Antony Pottier
email: antony.pottier@telecom-bretagne.eu

Francois-Xavier Socheleau
email: fx.socheleau@telecom-bretagne.eu

Christophe Laot
email: christophe.laot@telecom-bretagne.eu

Power-Efficient Spectrum Sharing for Noncooperative Underwater Acoustic Communication Systems

Keywords: Underwater acoustic communications, spectrum sharing, OFDM, interference channel, noncooperative game, power efficiency

This paper aims at studying underwater acoustic OFDM communication systems interfering with each others in the same channel. We propose a decentralized spectrum sharing method that minimizes the total power consumed while satisfying a constraint related to their information rate. The considered systems are supposed noncooperative, i.e. unable to communicate with each others so that they cannot agree on a fair resource sharing scheme. The problem is formulated within the framework of game theory and solved according to the Nash Equilibrium concept. Several results are presented and show that interfering UA systems can share the spectrum in a more efficient way, both in terms of energy consumption and information rate.

I. INTRODUCTION

Underwater acoustic (UA) communication channels feature important distance and frequency dependent attenuation that strongly limits the available communication bandwidth. This makes the UA spectrum a scarce resource potentially shared by many heterogeneous sources (communication systems, sonars, marine mammals, etc) and whose usage is not restricted by any regulatory body or standard. As a consequence, reliable UA communications are not challenging only because of the severe propagation channel, but also due to mutual interferences between several noncooperative entities wishing to use the same physical resource. This unintended jamming can drastically decrease the performance of UA systems, both in terms of information rate and energy efficiency.

Our aim in this paper is to propose a strategy able to improve the coexistence of UA communication systems transmitting in the same channel at the same time. Our interest lies in adaptive approaches, where transmitting devices are brought with the ability of automatically changing their transmission parameters according to the soundscape in which they operate.

So far, most of the works on similar topics have focused either on adaptive modulation for single user UA links [START_REF] Radosevic | Adaptive OFDM Modulation for Underwater Acoustic Communications: Design Considerations and Experimental Results[END_REF], [START_REF] Aval | On the Achievable Rate of a Class of Acoustic Channels and Practical Power Allocation Strategies for OFDM Systems[END_REF] or on cooperative multiusers UA systems evolving within the same network [START_REF] Wang | Power-efficient Resource Allocation for QoS Provisioning in Underwater MIMO-OFDM Acoustic Cooperative Wireless Networks[END_REF], [START_REF] Otnes | Underwater Acoustic Networking Techniques[END_REF]. The systems considered here are assumed to be fully noncooperative, which suppose the absence of signaling between the different communication links and the inability to agree on a resource sharing policy. In recent works [START_REF] Pottier | Distributed Power Allocation Strategy in Shallow Water Acoustic Interference Channels[END_REF], [START_REF] Pottier | Adaptive Power Allocation for Noncooperative OFDM Systems in UWA Interference Channels[END_REF], we proposed a decentralized, adaptive power allocation strategy based on game theory for noncooperative UA OFDM communication systems, where each transmitter seeks to maximize selfishly a criterion related to its information rate under average power constraint. It was shown that efficient power allocations over the available frequency band are attained by an iterative waterfilling solution. Numerical results have shown the benefits of this approach in high interference environments.

Here, we propose to study a situation where several interfering UA OFDM links try to minimize the total power needed to guarantee a minimum information rate. Energy consumption minimization problems are relevant for many UA applications requiring some energy autonomy or long battery life such as UA wireless networks or Autonomous Underwater Vehicles. Our contribution is to prove that UA systems can share the spectrum in an adaptive, decentralized and noncooperative manner to reach operating points where both their spectral and energy efficiencies are improved.

The paper is organized as follows: we first present the transmission and channels model, then formulate the problem of constrained total power minimization for multiple noncooperative users in Section II. A waterfilling solution based on the Nash Equilibrium concept is given in Section III. Finally, simulation results based on synthetic shallow water channels are analyzed in Section IV before conclusion in Section V.

Notations: Uppercase and lowercase boldface letters, e.g. A, x, denote matrices and vectors, respectively. The superscript T denotes transposition. The unitary column vector is denoted by 1. Finally, E{.} denotes expectation.

II. SYSTEM MODEL AND PROBLEM FORMULATION

Based on [START_REF] Pottier | Distributed Power Allocation Strategy in Shallow Water Acoustic Interference Channels[END_REF], we consider M UA communication links using OFDM modulation and transmitting at the same time on the same frequency band B divided in N subcarriers. The OFDM symbol duration and subcarrier spacing are denoted by T and ∆f respectively. Considering noncooperative setups, each receiver treats the interference generated by other users as colored additive noise. Let x i ∈ C N be the sequence of i.i.d symbols sent by transmitter i on the N subcarriers. For any i, the symbols x j =i sent by the other transmitters are independent of x i . The received symbol at receiver i on the n th subcarrier is

y i (n) = h ii (n)x i (n) + j =i h ji (n)x j (n) + w i (n) where w i (n) ∼ CN (0, σ 2 wi (n)) is a Gaussian noise indepen- dent of both x i (n) and x j =i (n). h ii (n) ∼ CN (µ ii (n), σ 2
ii (n)) is the complex gain of the direct subchannel n and h ji (n) ∈ C are those of the subchannels through which transmitters j = i interfere on the receiver i.

In scenarios where all the links are located in the same area it may be that some (or even all) links are unreliable, due to a high interference level. Trying to establish a communication without taking into account the presence of interfering sources would lead to a waste of energy.

Our goal is to minimize the total power allocated on the whole band B by each transmitter while complying to a specified information rate. As the information rate of the link i will depend of the interference generated by the other links, we denote this rate by u i (p i , p -i ) where

p i = [p i (1), • • • , p i (N )]
T ∈ R N + is the vector of powers allocated on the N subcarriers by the transmitter i and

p -i = [p 1 , • • • , p i-1 , p i+1 , • • • , p M ]
are all the allocation strategies chosen by the other transmitters.

Formally, we need to solve simultaneously a set of M constrained optimization problems. For each individual problem, the optimization variables are the power allocations p i of transmitters i ∈ {1, • • • , M }, and optimal solutions p ⋆ i depend on the choice of p -i made by all others transmitters:

p ⋆ i = argmin pi N n=1 p i (n) subject to u i (p i , p -i ) ≥ R min i p i (n) ≥ 0, ∀ n ∈ {1, • • • , N } (1)
where

u i (p i , p -i ) ≥ R min i
is the constraint on the information rate. We follow [START_REF] Pottier | Distributed Power Allocation Strategy in Shallow Water Acoustic Interference Channels[END_REF] to define u i as

u i (p i , p -i ) = 1 N T ∆f N n=1 log 1 + g i (n)E{|h ii (n)| 2 }p i (n) σ 2 wi (n) + j =i E{|h ji (n)| 2 }p j (n) , (2)
where g i (n) = K i (n) K i (n) + 1 e -Ei(-Ki(n)) , K i (n) = |µ ii (n)| 2 /|σ ii (n)| 2 is the Rice factor of subchannel h ii (n) and Ei(-x) denotes the exponential integral function defined, for x > 0, as Ei(-x) = - +∞ x e -t t dt.
Note that u i should not be understood as an achievable rate in the sense of [START_REF] Passerieux | Achievable Rates over Doubly Selective Rician-Fading Channels under Peak-Power Constraint[END_REF] but rather as an optimization criterion allowing UA systems to find efficient power allocation strategies in a noncooperative way and with minimal knowledge about their environment. In the following, u i will thus be called "information rate" with a slight abuse of language.

Solving the minimization problem (1) requires that the transmitters have a knowledge only about the statistics of their direct channels h ii and the overall noise plus interference PSD. From a practical implementation point of view, this knowledge can be acquired via a feedback link from their respective receiver -which is supposed to estimate correctly the needed parameters. Computing these statistics on the long term can reduce the feedback activity of the receiver. It also copes with issues related to outdated channel state information (CSI) at the transmitter.

Given the structure of the problem, it is possible to reformulate it as a noncooperative game [START_REF] Han | Game Theory in Wireless and Communication Networks[END_REF] defined by the following triplet:

G = M, {P i (p -i )} M i=1 , P tot i M i=1 , (3)
where the set of players M = {1, • • • , M } are the active links in the same channel, P i (p -i ) is the strategy space of the player i ∈ M defined as

P i (p -i ) = p i ∈ R N + : u i (p i , p -i ) ≥ R min i ( 4
)
and the total transmit power P tot i (p i ) = 1 T p i is the objective function that the transmitter i has to minimize.

III. ITERATIVE WATERFILLING SOLUTION

A. Nash Equilibrium and waterfilling best-response functions

We propose to solve the noncooperative game defined by G according to the concept of Nash Equilibrium (NE) [START_REF] Nash | Non Cooperative Games[END_REF]. In game theory, a NE of a noncooperative game is a strategic choice which is unilaterally optimal for each player. In the previous context, it would correspond to a set of power allocation strategies

p ⋆ = [p ⋆ 1 , • • • , p ⋆ M ]
such that no communication link can choose another allocation strategy p i = p ⋆ i satisfying its information rate constraint, unless more transmit power is used. Mathematically, we have the following NE definition corresponding to the game G: Definition 1: A Nash Equilibrium of the game G as defined in (3) is a strategy profile

p ⋆ = [p ⋆ 1 , • • • , p ⋆ M ] such that ∀ i ∈ M and ∀ p i ∈ P i (p ⋆ -i ) we have N n=1 p ⋆ i (n) ≤ N n=1 p i (n). (5)
In order to drive our systems to a Nash Equilibrium point of the game, we need to define their best response functions [START_REF] Han | Game Theory in Wireless and Communication Networks[END_REF] :

Definition 2: Given a fixed strategic choice p -i ∈ R N + of his opponents, the best response function of the player i to p -i is the set of strategies p ⋆ i such that

N n=1 p ⋆ i (n) ≤ N n=1 p i (n), ∀ p i ∈ P i (p i ). (6)
In other words, the best response function of a player i corresponds to the unique solution of (1) for a fixed nonnegative p -i [START_REF] Pang | Distributed Power Allocation With Rate Constraints in Gaussian Parallel Interference Channels[END_REF] and can be found by solving the Karush-Kuhn-Tucker system of equations associated to the dual problem of (1). This yields the waterfilling solution

∀ i ∈ M and ∀ n = 1, • • • , N p ⋆ i (n) = 1 λ i - σ 2 wi (n) + j =i E |h ji (n)| 2 p j (n) g i (n)E {|h ii (n)| 2 } + , (7)
where [x] + is equivalent to max(0, x) and λ i is chosen to satisfy the information rate constraint u i (p i , p -i ) ≥ R min i with equality.

Then, combining Definitions 1 and 2, it appears that a NE of the game G in (3) is reached when all the communication links use the waterfilling strategy [START_REF] Passerieux | Achievable Rates over Doubly Selective Rician-Fading Channels under Peak-Power Constraint[END_REF] to allocate their power among the N subcarriers. In practice, the NEs of G have to be reached iteratively [START_REF] Pang | Distributed Power Allocation With Rate Constraints in Gaussian Parallel Interference Channels[END_REF], [START_REF] Bacci | Game Theory for Networks: A tutorial on game-theoretic tools for emerging signal processing applications[END_REF]. In this paper we choose to focus on a distributed sequential waterfilling algorithm where the communication links update their strategy one after the other, one link being chosen at each iteration. Questions that can arise are wether or not a bounded power allocation solution exists for a given set of channels and rate constraints and if it can be reached iteratively.

B. Existence of a solution and convergence of iterative algorithms

In general, existence of at least one NE is guaranteed for any game whose objective functions are concave and strategy spaces are closed and bounded convex sets [START_REF] Rosen | Existence and Uniqueness of Equilibrium Points for Concave N-Persons Games[END_REF]. However, given the problem stated in (1), the strategy spaces are not bounded since there is no constraints on the maximum total power. As a consequence, it is possible that the set of channels h ji and the rate constraints lead to a situation where some communication links have no other choice than increasing their transmit power each time they have to update their power allocation strategy in order to maintain their information rate constraint satisfied. Sufficient conditions on the existence of a non-empty, bounded set of solutions for the game G in (3) have been given in [10, Theorem 5] and will be adapted next to our context. We first need to introduce the matrices Ψ n (R min ) ∈ R M×M , given a specified set of rate constraints (i,j)

R min = R min 1 , • • • , R min M T > 0: Ψ n (R min ) ij ∆ = g i (n)E |h ii (n)| 2 if i = j -(e R min j -1)E |h ji (n)| 2 otherwise ( 8
Ψn | ≥ 0, ∀ n = 1, • • • , N with |C (i,j)
Ψn | the determinant of the cofactor matrix obtained by removing the i th raw and j th column from Ψ n (R min ). Moreover, an upper bound p = [p 1 , • • • , pM ] on the power allocation vectors at a NE can be given

∀ n = 1, • • • , N as    p1 (n) . . . pM (n)    = (Ψ n (R min )) -1    σ 2 w1 (n)(e R min 1 -1) . . . σ 2 wM (n)(e R min M -1).    (9)
Interestingly, one can verify that these conditions always hold in the two user case.

Corollary 1: Sufficient conditions for the matrices Ψ n (R min ) to have all their principal minors positive are :

R min i < log 1 γ max i + 1 , ∀ i ∈ M (10)
with

γ max i ∆ = max n j =i E |h ji (n)| 2 g i (n)E {|h ii (n)| 2 } .
The previous corollary is useful to derive a simple physical interpretation of Theorem 1: as the interferences become higher, having a bounded solution to the problem (1) requires that the rate constraints imposed on each communication link are not too high.

Usually, convergence of iterative best-response algorithms, the sequential iterative waterfilling being one example, is guaranteed only in games with some particular properties. In most of other communication games, convergence proofs are application-specific and only sufficient conditions can be given [START_REF] Bacci | Game Theory for Networks: A tutorial on game-theoretic tools for emerging signal processing applications[END_REF]. We focus on a sequential version of the iterative waterfilling algorithm, for which convergence conditions can be derived [START_REF] Pang | Distributed Power Allocation With Rate Constraints in Gaussian Parallel Interference Channels[END_REF]Theorem 14]

. Let first Ξ n (R min ) ∈ R M×M be Ξ n (R min ) ij ∆ = e -R min i if i = j -e R min j ξ max ij otherwise (11)
where

ξ max ij ∆ = max n E |h ji (n)| 2 g j (n)E {|h jj (n)| 2 } × σ 2 wj (n) + k =j E |h kj (n)| 2 pk (n) σ 2
wi (n) and pk (n) defined as in [START_REF] Nash | Non Cooperative Games[END_REF].

Theorem 2: [10, Theorem 14] Assume that the conditions of Theorem 1 are satisfied for the game G with rate constraints R min . If the matrix Ξ n (R min ) as defined in [START_REF] Bacci | Game Theory for Networks: A tutorial on game-theoretic tools for emerging signal processing applications[END_REF] has its principal minors all positive, then the sequential waterfilling algorithm converges to the (unique) NE of the game. Note that the previous theorem gives also sufficient conditions for uniqueness of the NE of the game G. Furthermore, it can also be interpreted as a requirement of sufficiently small interference level perceived by each communication link [START_REF] Pang | Distributed Power Allocation With Rate Constraints in Gaussian Parallel Interference Channels[END_REF]Remark 15].

The conditions of Theorems ( 1) and ( 2) can be hard to check and may be unsatisfied in many scenarios of practical interest where one can expect that good operating points can be reached by iterative waterfilling (see for instance [START_REF] Pottier | Distributed Power Allocation Strategy in Shallow Water Acoustic Interference Channels[END_REF], [START_REF] Pottier | Adaptive Power Allocation for Noncooperative OFDM Systems in UWA Interference Channels[END_REF]). Indeed, as these two theorems give sufficient conditions on solutions boundedness and algorithms convergence, it does not imply that their non-satisfaction will lead necessarily to divergence and unbounded power budget. Nevertheless, they are useful to warn us that if the level of interferences and/or the desired information rates are too high, the whole system cannot reach an equilibrium.

IV. NUMERICAL RESULTS

We here show some simulation results for three noncooper- UA shallow water channel simulator described in [START_REF] Socheleau | A Maximum Entropy Framework for Statistical Modeling of Underwater Acoustic Communication Channels[END_REF], [START_REF] Socheleau | Concise Derivation of Scattering Function from Channel Entropy Maximization[END_REF].

The impulse responses are obtained by ray tracing according to imput parameters describing the transmission geometry. Time fluctuations are then modeled by a maximum entropy Doppler spectrum given the mean Doppler spread σ D and Rice factor K max of the main arrival. The Rice factor of other arrivals decreases exponentially. In the following, we set σ D = 1 Hz and K max = 20 dB. The water depth is fixed to 50 m and the depth of each terminal is chosen arbitrarily between 5 and 20 m. Path losses and frequency-dependent absorption are taken into account using Thorp's formula [START_REF] Urick | Principles of Underwater Sound[END_REF]. The distances d ii between a transmitter and its intended receiver are set to 1 km and we set their initial total transmit power to 160 dB re µPa, distributed uniformly on the whole 6 kHz band. The noise PSD is modeled with a decay of 18 dB/decade and its power in the frequency band in use is such that the communication links experiences a signal to noise ratio (SNR) of 15 dB for their initial uniform power allocation (without considering interferences). Each receiver is supposed to estimate its direct channel statistics µ ii (n) and σ 2 ii (n) as well as the noise plus interference PSD without errors. These parameters are used by the corresponding transmitter to find the power allocation solving the problem (1), with the constraint u i (p i , p -i ) = R min i . The update period of each link is set to 30 seconds, which is long enough compared to the OFDM symbol duration and channel coherence time to assume ergodicity. The links update their power allocation strategy one after the other1 and each update (from any player) is called "an iteration" of the game in the following. The game is run during 50 iterations.

We will consider several scenarios by varying the interference links distances d ji and the rate constraints.

A. Medium interference scenario

The distances of the interference links are set to d ji = 1.5 km and the rate constraints are u i (p i , p -i ) = 1 bits/s/Hz for all the links. The time varying frequency responses of the channels for this setup are shown in Figure 1, where the diagonal shows what we call the direct channels h ii between a transmitter i and its intended receiver, and the other subplots depicts the interference channels h ji between the j th transmitter and the i th receiver. Here, we noted that the conditions required by Theorem 1 are not met.

Figure 2 depicts the total power in use by the three communication links as a function of iterations of the game. After 15 iterations -corresponding to 2.5 minutes given the update period -the users are close to a state where none of them has an incentive to decrease or increase its transmit power to satisfy the information rate constraint. The evolution of the information rate metric u i (2) is depicted in Figure 3. In dashed lines, we compare these results with the initial uniform power strategy with the total power of 160 dB re µPa (denoted by P IN IT i in Figure 2). A clear improvement both in terms of spectral efficiency and total power consumption can be observed since our proposal of noncooperative and adaptive spectrum sharing strategy yields a better information rate metric u i with only 30 % of the initial total power (approximately 5 dB less).

B. High interference scenario

In this scenario we decrease the distance separating the interfering links to simulate a high interference setup. The distances d ji are set to 500 m, so that at the initial uniform power allocation state, each link perceives approximately twice more interference than signal of interest. 2 The results of the noncooperative game after 50 iterations in terms of total power and information rate functions are shown in Figures 4 and5 respectively.

After 25 iterations the three communications links are in an equilibrium state. Most importantly we see that they have considerably increase their information rate function u i compared to the initial state (in dashed lines), and with a decrease of total power in use of more than 5 dB. This is due to the fact that as the interference level is high, the best strategic choice for the players tends to a FDMA-like power allocation as the Figure 6 depicts. This fact has been pointed out in [START_REF] Lesherm | Game Theory and the Frequency Selective Interference Channel[END_REF], [START_REF] Scutari | Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems Based on Game Theory-Part I: Nash Equilibria[END_REF].

However, it can be seen from Figure 4 that before reaching the equilibrium state, all links need to increase considerably their total transmit power during the convergence phase. Depending on the initial power, such an increase could be prohibitive for many UA systems. During the first iterations, each player increases its total power one after the other and releases or decreases its power on some subcarriers at the same time. They act this way repeatedly until each of them have succeed in pushing the others out of its subcarriers of most interest, leading to a strategy profile close to FDMA. Then, the next iterations lead them to reduce the power allocated where they experience still some interference and increase it on their good subcarriers, until the information rate constraints are simultaneously satisfied. Interestingly, it has been proven that the sum-rate optimal power allocation is an FDMAtype strategy when the crosstalk between the different links is sufficiently high [START_REF] Hayashi | Spectrum Management for Interference-Limited Multiuser Communication Systems[END_REF]. In the previously cited reference, a locally optimal FDMA power allocation is found by means of a centralized algorithm, assuming the knowledge of all the direct and interference channels. In contrast, our present work assume only little knowledge of the environment from the communication links involved in the problem -namely, only the direct channels statistics (h ii ) and noise plus aggregate interference PSD.

V. CONCLUSION The proposed distributed power allocation strategy allows several interfering UA OFDM communication links to share the spectrum in an efficient way regarding the total transmit power in use, compared to the naive uniform transmit PSD strategy which leads to waste of energy in the studied scenarios. Our method has been developed for fully noncooperative systems competing for the same physical resource. Moreover, it requires only a little knowledge on the ambient soundscape by the transmitters to adapt their power allocation strategy. The main drawback of this method relies on the fact that convergence of distributed algorithms used to reach the Nash Equilibrium solutions is not guaranteed in many scenarios of practical interest, where the interference level is high. In addition, situations where an equilibrium state is reached at the cost of a considerable increase of the power budget have been observed. To be closer from practical UA systems requirements, future works on the topic could consider a modified game, with for instance an additional constraint on the maximum average power or systems having the ability to adapt their rate constraints automatically when the use of too high powers is observed.

) Theorem 1 : 1 ,

 11 [START_REF] Pang | Distributed Power Allocation With Rate Constraints in Gaussian Parallel Interference Channels[END_REF] Theorem 5] The game G with rate constraintsR min = R min • • • , R min MT > 0 has a non-empty and bounded solution set if Ψ n (R min ) in[START_REF] Han | Game Theory in Wireless and Communication Networks[END_REF] are such that all their principal minors are positive i.e.|C

Fig. 1 .

 1 Fig.1. Time-varying frequency responses of the directs and interference channels obtained from the simulator described in[START_REF] Socheleau | A Maximum Entropy Framework for Statistical Modeling of Underwater Acoustic Communication Channels[END_REF]. d ii = 1 km, d ji = 1.5 km.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Total power in use versus iterations of the game (medium interference).

Fig. 4 .Fig. 5 .

 45 Fig. 4. Total power in use versus iterations of the game (high interference).

Fig. 6 .

 6 Fig. 6. Power allocated by the users at the last iteration of the game (in % of the initial power P INIT i

Note that it is not necessary to assume synchronism among the links, since we can consider systems having the same update period but starting to transmit at different times.

In a real setup this would obviously impact the performances of the channel estimations required to solve the minimization problem (1).


Bruno S Chang
email: bschang@utfpr.edu.br

Franc ¸ois-Xavier Socheleau
email: fx.socheleau@telecom-bretagne.eu

Christophe Laot
email: christophe.laot@telecom-bretagne.eu

Widely Linear SC-FDE Systems for Underwater Acoustic Communication: Experimental Results

This work presents experimental results for single carrier underwater communication systems using widely linear frequency domain equalization. The underwater channel models were obtained from a stochastic replay-based channel simulator, which was fed with data from channel measurements conducted in the harbor of Brest (France). It was seen that when symbols from improper constellations are considered it is possible to obtain a performance gain in this scenario for different conditions if widely linear equalization is used.

I. INTRODUCTION

The underwater environment is one of the toughest ones for data communication. The electromagnetic waves typically used in wireless communications have poor underwater propagation, making acoustic waves the best choice to transmit data in this environment [START_REF] Urick | Principles of Underwater Sound[END_REF]. Also, in this case the bandwidth is a function of distance and frequency, while to further complicate the task of the receiver, the channel is highly selective in frequency and the noise power spectral density is non-white [START_REF] Stojanovic | On the relationship between capacity and distance in an underwater acoustic communication channel[END_REF]. Thus, efficient equalization performs a vital role in ensuring that higher data rate transmissions in this environment become possible.

Appropriate time-domain equalizers for this environment are long and complex; thus, frequency domain equalization (FDE) is desirable to reduce the computational complexity of this process. The most popular systems where this type of equalization is employed are multicarrier ones. Single carrier systems using frequency-domain equalization (SC-FDE) maintain the convenient low complexity equalization in the frequency domain of multicarrier systems while avoiding their characteristic high peak-to-average power ratio (PAPR) [START_REF] Falconer | Frequency domain equalization for single-carrier broadband wireless systems[END_REF], which can be a strain on the transducers used to transmit acoustic waves [START_REF] He | Single carrier frequency domain equalizer for underwater wireless communication[END_REF]. SC-FDE systems operating in the underwater environment have been presented in [START_REF] Youcef | Single carrier frequency division multiple access for underwater acoustic communications[END_REF], [START_REF] Xia | Underwater acoustic communication in a highly refractive environment using sc-fde[END_REF].

These systems transmit symbols from a complex quadrature amplitude modulation (QAM) constellation. QAM symbols can be described as proper, that is, their second-order statistics are completely described by the autocorrelation. The PAPR of the transmitted symbols can be further reduced by the usage of symbols from real or offset constellations instead of QAM ones, since their envelope is constant or quasi-constant [START_REF] Luzio | On the Use of Multiple Grossly Nonlinear Amplifiers for an Efficient Amplification of OQAM Signals with FDE Receivers[END_REF]. These constellations are known as improper. Widely linear (WL) processing takes advantage of the non-vanishing pseudoautocorrelation of these improper sequences to improve the symbols' estimation performance [START_REF] Schreier | Second-order analysis of improper complex random vectors and processes[END_REF], [START_REF] Chevalier | New Insights Into Optimal Widely Linear Array Receivers for the Demodulation of BPSK, MSK, and GMSK Signals Corrupted by Noncircular Interferences -Application to SAIC[END_REF]. In order to do that, the received signal must be processed together with its conjugate version. WL processing has been used in SC-FDE systems in [START_REF] Lin | Analysis of receiver algorithms for LTE SC-FDMA based uplink MIMO systems[END_REF], [START_REF] Chang | Widely linear mmse precoding and equalization techniques for sc-fde systems[END_REF], [START_REF] Kim | Asymptotically optimal lowcomplexity sc-fde with noise prediction in data-like improper-complex interference[END_REF]. It was seen that widely linear equalizers have better error performance than linear ones, due to their full usage of the available second order statistics, i.e., the autocorrelation together with the pseudoautocorrelation.

This work further develops [START_REF] Chang | On the performance of widely linear sc-fde systems for underwater acoustic communication[END_REF], in which a preliminary analysis of the usage of widely linear equalizers for SC-FDE systems in the underwater environment was presented. Differently from [START_REF] Chang | On the performance of widely linear sc-fde systems for underwater acoustic communication[END_REF], in this work underwater channel models were obtained from a stochastic replay-based channel simulator, which was fed with data from channel measurements conducted in the harbor of Brest (France). Replay-based channel simulators are able to generate new random time-varying impulse responses with statistical properties (almost) identical to the original measurement, providing a high degree of realism. It was seen that in this environment SC-FDE systems using WL equalization have better performance than when using linear equalizers, because they are able to exploit the pseudoautocorrelation contained in the transmitted improper sequences.

The remainder of the paper is organized as follows: Section II presents and the system model considered in this paper. In Section III the underwater channel models used in this work are introduced, together with an analysis of the results. Concluding remarks are presented in Section IV.

Notation: vectors are represented by bold lowercase letters, while bold capital letters denote matrices. Time domain elements have a tilde appended to them. The superscripts () * , () T and () H denote, respectively, conjugate, transpose and Hermitian operations. The i-th element of the vector v is given by v i and the (i, j)-th element of the matrix M is given by M i,j . The identity matrix of size N × N is denoted by I N . Finally, the mathematical expectation is E {.}.

II. SYSTEM MODEL

The system model considered in this paper is presented in Figure 1. Consider a signal block s of size N , whose symbols come from an improper constellation (such as binary phase shift keying (BPSK) or offset quadrature amplitude modulation (OQAM)). Before transmission, a cyclic prefix of length L CP Fig. 1: The system model for a SC-FDE system using a WL-MMSE equalizer.

is appended to the block of symbols, forming sCP with length N + L CP . Before transmission, sCP will be oversampled.

This symbol block is transmitted through a doubly selective channel model, modeled as a random linear time-varying system that maps an input signal s(t) onto the output r(t) according to the following I/O relationship:

r(t) = τ h(τ, t)s(t -τ )dτ + ñ(t), (1)
where h(τ, t) is the channel impulse response between the transmitter and the hydrophone and ñ(t) denotes the ambient noise. We recall that noise in the underwater environment is considered to come mainly from four sources: turbulence, shipping, waves and thermal noise [START_REF] Stojanovic | On the relationship between capacity and distance in an underwater acoustic communication channel[END_REF].

In the receiver, the signal block is first downsampled; after, it is stripped of its cyclic prefix and converted to the frequency domain. Thus, the vector r at the input of the equalizer with size N can be expressed as

r = Hs + n, (2)
where H is a N × N diagonal matrix with its (k,k)-th entry H k,k corresponding to the k-th coefficient of the N -sized DFT of the time domain channel impulse response h, s is the frequency domain version of s and the N -sized vector n contains the noise, with variance σ 2 n . Equalization is performed in the frequency domain by filters based on the minimum mean square error (MMSE) criterion. However, since the equalizer is dealing with a signal from an improper constellation (which has non-zero pseudoautocorrelation), it can employ widely linear processing to use all the second-order statistics made available by the received signal and improve its performance. In order to do that, the original version of the received signal in the frequency domain r together with its conjugate version r * is processed by a widely linear equalizer R W L , expressed as [START_REF] Chang | Widely linear mmse precoding and equalization techniques for sc-fde systems[END_REF]

R W L = HH H + σ 2 n I N HUH T H * UH H H * H T + σ 2 n I N -1 H H * U , (3)
where U is given by

U =        1 0 0 . . . 0 0 0 0 . . . 1 . . . . . . . . . . . . . . . 0 0 1 . . . 0 0 1 0 . . . 0        . (4)
R W L can be separated as R 1 (which processes the received signal in the frequency domain) and R 2 (which processes its conjugate version), which are respectively given by

R 1 = H mod + σ 2 n I N -1 H (5)
and

R 2 = H mod + σ 2 n I N -1 H * U, (6)
with

H mod = HH H + UHH H U. (7)
Thus, the equalized signal z can be expressed as

z = R H 1 r + R H 2 r * = R H W L t, (8)
with t = [r r * ].
We recall that if this equalizer is dealing with a proper constellation the pseudoautocorrelation is zero and the WL equalizer is reduced to the linear one, expressed by

R L = HH H + σ 2 n I N -1 H. (9)
Then, the equalized signal z in the frequency domain passes through an IFFT so that symbol decision is done on the time domain symbol z.

III. RESULTS

To obtain impulse responses for the channel model used in this paper, measurements were conducted in the harbor of Brest, France in May 2015 to collect real data. The transmissions were realized between two docks over a 800 m distance, in a 20 m water depth. At the transmitter side, an omnidirectional transducer ITC-1032 (resonant frequency: 35 kHz) immersed at a depth of 2 m was used. At the receiver side, a broadband omnidirectional BK-8106 hydrophone was vertically deployed at a depth of 3 m. Estimates of the timevarying channel impulse response (TVIR) were obtained by successive matched filtering to a known probe signal transmitted repeatedly. The probe signal used during the experiments was a m-sequence of 255 BPSK chips transmitted at a symbol rate of 5 kbds. Such a sequence can capture arrivals delayed up to 51 ms and channel estimates can be updated up to 19.6 times per second. Measurements were made at a carrier frequency of 35 kHz and transmitted symbols were pulse-shaped by a root raised cosine filter with a roll-off factor of 0.1. Figure 2 shows the channel estimate obtained in this experiment, while At the receiver side, the recorded signal is first downconverted into complex-baseband and downsampled. Then, time-varying Doppler shifts mitigated by an iterative resampling procedure presented in [START_REF] Van Walree | A discrete-time channel simulator driven by measured scattering functions[END_REF].

This measured at sea data is fed to a stochastic replay-based channel simulator [START_REF] Socheleau | Stochastic replay of non-wssus underwater acoustic communication channels recorded at sea[END_REF] to obtain new random TVIRs with statistical properties (almost) identical to the original measurement; these TVIRs are used for the actual simulation. The time-varying Doppler shift of this channel impulse response has been removed in order to mitigate the drift of multipath arrivals that could obscure the analysis of the taps statistics. For the bit error rate (BER) results presented in this section, the carrier frequency f c was 35 kHz, the bandwidth 5.5 kHz, 100 channel realizations were made and BPSK symbols were transmitted. The experimental conditions at the port allowed us to obtain a SNR of 19 dB for a transmitted power of 190 dB re µPa at 1 m. For this SNR, a block size N = 128 and a cyclic prefix (CP) L CP = 32 Figure 4 shows constellations from random symbols at the output of the SC-FDE systems when using a linear equalizer (in Figure 4a) and a widely linear equalizer (Figure 4b). A BER of 2.3 × 10 -3 was obtained when using the linear equalizer, while when using widely linear equalization the BER value was 3.4 × 10 -4 for this scenario. This performance gain is due to the fact that the receiver employing widely linear processing takes into account all of the available second order statistics when processing the improper received signal, leading to a better estimate.

An interesting characteristic when using the stochastic replay method to obtain the channel impulse responses is that it is possible to change the SNR values for a given TVIR. With this feature it is possible to test the WL-MMSE equalizer with other SNR values, to see if the performance gain seen above is upheld. Figure 5 Finally, in Figure 6 the impact of the block size N on the error performance of these systems is seen. For these results, the CP length was fixed at L CP = 64 and the values of N considered were 256 and 512. An increase of the block size brings better error performance for both systems, because this larger block size allows the MMSE equalizers in SC-FDE systems to better harness the available diversity [START_REF] Tajer | Diversity Order in ISI Channels with Single-Carrier Frequency-Domain Equalizers[END_REF]. For both block sizes there is a performance advantage for the systems employing widely linear processing.

IV. CONCLUDING REMARKS

In this work, results from SC-FDE systems using widely linear MMSE equalization operating with channel impulse responses coming from a replay-based simulator fed with realistic underwater acoustic channel models were presented. These realistic CIRs were obtained in Brest harbor, France. It is possible to see that when transmitting improper sequences the usage of widely linear equalization brings a performance gain with respect to systems using linear equalizers, due to the fact that full second-order statistics are taken into account in the equalization process. For a carrier frequency of 35 kHz and a bandwidth of 5.5 kHz the system using WL equalization has a single-channel average BER of 3.4 × 10 -4 with BPSK modulation for a experimental SNR of 19 dB, N = 128 and L CP = 32; this BER was better than the one obtained when using linear equalization (2.3 × 10 -3 ). For other values of SNR and block size there is also a performance advantage when using WL equalization. Future developments of this work could include a performance evaluation using multiple hydrophones in the receiver [START_REF] Socheleau | Stochastic replay of simo underwater acoustic communication channels[END_REF] and/or using iterative widely linear frequency domain equalization [START_REF] Chang | Widely linear iterative equalizers for sc-fde systems[END_REF].

ACKNOWLEDGMENT

This work has been partially sponsored by CNPq (Brazil).

Figure 3 Fig. 2 :Fig. 3 :

 323 Figure3shows the average power delay profile of this channel model. It is possible to see in these Figures that the main tap of this channel, which corresponds to the direct path, is quite stable and the rms delay spread is approximately 6.5 ms.

Fig. 4 :

 4 Fig. 4: Constellation output of the different MMSE equalizers in SC-FDE systems for a SNR of 19 dB, N = 128 and L CP = 32.

  presents a comparison of the error performance of these systems for different values of SNR, again with N = 128 and L CP = 32. As it is possible to see in this Figure, the WL performance gain is obtained throughout the considered SNR range.

Fig. 5 :Fig. 6 :

 56 Fig. 5: Error performance comparison for N = 128 and L CP = 32.


Liangshu Shu

Hongwei Yin

Michel Faure

Yan Chen

Yan Chen Highlights

Mesozoic intracontinental underthrust in the SE margin of the North China Block: insights from the Xu-Huai thrust-and-fold belt

Keywords: Thrust, Fault-related fold, Intracontinental underthrust, Mesozoic, Xu-Huai belt, North China Block

diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The Qinling-Dabie Orogen, also referred to as the Central China Orogen, is an important tectonic unit, separating the North China Block to the north from the South China Block to the south [START_REF] Wang | An outline of the tectonic evolution of China[END_REF]. To its western segment, an early Paleozoic Ocean subducted northwards beneath the North China Block, followed by the collision of North China and South China blocks in Silurian, building the Qinling Orogen [START_REF] Zhang | The major suture zone of the Qinling orogenic belt[END_REF]. To its eastern segment (Dabie area), no rock record related to the early Paleozoic subduction and collision was preserved because of likely late erosion [START_REF] Faure | Tectonics of the Dabieshan (eastern China) and possible exhumation mechanism of ultra high-pressure rocks[END_REF], as an early Mesozoic continental subduction of the South China Block beneath the North China Blocks took place, which is proven by the development of coeval UHP coesite-bearing eclogite and HP blue-schist [START_REF] Faure | Doming in the southern foreland of the Dabieshan (Yangtse block, China)[END_REF][START_REF] Faure | Continental subduction and exhumation of UHP rocks: structural and geochronological insights from the Dabieshan (East China)[END_REF], building the Dabie and the Su-Lu orogens [START_REF] Gilder | Tectonic evolution of the Tancheng-Lujiang (Tanlu) fault via middle Triassic to early Cenozoic paleomagnetic data[END_REF][START_REF] Schmid | How did the foreland react? Yangtze foreland fold-and-thrust belt deformation related to exhumation of the Dabie Shan ultrahigh-pressure continental crust (eastern China)[END_REF][START_REF] Faure | Continental subduction and exhumation of UHP rocks: structural and geochronological insights from the Dabieshan (East China)[END_REF]. At the same time, widespread intracontinental deformation took place within the South China Block [START_REF] Song | Late Early Paleozoic and Early Mesozoic intracontinental orogeny in the South China Craton: geochronological and geochemical evidence[END_REF][START_REF] Shu | Late Paleozoic-Early Mesozoic geological features of South China: response to the Indosinian collision event in Southeast Asia[END_REF]and Shu et al., 2015). Despite that the SE-ward continental crust underthrust of the North China Block beneath the Su-Lu Orogen has rarely been studied, numerous syn-orogenic and post-orogenic rocks and structural records related to early Mesozoic tectonic events are widely exposed in the SE margin of the North China Block near the Su-Lu Orogen, including the thrust and fold structures and strike-slip ductile shear zones [START_REF] Faure | Doming in the southern foreland of the Dabieshan (Yangtse block, China)[END_REF][START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF][START_REF] Zhu | Sinistral to normal faulting along the Tan-Lu Fault Zone: evidence for geodynamic switching of the East China continental margin[END_REF], UHP metamorphic rocks [START_REF] Li | Two-stage collision-related extrusion of the western Dabie HP-UHP metamorphic terranes, central China: evidence from quartz c-axis fabrics and structures[END_REF] and two-stage extrusion of UHP-HP metamorphic rocks [START_REF] Li | Two-stage collision-related extrusion of the western Dabie HP-UHP metamorphic terranes, central China: evidence from quartz c-axis fabrics and structures[END_REF][START_REF] Li | Two-stage Triassic exhumation of HP-UHP terranes in the western Dabie orogen of China: constraints from structural geology[END_REF], foreland basin [START_REF] Zhu | Tectonic controlling on formation of the lower Yangtze foreland basin[END_REF] and post-orogenic extension followed by emplacement of dioritic-granitic magma [START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF][START_REF] Xu | Mesozoic adakitic rocks from the Xuzhou-Suzhou area, eastern China: evidence for partial melting of delaminated lower continental crust[END_REF][START_REF] Xu | Geochemistry of eclogite xenoliths in Mesozoic adakitic rocks from Xuzhou-Suzhou area in central China and their tectonic implications[END_REF]. Tectonic evolution was related to regional-scale thrust, fault-related fold, and strike-slip shearing. The arcuate Xuzhou-Huainan thrust-and-fold belt (the Xu-Huai belt in short) was formed under this geodynamic setting [START_REF] Xu | The Xu-Huai thrust body[END_REF][START_REF] Shu | Thrust tectonics of Xuzhou-Suzhou region, eastern China[END_REF].

The Xu-Huai belt is located in the SE margin of the North China Block and to the western side of the Su-Lu Orogen, near the Tan-Lu Fault Zone (Fig. 1). Structurally, it appears as a NW-ward convex thrust-and-fold belt, which was intruded by early Cretaceous granitoids. Several large-scale coal mines are distributed in the late Paleozoic strata and were covered by thrust slices near the western boundary of this belt. Thus this arcuated belt is a suitable place to investigate the geological setting and tectonic evolution of the SE margin of the North China Block.

Despite its importance, the geodynamic mechanism and tectonic evolution of the Xu-Huai belt are poorly studied and were debated in the last decades. Several models have been proposed, such as the syn-tectonic thrust [START_REF] Xu | The Xu-Huai thrust body[END_REF][START_REF] Shu | Thrust tectonics of Xuzhou-Suzhou region, eastern China[END_REF][START_REF] Shu | Balanced sections in the Xuzhou-Suzhou area[END_REF][START_REF] Wang | The thrust fault system of arc-shaped dupleximbricated fan in the Xuzhou-Suzhou region[END_REF], a result from the clockwise-rotated South China Block suturing with the North China Block [START_REF] Zhao | Palaeomagnetic constraints on the collision and rotation of North and South China[END_REF][START_REF] Zhang | North and South China collision along the eastern and southern North China margins[END_REF][START_REF] Gilder | Tectonic evolution of the Tancheng-Lujiang (Tanlu) fault via middle Triassic to early Cenozoic paleomagnetic data[END_REF], an effect from syntectonic transformation [START_REF] Zhu | 40 Ar/ 39 Ar dating of strike-slip motion on the Tan-Lu fault zone, East China[END_REF][START_REF] Zhu | Syn-collisional transform faulting of the Tan-Lu fault zone, East China[END_REF][START_REF] Zhao | Indentation-induced tearing of a subducting continent: evidence from the Tan-Lu Fault Zone, East China[END_REF], and the post-orogeny gravity collapse [START_REF] Ma | Large-type deep-seated collapse tectonics in the Xu-Huai region, North China[END_REF]. All previous studies mainly focus on the Dabie Orogen, however, rarely on the Su-Lu Orogen and the Xu-Huai belt, little attention has been paid to the structural analysis and geodynamic mechanism forming the Xu-Huai belt.

In the 1980s, the balancing cross-section technique was used firstly for study of thrust deformation and deep-seated structure in foreland and piedmont basins of orogenic belt, such as the North Sea (England) and the Rocky Mountains (North American) [START_REF] Gibbs | Balanced section constructions from seismic sections in areas of extensional tectonics[END_REF][START_REF] Mitra | Energy balance and deformation mechanisms of duplexes[END_REF][START_REF] Cooper | Thrust-surface geometry: implications for thrustbelt evolution and section-balancing techniques[END_REF], and then was quickly accepted by geologists all around the world. The balancing of structural section and the restoration of balanced cross-section were mainly used to interpret brittle deformation [START_REF] Suppe | Geometry and kinematics of fault-bend folding[END_REF][START_REF] Suppe | Reactivalted normal faults in the western Taiwan fold-and-thrust belt[END_REF][START_REF] Ramsay | The Techniques of Modern Structural Geology[END_REF][START_REF] Fossen | Structural Geology[END_REF]. Numerous buried thrust faults and folds (Suppe and Medwedeff, 1990; [START_REF] Wilkerson | Geometrical modeling of faultrelated folds: a pseudo-three dimensional approach[END_REF][START_REF] Epard | Excess area and depth to detachment[END_REF] and some coal-trapping and oil-gas-trapping structures [START_REF] Chamberlin | The Appalachian folds of central Pennsylvania[END_REF][START_REF] Brewer | Restoration of across sections above intrusive salt domes[END_REF][START_REF] Groshong | Area balance, depth to detachment and strain in extension[END_REF][START_REF] Yin | Balancing and restoration of piercement structures: geologic insights from 3-D kinematic models[END_REF] were well prognosticated by interpretation of balancing cross-sections and restoration of their initial geometry.

In order to understand the forming process of the Xu-Huai belt, based on first-hand data from geological mapping, field observations and drilling, we have carried out a structural analysis and balancing and restoration of structural profiles throughout the outcrop areas of the Xu-Huai belt. Combined with published geochronological and geochemical data, a tectonic evolution forming the Xu-Huai belt was reconstructed in this study.

Geological setting

Tectonic framework

The Xu-Huai thrust-and-fold belt in the SE margin of the North China Block is developed upon the pre-Neoproterozoic crystalline basement. The North China Block consists mainly of Archean TTG to Proterozoic marine facies carbonate rocks, sandy-muddy rocks intercalated with various volcanic rocks [START_REF] Sdbgmr | Regional Geology of Shandong Province: Beijing[END_REF][START_REF] Li | Two-stage collision-related extrusion of the western Dabie HP-UHP metamorphic terranes, central China: evidence from quartz c-axis fabrics and structures[END_REF], which were metamorphosed into marble, mica schist, amphibolite or amphibole-schist, para-gneiss and orthogneiss. The oldest rock outcrop of this block, called Taishan Group, was dated at 2800 Ma [START_REF] Jahn | Archean crustal evolution in China: the Taishan complex, and evidence for Juvenile crustal addition from long-term depleted mantle[END_REF][START_REF] Jahn | Archean crustal evolution of the Jiaodong Peninsula, China, as revealed by zircon SHRIMP geochronology, elemental and Nd-isotope geochemistry[END_REF].

The Dabie Orogen is located to the south of the Xu-Huai belt. The eastern boundary of the Xu-Huai belt is the NNE-trending Tan-Lu Fault Zone that directly contacts with the Su-Lu Orogen (Fig. 1) [START_REF] Zhao | Indentation-induced tearing of a subducting continent: evidence from the Tan-Lu Fault Zone, East China[END_REF]. The area between the Dabie and the Xu-Huai belts is mostly covered by Quaternary deposits. The Tan-Lu Fault Zone was generated from a NW-ward oblique convergence of the South China Block beneath the North China Block in early Mesozoic [START_REF] Zhao | Indentation-induced tearing of a subducting continent: evidence from the Tan-Lu Fault Zone, East China[END_REF]. The crustal thickness of the North China Block (32-35 km) in the west to the Tan-Lu Fault Zone is larger than one of the South China Block (30-31 km) that is located in the east to the Tan-Lu Fault Zone [START_REF] Sun | Geoscience TRANSECT of Fengxian, Shanghai to Alashanzuoqi, Inner Mongolia[END_REF][START_REF] Zhu | Lithospheric textures of the Tan-Lu Fault Zone and their genetic analysis[END_REF], and the lithospheric thickness of the North China Block (110 km) is obviously larger than one of the South China Block (85-88 km) [START_REF] Sun | Geoscience TRANSECT of Fengxian, Shanghai to Alashanzuoqi, Inner Mongolia[END_REF][START_REF] Zhu | Lithospheric textures of the Tan-Lu Fault Zone and their genetic analysis[END_REF]. A threestage deformation was identified [START_REF] Zhu | Sinistral to normal faulting along the Tan-Lu Fault Zone: evidence for geodynamic switching of the East China continental margin[END_REF], i.e., a late Triassic thrust dated at 220-210 Ma ( 40 Ar/ 39 Ar on phengite of mylonite), an early Cretaceous sinistral shearing with the age of 135-125 Ma ( 40 Ar/ 39 Ar on mica) [START_REF] Zhu | 40 Ar/ 39 Ar dating of strike-slip motion on the Tan-Lu fault zone, East China[END_REF] and an extension in late Cretaceous -Paleogene [START_REF] Zhu | Syn-collisional transform faulting of the Tan-Lu fault zone, East China[END_REF].

The Neoproterozoic Zhangbaling Group is widely distributed along the Tan-Lu Fault Zone [START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF], which consists of meta-volcanic and meta-volcanoclastic rocks dated at 750 Ma [START_REF] Zhao | Indentation-induced tearing of a subducting continent: evidence from the Tan-Lu Fault Zone, East China[END_REF]. Some UHP-HP metamorphic rocks and mylonitic schists dated at 240-235 Ma ( 40 Ar/ 39 Ar on mica) [START_REF] Xu | Exhumation structure and mechanism of the Su-Lu ultrahigh-pressure metamorphic belt, central China[END_REF][START_REF] Zhang | Oblique collision between North and South China recorded in Zhangbaling and Fucha Shan (Dabie-Su-Lu transfer zone)[END_REF] are exposed in the Zhangbaling belt of the Su-Lu Orogen (Fig. 1). In the northern segment of the Zhangbaling belt, the rocks of ductile deformation with foliation and stretching lineation show a top-to the southeast sense of shearing, and its southern segment is a sinistral shear zone [START_REF] Zhang | Oblique collision between North and South China recorded in Zhangbaling and Fucha Shan (Dabie-Su-Lu transfer zone)[END_REF][START_REF] Zhao | Indentation-induced tearing of a subducting continent: evidence from the Tan-Lu Fault Zone, East China[END_REF]. The Zhangbaling group shows a geochemical affinity with the Yangtze Block [START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF][START_REF] Zhang | Oblique collision between North and South China recorded in Zhangbaling and Fucha Shan (Dabie-Su-Lu transfer zone)[END_REF].

Stratigraphic sequences

The neighboring areas of the Xu-Hai belt are widely covered by Quaternary alluvial deposits, the exposed rocks are mostly nonmetamorphosed Neoproterozoic to middle Ordovician marine facies limestone, dolomite and sandy-muddy rocks (Fig. 2). The metamorphosed Mesoproterozoic rocks are distributed on the eastern side of this belt, near the Tan-Lu Fault Zone.

Neoproterozoic strata

It is called the Qingbaikou system (''Pt 3 ", in Fig. 2) with a thickness of 750 m and consists of limestone, dolomite and stromatolite limestone intercalated with sandstone, siltstone and mudstone. This system is widely distributed in the eastern part of the Xu-Huai belt and is divided into seven formations, namely, the Niuyuan, Jiudingshan, Zhangqu, Weiji, Shijia, Jinshanzai and Wangshan formations (Fig. 3) (Nanjing University, 1996). The Niuyuan Formation, as the base of the Xu-Huai belt, overlies unconformably the metamorphosed Mesoproterozoic basement whereas on the top, the Wangshan Formation contacts disconformably with the Cambrian sequence (Fig. 3).

Cambrian to middle Ordovician strata

The strata of this age are widely distributed in the Xu-Huai belt (Fig. 2). The Cambrian system with a thickness of 964 m consists of various limestone, dolomite, bioclastic limestone and intercalations of sandstone, siltstone and shale. It is divided into five formations, namely, the Houjiashan, Mantou, Zhangxia, Gushan and Chaomidian formations (Fig. 3). Various stromatolite fossils are preserved well in this system. The evident negative C and O isotopic anomalies (dC 13 and dO 18 ) in the boundary of Cambrian and Ordovician sequences indicate an important event of biomass extinction [START_REF] Fang | Study of C and O isotopes in the boundary strata between Cambrian and Ordovician in the Jiagou of Suxian, Anhui Province[END_REF]. The Ordovician system is composed of dolomite, limestone, wormtalk, bioclastic limestone and intercalations of shale, and is divided into three formations (Sanshanzi, Jiawang and Majiagou), totally thick 610 m. The gypsum beds are widely developed in the top of the Majiagou Formation (Fig. 3). The depositional sequence from middle Ordovician to early Carboniferous is regionally absent due to a long-time uplift and erosion [START_REF] Fang | Study of C and O isotopes in the boundary strata between Cambrian and Ordovician in the Jiagou of Suxian, Anhui Province[END_REF][START_REF] Shu | Thrust tectonics of Xuzhou-Suzhou region, eastern China[END_REF].

Carboniferous and Permian strata

In the studied area, only the upper Carboniferous Benxi and Taiyuan formations and the lower Permian Shanxi Formation are locally exposed in the western segment. They are composed of coal-bearing sandy and muddy rocks, thick 230 m (Fig. 3), and are mostly covered by allochthonous thrust slices or Quaternary alluvial depositions.

Mesozoic depositional sequence

They are not exposed in the studied area; the youngest stratum exposed in the western part of the Xu-Huai belt is the early Permian Shanxi Formation (coal-bearing mudstone). According to 1:50,000 geological map of the Jiagou-Heifengshan region (The 325 Geological Brigade of Anhui Bureau, 1992;[START_REF] Xu | Tectonic Framework and Setting of Xu-Huai district, Eastern China[END_REF], the early Cretaceous rhyolitic, volcanoclastic and sandy-muddy rocks (K 1 ) were deposited in the areas to the south and southeast of Xuzhou City, and the late Cretaceous-Paleogene red colored sandy-muddy rocks (K 2 -E) were exposed in the areas to the northwest and the southeast of Xuzhou City (see Fig. 2). The late Cretaceous-Paleogene red beds were disconformably deposited on the early Cretaceous strata (Fig. 2) [START_REF] Xu | Tectonic Framework and Setting of Xu-Huai district, Eastern China[END_REF]. Previous authors reported that the middle Triassic thin-bedded carbonate rocks intercalated with muddy-sandy rocks are sparsely exposed in the Mengcheng area to the south of the studied area [START_REF] Wang | The thrust fault system of arc-shaped dupleximbricated fan in the Xuzhou-Suzhou region[END_REF].

Magmatic intrusion

Within the Xu-Huai belt, the pre-Mesozoic carbonate strata were intruded by small-scale granite, diorite and monzodioritic porphyrite, these intrusions were dated at 135 ± 4 Ma (U-Pb on zircon) [START_REF] Wang | The thrust fault system of arc-shaped dupleximbricated fan in the Xuzhou-Suzhou region[END_REF] and 131-132 Ma (SHRIMP U-Pb) [START_REF] Xu | Mesozoic adakitic rocks from the Xuzhou-Suzhou area, eastern China: evidence for partial melting of delaminated lower continental crust[END_REF]. The diorite and monzodioritic porphyrite contain the xenoliths of eclogite, garnet-clinopyroxenite and garnet amphibolite, these intrusions were originally emplaced in the late Mesozoic extensional setting [START_REF] Xu | Geochemistry of eclogite xenoliths in Mesozoic adakitic rocks from Xuzhou-Suzhou area in central China and their tectonic implications[END_REF][START_REF] Xu | Geochemistry of peridotite xenoliths in Early Cretaceous high-Mg# diorites from the Central Orogenic Block of the North China Craton: the nature of Mesozoic lithospheric mantle and constraints on lithospheric thinning[END_REF].

Geological features of the Xu-Huai thrust-and-fold belt

Petrological and structural units

According to field observations, 1:50,000 geological mapping (Nanjing University, 1996), drill-hole data [START_REF] Yin | The Thrusting Tectonics and the Proterozoic Basement[END_REF] and geophysical data [START_REF] Zhang | North and South China collision along the eastern and southern North China margins[END_REF], petrologically, three units were identified from the bottom to top: (1) the Pre-Neoproterozoic crystalline basement unit consisting of sandstone, mudstone, basalt, greywacke and granitic rock that were metamorphosed into mica schist, amphibole schist, para-gneiss, meta-basalt and orthogneiss; (2) the Neoproterozoic to early Permian rock unit, consisting of un-metamorphosed Neoproterozoic, Cambrian and Ordovician carbonate rocks as well as Carboniferous-Permian coal-bearing terrigenous clastic sequence, 2600 m thick in total. Various stromatolith carbonate rocks developed in the Neoproterozoic to middle Ordovician strata show a typical character of the North China biostratigraphic province. This depositional sequence was involved in an intensive thrusting and folding event; and (3) the Cretaceous-Paleogene rock unit, composed of the sub-horizontal early Cretaceous coarse-grained terrigenous clastic rocks (conglomerate and sandstone), volcanic and volcanoclastic rocks and late Cretaceous-Paleogene red beds [START_REF] Xu | Tectonic Framework and Setting of Xu-Huai district, Eastern China[END_REF].

Structurally, the Xu-Huai belt can be subdivided into three zones from the east to west (Fig. 2): (1) the pre-Neoproterozoic crystalline basement at the depth and near the Tan-Lu Fault Zone [START_REF] Shu | Thrust tectonics of Xuzhou-Suzhou region, eastern China[END_REF]. It contacts with the overlying thrust slice by a large-scale decollement fault; (2) the thrust and fold zone, being the principal part of the Xu-Huai belt is composed of allochthonous thrust slices with ramp-flat structure, imbricated slices, klippes and fault-related folds; and (3) the western frontal zone, composed of sandy-muddy and carbonate rocks and numerous coal measures.

The major decollement fault and six decollement layers

A NE-SW-trending major decollement fault occurs between the Neoproterozoic -Permian thrust-and-fold zone and the pre-Neoproterozoic crystalline basement. It has a listric thrust plane dipping to the southeast and disappears near the Tan-Lu Fault Zone (Fig. 2). The Xu-Huai belt is limited in the area between the Taierzhuang-Guzhen fault (eastern boundary) and the Molou-Nangang fault (western boundary). Numerous second-order thrust faults and fault-related folds are developed upon this major decollement fault [START_REF] Xu | Tectonic Framework and Setting of Xu-Huai district, Eastern China[END_REF][START_REF] Shu | Thrust tectonics of Xuzhou-Suzhou region, eastern China[END_REF].

Our investigation suggests that each second-order decollement fault occurs between competent-rock (roof) and uncompetent-rock (floor) layers, leading to variable-scale thrusting. The second-order decollement fault and its roof rock slice constitute a thrust body. In the Xu-Huai belt, uncompetent-rock layers are composed of shale, muddy rock, siltstone, gypsum-bearing dolomite and coal-bearing rocks, however, the competent-rock layers consist mainly of sandstone and massive limestone beds.

According to our field observation and structural analysis, six uncompetent-rock layers have been identified, namely, (1) the siltstone and marlite beds of the upper Proterozoic Niyuan formation (Pt 3 n), (2) the shale and marlite beds of the lower Cambrian Houjiashan formation (2 1 h), (3) the shale and muddy siltstone beds of the lower Cambrian Mantou formation (2 1-2 m), ( 4) the shale bed of the lower Ordovician Jiawang formation (O 1 j), (5) the gypsum bed of the lower-middle Ordovician Majiagou formation (O 1-2 m), and (6) the shale and coal beds of the Carboniferous-Permian (C-P). The thickness of each uncompetent-rock layer varies from meters to hundreds of meters. The scale of thrust is positively correlated with the thickness of uncompetent-rock layers.

Structural patterns

Two-phase folding

Folding is widely recorded in the pre-Mesozoic carbonate and clastic rocks. The first-phase deformation (D 1 ) is characterized by recumbent fold (F 1 ) with NE-striking axial-plane (S 1 ) dipping 8-15°toward to the southeast (Fig. 4a). The meter-to dozen meter-scale fault-bend fold, fault-propagation fold, asymmetric fold and isoclinal fold are widely developed, indicating a NWward motion direction.

Fault-bend fold is a fold formed in the hanging wall or above a fault ramp in response to a bend in the fault surface; and faultpropagation fold means a fold formed ahead of a propagating thrust fault tip [START_REF] Suppe | Geometry and kinematics of fault-bend folding[END_REF][START_REF] Suppe | Reactivalted normal faults in the western Taiwan fold-and-thrust belt[END_REF]. These two kinds of folds are dominant structures in the studied area. The decollement layers are widely developed in the thrust slices with SE-dipping planes. The fault-bend (Fig. 4d) and fault-propagation folds with an axial plane dipping 30°to the southeast are mainly outcropped in the Lihuashan area (Fig. 6). Kinematic indicators such as drag fold, intrafolial fold, crenulation, boudinage, slickensides on the fault plane, and the relationship between fracture cleavage and fault plane (Fig. 4b) indicate a top-to-the NW thrusting.

The second-phase deformation (D 2 ) is locally developed in the western frontal zone and is characterized by intrafolial fold and ''S-shape" asymmetric fold (F 2 ) with axial-plane (S 2 ) dipping to the NW. Associated sharp faults dipping 70°to the NW were observed, cutting the D 1 structural trace. Kinematic indicators, such as the NW-ward intrafolial fold (Fig. 4c), the asymmetric boudinage and the relationship between fracture cleavage and fault plane suggest a normal fault nature with a top-to-the NW dip-slip movement. This second-phase deformation was likely related with late Mesozoic collapse and extensional tectonics (no dating data).

The Xu-Huai belt was affected by the emplacement of late Mesozoic diorite and granite plutons (131-135 Ma) with high MgO and low Epsilon Nd (t) values [START_REF] Xu | Mesozoic adakitic rocks from the Xuzhou-Suzhou area, eastern China: evidence for partial melting of delaminated lower continental crust[END_REF] in an extensional setting. Both the late Mesozoic intrusions and the above-mentioned basaltic xenoliths were considered to be related with the delamination of the sub-continental lithospheric mantle [START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF][START_REF] Xu | Geochemistry of eclogite xenoliths in Mesozoic adakitic rocks from Xuzhou-Suzhou area in central China and their tectonic implications[END_REF][START_REF] Xu | Geochemistry of peridotite xenoliths in Early Cretaceous high-Mg# diorites from the Central Orogenic Block of the North China Craton: the nature of Mesozoic lithospheric mantle and constraints on lithospheric thinning[END_REF].

The strike-slip shear structures are exposed locally in the west of Guzhen, and cut the early thrusting structures (Fig. 2). Sinistral sense of shear is demonstrated by sub-vertical fault and displacement of strata along both sides of the fault (Fig. 5a, left).

Three kinds of fault

Many faults in the Xu-Huai belt display a composite pattern including imbricated, ramp-flat and listric ones, which closely relate to the formation of fault-related folds and imbricate thrust slices (Figs. 6 and7).

The imbricated fault displays a parallelism of thrust fault and the related fold axial plane. The ramp-flat fault is composed of two parts, one part cross-cuts strata (ramp) and another is parallel to strata (flat). These two parts are spatially connected with each other (Fig. 4d). Generally, folds were generated when the rampflat fault moved forward. The ramp part was developed within the competent-rock layers (sandstone and massive limestone), while the flat part occurs between the competent-and uncompetent-rock layers. This composite fault is mainly dis-tributed in the thrust and fold zone of the Xu-Huai belt. The listric fault displays distinct geometry, including a high-angle dip in the upper part and a low-angle dip in the lower part parallel or subparallel to the major decollement fault; this kind of fault is widely developed in both the thrust and fold zone and the western frontal zone of the Xu-Huai belt.

Regionally, the listric-shape major decollement fault dipping to the southeast reveals a NW-ward raising of the buried basement, implying that the original place of the Xu-Huai belt is likely seated in the eastern segment, near the Tan-Lu Fault Zone.

Four kinds of thrust pattern

Four kinds of thrust were identified from field investigations, including ramp-flat, imbricated (Figs. 6 and7), klippe (Fig. 5) and duplex (Fig. 5b) thrust. As aforementioned, the ramp-flat and imbricated thrust structures are the most developed structure in the Xu-Huai belt. The rootless structural block was often thrust on other slice by a thrust fault. A later erosion can make the structural block to be appeared as isolated allochthonous body, forming a klippe. The klippe structures are distributed in the thrust and fold zone of the Xu-Huai belt, such as Jiawang, Jingpinshan (Fig. 2), Dashankou (Figs. 2 and5a), Donggushan and Dushanzi (Fig. 5c) areas.

Duplex structure is a compressive zone confined between two decollement faults, with the interbedded fault slice. This pattern is well developed in the thrust and fold zone and formed when the flat and ramp move. At Wuyanquan, the interbedded fault slices of carbonate rocks (2 2 to 2 3 ) are trapped well between two thrust faults (Fig. 5b). To the western side of Wuniushan, a dozens-meter-scale duplex structure, consisting of coal-bearing Carboniferous and Permian clastic rocks, is developed between floor and roof thrust faults (Fig. 6).

Inferring formation time of the Xu-Huai thrust-and-fold belt

Field observations suggest that a thrust and fold event took place in the interval of Permian and early Cretaceous. This was confirmed by the following evidence: (1) the Permian depositional sequence has been involved in a thrust and fold unit (Figs. 6 and7): (2) the drill-hole data with a depth of 400-900 m suggest that the sub-horizontal early Cretaceous volcanic and clastic rocks unconformably overlie the folded late Paleozoic strata [START_REF] Shu | Thrust tectonics of Xuzhou-Suzhou region, eastern China[END_REF][START_REF] Wang | The thrust fault system of arc-shaped dupleximbricated fan in the Xuzhou-Suzhou region[END_REF] although no Cretaceous rock is exposed in the Xu-Huai belt. Thus, we suggest that the thrust and fold event took place in the period between the Permian and early Cretaceous, likely in the middle Triassic, corresponding to the time of continental subduction and exhumation of UHP-HP rocks in the Dabie and Su-Lu orogens.

Balancing and restoration of geological cross-section

General principles

Balancing of structural cross-section is a method to construct or interpret a geological profile that can be reconstructed by means of geologically realistic processes to a geologically un-deformed state. Balancing adjusts a geological interpretation so that it is not only reasonable in its present state, but also restorable to its predeformational state according to some assumptions about the deformation [START_REF] Suppe | Principles of Structural Geology[END_REF][START_REF] Fossen | Structural Geology[END_REF]. The ''balance" occurs when bed-lengths or cross-section areas are equal in both deformed and un-deformed states. If not, a section is not balanced. A balanced cross-section does not mean that it is correct. However, if it is not balanced, it cannot be correct, assuming plane strain and no area or volume change. In the metamorphosed areas with penetrative foliations, the balancing of cross-section is difficult [START_REF] Lisle | Basic Geological Mapping[END_REF].

According to [START_REF] Fossen | Structural Geology[END_REF], five conditions must be followed for balancing of cross-sections: (1) sound geologic interpretations; (2) plane strain deformation; (3) the section should be parallel to the motion direction of the geological body, and ramp cuts upward strata; (4) the choice of deformation (vertical shear and rigid rotation, etc.) must be reasonable and based on the general knowledge of deformation in a given tectonic setting; and (5) the results must be reasonable and admissible based on the geological observations and experience. Two methods can be adopted for balancing crosssections, namely, equal-length and equal-area. In practice, these two methods are often combined to obtain a better result.

If the deformed section is presented without a restored section, it may be not balance. The so-called ''restoration section" is an expression used for the reconstruction of a geological section to its pre-deformed state.

Making procedures of cross-section balance

Choosing suitable cross-section

In order to understand deformation features of the Xu-Huai belt, we carried out a study of balancing and restoration of two measured cross-sections (the Shangqiao to Jinpingshan and the Wangshan to Malou sections) (Figs. 6 and7) with the deformed length ranges from 26.6-34.1 km, respectively. To get the best results, we also collected data from more than 80 drill-holes, the depth of each drill-hole ranges from 404 to 885 m. In these two measured sections with detailed structural observations, the Neoproterozoic to late Paleozoic strata outcrop successively together with the deformed structures, and their geological settings are clear. Minor penetrative fabrics occur in rocks, with neither loss of area or volume nor formation of neo-formed mineral and texture, which belong to brittle deformation at a shallow crustal level. Thus, these two sections can satisfy the making conditions of crosssection balance.

Working procedures

Balancing of cross-section is a complex work, consisting of 18 working steps. The most critical steps could be summarized as follows [START_REF] Woodward | Balanced Geological Cross-Sections: An Essential Technique in Geological Research and Exploration[END_REF][START_REF] Fossen | Structural Geology[END_REF].

(1) To collect drill-holes and structural data as well as seismic reflection profiles, if possible. (2) To check and verify the location and orientation of profile line, to precisely project and mark the buried structures in the cross-section.

(3) To confirm all pre-deformation strata with thickness that were late involved in a thrust and fold event. (4) To determine nail line. Nail line is an important reference element of balancing length and conserving area. It must be vertical to the bedding plane and should be located in places with minimum shearing, also, could be divided in regional and local ones, the former can be settled at the frontal terminal of the thrust zone whereas the latter is placed at the trail terminal of a secondary thrust slice. In this study, the regional nail line followed by 6-7 local nail lines is settled nearby the Huaibei coalfield in the western boundary of Xu-Huai belt that has rarely late structural disturbances. (5) To make the balancing of cross-sections. From settled parameters like the intersection relation between axial planes, the depth of the deformation zone and fault displacement, the deformed structures can be extended to the underground, making the trail part of each nappe extends to corresponding location of stratum. Meanwhile, the geometrical shapes will be drawn from fold features of footwall and from the ramp and flat of corresponding hanging wall, and then, to fill all lines and areas of strata in the underground according to their structural patterns (imbricated, ramp-flat and duplex). ( 6) To make the restoration of balanced cross-section. This step requires to pull backward the frontal and local nail lines, to retract each thrust slice to its original location (horizontal depositional beds). The original main fractures should be appeared in this restoration section.

(7) To check all works, including the ramp and flat structure and area conservation, etc. If this cross-section can pass all inspections, it would be a balanced section. And then, we could estimate the shortened distance and shortening ratio.

4.3. Geological implications from balanced cross-sections 4.3.1. Direction of nappe movement Field investigations suggested a principal NW-ward thrust polarity for the Xu-Huai belt. All the faults display an upward motion trend. This NW-ward thrust direction has been verified from the Jinpingshan-Shangqiao and the Wangshan-Malou balanced cross-sections, they show a NW-ward young trend of thrust slices from Neoproterozoic in the eastern segment to Cambrian-Ordovician in the major thrust-and-fold zone and then to Carboniferous-Permian coal measure strata in the western segment (frontal zone) (Figs. 6 and7). Correspondingly, the structural level of major decollement fault is gradually raised westward. In the Malou-Nangang area (Fig. 2), Carboniferous and Permian coal measure strata were thrust to the surface, revealing that the frontal zone is located to the west.

Decollement layers

Six uncompetent-rock layers, as decollement ones, were identified in the Xu-Huai belt as mentioned above. These six layers occur mainly in the footwall top of nappe, which can be checked and verified from the two balanced cross-sections. The larger-scale nappes are well developed in the four places close to uncompetent-rock layers, namely, the Niyuan, Mantou, Jiawang formations and Carboniferous-Permian coal measure; the first one occurs between the pre-Neoproterozoic crystalline basement and Neoproterozoic strata, while the second one is located in the boundary of Neoproterozoic and Cambrian strata, the third one is observed in the area between Cambrian and Ordovician strata, and the fourth one is developed in the contact between the Majiagou dolomite and Carboniferous-Permian coal-bearing mudstone. The decollement layers often form duplex structures intercalated with the Cambrian and Ordovician fault blocks (Fig. 5b).

Ramp-flat fault

Ramp-flat shape thrust faults appeared gently on each balanced cross-section (Figs. 6 and7). Due to late structural disturbances, the ramp-flat fault is less observed than imbricate fault on the surface. Actually, the geometry of thrust structure from balanced cross-section is more reasonable and more admissible. In Fig. 6, the footwall ramp structure outcrops to the west of the Lihuashann whereas hanging wall ramp is exposed in areas to the east of the Lihuashan. Similar structures also occur in Fig. 7. The ramp-flat fault, therefore, is a major structural pattern in the Xu-Huai belt.

Break through fault, as a decollement structure resulted from fracture propagation gradually as slip accumulates [START_REF] Suppe | Geometry and kinematics of fault-propagation folding[END_REF], was distinguished from balanced crosssections. This kind of fault is related to the propagation fold and took place along the fold axial plane, leading to upward displacement of the roofwall block. The break through fault is mainly observed in the western Wuniushan (Fig. 6).

Fault-related folds

Fault-related folds are widely distributed in the two balanced cross-sections. Five fault-related folds with asymmetric geometry are developed in the Jinpingshan-Shangqiao balanced crosssection (Fig. 6). Generally, the axial plane of fold dips to the SE, the SE-limb of fold extends a larger length with lower dip-angle, while the NW-limb shows a less length with high dip-angle and terminates directly on the fault plane (Figs. 6 and7). The hanging wall ramp of fault-related fold is mostly thrust to the surface and then eroded (Fig. 8a andb). In the restored sections, the eroded parts are shown by dotted lines.

Geological information from dozen drill-holes (several ones are up to 900 m in depth) has been partly marked in the two measured cross-sections (Fig. 2) and used for balancing and restoration of the cross-sections. Results verify the existence of duplex structures, revealing that the thrust slices composed of Cambrian and Ordovician carbonate rocks structurally overlie the coal-bearing strata in the western frontal zone. From this we estimated that Carboniferous-Permian coal measure strata may occur below thrust slices of Cambrian and Ordovician strata, which has been verified by late practical drillings (Nanjing University, 1996). Duplex structures are developed in the Jinpingshan, Lihuashan and Xiaoshankou areas (Fig. 6); in the Lihuashan, the fault blocks of lower Permian coal-bearing rocks occur between the roof wall of the Ordovician gypsum-bearing dolomite and the floor wall of Cambrian limestone.

Shortening amount and rate

The two balanced cross-sections have been restored in order to estimate the shortening rate of nappe structure. Restoration was carried out according to strict requirements as mentioned above, and each step has been carefully checked. Results are reasonable and admissible and thus the two restored sections can be used for an estimation of shortening rate. On this basis, lengths of cross-section in the pre-and post-deformation were measured and then shortening rate was estimated.

The Jinpingshan-Shangqiao restored section has a predeformation length of 47.16 km (Fig. 8a) and was shortened to 26.6 km in the balanced cross-section (Fig. 6) due to thrust and fold, yielding a shortening length of 20.56 km and a shortening rate of 43.6%. Similarly, the restoration of the Wangshan-Malou balanced cross-section indicates a pre-deformation length of 63.68 km (Fig. 8b), whereas the balanced cross-section is a length of 34.1 km (Fig. 7), suggesting a length of 29.58 km was shortened, corresponding to a shortening rate of 46.4%.

Therefore, in the Xu-Huai belt, thrust caused an upper crust shortening of 43.6-46.4%, indicating an extensively compressive setting, which was likely related to the intracontinental underthrust.

Discussion

Quality evaluation of the balanced cross-sections

Profile lines of two structural sections in this study are parallel to the regional motion direction. Along the two cross-sections, no metamorphism has been observed. Each section shows complete strata sequence, abundant structures and successive outcrops. The geological attitudes are obtained from 1:50,000 geological mapping and more than 80 drill-holes. The basement is composed of pre-Neoproterozoic metamorphic rocks. The oldest stratum involved into thrust and fold is of the upper Proterozoic Niyuan Formation and the youngest one is of the lower Permian Shanxi Formation. The thickness of the pre-deformed strata is about 2600 m, which represents the minimum burial depth of the pre-Neoproterozoic crystalline basement.

All working steps for making the two balance cross-sections have been carefully checked, suggesting that their lengths and areas are conserved, and other factors, such as upward movement of thrust faults and invariable thickness of strata along the strike direction as well as same fault displacement distance, are up to standard. Thus, they can be considered as balanced sections.

Mechanism of NW-ward thrusting

In the Su-Lu Orogen, kinematic analysis yielded a top-to-the SE sense of shearing for the crustal slabs, implying a NW-ward continental subduction of the South China Block beneath the North China Block [START_REF] Faure | Continental subduction and exhumation of UHP rocks: structural and geochronological insights from the Dabieshan (East China)[END_REF][START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF]. However, different from the SE-directed thrust in the Su-Lu Orogen, almost all the kinematic fabrics from the deformed rocks and thrust fault zones within the Xu-Huai belt show a top-the NW thrusting. This NWward thrusting was not dated, although the neighboring Tan-Lu Fault Zone recorded an early Mesozoic thrusting event around 205-190 Ma ( 40 Ar/ 39 Ar on phengite) [START_REF] Zhu | 40 Ar/ 39 Ar dating of strike-slip motion on the Tan-Lu fault zone, East China[END_REF][START_REF] Zhu | Syn-collisional transform faulting of the Tan-Lu fault zone, East China[END_REF], which was considered as a response to the intracontinental subduction [START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF].

Previous studies suggest that the continental subduction in the Dabie and Su-Lu areas occurred during 240-230 Ma and subsequently the UHP-HP metamorphic rocks were rapidly exhumed from late Triassic to early Jurassic time [START_REF] Hacker | Exhumation of ultrahigh-pressure continental crust in east central China: late Triassic-early Jurassic tectonic unroofing[END_REF][START_REF] Liu | Fluid inclusions hidden in coesite-bearing zircons in ultrahigh-pressure metamorphic rocks from southwestern Su-Lu terrane in eastern China[END_REF][START_REF] Li | Thermochronological constraints on two-stage extrusion of HP/ UHP terranes in the Dabie-Sulu orogen, east-central China[END_REF]. [START_REF] Shu | Thrust tectonics of Xuzhou-Suzhou region, eastern China[END_REF] introduced an SEward continental subduction of the North China Block beneath the South China Block to interpret the mechanism of the Xu-Huai belt. [START_REF] Zhu | 40 Ar/ 39 Ar dating of strike-slip motion on the Tan-Lu fault zone, East China[END_REF][START_REF] Zhu | Syn-collisional transform faulting of the Tan-Lu fault zone, East China[END_REF] noted a curved boundary along the Dabie and Su-Lu orogens and obtained kinematic evidence of sinistral strike-slip with a thrust component, suggesting that a syntectonic transform displacement [START_REF] Zhao | Indentation-induced tearing of a subducting continent: evidence from the Tan-Lu Fault Zone, East China[END_REF] took place among the Su-Lu, Dabie and North China. They proposed that the Su-Lu Orogen moved rapidly northwards followed by a shearing and rotation, and the transform displacement was initiated by differential rates of continental subduction in different places along the Dabie and Su-Lu orogens, resulting in the sinistral offset of Tan-Lu Fault Zone. The Xu-Huai belt with NW-ward verging folds and thrust shows a NW-directed shortening deformation. If considering coeval SEward continental underthrust of the SE margin of the North China Block beneath the Su-Lu Orogen along the Tan-Lu Fault Zone, the mechanism forming the Xu-Huai thrust-and-fold belt could be supported by kinematic indicators of the top-to the NW as mentioned above. In fact, from our results in this study, the extensive thrusting and folding in the Xu-Huai belt took place in the upper crustal level, less than 10 km in depth. It belongs to ''thin-skin tectonics" that was likely related to the underthrust of continental crustal slabs in the SE margin of the N-China Block beneath the Su-Lu Orogen along the Tan-Lu Fault Zone. Unfortunately, the southeastern segment of the studied area is widely covered by Quaternary alluvial deposits whereas available seismic data are absent, leading to rare preservation of the geological records.

Tectonic evolution

We have not obtained reliable age constraint on the Xu-Huai belt because neither the Mesozoic strata are exposed and nor the newly-formed metamorphic minerals were found. Furthermore, the field observations and drill-hole data demonstrated that the thrusting and folding of the Xu-Huai belt took place after the deposition of early Permian coal-bearing rocks and before the deposition of early Cretaceous volcano-clastic beds, suggesting an early Mesozoic, i.e. Triassic to Jurassic age for the deformation. Thus the following tectonic evolution is only a preliminary discussion considering the available information from regional geology and previously published references.

The early Mesozoic event was coeval with ductilely sheared rocks [START_REF] Mattauer | Tectonics of the Qinling belt: build-up and evolution of Eastern Asia[END_REF][START_REF] Xu | Exhumation structure and mechanism of the Su-Lu ultrahigh-pressure metamorphic belt, central China[END_REF], UHP-HP metamorphic rocks dated at 240-220 Ma in the Dabie and Su-Lu areas [START_REF] Jahn | Crust-mantle interaction induced by deep subduction of the continental crust: geochemical and Sr-Nd isotopic evidence from post-collisional mafic-ultramafic intrusions of the northern Dabie complex, central China[END_REF][START_REF] Hacker | Exhumation of ultrahigh-pressure continental crust in east central China: late Triassic-early Jurassic tectonic unroofing[END_REF][START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF][START_REF] Li | Thermochronological constraints on two-stage extrusion of HP/ UHP terranes in the Dabie-Sulu orogen, east-central China[END_REF], and Jurassic-Cretaceous foreland basins in the Hefei area [START_REF] Faure | Tectonics of the Dabieshan (eastern China) and possible exhumation mechanism of ultra high-pressure rocks[END_REF][START_REF] Zhu | Tectonic controlling on formation of the lower Yangtze foreland basin[END_REF] as well as post-orogenic emplacement of granitoids around 130 Ma in the Xu-Huai belt [START_REF] Xu | Exhumation structure and mechanism of the Su-Lu ultrahigh-pressure metamorphic belt, central China[END_REF]. From the early Mesozoic geological records of the Dabie and the Su-Lu belts, [START_REF] Li | Two-stage collision-related extrusion of the western Dabie HP-UHP metamorphic terranes, central China: evidence from quartz c-axis fabrics and structures[END_REF][START_REF] Li | Two-stage Triassic exhumation of HP-UHP terranes in the western Dabie orogen of China: constraints from structural geology[END_REF] proposed a two-stage extrusion model, the first one was an upward extrusion that took place during the middle Triassic, and the second one, an eastward extrusion, occurred during late Triassic to early Jurassic, which can be correlated with the two stages of rapid exhumation of HP-UHP rocks, respectively.

Following the Early Mesozoic continental subduction in the Dabie and Su-Lu areas (Fig. 9a), a bi-direction underthrust of continental crust developed between the South and North China blocks (Fig. 9b). The NW-ward continental subduction of the South China Block formed the NE-trending Su-Lu belt and SE-ward thrust slices within the Su-Lu belt, whereas the SE-ward underthrust of the crustal slabs in the southeastern North China Block generated a top-to the NW nappe tectonics, building the Xu-Huai thrustand-fold belt (Fig. 9c) [START_REF] Shu | Thrust tectonics of Xuzhou-Suzhou region, eastern China[END_REF][START_REF] Faure | Continental subduction and exhumation of UHP rocks: structural and geochronological insights from the Dabieshan (East China)[END_REF][START_REF] Lin | Polyphase deformation in the Feidong-Zhangbaling Massif (Eastern China) and its place in the collision between North China and South China Blocks[END_REF]. The late Triassic-early Jurassic coarse grained clastic sequence deposited in a foreland setting that overlaid the metamorphosed and deformed pre-Mesozoic rocks in the Zhangbaling segment of the Su-Lu Orogen and the Hefei Jurassic basin of the northern margin of the Dabie Orogen [START_REF] Zhu | Tectonic controlling on formation of the lower Yangtze foreland basin[END_REF], suggesting that the deformation took place in the pre-Jurassic time [START_REF] Faure | Continental subduction and exhumation of UHP rocks: structural and geochronological insights from the Dabieshan (East China)[END_REF]. In this process, a tectonic transformation was recorded by deformed structures from the sub-E-W-trending in the Dabie orogenic belt into the NE-striking in the Su-Lu orogen and Xu-Huai belts. [START_REF] Zhu | Syn-collisional transform faulting of the Tan-Lu fault zone, East China[END_REF] attributed this change to the synconvergent faulting and continental subduction of the South China and North China blocks, which occurred simultaneously in the Dabie and Su-Lu areas, constructing a curved structure.

After the orogeny, some basins parallel to the orogenic belt were filled by middle-late Jurassic-Cretaceous clastic deposits of more than 1000 m in thickness [START_REF] Zhu | Tectonic controlling on formation of the lower Yangtze foreland basin[END_REF]. A SE-ward paleo-current predominates in the Hefei Jurassic terrigenous clastic basin located to the southeast of the Xu-Huai belt [START_REF] Zhu | Tectonic controlling on formation of the lower Yangtze foreland basin[END_REF][START_REF] Zhao | Indentation-induced tearing of a subducting continent: evidence from the Tan-Lu Fault Zone, East China[END_REF], indicating that the Xu-Huai belt is likely a source of fragments for Hefei Jurassic clastic basin.

Concluding remarks

(1) The Xu-Huai belt in the SE margin of the North China Block was subjected to two-phase deformation, the early-phase, a NW-ward thrusting and folding, and the late-phase, an extension followed by the emplacement of dioritic and monzodioritic porphyrites dated at 131-135 Ma.

(2) The Xu-Huai belt can be subdivided into three units, (1) the pre-Neoproterozoic crystalline basement in the eastern segment, (2) the thrust and fold zone composed of Neoproterozoic to middle Ordovician carbonate rocks and Carboniferous-Permian coal-bearing rocks, 2600 m thick in total, and (3) the western frontal zone. A major decollement fault was identified in the base of the thrust and fold zone.

All pre-Mesozoic depositional sequences were involved into a tectonic event and then were overlain unconformably by late Mesozoic strata. Six uncompetent-rock layers have been recognized and each occurs in the top of a footwall nappe.

(3) The two geological cross-sections are chosen for structural balancing and restoration, from which ramp-flat faults and fault-related folds were identified. A ca 20-30 km shortening was obtained from the restoration of balanced sections, corresponding to a shortening rate of 43-46%. This shortening deformation was likely related to the SE-ward underthrusting of the crustal slices of the North China Block beneath the South China Block in Mesozoic.

Fig. 1 .

 1 Fig. 1. Tectonic location of the Xu-Huai thrust-and-fold belt in the SE margin of North China Block (modified from Xu et al., 1987; Faure et al., 1999; Zhu et al., 2009; Li et al., 2009). Fault names: (1) Liyang-Jiangyin fault; (2) Chaohu-Gaoyou fault; (3) Qingjiang-Xiangshuihe fault; (4) Shuanggou-Liangyungang fault; (5) Tancheng-Qingdao fault; (6) the western boundary fault of Xu-Huai belt; (7) Tan-Lu Fault Zone.

Fig. 6 .

 6 Fig. 6. The Shangqiao to Jinpingshan balanced cross-section in the Xu-Huai belt.

L

  . Shu et al. / Journal of Asian Earth Sciences xxx (2016) xxx-xxx

Fig. 9 .

 9 Fig. 9. Tectonic evolutional model of the Xu-Huai thrust-and-fold belt (the crustal features of the North and South China blocks, from Sun et al., 1992; Zhu et al., 2002).

Acknowledgements

Prof. Sanzhong Li and Prof. Guang Zhu are appreciations for their constructive comments and valuable suggestions, which have greatly improved this manuscript. We acknowledge Dr. Yao JL, Dr. Song MJ, Dr. Yan CL and Dr. Wang Wei for their many helps during this study. Prof. Brewer RC is acknowledged for his valuable investigations in the early period of this study and a drawing of Figs. 6 and 8a. This study is financial supported by the national special project of South China geology by the Ministry of Science and Technology, China (No. 2016YFC0600202), National Natural Science Foundation of China (Nos. 41572200, 41272226) and State Key Laboratory for Mineral Deposits Research (Nanjing) (ZZKT-201603).