D Pageot

M Le Feuvre

D Leparoux

P Côte

Y Capdeville

Assessment of physical properties of a sea dike using multichannel analysis of surface waves and 3D forward modeling

Keywords: Controlled source seismology, Surface waves and free oscillations, Wave propagation, Inversion

Seismic surface waves analysis methods have been widely developed and tested in the context of subsurface characterization and have demonstrated their effectiveness for sounding and monitoring purposes. Given their efficiency, surface waves methods have been used in a variety of contexts, including civil engineering applications. However, at this particular scale, many structures exhibit 3D geometries which drastically limit the efficiency of these methods since they are mostly developed under the assumption of a semi-infinite 1D layered medium without topography. Taking advantages of wave propagation modeling algorithm development and high-performance computing center accessibility, it is now possible to consider the use of a 3D elastic forward modeling algorithm for the inversion of surface wave dispersion. We use a parallelized 3D elastic modeling code based on the spectral element method which allows to obtain accurate synthetic data with very low numerical dispersion and a reasonable numerical cost. In this study, we choose a sea dike as a case example. We first show that their longitudinal geometry and structure may have a significant effect on dispersion diagrams of Rayleigh waves. Then, we investigate the sensitivity of the dispersion diagrams to small velocity and layer thickness perturbations, and show the limitations of the standard 1D surface wave methods approach. Finally, we demonstrate in this context the benefits of using both a 3D forward modeling engine and the whole dispersion diagram, instead of the dispersion curves only.

Introduction

Sea dikes are of critical importance to protect coastal areas from flooding events, but defects can form within or below the dike body, and weaken the structure [START_REF] Kortenhaus | Failure mode and fault tree analysis for sea and estuary dikes[END_REF]. Following the recent storm surges in Western Europe, leading to numerous catastrophic sea dikes breaching, assessment and monitoring of sea dikes became an important task in civil engineering [START_REF] Nazarian | Evaluation of geophysical techniques for dike inspection[END_REF][START_REF] Samyn | Integrated geophysical approach in assessing karst presence and sinkhole susceptibility along flood-protection dykes of the Loire River[END_REF][START_REF] Antoine | Detection of leakage areas in an earth embankment from GPR measurements and permeability logging[END_REF]. However, many dikes were built, at least, several decades ago and orignal construction drawings and maintenance history may not be reliable, when they exist at all. That leads to a lack of knowledge of the internal structure and of the geotechnical parameters required to make sure of the integrity and effectiveness of the dikes. Even if the relationship between geotechnical and geophysical parameters is not straightforward, geophysicals methods are the best candidates to sound and to monitor sea dikes.

Among geophysical methods already in use for sea dike sounding, electric-resistivity imaging (ERI) is the most common one [START_REF] Johansson | Seepage monitoring in an earth embankment dam by repeated resistivity measurements[END_REF][START_REF] Fargier | 2D-Electrical Resistivity Imaging for Sike Survey: Impact of the a Priori Information Management[END_REF][START_REF] Arosio | A customized resistivity system for monitoring saturation and seepage in earthen levees: installation and validation[END_REF][START_REF] Weller | Geotechnical and geophysical long-term monitoring at a levee of Red River in Vietnam[END_REF]. Yet, while this method is suitable to determine water content in the dike body, and to infer the nature of materials, it does not allow to assess mechanical parameters without other site-specific experiments. In the geotechnical point of view, seismic methods seem to be more adapted since the seismic wave velocities are related to geotechnical parameters such as the dynamic stiffness of the material [START_REF] Karl | Geotechnical characterization of a river dyke by surface waves[END_REF]. In particular, Spectral Analysis of Surface Waves, SASW [START_REF] Nazarian | Evaluation of geophysical techniques for dike inspection[END_REF] and Multichannel analysis of surface waves, MASW [START_REF] Park | Multichannel analysis of surface waves (MASW)active and passive methods[END_REF], are commonly used for geotechnical investigations and have been recently used to assess mechanical properties of river dikes with symmetric geometries [START_REF] Karl | Geotechnical characterization of a river dyke by surface waves[END_REF]. Recently, ERI and MASW are used in combined geophysical survey of river dikes [START_REF] Samyn | Integrated geophysical approach in assessing karst presence and sinkhole susceptibility along flood-protection dykes of the Loire River[END_REF][START_REF] Busato | Combined geophysical surveys for the characterization of a reconstructed river embankment[END_REF], sometimes with the integration of geotechnical methods [START_REF] Perri | River embankment characterization: The joint use of geophysical and geotechnical techniques[END_REF][START_REF] Bièvre | Integration of geotechnical and geophysical techniques for the characterization of a small earth-filled canal dyke and the localization of water leakage[END_REF]. Le [START_REF] Le Feuvre | Passive multi-channel analysis of surface waves with cross-correlations and beamforming. Application to a sea dike[END_REF] develop crosscorrelation-based passive MASW methods suitable for sea dike monitoring using sea waves or anthropogenic noise as continuous seismic sources to retrieve surface wave signal and produce highquality dispersion diagrams. [START_REF] Planès | Monitoring the tidal response of a sea levee with ambient seismic noise[END_REF] successfully test a seismic-interferometry technique on an earthen levee using retrieved impulse signal from cross-correlation of anthropogenic ambient seismic noise. [START_REF] Joubert | Passive monitoring of a sea dike during a tidal cycle using sea waves as a seismic noise source[END_REF] develop a passive monitoring method, using sea waves as seismic sources, and retrieve shear-wave velocity perturbations, related to water content in the sea dike body, with respect to a background velocity model previously inferred using effective dispersion curve inversion. The latter aims, as other monitoring methods, to detect and locate as precisely as possible the heterogeneities in the dike body to facilitate future geotechnical intervention. This need for precision can only be achieved with the use of an accurate background velocity model. However, the inversion process of dispersion curves is widely based on 1D forward modeling algorithms with the assumption of a layered, laterally invariant, half-space models [START_REF] Xia | Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves[END_REF][START_REF] Wathelet | Array recrecord of ambient vibrations: surface-wave inversion[END_REF], while sea dikes present strong 3D surface variations which can limit the accuracy of the process [START_REF] Wang | Effect of near-surface topography on high-frequency Rayleighwave propagation[END_REF][START_REF] Borisov | 3D elastic full-waveform inversion of surface waves in the presence of irregular topography using an envelope-based misfit function[END_REF]. Indeed, side reflections can disturb the dispersion diagram of Rayleigh waves for dikes with a width-to-height ratio lower than four [START_REF] Karl | Geotechnical characterization of a river dyke by surface waves[END_REF] which can be the case for coastal sea dikes exhibiting asymmetric geometries and seafront promenade showing sometimes sub-vertical slopes. [START_REF] Pageot | Importance of a 3D forward modeling tool for surface wave analysis methods[END_REF] have also shown that, even for sea dikes with symmetric geometries, internal structure layering can emphasize geometrical effects, and produce dispersion curves very different from the theoretical 1D case, for both the fundamental and superior modes. Consequently, a multi-modal inversion approach will also fail to infer accurate shear-wave velocity models.

Taking advantages of high-performance computing center accessibility and wave propagation modeling algorithm development, it is now possible, as recommended by [START_REF] Min | Feasibility of the surface-wave method for the assessment of physical properties of a dam using numerical analysis[END_REF], to consider the use of a 3D elastic forward modeling as an engine for least-square minimization method, in order to assess directly mechanical parameters, or to improve the results of 1D dispersion curves inversion. Here, we use a parallelized 3D elastic modeling code based on the spectral element method [START_REF] Komatitsch | The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures[END_REF] which allows to obtain accurate synthetic data with very low numerical dispersion and a reasonable numerical cost.

In this study, we choose simplified coastal sea dike geometries as case examples. We first show that both the shape of their cross-section, and the presence of a lateral reflector, may have a significant effect on Rayleigh waves dispersion diagrams. We demonstrate the limitations of the classical 1D inversion process and show the importance of taking into account the full dispersion diagram as an input instead of dispersion curves only. Then, we demonstrate the necessity of 3D elastic modeling as a forward problem for the inversion of dispersion diagrams.

Modeling surface wave dispersion in sea dikes

Multichannel analysis of surface waves

Currently, in civil engineering, Multichannel Analysis of Surface Waves, MASW, [START_REF] Park | Imaging dispersion curves of surface waves on multi-channel record[END_REF][START_REF] Park | Multichannel analysis of surface waves[END_REF][START_REF] Park | Multichannel analysis of surface waves (MASW)active and passive methods[END_REF] is a common method to obtain a dispersion diagram and the first step through the determination of the effective dispersion curve. Compared to Spectral Analysis of Surface Waves (SASW, [START_REF] Nazarian | Evaluation of geophysical techniques for dike inspection[END_REF]), the main advantages of MASW are: the multichannel acquisition (efficient routine), the fast data processing, the identification of dispersion modes and the limitation of the impact of noise.

MASW is a wavefield transformation method in which data are transformed from space-time domain to, in most cases, frequency-wavenumber domain or frequency-velocity domain. Frequencywavelength and frequency-slowness [START_REF] Mcmechan | Analysis of dispersive waves by wave field transformation[END_REF] are two other way to represent surface wave dispersion. First, this transformation involves a Fourier transform of the signal. Then, the principle of MASW is to test phase propagation at a given frequency and velocity with respect to the source-receiver offset. For a given common shot gather, the dispersion diagram D, in the frequency- velocity domain, is calculated as:

D (v , ω)= ∑ i= 1 N r S i (ω)e i ω d i v , ( 1
)
where v is the phase velocity, ωis the angular frequency, N r is the number of receivers and d i is the source-receiver offset. S i (ω) is the real to complex Fourier transform of the signal recorded at receiver i.

Each signal S i (ω) is phase-shifted using a test velocity v and the results are summed for each set of ω and v.

The effective dispersion curve (and potentially superior dispersion modes) is then extracted from the dispersion diagram using (semi-)automatic picking of the maximas. Note that a whitening of the complex signal at each frequency, as well as the normalization by frequency of the dispersion diagram, can be done to improve the visibility of the different propagation modes.

Spectral element method

For this study we need a numerical modeling method whose spatial discretization is suitable for representing complex environments, and which provides both high precision results and low numerical dispersion. Thus, we use the Spectral Element Method (SEM) for three-dimensional elastic wave propagation modeling [START_REF] Komatitsch | The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures[END_REF][START_REF] Komatitsch | The spectral element method for elastic wave equations-application to 2-D and 3-D seismic problems[END_REF][START_REF] Komatitsch | The spectral-element method in seismology[END_REF][START_REF] Festa | The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics[END_REF].

SEM is a variant of the Finite Element Method (FEM) [START_REF] Lysmer | A finite element method for seismology[END_REF][START_REF] Hulbert | Space-time finite element methods for second-order hyperbolic equations[END_REF][START_REF] Tromp | Spectral-element and adjoint methods in seismology[END_REF] based on a high-order piecewise polynomial approximation of the weak formulation of the wave equation, which leads to a spectral convergence ratio as the interpolation order increases. Considering near-surface experiments, one advantage of SEM is that the weak formulation naturally satisfies the free-surface condition used to simulate surface wave propagation with considerable accuracy [START_REF] Komatitsch | The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures[END_REF][START_REF] Komatitsch | The spectral element method for elastic wave equations-application to 2-D and 3-D seismic problems[END_REF][START_REF] Komatitsch | The spectral-element method in seismology[END_REF]. Contrary to FEM, which calls on a wide range of available element geometry [START_REF] Dhatt | A new optimizer using particle swarm theory[END_REF], SEM is limited to quadrilateral elements in 2D and hexahedral elements in 3D. Note that although SEM with tetrahedral elements exists [START_REF] Komatitsch | Wave propagation in 2-D elastic media using a spectral element method with triangles and quadrangles[END_REF]), it leads to theoretical complications. In any case, quadrangles and hexahedras are well suited for handling complex geometries and interface matching conditions [START_REF] Cristini | Some illustrative examples of the use of a spectral-element method in ocean acoustics[END_REF].

In SEM, the wave-field is expressed in terms of high-degree Lagrange interpolants and the calculations of integrals are based on the quadrature of Gauss-Lobatto-Legendre (GLL). Each element is discretized with Lagrange polynomials of degree n l and contains n l +1GLL points that form its local mesh. This combination of high-degree Lagrange interpolants with the GLL integration leads to a perfectly diagonal mass matrix, which in turn provides a fully explicit time scheme suitable for numerical simulations on parallel computers [START_REF] Komatitsch | The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures[END_REF][START_REF] Komatitsch | The spectral element method for elastic wave equations-application to 2-D and 3-D seismic problems[END_REF].

The spatial resolution of SEM is controlled by the typical size of an element ( Δ h) and the polynomial degree in use on an element (n l ). Typically, a polynomial degree n l =4 is optimal for seismic wave propagation modeling [START_REF] Moczo | 3-D finite-difference, finite-element, discontinuous-Galerkin and spectral-element schemes analysed for their accuracy with respect to P-wave to S-wave speed ratio[END_REF] although n l =8 remains numerically affordable in 2D. To obtain accurate results, the required Δ h is of the order of λ min /2<Δ h<λ min for n l =4 and λ min <Δ h<2λ min for n l =4, λ min being the smallest wavelength of the waves propagated in the model.

The time marching scheme is governed by the Courant-Friedrichs-Lewy (CFL) stability condition which ensures the stability of the scheme:

Δ t <C Δh c max (2)
where C is the Courant constant and c max is the maximum wave velocity, typically the P-wave velocity. The Courant constant C is determined empirically, depending on the application, and is fixed at a maximum of 0.30 for this study.

In our study, the models are meshed with hexahedra (3D) using the GMSH open-source software package [START_REF] Geuzaine | Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities[END_REF].

Models and acquisition

As said in the introduction section, we choose to focus on coastal sea dikes which can exhibit asymmetric geometries and strong slopes on the sea side, contrary to most of river dikes studied for example by [START_REF] Karl | Geotechnical characterization of a river dyke by surface waves[END_REF] and [START_REF] Planès | Monitoring the tidal response of a sea levee with ambient seismic noise[END_REF].

The reference geometry model (Fig. 1(a)) is a simplified version of the sea dike of Les Moutiersen-Retz (France) already studied by Le [START_REF] Le Feuvre | Passive multi-channel analysis of surface waves with cross-correlations and beamforming. Application to a sea dike[END_REF] and [START_REF] Joubert | Passive monitoring of a sea dike during a tidal cycle using sea waves as a seismic noise source[END_REF]. The body dike is represented as a right-angled trapezoid along a lateral block with an infinite extent on the right side. The dike body and the lateral block are laid on a two-layered media which represents the two substratum layers. For convenience, this two layers are called the substratum and the half-space layer (bottom layer) thereafter.

This geometry is declined into a flat geometry model (Fig. 1(b)) and a rough geometry model (Fig. 1(c)). All materials are chosen to have a constant Poisson's ratio η=0.25 and a constant density ρ=2000 kg . m -3 . Models are divided into four areas of distinct shear-wave velocities, including a lateral block right next to the dike body. Shear wave velocities are set to V S1 =800 m . s -1 for the half-space layer and V S 2 =600 m . s -1 for the substratum layer. Additionally, we consider two cases for each geometry : 1) the lateral block has the same shear velocity that the dike body (V S 4 =V S 3 =400 m . s -1 ) and 2) the lateral block has a different shear velocity (V S3 =400 m . s -1 and V S 4 =500 m . s -1 ) and acts consequently as a vertical reflector. The modeling of the sea (water layer) is not included here, since previous numerical tests showed that, in this particular context, an adjacent water layer does not have any significant effect on the dispersion diagram [START_REF] Pageot | Importance of a 3D forward modeling tool for surface wave analysis methods[END_REF].

Figure 2 shows the mesh corresponding to the model presents in Figure 1(a). This mesh has 11544 hexaedra elements with PML (9600 hexaedral elements without PML), the other two models have 11752 and 10712 hexaedras for the flat and the rough geometry, respectively. The lateral block always exists even when it has the same properties than the dike's body.

The linear acquisition composed of 80 receivers spaced of one meter, is placed on the crest of the sea dike body along the coast line as schematically represented on Figure 2. This study is carried out in the framework of sea dikes monitoring using ambient seismic noise. In this case, the elastodynamic Green's function of the medium can be retrieved from the cross-correlation of two recording of seismic ambient noises at different receiver location at the free surface [START_REF] Wapenaar | Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation[END_REF][START_REF] Gouedard | Cross-correlation of random fields: Mathematical approach and applications[END_REF]. The resulting Green's function is the wavefield that would be observed at one of these receiver positions if there were an impulsive source at the other. Taking one receiver of an array as virtual source, a complete shot gather can be retrieved and can be used to calculate a dispersion diagram using the MASW approach. Consequently, we consider a minimum source-receiver offset of one meter at the beginning of the array to act as a retrieved shot gather from ambient seismic noises. The source is a Ricker wavelet with a peak frequency of 25 Hz (f max ≈ 70 Hz).

Effects of geometry and lateral reflectors

In this section, we focus on the effect of the structure of the dike, i.e. the slope angle and the presence of a lateral reflector, on dispersion diagrams. We compare calculated effective dispersion curves with theoretical ones since they are the input data in classical 1D inversion processes. The theoretical dispersion curves are calculated using a one-dimensional three-layered model corresponding to a vertical profile going through the dike body, the substratum layer and the half-space.

Figures 3(a-f) show the resulting dispersion diagrams for the six models considered (two different internal properties distribution and three geometries). Figure 3(a) shows that the presence of a single reflecting side (part of the free surface) does not disturb the fundamental mode compared to the 1D theoretical one. However, Figure 3(b) shows that the presence of a lateral velocity variation, even with a moderate velocity constrast with the dike's body, has effects on both the fundamental and superior modes.

We also see that contrary to the flat geometry models (Fig. 3(c,d)), which has no important effects on the dispersion diagrams compared to the reference ones, the rough geometry models drastically affects the diagram. Indeed, for the first material distribution (Fig. 3(e)), the fundamental mode surface wave energy appears to be split in two branches, while for the second material distribution (Fig. 3(f)), the fundamental mode seems to move closer to the theoretical dispersion curve.

In Figure 3(e), the two branches would be considered as effective mode and superior mode, while they are, in reality, totally different from the theoretical one.

Note that whatever the geometry, models without lateral variation of velocity seems to strongly excited superior modes (relative to the fundamental one) around the point (750 m . s -1 ; 35 Hz). We deduce here that one effect of the lateral variation of velocity is to focus energy on an effective mode and consequently to decrease the amount of energy in the superior modes.

Given these results, it appears clearly that picking dispersion curves and assessing the physical properties by 1D inversion will be, on some cases, challenging. However, it is difficult, based only on the appearance of the dispersion diagram, to assess which parameter will be affected during the inversion and to what extent. In the next sections, we will focus on the reference geometry models with the lateral variation of velocity since it constitutes the closest approximation to the sea dike of Les Moutiers-en-Retz.

1D inversion using particle swarm optimization

Assessing S-wave velocity model of a targeted medium by the inversion of dispersion curves is a non-linear and mix-determined problem [START_REF] Socco | Surface-wave analysis for building near-surface velocity models -Established approaches and new perspectives[END_REF]. Among the methods developed and used for the inversion procedure, the least-square minimization method [START_REF] Tarantola | Generalized nonlinear inverse problems solved using the least squares criterion[END_REF] is the most widely used. However, since this method requires an accurate initial model located in the vicinity of the global minimum of the cost function, a strong \textit{a priori} on the true model parameters is needed.

In order to avoid this issue and to start with minimum prior information, one can chose to use global optimization methods such as Monte-Carlo [START_REF] Metropolis | Equation of state calculations by fast computing machines[END_REF][START_REF] Mosegaard | Monte Carlo sampling of solutions to inverse problems[END_REF][START_REF] Mosegaard | Monte Carlo analysis of inverse problems[END_REF][START_REF] Socco | Improved Monte Carlo inversion of surface wave data[END_REF], neighborhood algorithm (Sambridge, 1999a(Sambridge, , 1999b[START_REF] Sambridge | Finding acceptable models in nonlinear inverse problems using a neighbourhood algorithm[END_REF][START_REF] Wathelet | Array recrecord of ambient vibrations: surface-wave inversion[END_REF], simulated annealing [START_REF] Ryden | Fast simulated annealing inversion of surface waves on pavement using phase-velocity spectra[END_REF] or genetic algorithm [START_REF] Holland | Genetic algorithms and adaptation[END_REF][START_REF] Dal Moro | Rayleigh wave dispersion curve inversion via genetic algorithms and Marginal Posterior Probability Density estimation[END_REF].

In this work, we choose to use a global optimization method called Particle Swarm Optimization (PSO). PSO, first proposed by [START_REF] Dhatt | A new optimizer using particle swarm theory[END_REF], is a population-based algorithm which intends for simulating the social behavior of a bird flock (swarm of particles) to reach the optimum region of the search space.

PSO is quite recent in the framework of geophysical data inversion [START_REF] Shaw | Particle swarm optimization: A new tool to invert geophysical data[END_REF][START_REF] Yuan | Swarm intelligence optimization and its application in geophysical data inversion[END_REF] and is not yet as widely as the other global optimization methods mentioned previously. However, it was successfully applied to surface-wave analysis [START_REF] Song | Application of particle swarm optimization to interpret Rayleigh wave dispersion curves[END_REF][START_REF] Wilken | On the application of Particle Swarm Optimization strategies on Scholtewave inversion[END_REF], traveltime tomography [START_REF] Tronicke | Crosshole traveltime tomography using particle swarm optimization: A near-surface field example[END_REF][START_REF] Luu | A competitive particle swarm optimization for nonlinear first arrival traveltime tomography[END_REF], seismic refraction [START_REF] Poormirzaee | Introducing Particle Swarm Optimization (PSO) to Invert Refraction Seismic Data[END_REF], seismic wave impedance inversion in igneous rock [START_REF] Yang | Particle swarm optimization and its application to seismic inversion of igneous rocks[END_REF] and multifrequency GPR inversion [START_REF] Salucci | Multifrequency Particle Swarm Optimization for Enhanced Multiresolution GPR Microwave Imaging[END_REF]. Furthermore, [START_REF] Song | Application of particle swarm optimization to interpret Rayleigh wave dispersion curves[END_REF] have shown, in a comparative analysis, that PSO outperforms genetic algorithm and Monte-Carlo methods in terms of reliability and computational efforts. Added to this simplicity of implementation and the few number of control parameters, PSO appears as a promising method.

The standard PSO update formulas are \citep{eberhart1995new}:

v id k +1 =v id k +c 1 r 1 ( p id -x id k )+c 2 r 2 ( p gd -x id k ), (3)
x id k +1 =x id k +v id k+ 1 , ( 4
)
where r 1 and r 2 are random variables that induce stochacity [START_REF] Souravlias | Particle swarm optimization with neighborhood-based budget allocation[END_REF], c 1 is the cognitive parameter, c 2 is the social parameter and c 1 =c 2 =2 in most cases.

Classical improvements of PSO focus on the control of the velocity vector through the use of an inertia weight ω or a constriction factor κ (Shi and Eberhart, 1998; Clerc, 1999; Eberhart and Shi, 2000).

v id k +1 =ω v id k +c 1 r 1 ( p id -x id k )+c 2 r 2 ( p gd -x id k ), (5)
v id k +1 =κ [v id k +c 1 r 1 ( p id -x id k )+c 2 r 2 ( p gd -x id k )] , (6) κ= 2 2-ϕ-√ ϕ 2 -4 ϕ (7)
where ϕ=c 1 +c 2 and ϕ> 4.

Here, we choose to follow the recommendations of [START_REF] Eberhart | Comparing inertia weights and constriction factors in particle swarm optimization[END_REF] and to use the constrictor factor version of the algorithms and we chose c 1 =2.8 and c 2 =1.3 as recommended by [START_REF] Song | Application of particle swarm optimization to interpret Rayleigh wave dispersion curves[END_REF]. In addition, we use the toroidal topology since it was demonstrated best performances than the initial full topology [START_REF] Kennedy | Population structure and particle swarm performance[END_REF].

For each PSO process, we have set the swarm population to 20 particles and the number of iterations to 200. Ten processes were made for each inversion of the effective dispersion curve corresponding to the reference geometry model with lateral variation of velocity (Fig. 3(b)). Two parameterizations are considered: (1) 3-layer model with variable V S (200<V Si <1200m / s, i=1,2,3) and thickness h (1<h<10 m for the dike's body and 1<h<15 m for the substratum layer), and (2) same as (1) with a constant top layer thickness (dike's body height of 4.75 m).

Figure 4 shows the results of these inversions processes for the two parametrizations. At first, we observe that for the two parameterizations, retrieved dispersion curves are in very good agreement with the input one. However, in both cases, even if the velocities of each layer are well recovered, the depth of the interface between the substratum layer and the half-space is always over-estimated. It appears also that the height of the first layer (dike body) is under-estimated (3.75 m instead of 4.75 m) with the first parametrization. Finally, it must be noted that the inversion results with a constant dike height always have higher misfit values than those obtained for a non-constant dike height.

In this section, we have shown that 1D inversion of dispersion curves, even if the retrieved models are not so far from the true model, does not give sufficiently accurate velocity models for geotechnical purposes.

Further, whatever the parametrization, a global optimization method can provide a set of possible solutions that are very different from each other. In this case, it can be difficult to deduce a representative average model that can be used as an initial or background model.

Sensitivity

In this section, we explore the effects, on dispersion diagrams, of a 10% positive perturbation of shear-wave velocity in each block constituting the reference geometry model for the second material distribution case (with a lateral variation of velocity, V S3 =400 m/ s, V S 4 =500 m/ s). In Figure 5 and Figure 6, the resulting dispersion diagram of each perturbed model is compared to the original one in terms of ratio of differences (absolute value of the relative change: (x A -x B )/ x B . These results allow to determine in which frequency band the surface waves carry information about the S-wave velocity of each block.

As expected, when considering only the dispersion curve, it is seen that high-frequencies carry information about the superficial layer (dike's body) and the depth of investigation increases with lower frequencies. However, Figures 5 and6 show that information exists out of the dispersion curve domain. It is particularity significant in Figures 5(a) and Figure 5(b) where difference ratios are very important out of the dispersion curve domain. We see also ,on Figure 5(c), that the differences for a velocity perturbation of the bottom layer are weak compared to superficial layers (Fig. 5(a,b) and 6(c)) and are out of the dispersion curve domain. This means that the sensitivity of the effective dispersion curve to velocity perturbations in the bottom layer is null. This implies that an inverted S-wave velocity models obtained using only the effective dispersion curve cannot be accurate, especially for deep layers as found in the 1D inversion results presented in the previous section. This inaccuracy can have serious implications in terms of geotechnical engineering, in particular to determine the location of the potential defects or weak zones.

These results confirm that the exploitation of the full dispersion diagram, instead of dispersion curve only, is necessary to assess correctly all parameter of interest (S-wave velocity, layer thickness). For targets with strong 3D geometry such as sea dikes, it means that the use of 3D modeling engine is necessary to provide the full dispersion diagrams needed as input during an inversion process.

In the next section, we focus on 3D inversion using the least-square minimization approach.

3D inversion using the least-square minimization method

We have shown in the previous section that superior modes of dispersion diagrams carry additional information, and it is known that they allow to improve the model resolution [START_REF] Gabriels | In situ measurements of shear-wave velocity in sediments with higher-mode Rayleigh waves[END_REF][START_REF] Park | Imaging dispersion curves of surface waves on multi-channel record[END_REF][START_REF] Socco | Surface-wave method for near-surface characterization: a tutorial[END_REF][START_REF] Luo | Rayleigh-wave dispersive energy imaging and mode separating by high-resolution linear Radon transform[END_REF]. However, superior modes are not always easy to identify since they can be very close to the fundamental mode over some frequency bands, or not visible at all on the dispersion diagram due to a lack of energy. [START_REF] Maraschini | A new misfit function for multimodal inversion of surface waves[END_REF] have developed an efficient multi-modal inversion of surface waves, based on the module of theoretical dispersion diagram, which allows to avoid mode-misidentification errors, but the forward problem is still 1D.

Given that the differences between the true and the theoretical dispersion curves are related to the presence of a vertical reflector (lateral variation of velocity) and the footprint of the sensitivity of S-wave velocities is stronger outside the dispersion curve level, presented in the previous sections, any 1D modeling tool can encounter difficulties to retrieve accurately the velocities of a sea dike with strong 3D geometry. Consequently, we choose to use a least-square minimization method [START_REF] Tarantola | Generalized nonlinear inverse problems solved using the least squares criterion[END_REF], based on a 3D forward modeling tool, that minimizes the misfit between the reference and calculated dispersion diagrams, instead of the dispersion curves only. This allows to avoid the dispersion curve picking step and to exploit completely the dispersion diagram. The misfit function is defined as:

C (m)= 1 2 |d cal (m)-d obs (m)| 2 ,
where d cal and d obs are, in our case, the calculated and observed dispersion diagrams, respectively. In the framework of this local optimization method, the model m is update iteratively through the formulation:

m k+ 1 =m k +α Δ m ,
where k is the iteration number and α is scalar ≤ 1. The model update Δ m is deduced from:

H (m k )Δ m k =-∇ C (m k ),
where H (m k ) is the hessian matrix and ∇ C (m k ) is the gradient vector of the cost function.

Following the Gauss-Newton approximation, Equation 10 can be rewritten as:

J T (m k ) J (m k ) Δ m k =-J T (m k )(d cal (m k )-d obs ),
where J (m) is the Jacobian operator: J (m)=∂ d cal /∂ m.

Given there are few unknowns (one S-wave velocity per block and the thickness of the substratum layer), the calculations of the Jacobian and the model update are very fast at each iteration.

For the initial model, we use the reference geometry model with initial velocities and second layer thickness previously given by the best previous 1D inversion result (minimum misfit) obtained for a fixed dike height. We also set the initial velocity of the lateral block (V S 4 ) equal to the velocity of the dike body (V S3 ). Initial velocities for each material and the initial second layer thickness are marked in blue in Fig. 7(a). For the 3D modeling, a mesh is automatically generated before each forward problem to take into account the minimum S-wave velocity of each block and the thickness of the substratum layer.

Retrieved velocities using 3D least-square inversion are marked in green in Fig. 7(a). We see that all assessed velocities are almost identical to the true one (marked in blue) and more, that the inversion process allows to retrieve the velocity of the lateral block (V S 4 ). Even the thickness of the substratum layer is accurately inferred. Finally, these results show that the inversion process allows to retrieve both the fundamental (Fig. 7(e)) and the superior modes (Fig. 7(b), (c) and (d)) which contain additional informations on the structure and would allow for even more efficient 3D inversion from Rayleigh wave dispersion diagrams.

Conclusions

Civil engineering structures are more and more instrumented in a sustainable way, in order to ensure the security of populations. Perturbation-based seismic methods, such as the use of ambient noises in the context of sea dikes [START_REF] Le Feuvre | Passive multi-channel analysis of surface waves with cross-correlations and beamforming. Application to a sea dike[END_REF][START_REF] Planès | Monitoring the tidal response of a sea levee with ambient seismic noise[END_REF][START_REF] Joubert | Passive monitoring of a sea dike during a tidal cycle using sea waves as a seismic noise source[END_REF] may allow to better understand their evolution in the face of aging, by providing relative variations of the surface wave velocity as a function of time. Nevertheless, these methods require accurate reference models to start with to ensure a precise localization of heterogeneities.

We have shown here that the standard surface wave analysis workflow, which widely uses a 1D forward modeling engine and exploits only the fundamental dispersion curves, is not adapted to targets with strong 3D geometries. Even if the 1D retrieved velocity profiles are not far from the true velocity logs, they are not accurate enough for high stakes geotechnical studies such as sea dike monitoring and failure prevention.

We have proposed a new approach divided in two phases. First, a standard surface wave analysis workflow, based on particle swarm optimization, is used to obtain prior informations on the material properties. Then, the full dispersion diagram is exploited using a least-square minimization method combined with the use of a 3D forward modeling engine, in order to take into account the geometry. This approach has shown a very good efficiency to assess physical properties of the considered sea dike, even for materials outside the vertical plan defined by the source-receivers line: the resulting model is virtually identical to the true one. An evaluation with more realistic data such as data from experimental small-scale modeling [START_REF] Bretaudeau | Small-scale modeling of onshore seismic experiment: A tool to validate numerical modeling and seismic imaging methods[END_REF][START_REF] Pageot | Improving the seismic small-scale modelling by comparison with numerical methods[END_REF]) must be performed, but it seems at this stage that, even with field data, this method will be able to provide well defined image of the material distribution of a structure and an accurate reference model suitable for perturbation based imaging and monitoring.

Finally, the proposed method and workflow are not specific to sea dike imaging and can be easily transfered to others 3D objects such as bridges, dams, roads, rails and others infrastructures which need to be sounded and/or monitored.

Acknowledgments

We would like to thank the CEA for the SEM3D Spectral Element Method modeling code. We are also grateful to the CCIPL (Nantes, France) for providing access to its high-performance computing facilities and for the support given by its staff. This study was carried out within the framework of the VIBRIS project (OSUNA-IFSTTAR-University of Nantes -CNRS) and the WeaMEC PROSE project sponsored by the Region Pays-de-la-Loire (France). We would also like to thank ANR HIWAI (ANR-16-CE31-0022, Laboratory of Planetology and Geodynamics, University of Nantes, France) for its support.

Figure 1 :

 1 Figure 1: Three sea dike geometries. (a) Reference geometry close to the real one from Les Moutiers-en-Retz, France. (b) Flat geometry. (c) Rough geometry. The S-wave velocity of the lateral block (V S 4 ) can be equal or greater than the S-wave velocity of dike body (V S 4 ).

Figure 2 :

 2 Figure 2: The mesh uses for 3D modeling (here without PML). The red dot represents the source position while the red line represents the receiver line.

Figure 3 :

 3 Figure 3: (a,b) Dispersion diagrams for the reference geometry model (a) without lateral variation of velocity (V S3 =V S4 =400 m/ s) and (b) with lateral variation of velocity (V S3 =400 m/ s, V S 4 =500 m/ s). (c,d) Same as (a) and (b) for the flat geometry models. (e,f) Same as (a) and (b) for the rough geometry models. Black lines correspond to theoretical fundamental and superior mode. White solid circles correspond to effective mode extracted from the dispersion diagram.

Figure 4 :

 4 Figure 4 : Results of standard 1D inversion for the reference geometry model with a lateral variation of the velocity (a,b) with a variable top layer height and (c,d) with a fixed top layer height (dike height of 4.75 m). (a, c) Dispersion curves of the best model found during inversion (grey) compared to the effective dispersion curve (black). (b,d) Best S-wave 1D velocity profiles found during inversion (grey) compared to the S-wave 1D velocity profile below the receiver line.

Figure 5 :

 5 Figure 5: (a,c,e) Dispersion diagrams for a velocity perturbation in (a) the dike body (V S3 ), (c) the substratum layer (V S 2 ) and (e) the half-space(V S1 ). (b,d,f) Difference ratio between the dispersion diagram of the original model and the dispersion diagram of the perturbed models (a), (c) and (e) respectively. The red dot lines correspond to the effective dispersion curves extracted from the perturbed velocity models.

Figure 6 :

 6 Figure 6: (a) Dispersion diagrams for a velocity perturbation in the lateral block. (b) Difference ratio between the dispersion diagram of the original model and the dispersion diagram of the perturbed model (a). The red dot lines correspond to the effective dispersion curves extracted from the perturbed velocity model.

Figure 7 :

 7 Figure 7: (a) S-wave velocity for prior model (red), inverted model (green) and true model (blue, reference geometry model with a lateral variation of velocity, Fig.1(b). (b,c,d) Dispersion diagrams for (b) the true model, (c) the prior model and (d) the inverted model.(e) Dispersion curves extracted from dispersion diagrams for the prior model (red), the inverted model (green circles) and the true model (blue). Dashed circles emphasize higher-modes.


Isabelle Léglise
email: leglise@univ-tours.fr

Sophie Alby

Minorization and the process of (de)minoritization: the case of Kali'na in French Guiana

Minorization and the process of (de)minoritization: the case of Kali'na in French Guiana

Isabelle Léglise, Sophie

Introduction

The concept of diglossia, according to the broad definitions of [START_REF] Fishman | Sociolinguistique[END_REF][START_REF] Ferguson | Diglossia revisited. Studies in Diglossia[END_REF] i , has had a significant impact on the field of language contact studies, to the point that the "high variety/low variety" model often influences the scientific perception of any situation in which one or more contact or official languages are in contact with languages spoken by smaller groups, also known as minority languages [START_REF] Haugen | Minority language today[END_REF]. Macrolinguistic descriptions of multilingual situations seldom escape this influence, even when they are located -as it is the case here -outside models of linguistic conflict such as [START_REF] Aracil | Conflit linguistique et normalisation dans l'Europe nouvelle[END_REF] or Lafont (1997) whereby linguistic cohabitation is seen as a pairing of dominant language(s) versus dominated. Furthermore, the epilinguistic comments of speakers who belong to a linguistic minority often refer to hierarchies or conflicts between languages, to the point that the researcher is faced with emic categories which mirror the high/low and dominant/dominated models.

As such, in looking at the macrolinguistic situation of the French Overseas Department of Guiana, one tends to see uneven relationships between languages: an official language (French), contact languages (essentially Guyanese Creole and French) and vernacular languages, some of which are regional (Amerindian languages such as Kali'na and Wayana, English-based creoles like Ndyuka and Aluku, etc) while others are a product of immigration (and are vernacular in Guiana, such as Haitian Creole, Brazilian Portuguese, Spanish, etc).

A global approach to the languages of French Guiana, like the one presented above, gives us a rapid overview of the linguistic situation of the department. It is, however, imperfect on several levels: in terms of geography, in terms of the hierarchy between local and global levels, and in terms of the dynamics involved. For one thing, the approach needs to be qualified as far as Guyanese regional particularities are concerned, as seen in the appended map of regional languages: the vernacular languages are positioned in different ways across the territory, making it difficult to make any generalizations. Another point is that the language dynamics of each region are not necessarily the same and potentially contradict the global conclusions. For example, in Western Guiana, and particularly in Saint-Laurent of Maroni, Guyanese Creole is in strong competition with English-based creoles, namely Nenge variants (mostly Ndyuka) ii and Sranan Tongo (a contact creole from Surinam), allowing us to see the emergence of new contact languages. At the local level, the equilibrium is not the same, and languages classified as dominated at the global scale may in fact be contact languages, like, for instance, Nenge in Saint-Laurent of Maroni, or Brazilian Portuguese in St Georges of Oyapock, with positive associations [START_REF] Léglise | Langues frontalières et langues d'immigration en Guyane Française[END_REF]. We can thus raise the issue of how legitimate a global overview can be if it corresponds neither to any one particular exemplary case, nor to the sum of local particularities, nor even to their smallest common denominator.

While most speakers of these different languages do in fact belong to "minority" communities, their languages are not minorized as a direct consequence of this. The notion of "minorized language" refers in this case to a definition which acknowledges various macroand microlinguistic features, as proposed by [START_REF] Kasbarian | Langue minorée et langue minoritaire[END_REF]. Like Kasbarian, we retain of the different macro approaches that a "minorized language is a language whose lack of autonomy, status, diffusion, functional distribution and standardization makes up objective characteristics derived from macrolinguistic description." We retain from microlinguistic approaches the idea that they are "languages whose value is not recognized on the interactional scene by speakers of a sociolinguistically dominant language (official language, written language, contact language, language of schooling, backed by regulating and prescriptive norms), and that speakers of the minorized language conform to the usage and interactive norms set by their interlocutors." iii Indigenous languages in particular are often labelled "minority languages" and generally categorized as "endangered languages" according to UNESCO's definition of the term : "A language is endangered when it is on a path toward extinction" (2003 :2). In other words, the language does not fulfil the following criteria of linguistic vitality:

(1) Intergenerational language transmission

(2) Absolute number of speakers (the smaller a community is, the more likely it is to be endangered)

(3) Proportion of speakers within the total population (4) Use in existing language domains (5) Response to new domains and media (6) Materials for language education and literacy A language must fulfil all of these criteria to be considered in a situation of "linguistic vitality".

Kali'na, one of the six Indigenous languages of French Guiana, belonging to the Cariban family, is spoken in five countries: Brazil, France (French Guiana), Surinam, Guyana and Venezuela. It appears to be a minority language with respect to all the languages in Guyanese territory (official, regional, contact), as the number of speakers is estimated around 2800 iv , in other words less than 2% of the total population of the department. It is worth questioning whether this language is minorized, both at the departmental scale as well as at the more local scale of Kali'na-speaking communities, and if so, whether it is always minorized, or whether minoritizations and deminoritizations are sometimes perceptible in certain situations.

Minoritization -in French "minorisation"-here refers to the concept as it is defined by [START_REF] Py | Minorisation linguistique et interaction[END_REF], that is, as a way to conceptualize linguistic inequalities in a dynamic way, as a process "governed by the very development of oral interaction, constructed and constructible with each speech act." v From the point of view of Amerindianist linguists, Kali'na could be considered to be "endangered" due to its intensive contact with other languages in French Guiana, which could lead to quite substantial changes in the lexicon and the morphosyntactic structure of the language vi . Indeed, Kali'na has been in contact with different languages since the beginning of the period of colonization, resulting in different degrees of influence (Renault-Lescure, 2004), and, more recently, with French, which appears to have a strong influence on the linguistic practices of current generations.

The aim of this article is to document the case of Kali'na as a minority language in French Guiana by, on the one hand, using both micro-and macrosociolinguistic levels of analysis, and on the other, questioning the static descriptive categories ("dominated language", "minorized language", "endangered language") available in the literature as they apply to the contrasted situation of Kali'na over a large geographical area and in varied interactive contexts. The fact that contact situations for Indigenous languages are most often approached as matters of the language death or endangerment must be questioned. While the terms may be pertinent in some cases vii , they may not be for Kali'na.

The findings presented here are based on data gathered during three periods of field work. These data involve, on the one hand, a microsociolinguistic study of the interactions between children and young Kali'na speakers in a school setting and in the village [START_REF] Alby | Contacts de langues en Guyane française: une description du parler bilingue kali'na-français[END_REF], and on the other, the analysis of results, as they pertain to Kali'na, collected during a large-scale survey through guided interviews in a school setting about spoken languages and related attitudes (see Léglise 2007 for methodology). There is also an analysis of speeches collected from oral media or written about the language.

In the first part of this article we will look at the macrosociolinguistic indicators we have of the minorization -in French "minoration" -of Kali'na. At the departmental scale, we are interested in attitudes with regards to Kali'na language and culture, and to epilinguistic comments by speakers. We shall raise the question of whether the minorization of this language is internalized by its speakers and in particular by the children. In the second part of the article, we will present a more local view of relationships between languages. Looking at the Awala-Yalimapo township in Western Guiana, which has been recognized as autonomous since 1989 and is inhabited primarily by Kali'na speakers, we will explore whether the effects of minorization change at the local scale, and also at the broader scale of the Kali'na linguistic community. In the third part, we will attempt to determine to what extent, as far as interaction is concerned, the alternations and code switching observed between Kali'na, French and Creole offer clues about the process of minoritization or deminoritization currently underway.

Some indicators of the minorization of Kali'na in French Guiana

At the macrolinguistic level, the situation of Kali'na in French Guiana is one of a double minorization [START_REF] Alby | Une approche bilinguiste du contact de langues : discours bilingues d'enfants kali'na en situation scolaire[END_REF]. Two languages are majorized through their status and their function, namely French, as the language of schooling and public institutions in general but also more and more as a contact language, and creoles viii , in their role as contact languages.

This statutory domination is compounded by a "socio-racial stratification dating back to the period before the creation of the department", which has been uncovered by works in sociology and anthropology (namely [START_REF] Jolivet | Essai de sociologie sur la Guyane française[END_REF][START_REF] Collomb | La question amérindienne en Guyane. Formation d'un espace politique[END_REF]) which distinguish "primitive" peoples (Indigenous and Maroons ix ) and "civilized" peoples (White Peoples and Creoles).

Different elements indicate that there is indeed a minorization of Kali'na and internalization of this attitude by speakers.

Kali'na speeches depicting a situation of linguistic domination

Summing up the positions of Kali'na speakers with respect to the linguistic situation in French Guiana is a delicate matter. Nevertheless a number of arguments appear to converge in epilinguistic speeches. In July 2003, a special report called "Indigenous languages of Guiana are resisting" appeared in the Indigenous magazine Okamag. Two articles clearly point to the dominance of two languages, French and Guyanese Creole. We can "sound the alert for the preservation of Kali'na which is considered to be endangered" to the extent that "young people speak their mother tongue less and less" switching instead to French and Creole, considered by the author to be dominant languages. Another article makes the same claims: "At the dawn of the third millennium, I am saddened to see my mother tongue, Kali'na Aulan, disappearing under pressure from French and Creole." Furthermore, according to the author of the second article, the situation faced by Kali'na is the same in other countries where the language is spoken : "It is disappearing under pressure from Taki Taki x in neighbouring Surinam, and from Spanish in Venezuela."

Similarly, during a colloquium organized in Cayenne in May 2003 entitled "The writing of languages of Guiana", some participants brought up the fears of the Kali'na in the face of a Creole language hegemony, with the former accusing the latter of subjecting the language to the same domination which Guyanese Creole faced from French.

The overcautious or minorizing attitude of politicians and the media

The strong presence of French and, to a lesser extent, Creole in the Guyanese media (the majority of programs are in these two languages) majorizes them, even if over the last few years programs about Amerindian languages and English-based Creoles have started to appear. The Kali'na nonetheless generally believe that the media have no serious interest in their language. During a workshop testing the writing system adopted for Kali'na in 1998, not a single media representative was present to cover the event, despite invitations having gone out to them. These events, which take place every two months or so, are of great importance to the community, and the absence of the media was not appreciated by the organizers. xi Furthermore, Indigenous languages are only poorly represented, if at all, in the political arena, and completely absent from speeches made by non-Indigenous local politicians. As an example of this, during the 7 :30 PM news program by Tele Guyane on RFO on August 20 th 2003, in an interview on multilingualism in St Georges of Oyapock, the mayor of the small Eastern Guyanese town mentioned that St Georges has a tri-lingual population speaking French, Portuguese and Creole, and that efforts were being made to accommodate these three languages in school settings. The speech made no mention of another language spoken in St Georges, namely Palikur, which has a large number of speakers (Leconte, Caitucoli 2003).

The omission of any reference to this Indigenous language from the speech reinforces the hierarchy of official language/contact language(s), with the minorization of Indigenous vernacular languages.

Indigenous demands concerning the naming of towns (which recall the Kali'na origins of some of the current names-such as Kalani for Cayenne, Ilakupo for Iracoubo, etc) or buildings (such as a request to give a Kali'na name to a new middle school ) have led some speakers to comment on the limited response to such claims among politicians and the media: "In Guiana, people prefer large-scale public debates about changing the name of the Rochambeau airport, and attempt to stifle projects aiming to see Indigenous names given to buildings." (Okamag, 07.2003, 6)

Non-native minorizing speeches

According to a number of non-Kali'na social agents (postal workers, doctors, pharmacists, school principals) xii , there are several reasons which make it unnecessary to hire bilingual personnel for the benefit of the Kali'na-speaking population : "Kali'nas all speak French", "they give us no trouble", "they're a peaceful population". Pierre and Françoise [START_REF] Grenand | La Question amérindienne en Guyane française, éléments de synthèse[END_REF] have pointed out, concerning the reception of the foundation speech of the indigenous movement in Guiana, that "very few people could imagine that a Galibi xiii could be the author of such vigorous and violent words... Indigenous unfortunately live in the shadow of the image that they are timid people, populations of 'grown-up children'".

It seems to us that the widely circulated image of an "inoffensive population" leads to a minorization of their culture, as the group appears not to require any particular adaptations, unlike other populations present in Guiana.

Unlike Maroon children, who are often seen by the school administration as a "problem group" for disciplinary purposes, Kali'na children do not elicit discipline-related complaints from their teachers, and are seen as "very pleasant". Rather it is this very "absence of problems" which is an issue, and Kali'na children are criticized for not being outspoken enough in class. There are discussions about setting up means of intervening in problems relating to the language and culture of the Maroons, but none about the language and culture of the Kali'na. Nevertheless Kali'na children and Maroon children have the same failure rate at school, and the silence of the Kali'na in the classroom has been related to a cultural phenomenon known since the 1970's as the "silent Indian child" [START_REF] Dumont | Learning English and how to be silent: studies in Sioux and Cherokee classrooms[END_REF][START_REF] Philips | Participant structures and communicative competence : Warm Springs children in community classrooms[END_REF]).

The comments and attitudes of teachers, which often reveal a lack of training in the area of Guyanese cultural diversity [START_REF] Léglise | Usages et représentations linguistiques en milieu scolaire guyanais[END_REF], can lead to a minorization of languages even if this was not the intent of the speaker. For example, during a class-room observation at Saint-Laurent of Maroni, despite a teacher's desire to have the students' languages enter into the classroom, his questions were met with embarrassed silence. In a heterogeneous class, with a majority of Maroon children and five Indigenous children (2 Kali'na and 3 Arawak), the teacher asked how to say a particular word "in Indian". The Indigenous children had different linguistic backgrounds: the Kali'na individually told the observer that they spoke their language, but the Arawak said they no longer spoke the Amerindian language of their ancestors but rather an English-based Creole, Sranan Tongo, also spoken by the Maroon children in the class. The teacher's misunderstanding of the individual linguistic backgrounds of his students led him to some hasty conclusions: the Maroon children had answered his question satisfactorily, but not the Indigenous, and he turned to the observer and said: "You see, they don't even know how to say it in their language". This certainly does not help develop a valorization of the group of Indigenous children, who happen to be numerically inferior, nor an appreciation of their individual languages.

Declared practices of Kali'na-speaking children : an integration of several layers of minorization ?

A study carried out in a school setting, through individual semi-directive interviews with students around ten years old, showed that less than 4% of the studied population in the towns of Saint-Laurent of Maroni and Mana claims Kali'na as their first or second language [START_REF] Léglise | Langues frontalières et langues d'immigration en Guyane Française[END_REF]. On a numerical scale, then, Kali'na children are clearly a minority in both towns. One of the questions in the interview was a self-evaluation of their first language skills (defined as the language spoken before the beginning of schooling): "do you speak your first language a little, well, or very well?", "do you understand your first language a little, well, or very well?". The following table shows the percentages of positive responses: self-evaluation of the mother tongue was considered to be positive overall if the students' answers were "well or very well". In Saint-Laurent, only half the children with Kali'na as L1 claimed to speak the language well, unlike children claiming Haitian Creole or Aluku, other minority languages in this town [START_REF] Léglise | Contacts de langues issus de mobilités dans un espace plurilingue: approches croisées à St Laurent du Maroni. In Pratiques et représentations des contacts de langues dans des contextes de mobilité[END_REF].

L1 Positive self-evaluation for production

Positive self-evaluation for comprehension

Kali'na 50% 80% Aluku 78% 100%

Haitian Creole 100% 100%

Tab 1. Self-evaluation in three minority L1s in St Laurent

The rates are even lower for Kali'na-speaking children being educated in the town of Mana, where two thirds of the children claim they only speak and understand their mother tongue "a little". This seems to betray an attitude which minorizes the use of a language which is claimed as the L1 but which is diminished because the speaker claims: "I speak it, but not well, not really, etc" as if to be forgiven for speaking it and to not completely accept it. One

wonders to what extent these self-evaluations reflect an internalization for the children of the minorization of their language and culture on a more global level. One also wonders whether these attitudes reflect, at least partially, the negative evaluation by adults and elders of the competence levels of young speakers, a point to which we will return.

Taking into account the four preceding points, Kali'na appears to be a globally minorized language. This statement must however be further qualified with reference to two recent changes in different directions. On the one hand, we notice a tendency to deminoritize Kali'na through the media, thanks to the emergence of Kali'na media (a Kali'na-French bilingual newspaper and radio station, as well as a multilingual xiv radio station, Radio Galibi, broadcast from Surinam but available on the West Coast of Guiana) and also room for Kali'na xv on the local radio programs, whereas until recently, only Creole and French were used. xvi

On the other hand, we notice in the Kali'na language, but most specifically in the lexicon, the reinforced presence of French. The language is in the midst of a phase of massive borrowing from French, coupled with the loss of certain semantic categories already affected in previous generations (such as numerals, colors, or kinship terms). There are several explanations for this phenomenon: compulsory schooling since 1969 and the image of French as a prestige language (Renault-Lescure 1985) which allows speakers "a footing in the world of the Whites and Creoles who hold local power."

The minorization of Kali'na with respect to the particular situation in the village of

Awala-Yalimapo

The 900 inhabitants township of Awala-Yalimapo has a number of particularities which distinguish it from other Guyanese townships as well as from other Kali'na villages. These particularities have the potential to result in a majorization of the language of its inhabitants.

This township, almost a mono-community and rather isolated geographically, is the birth place of the Indigenous protest movement in French Guiana xvii , and some of the inhabitants are known at the local and national levels. Having become a symbolic place, Awala-Yalimapo has become a compulsory stop during any ministerial visit to Guiana [START_REF] Collomb | La question amérindienne en Guyane. Formation d'un espace politique[END_REF].

Kali'na is spoken almost everywhere there, not only at home and for shopping but at the town hall and post office, two main symbols of French Administration and French presence in Guiana. Some political speeches are in Kali'na and during the last municipal elections, the pamphlet for one of the two electoral lists was bilingual in French and Kali'na. An examination of exchanges between children at school [START_REF] Alby | Contacts de langues en Guyane française: une description du parler bilingue kali'na-français[END_REF]) reveals that Kali'na plays an important role in the playground and partly in the classroom, with bilingual speeches present at all times. The language is also present at school under the auspices of a project called "bilingual and cultural mediators" during which three hours are devoted to Kali'na language study every week. In Awala, Kali'na appears to be making inroads into domains usually reserved for French-or Guyanese Creole-in the rest of the department, to the point that we might posit the idea of a local minorization of French.

The specific situation in this township therefore has consequences on language use but also on instituted norms and related attitudes. We see, for example, that the inhabitants consider standard the way they speak, compared with other varieties of Kali'na spoken in French

Guiana. Thus a survey carried out in 1986 by Odile Lescure among the inhabitants of Awala-Yalimapo showed that a majority of adults there considered Awala and the neighbouring region to be the area where Kali'na is spoken best. Furthermore, the other varieties of Kali'na are being minoritized and their speakers are submitting to this minoritization, as seen in the following extract from an interview with a Kali'na woman (R) from the village of Yanou-Bellevue: "this is no good, I have made a mistake in Kali'na. The declared practices of Kali'na children from Awala show contrasting results on this point.

Results from an investigation in a school setting appear to confirm the fact that locally, minorizations seem to be reversible. In Awala, the numbers for self-evaluation for Kali'na production and comprehension are much higher than in other cities in the region, as two thirds of children claim to speak their language well or very well. As seen in table 2, the numbers jump from 36% or 50% positive self-evaluation to 76% for production xviii , which indicates a local majorization of Kali'na. Nonetheless, a rate of 76% positive self-evaluation is still considerably less than the very good results gotten for majority languages in other towns, which are closer to 100% (as is the case for speakers of French, Guyanese Creole, and Ndyuka, a majority English-based creole spoken in the West). There are therefore 24% of children in Awala who claim Kali'na as L1 who feel they can only speak it "a little", which supports the trend observed in the two cities in the region and which could again be explained as an effect of the comments of elders and adults.

Positive self-evaluation for production

Positive self-evaluation for comprehension

Kali claimed to speak French well or very well. We must therefore ask ourselves whether this relatively good evaluation of their competence levels in Kali'na, as well as the particular situation in this village, makes these children relatively linguistically insecure in French. This general tendency in Kali'na children-that which correlates a positive self-evaluation in one language with a negative evaluation in another xx -differs sharply from the observations made at this stage in the survey for responses of child speakers of other languages of Guiana.

Whatever the situation may be, Awala-Yalimapo is particular in the high value associated with Kali'na, with children claiming to speak Kali'na more than their peers, whether these be their friends or siblings. Indeed, 82% of children claim to speak Kali'na to their friends, and say that only 70% of their friends respond in the same language. These percentages are respectively 75% and 62% for siblings. There seems to be a positive connotation to declaring oneself a better speaker of Kali'na than one's friends and siblings.

All these elements lend support to the idea, on the one hand, of the local majorization of Kali'na and the local variety spoken there, and on the other hand, the resulting minorization of other spoken languages, such as French and other non-local varieties of Kali'na.

Interactions of youths as indicators of the minoritization or vitality of the language ?

In the bilingual speech of Kali'na children, we notice competition between French lexical items and Kali'na lexical items or older borrowings, the children preferring the French form even if they are familiar with the other. This process is manifested in bilingual speech in the form of insertions or inserted mixing, using terminology from [START_REF] Auer | From codeswitching via language mixing to fused lects: toward a dynamic typology of bilingual speech[END_REF]. This mixing is felt by a number of Kali'na to be an indicator of a process of minoritization. This is seen in the following extract from Okamag (2003): "Let us mention another serious problem: that of speaking one's language properly, with no borrowing, or as little as possible, of foreign words, which disfigure or denaturalize our language. [...]. When we hear some people speak Kali'na these days, there are sometimes more French or Creole words in their sentences than Kali'na. [...]. Some would be better off simply speaking French or Creole, rather than butchering their linguistic heritage!"

In children as well, mixing is felt to be very negative, as seen in the following comments by Kali'na thus appears for boys to be an in-group code, with a powerful identity-building function, as almost all exchanges with friends are said to be in Kali'na. Among girls, we see traces of the idea already found in the comments of elders and adults that it is better to speak both languages well rather than half-way: girls claim they never communicate partly in French but rather entirely in one language or the other. They point to a difference with their friends, who do mix (33% of communication from their friends is partly in French and partly These results conform to the actual practices of children, where we notice differences between the speech of girls and that of boys in the classroom and in the playground. [START_REF] Alby | Contacts de langues en Guyane française: une description du parler bilingue kali'na-français[END_REF] has

shown the net tendency for girls to use French in one situation and Kali'na in another, whereas for boys, code switching with a Kali'na matrix remains the same.

In contact situations, we often see a minoritization of mixing and code-switching in speech.

The observed mixed variety, however, is equally rich in meaning and different values. We can propose that the mixed variety in adolescent boys and young male adults is an in-group code, a variety with an identity-building value. Furthermore, it appears to us as a sign, in children learning their language, of exploratory and playful behaviour towards language [START_REF] Pochard | Profil(s) d'apprenant(s)[END_REF]. The laughter of two boys upon hearing the language mix produced by B attests to this:

B kama' [ go on !] JP do' (.) sikap(ˆ)i' (5) kama' [go on] B it 's a (.) PELO [it's a dog] (laughter)
Despite the fears of speakers in the face of language loss or death, which young speakers' speech represents to them, it is useful to observe in greater detail whether there is really a process of loss at the level of the language. Certainly at a lexical level we see many changes in several categories: nouns, adverbs, and, to a lesser extent, verbs. [START_REF] Thomason | Language contact: an introduction[END_REF] identifies different degrees of the process of borrowing and, in her opinion, a change is not major as long as the morphosyntactic structure is not affected. Renault-Lescure (2003) notes some changes at the morphosyntactic level in Kali'na, which we must examine to determine whether they represent an intrasystemic or intersystemic change.

Conclusion

In a situation of a "conflicting" multilingualism with official language, contact languages, and minority vernacular languages with very few speakers (as is the case for quite a few Indigenous languages in the world), language contact often eventually leads to the death of the minority languages involved. Of the twenty or so Indigenous languages spoken at the beginning of the period of colonization, only six remain in French Guiana, and in endangered conditions.

At the linguistic and microsociolinguistic levels, our conclusion regarding Kali'na is divided : language contact has led to numerous lexical changes and the question of whether language contact has brought about morphosyntactic change is still unresolved. Nonetheless, language games, alternations, bilingual speech as a code among adolescents [START_REF] Alby | Discours bilingue chez les jeunes kali'na d'Awala-Yalimapo: l'émergence d'un parler jeune ?[END_REF], with identitybuilding and cryptic functions, are signs of vitality in that the language is alive and functional as a linguistic resource [START_REF] Mondada | Pour une approche émique de la catégorisation des ressources linguistiques par les locuteurs[END_REF] for young speakers who, as the first generation attending secular schools, are experiencing the difficulties of drops in status and the creation of social outcasts [START_REF] Collomb | De l'indien à l'indigène. L'internationalisation des luttes amérindiennes en Guyane et les enjeux de l'autochtonie[END_REF].

At a global level, small victories have been won for outside recognition of Kali'na language and culture. At the community level, language use is maintained, and there is also the development of identity, linguistic and cultural claims, signs of increased awareness on the part of the speakers.

The specific situation in the Awala-Yalimapo community is paradoxical, with its majorization of Kali'na and the local minoritization of French and of mixed speech in some contexts. On the one hand, the community is a symbol of a linguistic and cultural conquest, an element of pride for the community, but on the other hand, this very same symbol participates in the minoritization that affects Kali'na speakers: the Awala variety sometimes appears as a standard variety, minorizing the varieties spoken outside the village as well as those of young speakers in the community.

The data we have presented call for the use of concepts which relate to processes, such as "minoritization" or "deminoritization", rather than static concepts such as "minorized language" or "minorization". These concepts are also useful in discussing the criteria for "endangered languages" proposed by UNESCO, such as intergenerational language transmission or use in existing language domains as well as in new domains and the media. It ii Particularly in some places, such as villages, markets, rivers.

iii «une langue minorée est une langue dont l'absence d'autonomie, de statut, de diffusion, de distribution fonctionnelle et de standardisation constituent des caractéristiques objectives issues de la description macrolinguistique. ». C' «est une langue dont les valeurs ne sont pas reconnues sur la scène interactionnelle par les locuteurs d'une langue sociolinguistiquement dominante (langue officielle, écrite, véhiculaire, scolaire, dotée de normes régulatrices et prescriptives), les locuteurs de la langue minorée se conformant pratiquement aux normes d'usage et d'interaction produites par leurs interlocuteurs. » iv From [START_REF] Collectif | Les langues de Guyane[END_REF].

v Un processus « régi par le développement même de l'interaction verbale, construit et à construire dans chaque instance de discours ».

vi Opinions vary on this point, some scholars considering that morphosyntactic criteria should be given more weight than lexical.

vii When the population becomes extinct, or when there are no remaining speakers for example. viii Traditionnaly a French-lexified creole, Guyanese Creole, and yet on the Western part of Guiana also Englishbased creoles such as Ndyuka or Sranan Tongo. ix The populations of African-descent who originate from Suriname (see [START_REF] Price | Maroons in Suriname and Guyane: How many and where[END_REF], also called Businenge.

x A term probably referring to Sranan Tongo but see Léglise and Migge (2004).

xi "RFO could not attend the second workshop, Saturday April 12th, which took place in Bellevue-Yanou and gave as an excuse that Bellevue was too far. If RFO had had to cover the preparation of aouara soup in Iracoubo, they would have been there, but a Kali'na workshop is somehow not worth their time. Thanks." (Okamag, 07.2003: 6) xii During non-directive interviews (see Léglise 2004b).

xiii Non-native name for the Kali'na until they reclaimed the use of their autonym. xiv Kali'na-Dutch-Sranan Tongo.

xv A popular Kali'na language program, on the radio at Awala, which gives local news. There is also a program on Palikur, another Indigenous language, as well as a radio presenter who is ethnically Palikur.

xvi This appearance of Indigenous languages in the media primarily concerns coastal languages, which raises the issue of the potential minoritization of languages of the interior.

xvii In 1982, the Indigenous protest movement emerged under the influence of a group of Kali'nas (from the generation educated in Catholic boarding schools), leading to, in 1983, the first explicit linguistic claim against the state which was deforming family names and refusing Indigenous first names. In 1984, during the first assembly of Indigenous in Guyana, a bilingual speech (written and oral) was produced, using "Ǹ" in writing, which differs from the French transcription system for the language. In 1998, after a number of workshops and collaboration with linguists, the Kali'na came to an agreement about their writing system, during the Yanou-Bellevue meeting. They created a workgroup about Kali'na language and culture at that time which is still active today. xviii We can also see a gap between production and comprehension, a phenomenon which is found in situations of immigration where, after a period of schooling and use of French by successive generations, there is a passive usage of L1 (comprehension) and less and less production. Kali'na children currently in CM2 (5th grade) correspond to the second schooled generation.

xix Girls and boys must be distinguished in Awala because unlike Kali'na L1 boys, who all claim they speak Kali'na very well, only 42% of girls claim they speak it very well. More than half the girls interviewed thought of themselves as only speaking Kali'na "a little". These numbers are much higher for comprehension. Boys claim to know French only poorly, whereas for girls, these numbers are higher by 20 to 35%! xx Similarly, if we look at children claiming Kali'na as L2, we are surprised to find that none of the investigated children claim to speak the language well or very well. These poor evaluations are often accompanied by very good self-evaluations for French, which is claimed as L1 (100% of interviewed children claimed to speak it well or very well).

  is very difficult to generalize along such lines, and to find clear answers concerning indicators of vitality or endangerment. The analyses of microsituations demonstrate quite clearly that linguistic practices vary tremendously from one family to another, from one village to another, or from one location within a village to another.Notesi See also the special issue of the International Journal of the Sociology of Language (2002) edited by J. A. Fishman: "Focus on Diglossia".

  't know (...) he knows (...) but we have to speak Kali'na (...) I mean (...) Kali'nas have an accent (.) but we' (.) we just speak Kali'na like that

	E	yes (.) but what does it mean to speak Kali'na well?
	R	well, I don
	E	but when you speak with the (.) with the people from Awala (.) they say things about
		the way you speak?
	R	they criticize it (quietly and with a smile)
	E	really? why do they criticize it?
	R	I don't know (2) because we don't speak (.) real KALI'NA' (...) because we mix it (...)
		that's why
	E	what do you mix it with'
	R	with Creole
	E	hmmm
	R	we mix Kali'na with Creole (...) but they criticize ours because THEY speak it well'

.. you see, the Indians of Awala say that the people of Iracoubo don't speak Indian well. They say that we mix it with Creole, whereas they speak Indian well." This comment led the researcher (E) to ask her to elaborate:

Positive self-evaluation in Kali'na L1 and French L2

  Furthermore, the positive evaluation rate in L1 xix correlates to a very low rate of positive evaluation in French L2 since only 35% of participating children in Awala(Kali'na L1)

		'na L1 French L2	Kali'na L1 French L2
	Mana	34%	66%	34%	66%
	St Laurent	50%	66%	80%	64%
	Awala	76%	35%	90%	60%
	Tab 2.

Exclusive use of Kali'na, among siblings or friends.

  This minoritization of bilingual speech is also seen in the declared practices of children from Awala: while only 18% of children claim their friends mix languages or alternate while speaking-low results which do not correspond to real practices we have just describednone of them admits to mixing himself. Students say they use either Kali'na (82%) or French (12%). The behaviour of girls and boys is different on this point, as seen in table 3:

	In interactions we see negative reactions when mixed forms are used, leading to a
	minoritization of bilingual speech:
	M-Y owi carbet		[a carbet]
	V	anekalikili anukutˆ pa wa français ta ?	[can't you say it in French?]
	V., a ten year old Kali'na girl:
	E	do you know anyone who speaks Kali'na poorly ?
	V	yes, M-Y
	E Communication what does it mean to speak poorly ? Friends / child	child / friends	Siblings / child Child / siblings
	V entirely in Kali'na she doesn't understand (.) she makes mistakes (.) when she doesn't know the Kali'na Awala girls 55% 77% 66% 77%
	word she says it in French Awala boys 90%	100%	72%	72%
	E	do you think you speak French well? Tab 3.
	V	no
	E	what do you not say right in French ?
	V	words
	E	do you sometimes mix French and Kali'na ?
	V	yes (.) it's a bad thing to mix
	E	who do you mix languages with?
	V	M-Y. (.) with J. (.) with the girls in my class

Use of French among siblings or friends

  in Kali'na, but they respond either in Kali'na, in 77% of cases, or in French, in 22% of cases, but never mixing the two), as seen in table 4. These claims are comparable to those made about communication among siblings, where Kali'na use seems to be stronger.

	Communication in	Friends to child Child to friends Siblings to child Child to siblings
	French (partly /
	entirely)
	Awala girls	33% / 0%	0%/22%	10% / 10%	0% / 10%
	Awala boys	0% / 0%	0% / 0%	9% / 0%	18%/ 0%
		Tab 4.