Olivier Lai

Mark Chun

Fatima Abdurrahman

Jessica Lu

Maxwell Service

Dora Fohring

Douglas R Toomey

Deconstructing turbulence and optimising GLAO using imaka telemetry

Keywords: optical turbulence, ground layer adaptive optics, dome seeing, tomography, turbulence profiling

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

INTRODUCTION

Imaka is a ground layer adaptive optics (GLAO) prototype/demonstrator installed at the University of Hawaii 88" telescope on Maunakea [START_REF] Lai | IMAKA: imaging from Mauna KeA with an atmosphere corrected 1 square degree optical imager[END_REF][START_REF] Chun | imaka: a ground layer adaptive optics system on Mauna Kea[END_REF]. The goal of this project is to analyze and optimize GLAO performance over large fields; indeed, the patrol field of the wavefront sensors is on the order of 0.4˚ (24' x 18') and the science field of view is on the order of 12'. Up to 5 Shack Hartman wavefront sensors can be positioned on guide stars; these have 8 x 8 subapertures of 12x12 pixels measuring 0.4" providing a relatively large 5" field, necessary for open loop and GLAO operation. The correction is provided by a 36-electrode bimorph mirror manufactured by CILAS, on loan from Subaru Telescope (it was the DM used in their first-generation facility AO system). Imaka was installed of the UH88" telescope in October 2016 and had its GLAO first light in November 2016. Observing runs took place in January, February and May 2017 (as well as March 2018 but data is not included in present analysis). A detailed description of the instrument can be found in [START_REF] Chun | [END_REF] and of its performance in [START_REF] Abdurrahman | Improved Image Quality over 10' fields with the `Imaka ground layer adaptive optics experiment[END_REF]. Here, we focus on the very useful tool of having 5 simultaneous wavefront sensors pointing in different directions to analyze the turbulence through its properties and its profile. This information can be also used to generate tomographic filters, such as a learn-and-apply method adapted from MOAO to GLAO applications. The measurements used were obtained in open loop, although the methods developed herein will be adapted to closed loop operation (by reconstructing pseudo-open loop measurements from the commands to the deformable mirror), where the sensitivity to altitude turbulence may be improved, but the detailed structure of the turbulence near the ground may be harder to extract as the ground conjugate but tilted DM will have a variable height of correction as a function of position in the pupil.

The analysis of the turbulence profile follows a method somewhat similar to that developed in [START_REF] Martin | William Herschel Telescope site characterization using the MOAO pathfinder CANARY on-sky data[END_REF] and used on the CANARY MOAO instrument on the William Herschell Telescope. Telemetry streams are recorded, containing all relevant real time AO variables of interest. These are usually of a length between 1024 and 2048 samples (sometimes multiple telemetry buffers were recorded sequentially, allowing to concatenate the circular buffers); as the sampling frequency is on the order of 180Hz, the buffers sample between 5.5 and 11 seconds of turbulence which may not be sufficient to properly sample the turbulence statistics. Nonetheless, we extract the centroids and compute the slopes covariance matrices: Cslopes = <m.m T >. We call the covariances of each wavefront sensor with itself the auto-covariance and the covariances of the wavefront sensors with each other the cross-covariances. The former contain the integrated the turbulence and the latter contain information on the ground layer and up to the altitude where the meta-pupil starts to become discontinuous (in practice, the highest levels are only poorly sampled as fewer subapertures are available for their measurement.

SLOPE COVARIANCE MATRIX MODEL

The analysis depends on being able to interpret the covariance matrices. To do so, we need a model against which to compare our data. Consider two subapertures of size d and a distance r apart. By virtue of Green's Theorem, we can write the slope vector s as:

(1)

The contour integral ∮ ϕx dy is the sum (i.e. normalized to the subaperture size, the average value) of the phase along the left edge of the subaperture ϕ<y>(x) minus the sum of the phase along the right edge, ϕ<y>(x + d). By virtue of the mean theorem, of the phase along the left edge can be approximated as the value of the phase halfway along the edge, point A for subaperture 1, point C for subaperture 2; similarly, the average value of the phase on the right side of the subaperture is approximated as the phase halfway along the subaperture, point B for subaperture 1, point D for subaperture 2, so we can write ∮ϕx dy ~ ϕy=A(x) -ϕy=B(x + d). To alleviate the notation, we write the x-slope of subaperture 1 as sx1 = ϕ(B) -ϕ(A) and the x-slope of subaperture 2 as sx2 = ϕ(D) -ϕ(C). We can then write the covariance matrix of the x-slopes as:

(2)

Recall that the phase structure function Dϕ is defined as: Similarly, we can compute the y-slope covariances <sy1 sy2> and the x-y covariances, although these contain less information at small separation. For the phase structure function, we can use either the Kolmogorov or the von Karman models, both of which have relatively straightforward analytical expressions. We can thus generate covariance matrices for layers at any altitude, simply by maintaining the proper geometrical relationship of the subapertures within each beam, through the distance r at the given altitude.

Direct inversion

It is possible to construct a large altitude-covariance matrix, where each column is the covariance matrix for a layer at a single altitude, unfolded into a vector. Such a matrix A would be of size [Nheight, (2 x Nsubaper x Nwfs) 2 ] for which a generalized inverse of the form A † = (A T .A) -1 A T can be found. In theory, it ought to be possible to multiply a measured covariance matrix-vector by this generalized inverse and obtain a vector containing the strength of each layer at each altitude of the model. Unfortunately, this method is limited both because the noise in the measurements propagates in the reconstruction, but also because the outer scale L0 varies with altitude. Specifically, it can lead to negative values of the turbulence strength when the off-diagonal response for an altitude layer is too narrow due to a small outer scale. One possible solution is to filter the tip-tilt from the measurements and compute a model covariance matrix with a van Karman spectrum and a small outer-scale, on the order of the telescope diameter, although this still does not prevent the turbulence strength to be negative at times. A disadvantage of filtering the tip-tilt is that information on the outer scale is essentially lost, although in the presence of vibrations, it usually required to filter it to reconstruct the turbulence profile. An advantage of this method is that once the model covariance matrices at altitude are calculated, extracting the profile from the measurements requires a simple matrix multiplication.

Covariance map fitting

The covariance matrices contain a lot of redundant information and the signal can be increased over the noise by averaging all the matrix elements that represent the same subaperture separation on the pupil. This is simply a reordering and averaging of the matrices but allows to reduce the size of the maps from (2 x Nsubaper x Nwfs) 2 to (2 x Nxsub x Nwfs) 2 , with Nsubaper = Nxsub 2 .

We first extract integrated properties of the turbulence, by using only the auto-covariance maps. We average the autocovariance maps of all the wavefront sensors under the assumption that the free atmosphere turbulence is independent of the direction of the guide star. We use a simplex algorithm to find the phase structure function that produces the best fit to the measured covariance maps, as given by equation 4. To simplify and constrain the phase structure function, we parametrize using the von Karman model, which has been shown to be representative of many different types of turbulence, indoors or outdoors [START_REF] Ziad | Lotuce: a new monitor for turbulence characterization inside telescope's dome[END_REF][START_REF] Chabé | The INdoor TurbulENce SEnsor (INTENSE) instrument[END_REF]. We use the formula given by Kellerer [START_REF] Kellerer | A Cookbook of Structure Functions[END_REF]: [START_REF] Martin | William Herschel Telescope site characterization using the MOAO pathfinder CANARY on-sky data[END_REF] with k=6.88. We then average the cross-covariances and the central peak of the covariance map will be due to the ground layer only. We use the same simplex algorithm to obtain the r0 and L0 of the ground turbulence. Once we have found the best fit to the ground layer covariance peak, we subtract it from the integrated covariance peak and estimate the free atmosphere turbulence strength and outer scale. Please verify that (1) all pages are present, (2) all figures are correct, (3) all fonts and special characters are correct, and (4) all text and figures fit within the red margin lines shown on this review document. Complete formatting information is available at http://SPIE.org/manuscripts Return to the Manage Active Submissions page at http://spie.org/submissions/tasks.aspx and approve or disapprove this submission. Your manuscript will not be published without this approval. Please contact author_help@spie.org with any questions or concerns. Single layers of turbulence at altitude will produce a decentered covariance peak. Using cross-covariance maps from which we have subtracted the ground layer and free atmosphere components, we try to estimate the turbulence profile by fitting our decentered altitude-dependent model covariance maps to these residuals. We use a priori information of the direction in which the secondary peaks are located for each pair of guide star, to increase the sensitivity, but the signal is usually quite tenuous, and it is therefore challenging to extract the outer scale at altitude. Increasing the number of samples in our circular buffers and obtaining very clean covariance maps could alleviate this issue. Note however, that since most of the data from the UH88" telescope is tainted by vibrations the accuracy of the methods only work reliably when tip-tilt is filtered, but L0 is consequently severely underestimated.

It should be possible to remove the vibrations and jitter of the circular buffers from their temporal properties; unfortunately, the temporal power spectrum of tip-tilt shows only a broad peak which is difficult to filter. Also, tip-tilt translates into a constant on the covariance maps, so subtracting a constant should correct this bias, although it is unclear how to estimate the contribution of the turbulence versus the vibrations, and this depends on both r0 and L0. If this could be done to any level of accuracy, then it would also be easy to simply estimate the strength of the turbulence from the modal variance spectrum, which it is not, unless using higher orders, where the effects of the outer scale become negligible.

Running a simplex optimization of r0 and L0 for each altitude is CPU intensive and probably not ideal to implement as a real time tool, although probably provides the best estimates of the turbulence profile (see e.g. Figure 5). Guesalaga et al. [START_REF] Guesalaga | Online estimation of the wavefront outer scale profile from adaptive optics telemetry[END_REF] have implemented a method where they compute covariance matrices at each altitude for various r0 and L0 and apply a sort of CLEAN peak finding algorithm. We have not implemented such a method but instead, for real time pruposes, we use predetermined outer scales for different altitudes. This method is obviously much faster but will generally overestimate the amount of turbulence near the ground.

It will be important to obtain good profiles, for example to examine the PSF variability as a function of the thickness of the ground layer. Also, in its current implementation, the learn and apply tomographic filter does require a profile to be optimized, as we use a simulated atmosphere to generate the tomographic filter.

Figure 4: Turbulence profile obtained from Simple fitting of the covariance maps with model covariance maps. We show the results for a Kolmogorov Spectrum on the top row, without (left) and with (right) filtering the tip tilt. The lower row shows the fit of a von Karman phase structure function for L0=20m (left) and 2m (right).

In the line plots, the full line is the integrated turbulence, the dashed line is the ground layer and the dotted line is the free atmosphere.

TURBULENCE PROFILING

In this section we present some of the turbulence profiles obtained with imaka during the February (for profiles) and May (for spatial properties of the turbulence) observing runs. No statistical study of the profiles has been performed and the data set is not very homogeneous (the three observing runs had very different atmospheric conditions, as well as different guide star constellations, and wavefront sensor orientations). The long-term goal is to have an automated tool that can reconstruct the profiles and populate an archive for statistical analysis and correlation with image plane data.

For comparison purposes, we include the measurements from MASS/DIMM obtained for the night of February 16 th for which we show the profile analysis. That nigh had strong ground layer turbulence and a free atmosphere seeing between 0.1 and 0.4".

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10703 -229 V. 10 (p.5 of 14) / Color: No / Format: Letter / Date: 6/4/2018 11:21:14 AM SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Comparison of methods for night of UT20170216

First, we show the profile obtained by direct inversion of the covariance matrix in Figure 3. We have a choice for the model to use and whether to filter the tip tilt or not. Note that filtering tip-tilt means that it is filtered from the covariance matrices in the fitting process, but not from results, so the estimated seeing contains the full turbulence. We find that a hybrid model with a von Karman phase structure function with L0=4m for altitudes below 700m and a Kolmogorov phase structure function above seems to minimize the artefacts, and the filtering of the tip tilt does not alter the results substantially, so this is encouraging. However, the layer at altitude 800m as well as the lack of free atmosphere turbulence (the highest layer represents the free atmosphere and is arbitrarily set to an altitude 3 times higher than the highest reconstructed layer). Next in Figure 4, we show the results of our model fitting algorithm (where we set the outer scale to a set value for the model). The main features of Figure 3 are still apparent but the profile is much cleaner, with less noise. Filtering tip-tilt increases the sensitivity to mid-altitude layers, because the off-centered peak become sharper and easier to fit. Reducing the outer scale also seems to increase the sensitivity to mid-altitude layers, for similar reasons. In the same figure we show a plot of seeing (integrated, full line; ground layer, dashed line and free atmosphere, dotted line) because these are each estimated independently of the actual profile. Estimates of these parameters are rather insensitive to which model is being used.

Please verify that (1) all pages are present, (2) all figures are correct, (3) all fonts and special characters are correct, and (4) all text and figures fit within the red margin lines shown on this review document. Complete formatting information is available at http://SPIE.org/manuscripts Return to the Manage Active Submissions page at http://spie.org/submissions/tasks.aspx and approve or disapprove this submission. Your manuscript will not be published without this approval. Please contact author_help@spie.org with any questions or concerns. Finally, we ran the Simplex fitting on the von Karman Model where both r0 and L0 were free parameters shown in Figure 5. Tip-tilt filtering is very time consuming because the covariance maps have to be converted into covariance matrices, for which we can build a tip-tilt filtering matrix. We then have to convert the covariance matrices back into a covariance maps, which prevents this method from being useful in real time. However, for a posteriori analysis, it is the most accurate and most useful as it provides not only the profile of r0 but also that of L0 (Figure 6), and we can start looking for systematic effects that one might expect, such as a smaller outer scale at low altitude.

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Seeing is formally defined as the FWHM at 500nm for a Kolmogorov PSF with given r0. However, a finite outer scale modifies (reduces) the FWHM obtained at the focus of the telescope. Since we have access to L0, we can correct for the effect of outer scale on seeing to predict the Image Quality (IQ), to compare directly to the FWHM of focal plane images. [START_REF] Ziad | Lotuce: a new monitor for turbulence characterization inside telescope's dome[END_REF] This correction factor was established by Martinez et al. [START_REF] Martinez | Atmospheric blur with finite outer scale or partial adaptive optics correction[END_REF] and is valid for L0/r0 > 20. However, we show in Figure 6 the actual r0 and L0 obtained as a function of time for both the covariance maps including tip-tilt and those with tip-tilt filtered. A few comments are needed to explain those profiles. The r0 profiles are shown clipped to below 1m; indeed, for r0 much larger than that, the signal of such a weak layer is effectively lost in the noise. Also, when r0 is large, the value of L0 is not very meaningful, since there is no peak in the covariance map to fit. The r0 profiles are qualitatively comparable to the seeing profiles obtained by direct inversion or fixed-model fitting, though we note that the resolution on the ground layer is improved when filtering tip-tilt (as would be expected) but also that the free atmosphere is better estimated when tip-tilt is filtered. The L0 profiles are interesting but rather speculative, as the SNR on the covariance maps obtained with 2048 samples is marginal to fit secondary off-axis peaks. When tip-tilt is included, there are times when the noise is too strong, and the fit is poor for the entire profile (e.g. at UT 6.5, 8.6 and 8.9). However, when filtering tip-tilt the values of L0 are consistently smaller than 20m. It is surprising that the L0 estimates show no correlation to the r0 profiles, as one would expect the noise on L0 to be larger when r0 is large.

The L0 profile is difficult to interpret. However, one thing appears clearly in the bottom left panel of Figure 6: The outer scale of the ground layer is large, quite opposite to what one might have expected. However, tip-tilt adds a constant pedestal to covariance maps, and the apparent large outer scale may be an artefact of the Simplex algorithm trying to fit this pedestal due to vibrations with a von Karman Structure Function, and the one that extends out furthest (effectively acting as a constant in the wings of the covariance maps) is for L0 ↝∞. Please verify that (1) all pages are present, (2) all figures are correct, (3) all fonts and special characters are correct, and (4) all text and figures fit within the red margin lines shown on this review document. Complete formatting information is available at http://SPIE.org/manuscripts Return to the Manage Active Submissions page at http://spie.org/submissions/tasks.aspx and approve or disapprove this submission. Your manuscript will not be published without this approval. Please contact author_help@spie.org with any questions or concerns.

10703

SPATIAL PROPERTIES OF THE TURBULENCE

To further characterize the turbulence, we want to infer its spatial properties, and this is best represented by the phase structure function. A von Karman phase structure function is able to represent most cases of turbulence by varying the outer scale, from ∞ for fully developed, Kolmogorov turbulence to L0~D for random walk, diffusive turbulence. However, since we have a model that allows to get the covariance from the phase structure function, we wanted to see if we could obtain the phase structure function empirically from the covariance maps, in other words, can we solve for Dϕ(r) in terms of <sx1 sx2> from equation 4? For r=0, we can write:

From which we deduce the following discrete sum:

We can then infer the phase structure function without having to parametrize it. This method however tends to amplify noise at long separations as it effectively performs an integration by linking up the variances of points B, C to get from A to D on Figure 1. Also, whereas we try to reconstruct the entire covariance map using our phase structure function-based model, this method only uses a one-dimensional cut through the covariance map to reconstruct the radial phase structure function, it is not trivial to generalize in two dimensions.

W reconstructed the phase structure function using the covariance matrix for the entire night of 2017/02/16, but instead of separating the ground layer and the free atmosphere from the cross-covariances and the difference between the autocovariance and the cross-covariance respectively, we tried to use a cleaner method whereby we obtained the integrated seeing from the auto-covariances as previously, but for the free atmosphere we subtracted the pairwise measurements of WFSn to those of WFSn+1: both contain the contribution of the ground layer which should subtract out perfectly, leaving a circular buffer with twice the variance of the free atmosphere. For the ground layer, we concatenated the various wavefront sensors into a single circular buffer and computed the covariance by matching different wavefront sensors:

Using such covariances, we reconstructed the phase structure function non parametrically from equation 8 and tried fitting it with either a variable exponent power law (of the form (r/r0) 𝛼 , with variable r0 and 𝛼) or with a von Karman spectrum with a finite outer scale. It was not possible to discriminate between these two models, especially given the coarse sampling of the phase structure function (equal to the number of subapertures, 8 in the case of imaka, and limited baseline imposed by the telescope diameter). In the following we report only on open loop von Karman fit values to alleviate the discussion.

In the case of a von Karman fit, it is also possible to fit covariance maps on the profile using our simplex algorithm. We can filter the tip-tilt from the data and from the model covariance maps and we can obtain estimates of r0 and L0 only from higher orders. We expect L0 to be smaller than in the case of the data with vibrations present in the tip-tilt signal. In theory it should be possible to compute the covariance map for a power law with tip-tilt subtracted but we did not pursue this, especially as GLAO PSFs seem to be very well fitted by a von Karman phase structure function with a small outer scale. In Table 1 and Figure 7 we compare the estimates of r0 and L0 obtained by fitting the tip-tilt-filtered covariance maps with a tip-tilt-filtered von Karman phase structure function to the r0 and L0 computed from fitting the one-dimensional empirical structure function obtained with equation 8. The presence of vibrations makes the interpretation of these curves difficult as it prevents a direct comparison of the tiptilt filtering as well as between x and y. This tool may become useful for systems with a greater number of subapertures, as it will improve the resolution of the reconstructed phase structure function. However, the noise reconstruction of the phase structure function will also increase due to the integration of noisy covariance maps. The phase structure function of tip tilt is a parabola (this is easy to see from first principles since D𝜙 2 (r) = <| 𝜙(𝜌)-𝜙(𝜌+r)| 2 >, but 𝜙(𝜌+r) = 𝜙(𝜌) + bx (with b=constant) for pure tip along x-axis, so D𝜙 2 (r) = <|bx| 2 > = b 2 x 2 and the same for tilt with y).

Unfortunately, it is difficult to separate which part of the tip-tilt comes from vibrations and which is part of the atmosphere. To try to circumvent that, we can also attempt to compute and fit the empirical phase structure function from covariance maps from which we have removed tip-tilt and compare it to fitting the tip-tilt filtered covariance map with a theoretical von Karman covariance map model from which we have not filtered tip tilt. This will certainly introduce a bias in the estimation of the outer scale, but we can at least check for agreement in r0 and between x and y. These results are presented in Figure 8 and Table 2.

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10703 -229 V. 8, and the dotted lines are von Karman fits with values reported in Table 2. The dashed lines are von Karman fits on the covariance maps directly, without reconstructing the phase structure functions. Left: free atmosphere, middle: ground layer and right, sum of left and middle panels. On the right panel, green and blue are integrated tip and tilt (respectively) from auto-covariances. The agreement between x and y is much better, indicating the impact of the jitter on the estimation of the phase structure functions.

This work will be greatly improved if we can reduce the telescope vibrations at the source, especially as the jitter is not restricted to a narrow frequency but is spread over a rather band and may even have a low frequency component that is most likely not well sampled given the length of our circular buffers. This jitter also affects the image plane analysis presented in the next section, which, if it were corrected at the source, would allow us to match the telemetry data with the delivered images at the focal plane.

Unfortunately, in the case of GLAO (or seeing limited), the MTF does not extend out to the cut-off frequency of the telescope, and the large separations on the phase structure function are dominated by numerical errors by taking the logarithm of an exceedingly small number. However, the small separations on the pupil are adequately estimated, as shown in Figure 9.

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Return the Manage Active Submissions page at http://spie.org/submissions/tasks.aspx and approve or disapprove this submission. Your manuscript will not be published without this approval. Please contact author_help@spie.org with any questions or concerns. It is more robust to try to fit the phase structure function in image plane using the Fourier Transform of equation 9. We then have to revert to a parametric phase structure function. In Figure 10, we show the r0 and L0 estimated for the run of May 2017 from image plane data (note that these images are elongated due to jitter and the analysis is only carried out on the narrow axis of the PSF). The range of r0 remains more or less unchanged between open and closed loop, but the outer scale is systematically reduced when the loop is closed (Figure 10, right). This suggests that the GLAO PSF may be well parametrized with a von Karman phase structure function with a small outer scale. Please verify that (1) all pages are present, (2) all figures are correct, (3) all fonts and special characters are correct, and (4) all text and figures fit within the red margin lines shown on this review document. Complete formatting information is available at http://SPIE.org/manuscripts Return to the Manage Active Submissions page at http://spie.org/submissions/tasks.aspx and approve or disapprove this submission. Your manuscript will not be published without this approval. Please contact author_help@spie.org with any questions or concerns. Since the fit in the image plane is more robust, we can also try to fit the PSF with a von Karman phase structure function to which we add a parabolic component in one dimension, representative of the broadening of the PSF due to vibrations. We let the amplitude and the angle of the parabola vary as free parameters of the fit and obtain the results shown inFigure 11. A major difference with the results obtained using the narrow axis of the PSF is that the r0 is smaller on average, for both open and closed loop images. The open loop L0 is also smaller, which makes the effect of the GLAO correction as a reduction of the outer scale less visible but compared toFigure 11, it is the estimated closed loop outer scale that remains relatively unchanged, while the open loop outer scale show more variation (indicating that some of the residual tip-tilt from the narrow axis PSF contributes to overestimating L0.

TAMING TURBULENCE

The reason why it is important to determine the turbulence profile and the spatial properties of the turbulence is to understand the physical properties of the turbulence, to determine whether the GLAO correction will be useful given the conditions but also to be able to produce optimal tomographic filters and understand which ones will perform better. We currently only consider implementing on two types of tomographic filters (described below), but the goal is to use the imaka prototype as a testbench for different algorithms.

Tomographic filters

We are developing two approaches to improve GLAO correction by attempting to reject the free atmosphere from the measurements. To do better than simple averaging, we need to include some a priori information, which helps to identify (and reject) turbulence not associated with the ground layer. Turbulence profiles and temporal filtering are such examples.

The learn and apply method, developed by Vidal etal, [START_REF] Martinez | Atmospheric blur with finite outer scale or partial adaptive optics correction[END_REF] is conceptually very simple: What is the matrix M which will produce the optimal measurements in the center (or any other part) of the field, given a set of measurements on the periphery (or anywhere else): mfield =MLA mWFS. We can multiply both side by mWFS T and take a time average to find: MLA = < mfield • mWFS > < mWFS • mWFS > -1 . The latter term is the inverse of the covariance matrix, which we have access to (though not always well conditioned), but the former term is harder to obtain. For MOAO applications, a truth sensor can be used at the location of the science target, but in GLAO, it is the average of the field, therefore only the measurements from the ground that we are interested in. We can try to average the measurements of the different WFS to obtain an estimate of the ground layer measurements, but these will still include the partially averaged FA from each direction. We propose to estimate mfield by open loop simulations, for which we need to know the thickness (and profile) of the ground layer. Knowing the outer scale is also useful. We draw many realizations of the phase screens maintaining the proper geometrical relationships between guide stars and layer height and can compute learn and apply tomographic filters in this way. We have tried this algorithm on the sky during the May 2017 run, but the results are not conclusive, as too much time had elapsed between obtaining measurements and producing the tomographic matrix.

Another promising method to improve GLAO correction is to use the spatio-temporal covariance maps to identify layers traveling at different speeds and generate a filtering matrix from these covariance maps. Such a filter should allow to isolate layers and their relative speed and only combine measurements from the current and N previous frames that contribute to the signal of these selected layers. We can observe these peaks in spatio-temporal covariance maps and work is ongoing to isolate them automatically and transform them into an optimal filter.

AIR-FLOW

GLAO performance will be strongly dependent on controlling the wings of the PSF to reduce the NEA as much as possible. The telescope, the dome and their interaction with the ground layer produce a complex environment for the turbulence and it is difficult to interpret data which can intermittently be very different from simple models. The wings of the PSF occur when there is an excess of high spatial frequencies with respect to low ones. This can occur if the outer scale of the turbulence is small, if the turbulence is not fully developed or in the case of diffusive turbulence. All these phenomena occur in the vicinity of or inside the dome, and this is a part of the environment we can control. To better understand the self-generated turbulence, we have developed a portable turbulence sensor, named AIR-FLOW [START_REF] Vidal | Tomography reconstruction using the learn and apply algorithm[END_REF]. Such a sensor will also be useful to control the dome vents of telescopes such as CFHT and Gemini, as well as to optimize the airflow in the domes of ELTs.

Airborne Interferometric Recombiner -Fluctuations of Light at Optical Wavelength is a turbulence sensor based on a nonredundant mask. Because the baselines are small, the induced turbulence phase perturbations are small. The variance of the phase of each frequency of the Fourier transform of the complex fringe pattern in the focal plane provides an estimate of the variance of the phase (within the linear range) at different separations and allows to measure the phase structure function directly. First tests using a small heat source show promising results (Figure 12). The instrument will be ruggedized and tested simultaneously with INTENSE/LOTUCE [START_REF] Ziad | Lotuce: a new monitor for turbulence characterization inside telescope's dome[END_REF][START_REF] Chabé | The INdoor TurbulENce SEnsor (INTENSE) instrument[END_REF] at Plateau de Calern before attempting to measure turbulence at the UH88" concurrently with imaka. Please verify that (1) all pages are present, (2) all figures are correct, (3) all fonts and special characters are correct, and (4) all text and figures fit within the red margin lines shown on this review document. Complete formatting information is available at http://SPIE.org/manuscripts Return to the Manage Active Submissions page at http://spie.org/submissions/tasks.aspx and approve or disapprove this submission. Your manuscript will not be published without this approval. Please contact author_help@spie.org with any questions or concerns.

CONCLUSION

We have presented ongoing work to use wavefront sensor telemetry from imaka to try to reconstruct the optical turbulence seen during our observations, both in its vertical profile as well as its spatial properties. We have presented three different methods to reconstruct the profile using an analytical model of the phase structure function (direct inversion, Simplex with fixed model, Simplex with variable r0 and L0). We have also presented the state of affairs of the estimation of the phase structure function both empirically and with a von Karman parametrization. Work is ongoing to separate the contribution of jitter using Moffat parametrization. We have also tried to estimate the phase structure function from image plane data and found that we cannot access it directly. We can however use a simplex fit to estimate r0 and L0 from the difference between the data and a theoretical PSF computed using a von Karman phase structure function. Because of the presence of vibrations, we can either use the narrow axis of the PSF or try to add a parabolic component to the phase structure function (the amplitude and angle of which are free parameters in the fit). The results of these algorithms are in the process of being integrated to a tomographic filter for GLAO. Finally, we report on the first measurements obtained with our AIRFLOW prototype, the goal of which is to chase down the turbulence inside the telescope dome and tube, and especially attempt to determine its physical properties.

With imaka and AIR-FLOW we hope to generate a coherent and quantitative account of the turbulence type and strength present in the telescope beam and to accurately match this detailed phase information to the focal plane images. Such a level of detail is required to understand and eventually be able to control the local environment for optimized image quality. We foresee this expertise will be especially valuable for ELTs, where the halo around the PSF will act like an extra source of background.

( 3 )

 3 By writing < ϕ(B) ϕ(D)> as 1/2 Dϕ(BD) -𝜎𝜙 2 , we can replace the covariances of equation 2 by the phase structure functions and all the variances cancel out:[START_REF] Abdurrahman | Improved Image Quality over 10' fields with the `Imaka ground layer adaptive optics experiment[END_REF]

Figure 1 :

 1 Figure 1: Two subapertures of side d and a distance r apart.

Figure 2 :

 2 Figure 2: MKAM Mass/DIMM measurement of the turbulence on the night of UT February 16 th 2017. The yellow box shows the time span during which we observed. The blue dots show the free atmosphere seeing, below 0.2" on average but with spikes up to 0.4". The red dots show the ground layer seeing, with two large spikes shortly after 06:00UT (20:00HST) and around 8:00UT (22:00HST).

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Figure 3 :

 3 Figure 3: Turbulence profiles for the night of UT20170216, obtained from direct covariance matrix inversion. On the top row from left to right, Kolmogorov, von Karman with L0=20m and L0=4m. The middle row shows the same turbulence models but with tip-tilt filtered. Both have systematic residual seen as horizontal and vertical persistent lines where the method simply fails. The bottom two panels show a hybrid model with a von Karman phase structure function with L0=4m for altitudes below 700m and a Kolmogorov phase structure function above.

Figure 5 :

 5 Figure 5: Turbulence profiles obtained by fitting the covariance maps to a von Karman Phase Structure function by Simplex, with r0 and L0 as free parameters at each altitude (top row, with tip-tilt, bottom row, tip-tilt filtered from covariance maps). On the right, we show the actual IQ, which differs from seeing.

Figure 6 :

 6 Figure 6: r0 (top) and L0 (bottom) profiles with tip tilt (left) and filtered (right). The color scale for r0 is clipped from 0 (black) to 1m (white) even though some values of r0 are estimated up to 20m. The color scale for L0 goes from 0 to 1000m (left) and from 2 to 10m (right).

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( 6 )

 6 as Dϕ(d) = Dϕ(-d) and Dϕ(0)=0. Similarly, for r=d, For r=2d, Etc…

Figure 7 :

 7 Figure 7: Phase structure functions. In all cases, full line is the phase structure function reconstructed from Equation8, dotted is the associated von Karman fit while dashed line is the tip-tilt filtered von Karman model fitted to the tip-tilt filtered covariance maps. The red and black curves show x and y for the free atmosphere (left), the ground layer (middle) and the integrated seeing (right); on this last panel green and blue are the integrated seeing (auto-covariances) and black and red are the sum of the left and middle panels. The fact that the red and blue curves, as well as the green and black curves almost overlap means that the integrated seeing matches well the sum of the ground layer and free atmosphere.

Figure 8 :

 8 Figure8: Tip-tilt filtered phase structure functions. As in Figure8, black is tip (x) and red is tilt (y). Thin full lines are the empirical reconstructed phase structure functions from Equation8, and the dotted lines are von Karman fits with values reported in Table2. The dashed lines are von Karman fits on the covariance maps directly, without reconstructing the phase structure functions. Left: free atmosphere, middle: ground layer and right, sum of left and middle panels. On the right panel, green and blue are integrated tip and tilt (respectively) from auto-covariances. The agreement between x and y is much better, indicating the impact of the jitter on the estimation of the phase structure functions.

1

 1 Phase structure function from image plane data To compare the wavefront sensor reconstructed phase structure function, we can try to obtain the phase structure function from focal plane image data. If we call the Optical Transfer Function (OTF) the autocorrelation of the pupil function and the Modulation Transfer Function (MTF) the Fourier transform of the PSF, then the following relations hold:

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Figure 9 :

 9 Figure 9: (left) Phase structure function obtained from image plane data on the night of My 18th 2017. Decreasing SNR from cyan to yellow, we can see the saturation of the phase structure function due to numerical errors of the logarithm of small numbers. The small separation regime is well fit by a Kolmogorov phase structure function with r0 of 0.25m.

Figure 10 :

 10 Figure 10: (Left) r0 and L0 obtained from fitting the narrow axis of image plane data for the entire May 2017 run; different colors indicate different nights. Stars are open loop and triangles are closed loop. (Right) r0 and L0 versus time from image data during the May 2017 run (same color coding). The open (star) and closed (triangle) loop r0 (bottom panel) are almost identical, but the outer scale (top panel: log scale showing some outliers, middle panel: linear scale) is systematically smaller when GLAO correction is turned on.

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Figure 11 ,

 11 Figure 11, left: r0 vs L0 and right: r0 (bottom) and L0 (middle and top) vs. time allowing for PSF broadening in one axis in the phase structure function by including a parabolic component, the amplitude and angle of which are free parameters of the fit.

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Figure 12 :

 12 Figure 12: First results of the AIRFLOW prototype. A point source is reimaged through a non-redundant mask (lower right inset) and produces the fringe pattern shown on the inset at the top left of the plot. A heat source was placed in the test area and produced the data shown on the right. The red line is a Kolmogorov spectrum.

  10703 -229 V. 10 (p.13 of 14) / Color: No / Format: Letter / Date: 6/4/2018 11:21:14 AM SPIE USE: ____ DB Check, ____ Prod Check, Notes:

  Please verify that[START_REF] Lai | IMAKA: imaging from Mauna KeA with an atmosphere corrected 1 square degree optical imager[END_REF] all pages are present, (2) all figures are correct, (3) all fonts and special characters are correct, and (4) all text and figures fit within the red margin lines shown on this review document. Complete formatting information is available at http://SPIE.org/manuscripts

Return to the Manage Active Submissions page at http://spie.org/submissions/tasks.aspx and approve or disapprove this submission. Your manuscript will not be published without this approval. Please contact author_help@spie.org with any questions or concerns. 10703 -229 V. 10 (p.8 of 14) / Color: No / Format: Letter / Date: 6/4/2018 11:21:14 AM SPIE USE: ____ DB Check, ____ Prod Check, Notes:

Table 1 :

 1 Average values of r0 and L0 for the night of UT February 16

	20170216	Integrated x	Integrated y	Ground Layer x	Ground Layer y	Free atmosphere x	Free atmosphere y
	r0 (m)	0.186	0.186	0.239	0.284	0.256	0.255
	L0 (m)	196.0	25.8	2.4 x10 5	58.7	13.1	10.6
	r0_noTT (m)	0.152	0.224	0.223	0.345	0.178	0.171
	L0_noTT (m) 5.1	10.1	6.3	57.3	2.7	2.3

th , 0217, obtained from fitting the reconstructed phase structure function from covariance maps by a von Karman phase structure function. It is worth noting that the vibrations were mostly in x, which may explain the large outer scale for the ground layer along that axis. It is maybe surprising that the outer scale of the free atmosphere is so small.

Table 2 :

 2 r0 and L0 estimated with tip-tilt filtered from circular buffers but not from model, leading to a bias in outer scale.

	20170216	Integrated x Integrated y Ground Layer x	Ground Layer y	Free atmosphere x	Free atmosphere y
	Tip-tilt filtered
	r0 (m)	0.117	0.131	0.197	0.196	0.175	0.189
	L0 (m)	3.5	4.0	3.9	3.9	3.5	3.9
	r0_noTT (m)	0.133	0.174	0.201	0.242	0.201	0.242
	L0_noTT (m)


Yves G Guglielmi

Pierre Henry

Christophe Nussbaum

Pierre Dick

Claude Gout

Florian Amann

Underground Research Laboratories for conducting fault activation experiments in shales

à la 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

Little is known about the rock mechanical characteristics of pre-existing tectonic faults and their influence on rock mass properties and behavior in clay rocks. Underground research laboratories provide exceptional conditions to observe unaltered fault zones in shales and to perform relatively well constrained experiments. Studies on induced macroscopic fracturing around tunnels in faulted shale indicate that reactivation of tectonic faults as a consequence of excavation-induced stress redistributions play an essential role in the development of the Excavation Damage Zone (EDZ) fracture network [START_REF] Bluemling | Development of an excavation disturbed zone in Claystone (Opalinus Clay)[END_REF][START_REF] Yong | A three-dimensional analysis of excavation-induced perturbations in the Opalinus Clay at the Mont Terri Rock Laboratory[END_REF][START_REF] Nussbaum | Analysis of tectonic structures and excavation induced fractures in the Opalinus Clay, Mont Terri underground rock laboratory (Switzerland)[END_REF][START_REF] Thoeny | Geomechanical analysis of excavation-induced rock mass behavior of faulted Opalinus Clay at the Mont Terri Underground Rock Laboratory[END_REF]. Hence, faults significantly alter the homogeneity of the rock mass in strength, stress and deformability, and thus have a significant effect on induced fracturing.

Another key point of interest is to evaluate the occurrence and processes controlling radionuclide or fluid (water, hydrocarbons, CO2) migration through the host rock, from the disposal system to the biosphere or out of the trap. Studies show that if fluid circulations in the undisturbed matrix are very slow (hydraulic conductivity of 10-14 to 10-15 m.s-1), the occurrence of clay-rich fault zones significantly enhance fluid circulation [START_REF] Guglielmi | ISRM Suggested Method for Step-Rate Injection Method for Fracture In-Situ Properties (SIMFIP): Using a 3-Components Borehole Deformation Sensor[END_REF]. Here we focus on two fault zones respectively affecting the Upper Toarcian shales at the Institut for Radiological protection and Nuclear Safety (IRSN) Underground Research Laboratory (URL) of Tournemire (Aveyron, France) and the Upper Toarcian-Aalenian Opalinus Clay in the Mont Terri Underground Rock Laboratory (St. Ursanne, Switzerland). We discuss some key architectural, stress and permeability characters of the two fault zones through the synthesis of different studies conducted at the two sites.

FAULT GEOLOGY

The Tournemire Laboratory is located 250m below ground surface in a monoclinic structure composed of three major stratigraphic units: a 250 m thick clay formation (Toarcian-Domerian) intercalated between 200m thick outcropping carbonate deposits of Bathonien-Bajocian-Aalenian and underlying Carixian-Sinemurian carbonates. The studied fault intersects the Toarcian shale formation being part of a complex kmscale fault network [START_REF] Dick | Estimating hydraulic conductivities in a fractured shale formation from pressure pulse testing and 3D modeling[END_REF]. The Mont Terri Laboratory is located in the southern limb of the SW-NE trending Mont Terri anticline which is a flat-ramp-flat structure thrust towards the NW (fault-bend fold) and where the studied fault, although called the "Main Fault" because it is the most deformed zone intersected by the laboratory facilities, is a minor splay (third order structure) of the thrust crossing the Opalinus clay formation, 300m below surface [START_REF] Nussbaum | Analysis of tectonic structures and excavation induced fractures in the Opalinus Clay, Mont Terri underground rock laboratory (Switzerland)[END_REF]. Both laboratories are dedicated to the study of the thermo-hydro-mechanical integrity of clay formations for application to the storage of nuclear deposits. The Tournemire shale is characterized by a low porosity (8-10 %) with a water content of 3-4% [START_REF] Matray | Desaturation and structure relationships around drifts excavated in the well-compacted Tournemire's argillite (Aveyron, France)[END_REF][START_REF] Constantin | Evolution of the structural fault permeability in argillaceous rocks in a polyphased tectonic context[END_REF] while the Mont Terri shale is characterized by a high porosity (12-18 %) and a water content of 7-8 % [START_REF] Amann | Insight into the brittle failure behavior of clay shales in unconfined and confined compression[END_REF][START_REF] Wymann | The influence of saturation on the uniaxial compressive strength of Opalinus Clay[END_REF].

The Tournemire Fault is a N05°-70-to-80°W anticlockwise strike slip fault crossing 0-to-10°N dipping Toarcian shale (Fig. 1a-b). This sinistral component on the fault is indeed the last observed movement in the recent stress field, however the main movement was clockwise [START_REF] Constantin | Fracturation et paléocirculations de fluide dans les formations géologiques de faible perméabilité matricielle : le cas des argilites de Tournemire[END_REF]. The fault zone has been intersected by several boreholes and outcrops in the URL's galleries walls (Fig. 1b). It is about 8-to-10 m thick with a 0.85-to-2.4 m thick anastomosing fault core (FC) and a dissymmetric fractured damage (FDZ) zone 2-to-3 times thicker in the western fault compartment than in the eastern one. Three families of fractures and faults affect the FDZ; respectively N110-to-140, 50°Nor-S, N160, 20-to-40W and N0-to-10, 70-to-80°W. The two first families display large calcite fillings while the third one is characterized by lustrated striated planes that may eventually contain thin gouge material. The fault core displays a high heterogeneity characterized by cataclastic zones of varying thicknesses from 0.4 to 0.01m intercalated with thin 0.1-to-0.2m highly fractured zones (Fig. 1b). In the cataclastic zones, shale clasts are bounded/coated by thin (0.001m) clay layers. In the highly fractured zones, most of the fractures are sealed with calcite. At the meter scale, contacts between breccia and highly fractured zones correspond to sliding surfaces. Relatively thick calcite veins are observed at the FDZ-FC boundary, and the FC calcite bulk content is lower than FDZ's, respectively of 5 and 10%. Outside the fault zone, the Toarcian shale is almost unfractured. The complex fault zone architecture is related to multiphase activations of the fault under two main tectonic stress regimes: normal faulting during Upper Jurassic to Lower Cretaceous [START_REF] Bles | Successive post-Variscan stress fields in the French Massif Central and its borders (western European plate): comparison with geodynamic data[END_REF][START_REF] Martin | Paleo-stresses inferred from macro-and microfractures in the Balazuc-1 borehole (GPF programme). Contribution to the tectonic evolution of the Cevennes border of the SE Basin of France[END_REF] followed by sinistral strike slip reactivation during the Eocene-Pyrenean compression. The Mont Terri Main Fault consists of a highly deformed zone of about 0.8-to-3m width composed of a complex network of single faults and scaly clays (Figure 1c). Around this thrust zone, the galleries are cut by many faults and fractures associated to the same deformation regime. Compared to Tournemire, what is called the "Main Fault" could correspond to Tournemire's fault core, the damaged zone being, in Mont Terri, much more extended or "hidden" by other satellite fault zones. Indeed, an increase in the fault density was observed close to the "Main fault" while boundaries of the FDZ are unclear. In the tunnel, the Main Fault plunges to the SE with a mean dip of about 50° and intersects the stratification which gently dips 35° to the SE. The detailed fracture network visible at the outcrop scale and strain intensity within the zone of the Main Fault is heterogeneous [START_REF] Nussbaum | Analysis of tectonic structures and excavation induced fractures in the Opalinus Clay, Mont Terri underground rock laboratory (Switzerland)[END_REF], characterized, as in Tournemire's FC, by zones with fault gouge, C'-type shear bands, meso-scale folds, micro-folds, numerous fault planes and apparently undisturbed parts (Figure 1c). Parts of the Main Fault comprise a 'scaly' fabric [START_REF] Laurich | Microstructural evolution of an incipient fault zone in Opalinus Clay: Insights from an optical and electron microscopic study of ion-beam polished samples from the Main Fault in the Mt-Terri Underground Research Laboratory[END_REF], where the rock splits progressively into smaller fish-like flakes. The different sets of faults in the Main Fault can be interpreted as Riedel P-and R-shears (Fig. 2e). The Main Fault can be interpreted as a shear fault-bend fold [START_REF] Nussbaum | Analysis of tectonic structures and excavation induced fractures in the Opalinus Clay, Mont Terri underground rock laboratory (Switzerland)[END_REF], which was passively steepened from 20° to the range of 40°-45° in sequence with the folding of the Mont Terri anticline over a basal ramp during the folding of the Jura belt in late Miocene. The offset of the Main Fault is inferred to be relatively small (~10 m) but difficult to determine precisely in absence of reliable markers. The Main Fault is an aborted blind thrust and is interpreted to be an internal thrust within the Opalinus Clay, soling at the base of the Opalinus Clay formation. The kinematics of the Main Fault have been inferred by paleostress analysis of slickenlines, showing a1 to be sub-horizontal, trending NNW-SSE for a reverse faulting mode [START_REF] Nussbaum | Analysis of tectonic structures and excavation induced fractures in the Opalinus Clay, Mont Terri underground rock laboratory (Switzerland)[END_REF]. This geometry agrees with the "distant push" or "Fernschub" theory of the Jura folding as a consequence of the propagation of the Alpine foreland towards NNW [START_REF] Laubscher | Die Fernschubhypothese der Jurafaltung[END_REF]. Kinematic criteria support the thrust movement towards the NNW with a slight dextral component. A second generation of oblique slickenlines attests that part of the deformation was probably not plane strain. P-T conditions at the time of the onset of motion of the Main Fault are inferred by [START_REF] Mazurek | Unravelling the multi-stage burial history of the Swiss Molasse Basin: integration of apatite fission track, vitrinite reflectance and biomarker isomerisation analysis[END_REF] to be about 55°C under an overburden of maximum 1000 m. In comparison, the P-T conditions of the Tournemire fault was 110° C under an overburden of 2.5 km [START_REF] Peyaud | Mid-Cretaceous uplift and erosion on the northern margin of the Ligurian Tethys deduced from thermal history reconstruction[END_REF].

The two studied faults show common architectural characteristics defined by a decameter thick fractured damage zone and a complex 1-to-2m thick fault core where meter scale Riedel planes bound cataclastic and/or highly fractured lenses. In the fault core, thin clay layers are observed in the Riedel planes or between the clasts in the cataclastic lenses showing that a reorganization of the clay minerals occurs during shear deformation. FDZ fractures are more or less sealed with calcite, and a decrease of the calcite content is observed in the FC.

FAULT STRENGTH/STRESS PROPERTIES

The in-situ stress state at the level of the Mont Terri URL was estimated by [START_REF] Martin | Measurement of in-situ stress in weak rocks at Mont Terri Rock Lab[END_REF] using three-dimensional numerical modeling and field data from stress-induced borehole breakouts and different stress measurement methods in the shale facies (Fig. 1a). Their analyses suggest a sub-vertical maximum principal stress direction which is steeply (70°) inclined towards SSW with a magnitude of 6.5 MPa, a sub-horizontal intermediate principal stress direction trending with 10° towards NW with a magnitude of 4 MPa, and a sub horizontal minimum principal stress direction trending towards NE with a magnitude of 0.6-to-2.9 MPa (Fig. 1a). During the excavation of a gallery across the Main Fault, excavation-induced displacements of the gallery wall and deformations of natural pre-existing faults were continuously monitored [START_REF] Thoeny | Geomechanical analysis of excavation-induced rock mass behavior of faulted Opalinus Clay at the Mont Terri Underground Rock Laboratory[END_REF].

Gallery Meier (GM) when activating the Tournemire fault. We used the dihedral method [START_REF] Cornet | Détermination du champ de contrainte au voisinage du laboratoire souterrain de Tournemire[END_REF] to determine the compression P and tension T zones between the fault plane and the auxiliary plane.

Data revealed that the rock mass response is substantially governed by both the rock anisotropy and the kinematic failure of individual fault planes. Fault plane reactivations mainly occured at the tunnel face (Figure 2a), crown and the invert, and less in the sidewalls and at larger depths in the rock mass, respectively, because of the unfavorable orientation of the planes towards excavation induced stress perturbations and the attenuation of the excavation induced stress magnitude perturbation. The rock mass response was dominated by extensional fracturing through the intact rock matrix resulting in large displacements (up to 40 mm) adjacent to fault zones. Considering a bilinear Mohr-Coulomb failure criterion deduced from direct shear laboratory tests on fault planes in a three-dimensional finite differences representation of both the gallery and the fault zone geology, [START_REF] Angelier | Tectonic analysis of fault slip data sets[END_REF] calculated that such displacements were induced by a minimum principal stress decrease of about 1 MPa and maximum principal stress increase of about 2 MPa at 0.3m depth from the gallery walls close to the fault zones. Using about the same state of stresses and fault properties, characterized by a cohesion of 0.2-to-0.6 MPa and a peak static friction angle of 22°, Main Fault slip tendency analyses confirmed that given the Mt Terri's range of pore pressures of about 2 MPa (far from the galleries), the fault is close to a critical state for normal slip and dilation on a varying activated area of 1425 -to -1460 m2.

In Tournemire, the actual state of stresses was determined with a series of leak off tests performed in a vertical 180 m deep borehole located in the intact shale 50 m from the fault zone [START_REF] Cornet | Détermination du champ de contrainte au voisinage du laboratoire souterrain de Tournemire[END_REF], revealing a strike slip regime at the experiment depth characterized by o1= 4±2 MPa, horizontal and oriented N162°±15°E, o2= 3.8±0.4 MPa, 7-8° inclined from vertical in the N72° direction and o3= 2.1±1 MPa, 7-8° inclined from horizontal in the N72° direction (Figure 1a). An inclined borehole was drilled to intersect the fault zone at a distance of about 10-to-15m from the tunnel where the fault was pressurized using a straddle packer system defining a 2.4 m long injection chamber normal to the fault surface (Fig. 3b). Several fault zone intervals were tested in the fault damage zone and in the fault core. A three-dimensional displacement sensor set in the chamber allowed continuous synchronous coupled monitoring of fault movements, injection pressure and flow rate [START_REF] Guglielmi | ISRM Suggested Method for Step-Rate Injection Method for Fracture In-Situ Properties (SIMFIP): Using a 3-Components Borehole Deformation Sensor[END_REF]. An anticlockwise 0.05-to-0.22 mm fault slip was captured in good accordance with the orientation of preexisting fault surface towards the principal stresses. Depending on the tests, the fault activation occurred at injection pressures of 1.5-to-3.2 MPa revealing the effects of both a heterogeneity of the stress tensor within the fault zone and strong strength contrasts between the FDZ and the FC characterized by peak static frictions of 34 and 22° and cohesions of 0.5 and 0 MPa respectively. Experiments conducted in both URLs show similar results given the highly similar principal stress magnitudes but different stress regimes respectively normal in Mt Terri and strike slip in Tournemire. Faults are activated at stress variations that are within the range of the perturbations induced by galleries excavations. The same 22° peak static friction properties of the FC were deduced from laboratory tests and numerical analyses in Mont Terri, and from the field fault activation experiment in Tournemire. In detail, friction values much higher (34°) were obtained in the Tournemire's fault FDZ and same range of cohesion was found. These experiments show that faults may easily reactivate during tunnel excavation if they are favorably oriented in respect to the in-situ state of stress. Reactivation may not be simple since a significant friction contrast appears between the shale fault core and damage zone.

FAULT PERMEABILITY VARIATIONS

To assess the transport properties associated with the Tournemire fault, a modular mini-packer system (MMPS) hydraulic testing was conducted in multiple boreholes to characterize hydraulic conductivities within the formation. Pressure data collected during the hydraulic tests were analyzed using the nSIGHTS (ndimensional Statistical Inverse Graphical Hydraulic Test Simulator) code to estimate hydraulic conductivity and formation pressures of the tested intervals. Preliminary results indicate hydraulic conductivities of 5.10-12 m.s-1 in the fault core and damaged zone, and 10-14 m.s-1 in the adjacent undisturbed shale. At Mont Terri, a compilation was done of all data concerning the permeability obtained from hydraulic packer tests performed in different boreholes within the framework of various experiments [START_REF] Nussbaum | Compilation of Kvalues from packer tests in the Mont Terri rock laboratory[END_REF]. The statistical analysis of data shows that the hydraulic conductivities of intact shale and fault zones are ranging between 9 x 10-15 and 6 x10-12 m.s-1. All these tests were performed at low imposed pressure below 1 MPa, considering that no movement of the fault was occurring.

There are few field data on stress induced hydraulic conductivity variations of clay faults. In the laboratory, low 1-2 MPa effective normal stress variations induced hydraulic conductivity variations of clay fractures may result from a complex combination of clay minerai swelling, consolidation and creep [START_REF] Bastiaens | SELFRAC : experiments and conclusions on fracturing, self-healing and self-sealing processes in clays[END_REF][START_REF] Gutierrez | Stress-dependent permeability of a mineralised fracture in shale[END_REF]. Some laboratory experiments conducted on Opalinus clay fractures by [START_REF] Cuss | Fracture transmissivity as a function of normal and shear stress: First results in Opalinus Clay[END_REF] show that conductivity may decrease initially at low shear strain then increase at high strains through fracture generation out of the main shear plane. Recently, a fault pressurization experiment has been conducted in the core of Tournemire fault (location in Fig. 2). Water pressure was increased step-by-step in a straddle packer interval set across the fault core. At each pressure step, pressure was held for a given amount of time (about 250 seconds), then increased to the next step until reaching the fault opening pressure which is when pressure 'break-over" occurs i.e. large increase in flow rate results in small pressure increases. A 300 seconds long constant pressure was then held at a pressure above the fracture opening pressure. Then a step-down procedure was performed until the pressure returned to its initial value. Pressure and flow rate-vs-time curves show a complex fault core leakage activation (Fig. 3a) characterized by transient fiow rate pulses occurring between 1.5 and 2.2 MPa, followed by a no-leakage period and the progressive transition from transient pulses to quasisteady state flow at 3.6MPa. Using an analytical pseudostate solution of the radial diffusivity equation for a relatively incompressible fluid to describe the pressureversus-flow rate curve above 3.6MPa yields a 10-to-30x10-6 m.s-1 permeability value at fault opening. Below 3.6 MPa, no steady state flow was measured into the fault because of the relatively low sensitivity of the straddle packer apparatus at low injected pressures. Taking the values at low stress given by [START_REF] Gutierrez | Stress-dependent permeability of a mineralised fracture in shale[END_REF] from tests conducted in the same fault, we conclude that the effective stress variation in the fault induced a five orders of magnitude permeability increase from 5.10-12 to 1-to-3x10-7 m.s-1. Interestingly, if we consider the state of stresses in the fault core with strength properties characterized by no cohesion and a peak static friction angle of 22°, we can calculate that this permeability increase should occur at shear failure for a 1.8MPa pressure variation (Figure 3b). This value matches the pressure when the transient pulse of flow rate initiates (at 1.5-to-2.2 MPa in Fig. 3a) but does not match the significant quasi-steady-state flow rate regime occurring for injection pressures much higher than the yield point in the Mohr-Coulomb diagram (Figures 4a andb). Such observations highlight that permeability variation of the fault core is related to complex mixed failure modes associated with both the microscopic evolution of fabric elements in clay rich fault gouge and to the macroscopic reactivation of pre-existing discontinuities (potentially the Riedel faults as shown in Fig. 3b).

CONCLUSIONS

Both underground research laboratories at Tournemire and Mont Terri provide access to unaltered fault zones in shales. Although the geological history of the faults is different, some common architectural characteristics may be observed: a fractured damage zone where many fractures are sealed with calcite and a core zone where intense deformation is characterized by complex mechanisms of cataclasis, clay minerals reorientation and macroscopic scale Riedel planes. It results in a high potential instability of some faults elements to relatively small stress variations within the range of magnitudes of the ones induced by galleries excavation. Such instability is explained by the orientation of fault surfaces to stress and by high contrasts in strength properties characterized by a low peak static friction of the fault core and cohesive sealed-with-calcite fractures of the fault damage zone. Understanding permeability variations related to shale faults activation appears as one of the most promising challenge that can be studied in the URL's. Indeed, permeability tests conducted at pore pressures that cannot induce any fault deformation tend to show relatively reduced contrasts of values between fault and intact shale permeability. Recently, URL facilities allowed one to conduct local suprahydrostatic pore pressure increases in a fault while many hydrogeophysical parameters were monitored close to the source, showing permeability increase of several orders of magnitude at low strain rates on critically stressed shale faults. These experiments may thus help refine the physics of fluids hydromechanical effects during shale fault reactivation, opening new experimental perspectives to relate these effects to aseismic-to-seismic fault movements.

Fig. 1 .

 1 Fig. 1. (a) Stereographic projection of the main fault planes and state of principal stresses (dark is Tournemire, grey is Mont Terri); (b) Fault core-damage zone boundary (red line) outcropping in the Tournemire gallery wall and CT-scanned view of the same boundary (yellow line) on a core of the borehole intersecting the fault. Core shows thin black zones with reoriented clay material that alternate with brecciated (cataclastic) zones; (c) Main Fault outcropping in the Mont Terri gallery wall and (d) Riedel faults network conceptual model of Mont Terri fault core.

Fig. 2 .

 2 Fig. 2. (a) -Conceptual model of [19] which illustrates the generalized structural and kinematic relationships between pre-existing tectonic faults (RF) and excavation-induced fractures (IF) around the Mont Terri gallery intersecting the Main Fault (bedding is in grey dotted lines parallel to the SSEdipping faults (red lines), excavation induced fractures are shown by grey lines); (b) -Slip vector orientation and modulus measured above the fault opening pressure point (FP)when activating the Tournemire fault. We used the dihedral method[START_REF] Cornet | Détermination du champ de contrainte au voisinage du laboratoire souterrain de Tournemire[END_REF] to determine the compression P and tension T zones between the fault plane and the auxiliary plane.

Figure 3 :

 3 Figure 3: (a) -Pressure and Flow rate time variations during the injection in the Tournemire fault core; (b) -Mohr-Coulomb representation of the strength and state of stresses during the test.