebel Rihane, Bou Ftis, Jebel Bessioud and Taref Ech Chena (Fig. 9). This mode of extension tectonics and crustal opening is comparable with the evolution of the Upper Rhine graben [START_REF] Bergerat | Le rôle des décrochements dans les liaisons tectoniques entre le Fossé de la Saône et le Fossé Rhénan[END_REF][START_REF] Granet | Des images du système lithosphèreasthénosphère sous la France et leurs implications géodynamiques : l'apport de la tomographie télésismique et de l'anisotropie sismique[END_REF] which is contemporary to the building of the Numidian basins in Tunisia [START_REF] Talbi | Le Numidien de la Tunisie septentrionale: données stratigraphiques et interprétation géodynamique[END_REF]. These extension movements are as well coeval to the opening of the Algerian-Provençal basin [START_REF] Tapponnier | Evolution tectonique du système alpin en méditerranée: poinçonnement et écrasement rigide-plastique[END_REF]Belon and Brousse, 1977) and can be considered as a response to the ongoing convergence between Africa and Eurasia [START_REF] Biju Duval | From the Tethys ocean to the Mediterranean Sea: a plate tectonic model of the evolution of the western Alpine system[END_REF][START_REF] Dercourt | Présentation de 9 cartes paléogéographiques au 1/20000000 s'étendant de l'Atlantique au Pamir pour la période du Lias à l'Actuel[END_REF].

(iii)-The Middle Miocene ultimate compressive phase responsible for the installation of the Tunisian Atlas [START_REF] Ben Chelbi | Précision sur l'évolution structurale de l'Atlas septentrional de Tunisie depuis le Crétacé (Bassin de Bir M'Cherga). Echos d'une évolution polyphasée de la marge tunisienne dans son cadre méditerranéen[END_REF]) was characterised by a N334 horizontal maximum compression strain, a vertical intermediate extension strain and a N241 oriented minimal strain (Fig. 12 A). These forces reactivated the NE-SW and NW-SE oriented faults in sinistral reverse and dextral to dextral normal movement, respectively (Fig. 12 B). The interaction of movements recorded on these faults may likely guide the continuous opening and subsidence movement of BAT (Fig. 12 C and D). This tectonic configuration is attested by the thick accumulation of Late Miocene continental deposits in the trough centre and their absence in the basin borders.

During the Middle Miocene, the North African plate subduction under the Southern European margin was blocked [START_REF] Dercourt | Présentation de 9 cartes paléogéographiques au 1/20000000 s'étendant de l'Atlantique au Pamir pour la période du Lias à l'Actuel[END_REF], whereas, the Ionian and Adriatic plates continued to subduct [START_REF] Aubouin | Les grands traits de l'évolution des chaînes de montagnes ; Téthys et Pacifique, collision et subduction[END_REF][START_REF] Carminati | The role of slab detachment processes in the opening of the western-central mediterranean basins: some geological and geophysical evidence[END_REF][START_REF] Doglioni | Orogens and slabs vs. their direction of subduction[END_REF][START_REF] Faccenna | Lateral slab deformation and the origin of the western Mediterranean arcs[END_REF][START_REF] Panza | Geophysical and petrological modelling of the structure and composition of the crust and upper mantle in complex geodynamic settings: The Tyrrhenian Sea and surroundings[END_REF].

(iv) -During the Late Miocene-Pliocene period, the tectonic regime was essentially extensive to transtensive implying a N241 minimal strain and N150 compressive intermediate strain (Fig. 13 A). This couple of strain distribution reactivated the two pre-existing systems of fractures into normal movement with sinistral and dextral sliding component respectively (Fig. 13 B), thus involving the downthrown of the BAT (Fig. 13 C andD). This activity is here also attested by the strong accumulation of the Mio-Pliocene continental deposits in the centre of the trough, and their absence in its borders. This basin formation mode is similar to that described by [START_REF] Hurwitz | The tectonic framework of a complex pull-apart basin: seismic reflection observations in the Sea of Galilee, Dead Sea transform[END_REF] to explain the mode of opening of the Sea of Galilee and the scenario of installation of some troughs of the Pelagean Sea [START_REF] Chihi | Les fossés de l'extrémité orientale du Maghreb (Tunisie et Algérie orientale) : tectonique mio-plio-quaternaire et implication dans l'évolution géodynamique récente de la Méditerranée occidentale[END_REF].

(v) -Since the Quaternary until Present day, the tectonic regime affecting the Tunisian Atlas and North Africa Mountain ranges is compressive as shown by the N359 horizontal compressive stress [START_REF] Meghraoui | Seismotectonics of the Cheliff basin: Structural background of the El Asnam earthquake[END_REF][START_REF] Rebai | Modern tectonic stress field in the Mediterranean region: evidence for variation in stress directions at different scales[END_REF]; Fig. 14 A). This most recent tectonic regime reactivates the NE-SW to ENE-WSW and NW-SE to WNW-ESE pre-existent faults in reverse movement with sinistral and dextral sliding component respectively (Fig. 14 B). This tectonic phase involves normal faulting and final trough installation in its current architecture (Fig. 14 C). The persistence of this compressive activity causes the reverse movements recorded by all the faults without compensation of the normal movements recorded since the first extensional phases of this basin's evolution. This configuration is attested, especially, on the P1 and P2 seismic sections. This situation will lead to the beginning of closing of this structure. This period is contemporary to the phase of installation of troughs in the central Tunisian Atlas [START_REF] Philip | Evolution tectonique mioplio-quaternaire du fossé de Kasserine (Tunisie centrale): implications sur l'évolution géodynamique récente de la Tunisie[END_REF][START_REF] Chihi | Les fossés de l'extrémité orientale du Maghreb (Tunisie et Algérie orientale) : tectonique mio-plio-quaternaire et implication dans l'évolution géodynamique récente de la Méditerranée occidentale[END_REF].

Conclusions

The BAT has developed during a succession of phases of crustal deformation since the Maastrichtian, in association with slip on major faults oriented NE-SW and NW-SE. It is inferred that during extensional phases the BAT has developed as a rift basin whereas during compressive and transcurrent phases it has developed as a pull-apart basin. Seismic data confirm field observations and indicate that the BAT is segmented into three sub-basins with an overall negative flower structure. Its complex history of development reflects the complex deformation of the wider region as a result of changes in the relative motions of the African and Eurasian plates.

During periods of extensional tectonics the basin subsidence is attributed to a simple rifting model, while during the compressive and transcurrent tectonic periods the opening of this graben occurred according to a pull-apart mechanism. This scenario implies a continuous subsidence in the graben. The examination of seismic profiles combined with field observations reveal 1) the NE-SW oriented faults allowed the fragmentation of this trough in three adjacent grabens, and 2) the bordering faults of this depressed structure show flower structures. Furthermore, the sub-surface observations in seismic profiles confirm those performed at the surface and show that the subsidence process is continuous either in extensional period according to a mechanism of the rifting type or in compression movement period according to a pull-apart mechanism of opening.

Our evolution model of the BAT is different from that proposed to explain the modes of graben formation in the central Tunisian Atlas during the Mio-Plio-Quaternary [START_REF] Philip | Evolution tectonique mioplio-quaternaire du fossé de Kasserine (Tunisie centrale): implications sur l'évolution géodynamique récente de la Tunisie[END_REF]. The BAT records the complex tectonic evolution in a convergence, subduction and collision system between the African and Eurasian plates outlined here since the Maastrichtian. Moreover, the BAT structural building could be a potential site for oil and water reservoir because formed by thick Cretaceous and Early Eocene limestone series rich in organic matter and a thick Oligocene and Neogene sandy deposits. Detailed geochemical and hydro-geochemical studies, complementary to this structural analysis, are necessary in order to understand the importance of hydrocarbon and hydrological potentialities within the BAT.

Figure captions

  . The cumulative vertical displacement affecting the top of the Campanian limestone series cropping out at Jebel Zemala and in the centre of the trough is estimated as 2000m. At the surface, the northern fault corresponds to the Jebel Sidi Brahim fault whereas the southern fault corresponds to the Jebel Zemala fault (Figs 2B and 5A).

Fig. 1 :

 1 Fig. 1: A-Simplified structural map of the northern and central Tunisian Atlas and localization of the studied area (T2: Zaghouan Fault, T3: Tunis-Ellès fault, T4: El Alia-Teboursouk Fault; After Melki et al. 2010). B-Structural zoning of Tunisia showing the structural position of the Bou Arada Trough (After Ben Chelbi et al. 2008).

Fig. 2 :

 2 Fig. 2: A-Geomorphologic context of the studied area (SRTM 30m). B-Geologic map of the studied area (1-Triassic; 2-Early Cretaceous; 3-Late Cretaceous; 4-Campanian-Maastrichtian; 5-Palaeocene-Middle Eocene; 6-Late Eocene-Oligocene-Aquitanian; 7-Mio-Pliocene; 8-Quaternary; 9: Fault; 10: Localization of the seismic lines; 11: Localization of the cross sections).

Fig 3 :Fig. 4 :

 34 Fig 3: Lithostratigraphic column of the study area

Fig. 5 :Fig. 6 :Fig. 7 :

 567 Fig. 5: Geological cross sections (for localization see Fig. 3C) showing the northernmost contacts of the graben of Bou Arada with the neighbouring structures (Apt.: Aptian; Alb.: Albian; Cen.: Cenomanian; Con.: Coniacian; Sant.: Santonian; Maast.: Maastrichtian; La. Eoc.: Late Eocene; Olig.: Oligocene; Mio-Plio.: Mio-Pliocene; Q.: Quaternary)

Fig. 8 :

 8 Fig. 8: Raw (P3, P4) and interpreted (P'3, P'4) E-W and NW-SE oriented seismic lines showing the configuration and the geometry of the Bou Arada Trough (see Fig. 2B for locations). Notation is the same as for Fig. 7.

Fig. 9 :

 9 Fig. 9: Correlation proposed in this study between the lithostraigraphic series on both sides of the Bou Arada Trough (A, B, C) showing modes of formation (A', B', C') and the evolution of this trough since the Campanian.

Fig. 10 :

 10 Fig. 10: Evolution of the Bou Arada Trough in response to the various tectonic constraints during Maastrichtian-middle Eocene. A depicts a stereographic representation (Schmidt's projection, lower hemisphere) of the various populations of faults affecting the different layers in studied area (continuous lines); a strike rose diagram, showing principal stress axes orientation and value (σ1, σ2 and σ3)). B depicts interpretations of the stereograms showing the various activities recorded on major faults. C depicts schematic block diagram showing the paleostructuration of the studied area ( extension regime, Compression regime). D depicts an evolutionary model of BAT in relation to the bordering system of faults).

Fig. 11 :

 11 Fig. 11: Evolution of the Bou Arada Trough in response to the various tectonic constraints during Late Eocene-Aquitanien (same legend as Fig. 11).

Fig. 12 :

 12 Fig. 12: Evolution of the Bou Arada Trough in response to the various tectonic constraints during Middle to Late Miocene (same legend as Fig. 11).

Fig. 13 :Fig. 14 :

 1314 Fig. 13: Evolution of the Bou Arada Trough in response to the various tectonic constraints during Late Miocene-Pliocene (same legend as Fig. 11).

Fig. 15 :Table 1 :

 151 Fig. 15: A) Block diagram schematically showing the pull-apart model of formation of the BAT during transpression. B) Simplified sketch showing the faults that controlled the evolution of the BAT.

Table 1

 1

	882	:
		Chronostratigraphy Formation N	σ1	σ2	σ3	Ф	R
		Quaternary			12	359.16/	91.9/	210.71/	0.094	C
						-0.51	-0.37	0.88
		Late Mio-Pliocene			11	334.52/	150.38/	241.20/	0.314	SS
						-0.70	-0.20	0.9
		Middle Miocene	Beglia		18	335.13/	119.73/	242.9/	0.855	C to
						-0.97	0.37	0.60		TP
		Oligocene-	Fortuna							E
		Aquitanian			15	112.29/	269.50/	16.10/	0.147	To
		Late Eocene	Souar			-0.55	-0.34	0.88		TT
		Lower Eocene	Bou							C
			Dabbous		12	319.9/	220.44/	58.45/	0.696	To
		Paleocene	Al Haria			-0.95	0.23	0.77		TP
		Maastrichtian	Top Abiod
		Campanian	Base	to	05	95.63/	202.8/	296.26/	0.834	E
			Middle			-0.95	0.35	0.61		to
			Abiod							TT

Fig.1:

Fig.3:

Fig.5:

Acknowledgements: This work was made possible with the collaboration of ETAP (Tunisian Petroleum Company) and funding from the Ministry of Higher Education. Field observations and modelling benefited from fruitful discussion with Chedly Abbès and Noureddine Boukadi (Professors at the University of Tunis). We are thankful to Rob Westaway and two anonymous reviewers for the critical reading of an earlier version of the manuscript.