Raphaël Paris

Simon Falvard

Catherine Chagué

James Goff

Samuel Etienne

Pascal Doumalin

Sedimentary fabric characterised by X-ray tomography: A case-study from tsunami deposits on the Marquesas Islands, French Polynesia

Keywords: Grain size, Marquesas Islands, sedimentary fabric, tsunami deposits, X-ray tomography

X-ray tomography is used to analyse the grain size and sedimentary fabric of two tsunami deposits in the Marquesas Islands (French Polynesia, Pacific Ocean) which are particularly exposed to trans-Pacific tsunamis. One site is located on the southern coast of Nuku Hiva Island (Hooumi) and the other one is on the southern coast of Hiva Oa Island (Tahauku).

Results are compared with other techniques such as two-dimensional image analysis on bulk samples (particle analyser) and anisotropy of magnetic susceptibility. The sedimentary fabric is characterised through three-dimensional stacks of horizontal slices (following a vertical step of 2.5 mm along the cores), while grain-size distribution is estimated from twodimensional vertical slices (following a step of 2 mm). Four types of fabric are distinguished: (a) moderate to high angle (15 to 75°); (b) bimodal low-angle (<15°); (c) low to high angle with at least two different orientations; and (d) dispersed fabric. The fabric geometry in a tsunami deposit is not only controlled by the characteristics of the flow itself (current strength, flow regime, etc.) but also sediment concentration, deposition rate and grain-size distribution.

There is a notable correlation between unimodal high-angle fabrictype (a)and finelyskewed grain-size distribution. The two tsunami deposits studied represent two different scenarios of inundation. As demonstrated here, X-ray tomography is an essential method for characterising past tsunamis from their deposits. The method can be applied to many other types of sediments and sedimentary rocks.

INTRODUCTION

Despite considerable progress over the last decade, the interpretation of tsunami deposits still suffers from a lack of both qualitative and quantitative criteria that would allow for a better description of flow characteristics (e.g. [START_REF] Chagué-Goff | Expanding the proxy toolkit to help identify past events -Lessons from the 2004 Indian Ocean Tsunami and the 2009 South Pacific Tsunami[END_REF][START_REF] Goff | Progress in palaeotsunami research[END_REF][START_REF] Sugawara | Numerical models of tsunami sediment transport current understanding and future directions[END_REF][START_REF] Falvard | X-ray tomography of tsunami deposits: towards a new depositional model of tsunami deposits[END_REF]and references therein). Little attention has been paid to the fabric of tsunami deposits. The fabric of a sedimentary formation corresponds to the spatial arrangement of its grains [START_REF] Sander | Gefügekunde der Gesteine mit besonderer Berücksichtigung der Tektonite[END_REF] and its value in deducing depositional processes has been emphasised by early workers (e.g. [START_REF] Dapples | Orientation analysis of fine grained clastic sediments[END_REF][START_REF] Rusnak | Orientation of sand grains under conditions of unidirectional flow[END_REF][START_REF] Hand | Grain orientation in turbidites[END_REF][START_REF] Rees | The production of preferred orientation in a concentrated dispersion of elongated and flattened grains[END_REF]. Anisotropy of magnetic susceptibility (AMS) is commonly used to infer fabric patterns from the magnetic fabric (e.g. [START_REF] Rees | The Use of Anisotropy of Magnetic Susceptibility in the Estimation of Sedimentary Fabric[END_REF][START_REF] Taira | The comparative reliability of magnetic, photometric and microscopic methods of determining the orientations of sedimentary grains[END_REF].

The technique has been applied to different types of sedimentary rocks and soft sediments, including tsunami deposits (e.g. [START_REF] Wassmer | Use of anisotropy of magnetic susceptibility (AMS) in the study of tsunami deposits: Application to the 2004 deposits on the eastern coast of Banda Aceh, North Sumatra, Indonesia[END_REF][START_REF] Cuven | High-resolution analysis of a tsunami deposit: Case-study from the 1755 Lisbon tsunami in southwestern Spain[END_REF][START_REF] Schneider | Using Magnetic Fabric to Reconstruct the Dynamics of Tsunami Deposition on the Sendai Plain, Japan -The 2011 Tohoku-Oki Tsunami[END_REF][START_REF] Kain | Determining flow patterns and emplacement dynamics from tsunami deposits with no visible sedimentary structure[END_REF]. Direct measurements of grain orientation on thin sections under the microscope give more reliable results, but the geometry of the plane of section introduces uncertainties and the technique is time-consuming [START_REF] Taira | The comparative reliability of magnetic, photometric and microscopic methods of determining the orientations of sedimentary grains[END_REF]. As stated by [START_REF] Rees | The Use of Anisotropy of Magnetic Susceptibility in the Estimation of Sedimentary Fabric[END_REF]: "any rapid method of finding preferred grain orientation is, therefore, potentially of great interest".

The observed grain orientation in sediment reflects a final state of deposition and depends on different parameters related to sediment (grain size, shape, density, sorting, etc.), bed roughness and the flow itself (regime, sediment concentration, etc.). The primary fabric corresponds to the grain preferred orientation during transport and is particularly wellpreserved in highly-concentrated flows that settle rapidly. When grains settle more slowly as suspension fallout, they might be reoriented by rolling or sliding near the bed [START_REF] Gupta | An experimental study of fabric development in plane-bed phases[END_REF]. Thus, the observed fabric does not always reflect the primary fabric. X-ray tomography (XRT) provides a unique opportunity to characterise the three-dimensional structure and texture of rocks and sediments, as demonstrated by its recent application to tsunami deposits [START_REF] Falvard | X-ray tomography of tsunami deposits: towards a new depositional model of tsunami deposits[END_REF][START_REF] Falvard | Scenario of the 1996 volcanic tsunamis in Karymskoye Lake, Kamchatka, inferred from Xray tomography of heavy minerals in tsunami deposits[END_REF]. This study characterises in detail the vertical variations of grain size and clast fabric of tsunami deposits in the Marquesas Islands (French Polynesia) using 2D and 3D analyses at the grain-scale.

TSUNAMIS IN THE MARQUESAS ISLANDS

The Marquesas Islands are located in French Polynesia (South Pacific Ocean) ca 1400 km north-east of Tahiti and ca 4700 km from the nearest continent (Fig. 1). Over the past 26 kyr, four successive phases of coral reef growth were interrupted by periods of sea-level rise and reef drowning and thus the reefal shelf around the islands is poorly developed [START_REF] Cabioch | Successive reef depositional events along the Marquesas foreslopes (French Polynesia) since 26 ka[END_REF][START_REF] Montaggioni | Récifs coralliens et paysages géomorphologiques des îles Marquises[END_REF]. The youngest reef terrace, dated 9 to 9.6 ka, is now at 60 to 55 m water depth on the foreslope of the islands. Reef building has stopped over the past 9 ka.

The largest islands have a shield-volcano morphology dissected by deep valleys that exit to the sea as narrow open bays. The coastline of the Marquesas Islands is dominated by rocky coasts with plunging cliffs or fringing shore platforms, whereas beaches and dunes are found at the mouth of the river valleys and embayments.

Due to its central position in the Pacific Ocean, the archipelago is particularly exposed to trans-Pacific tsunamis caused by earthquakes in Japan (2011), Kamchatka (1952), the Aleutian (1946 and[START_REF] Rusnak | Orientation of sand grains under conditions of unidirectional flow[END_REF], Alaska (1964), Peru (1868Peru ( , 1996Peru ( and 2001) ) and Chile (1837Chile ( , 1877Chile ( , 1922Chile ( , 1960Chile ( and 2010)). Since the narrow bays are not protected by outer reefs, their morphology is prone to tsunami amplification [START_REF] Hébert | Tsunami risk assessment in the Marquesas Islands (French Polynesia) through numerical modeling of generic far-field events[END_REF]. Tsunamis are part of the Marquesian culture and the local expression 'tai toko' refers to catastrophic wave events [START_REF] Candelot | Tai Toko ! ou l'imminence d'un cataclysme dans les Marquises[END_REF]. The oldest tsunami reported in the area dates back to 1806 [START_REF] Candelot | Tai Toko ! ou l'imminence d'un cataclysme dans les Marquises[END_REF], and since 1837 there have been 17 reported tsunamis, seven of them with wave runups exceeding 3 m [START_REF] Schindelé | L'aléa tsunami en Polynésie française : synthèse des observations et des mesures[END_REF][START_REF] Sladen | Evaluation of far-field tsunami hazard in French Polynesia based on historical data and numerical simulations[END_REF][START_REF] Reymond | The 2010 and 2011 Tsunamis in French Polynesia: Operational Aspects and Field Surveys[END_REF]. The 1946 Aleutian tsunami impacted all of the islands, with runups up to 18 m in the valleys [START_REF] Schindelé | L'aléa tsunami en Polynésie française : synthèse des observations et des mesures[END_REF]. No tropical cyclone has been ever recorded in the Marquesas Islands Archipelago since the onset of meteorological observations in 1831. This is explained by the geographical proximity of the equator inhibiting the organisation of convective clouds in spiral bands [START_REF] Larrue | Les îles de Polynésie française face à l'aléa cyclonique[END_REF][START_REF] Laurent | Historique des cyclones de Polynésie française de 1831 à 2010[END_REF].

Tsunamis have left their mark on the coastal landscapes of the Marquesas Islands. During a field survey in June 2012 the present authors noted numerous traces of sediments, driftwood and erosion by extreme sea waves at altitudes up to 36 m above sea level (a.s.l.) (Fig. 2: coral conglomerate at Hanateio, eastern coast of Tahuata Island). Coral boulders in the valleys (for example, Hooumi in Nuku Hiva and Hanamenu in Hiva Oa) represent another compelling line of evidence for tsunami inundation since there are no elevated reefs in the Marquesas.

Trenches made in low-energy morpho-sedimentary systems revealed fine-grained (mud to sand) deposits fulfilling the typical trench-scale criteria of tsunami deposits (e.g. [START_REF] Shiki | Characteristic features of tsunamiites[END_REF][START_REF] Goff | Progress in palaeotsunami research[END_REF]. The main sedimentary facies observed are laminated sands in a discontinuous contact overlying soil or lagoonal muds that are reworked as rip-up clasts and mud lines. Some of the sedimentary successions observed have recorded several tsunamis (for example, Haatuatua in Niku Hiva and Taipivei in Hiva Oa), including the 2011 Japan tsunami deposits that were still well-preserved in June 2012. Satellite imagery of Haatuatua Bay (eastern coast of Nuku Hiva) before and after the 2010 and 2011 tsunamis illustrates the morphological imprint of recent tsunamis on coastal landscapes (Fig. 3). A comparison between images from June 2005 and April 2013 shows erosion of the lower sand ridge, driftwood deposition up to 9 m a.s.l. (Fig. 2) and progression of the sand washover fans inland at altitudes up to 15 m a.s.l. (Fig. 3). There are no runup estimates available for the eastern coast of Nuku Hiva, but [START_REF] Reymond | The 2010 and 2011 Tsunamis in French Polynesia: Operational Aspects and Field Surveys[END_REF] reported maximum runups of 3.8 m and 4.5 m for the 2010 and 2011 tsunamis, respectively, on the southern coast.

SAMPLING SITES AND METHODS

Extensive field work aiming at reconstructing the tsunami chronology of the Marquesas

Islands would cover the entire archipelago and document tens of sites with absolute dating of the different sedimentary units, but this is not the aim of the present study. This work focuses on two sites (Fig. 4): (i) on the southern coast of Nuku Hiva Island (Hooumi); and (ii) on the southern coast of Hiva Oa Island (Tahauku). Both of these sites were impacted by the 2010 and 2011 tsunamis, with wave runups of 2.5 to 3.5 m [START_REF] Reymond | The 2010 and 2011 Tsunamis in French Polynesia: Operational Aspects and Field Surveys[END_REF]. The 1946 and[START_REF] Schindelé | L'aléa tsunami en Polynésie française : synthèse des observations et des mesures[END_REF].

Hooumi is located at the end of a funnel-shaped branch of the Baie du Contrôleur (Fig. 4A).

There is no river outlet, and a small lagoon has formed behind the sandy beach. The sampling site is a low altitude (<2 m a.s.l.) hand dug trench on the western side of the lagoon, 210 m from the shoreline. Tahauku is another example of a funnel-shaped bay located east of Atuona village (Fig. 4B). The site is particularly exposed to tsunami wave amplification [START_REF] Hébert | Tsunami risk assessment in the Marquesas Islands (French Polynesia) through numerical modeling of generic far-field events[END_REF]. A large trench was dug mechanically between the lagoon and the river outlet. Note that the lagoon that was still visible on the November 2004 satellite imagery (Google Earth©) has now disappeared due to successive sediment inputs from anthropic activities and tsunamis.

A complete dataset of the structure and texture of a tsunami deposit was collected in the Tahauku trench. Two sections were sampled: a shore-parallel section oriented N115° and a shore-perpendicular section oriented N190° (Fig. 5). Bulk samples of sediments were collected vertically along both sections. Sampling includes pre-tsunami soil, a 30 cm thick tsunami deposit (tsunami 2 on Fig. 5) and deposits of the 2011 tsunami.

Grain size of bulk samples was analysed using a particle analyser (Morphologi G3; Malvern Panalytical, Malvern, UK). The G3 analyser separates particles using an integrated disperser, and captures thousands of images of individual particles down to 0.5 µm and up to 1.5 mm using a microscope linked to a digital camera. Image analysis then provides quantitative parameters related to the size (for example, equivalent spherical diameter, perimeter, width, length and area) and shape of the particles (for example, aspect ratio, circularity, solidity, convexity and elongation). The method has been applied successfully to volcanic ash [START_REF] Leibrandt | Towards fast and routine analyses of volcanic ash morphometry for eruption surveillance applications[END_REF] and tsunami deposits [START_REF] Ulvrova | Source of the tsunami generated by the 1650 AD eruption of Kolumbo submarine volcano (Aegean Sea, Greece)[END_REF]. Particles were captured at a focal length of 0.130 to 0.160 mm, a magnification of ×2.5, and a resolution of 5 megapixels. The dataset is then filtered at 20 µm in order to eliminate post-sampling artefacts (for example, dust), yielding particle numbers between 2800 and 11700 (Fig. 6).

The anisotropy of magnetic susceptibility (AMS) was analysed using a Kappabridge KLY-2 (Agico, Brno, Czech Republic). Samples from the Tahauku trench were collected in 2 cm sided oriented boxes, as described in [START_REF] Wassmer | Use of anisotropy of magnetic susceptibility (AMS) in the study of tsunami deposits: Application to the 2004 deposits on the eastern coast of Banda Aceh, North Sumatra, Indonesia[END_REF]. Each sample was analysed in 15 directions to determine the magnitude and directions of the maximum, intermediate and minimum AMS axes. The anisotropy of each sample (i.e. each cubic box) can be represented by a triaxial ellipsoid (the maximum K1 or K max , intermediate K2 or K int and minimum K3 or K min axes corresponding to principal eigenvectors). The stereographic projection (lower hemisphere equal-area projection) of the three axes of the ellipsoid gives information on the preferential orientation of the ferromagnetic minerals (for example, magnetite from volcanic rocks in the case of the Marquesas Islands).

Oriented cores of tsunami deposits were retrieved in carbon fibre tubes (10 cm long and 2 cm wide), thus preserving their structure and vertical variations of texture. Roots and cobbles locally prevented coring the entire thickness of the tsunami deposit. Four cores of tsunami deposits were sampled: two cores at Tahauku (TK03-A and TK03-B on Fig. 5) and two cores at Hooumi (Ho1-A and Ho1-B on Fig. 7). Cores were scanned at the Institut P' using an X-ray tomography system (UltraTom; RX-Solutions, France) at 70 kV and 140 µA. The acquisition time per core ranged between 22 and 25 hours (eight successive scans by translating the core along the beam were necessary to cover the entire volume of each core). Reconstructed data are sets of 16 bits Tiff image files representing cross-sections of the cores (horizontal slices from top to base). Image resolution (voxel size) is 11 µm. The total number of images available for each core ranges from 7618 to 9230. Particles (grains) were semi-automatically separated using the morphological segmentation tool of the MorphoLibJ collection [START_REF] Legland | MorphoLibJ: integrated library and plugins for mathematical morphology with ImageJ[END_REF] included in the Fiji distribution of ImageJ [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. Sedimentary fabric data were obtained from threedimensional stacks of horizontal slices, while statistics on grain size (following a vertical step of 2 mm along the cores) and grain-size maps were calculated from a two-dimensional vertical slices of each core, using new versions of the grainstat and grainmap codes rewritten in Python 3.5 (modified from [START_REF] Falvard | X-ray tomography of tsunami deposits: towards a new depositional model of tsunami deposits[END_REF]. Blob3D program [START_REF] Ketcham | Three-dimensional grain fabric measurements using high-resolution X-ray computed tomography[END_REF] was used to obtain data on the 3D orientation of particles. Resolution and image quality allowed characterisation of the sedimentary fabric with a vertical step of 2.5 mm along the cores, which represents an eight-fold increase in spatial resolution compared to a previous study [START_REF] Falvard | X-ray tomography of tsunami deposits: towards a new depositional model of tsunami deposits[END_REF]. Fabric data were plotted as stereographic projections of the orientations of the longest grain axes (900 to 3500 grains at each step, representing a total number of >60000 grains). Particles with a short axis lower than 10 voxels were excluded in order to avoid artefacts from potential over-segmentation of some grains or from noise. The geometry of the fabric at each vertical step is inferred from the characteristics of the ellipsoid (degree of anisotropy, elongation, azimuth and plunge) of preferred grain orientation.

RESULTS

Tahauku trench

At Tahauku, two successive tsunami deposits overlying soil are preserved (Fig. 5). The upper tsunami deposit has a thickness of 15 to 20 cm and corresponds to the 2011 Tohoku-oki tsunami (as confirmed by local residents). The deposit is poorly sorted, with grain size ranging from very fine sand to pebbles, including bioclasts (fragments of shells and corals). It is difficult to observe any internal structure and bedform, due to bioturbation (note abundant roots in the deposit on Fig. 5). The lower tsunami deposit is thicker (30 cm) and structured in different subunits. Basal contact with the soil is erosive (note erosional contact at 45 to 50 cm depth on Fig. 5). Because the trench is located at the border of a former lagoon, the soil has a bimodal composition due to a mixing of mud (lagoon) and fine sand (fluvial and coastal inputs). The soil corresponds to samples 8 and 9 on Figs 5A and 6.

The lowermost tsunami subunit has an irregular thickness and consists of crudely laminated, poorly-sorted medium sand (subunit 7 on Figs 5A and 6; subunit 4 on Figs 5B and6). The lower part of the subunit is particularly rich in heavy minerals and inversely graded (Fig. 7). This vertical grading is not uniform and rather corresponds to an inversely-graded sequence of multiple poorly-defined laminae. The upper part of the subunit displays mud clasts (from the underlying soil) and high-angle lamination dipping towards the south-west, which is associated with small variations of grain size and sorting (Fig. 7). Detailed analysis of the fabric at a vertical step of 2.5 mm reveals complex variations along the 10 cm long core (Fig. 8). Four types of clast fabric can be distinguished: (a) moderate-angle (15 to 35°) fabric oriented north-east (i.e. dipping towards the south-west); (b) bimodal low-angle (<15°) fabric (two orientations with opposite angles); (c) low to moderate angle fabric with at least two orientations; and (d) dispersed fabric. Type-b fabric has a majority of south-west/north-east orientations, but north-west/south-east orientations are recorded locally (for example, 38.5 cm depth on Fig. 8). The AMS samples near the base of the core have K max axes oriented NE/ENE at angles of 5 to 15° (samples TK03-43 and TK04-48 on Fig. 5C), an orientation that is concordant with fabric obtained from XRT at a similar depth (Fig. 8). The lower part of the subunit (42 to 44 cm depth) shows a succession of b-d-a fabric, followed by a coarse-grained interval with poorly-defined fabric (40.5 to 42.0 cm depth). The upper laminated part of the core (39.5 to 35.0 cm depth) displays alternating b and d fabrics.

The aforementioned basal subunit of the tsunami deposit is deeply eroded by a chaotic coarsegrained and poorly-sorted subunit (too coarse to be sampled for XRT). Medium to coarse sand is mixed with corals and numerous pebbles over a thickness of 15 to 20 cm (subunit 6).

At a depth of 30 cm below the surface, another erosional contact marks the onset of a new phase characterised by finer sediments (Fig. 5) with abundant bioclasts (Fig. 9). The contact is fossilised by a 2 to 5 cm thick assemblage of medium sand and shells with abundant mud clasts, as confirmed by X-ray imagery (subunit 5). The relative abundance of mud clasts decreases upward and the deposit progressively turns to silty sand. As observed on the shoreperpendicular section (Fig. 5B) and XRT (Fig. 7), subunits 2 and 4 are crudely laminated: horizontal lamination at the base of subunit 4, cross-lamination in upper subunit 4, and lowangle lamination dipping seaward (towards the south-west) in subunit 2. This lamination is associated with vertical variations of grain size. However, the laminated silty sand is not homogeneous. Some laminae are coarser-grained (for example, lens of coarse sand on Figs 7 and9) or enriched in heavy minerals (for example, at 19.5 and 22.5 cm depth on Fig. 9). Different facies of mixing between sand and clay are observed (Fig. 9): (i) interstitial clay acting as a matrix between sand grains; (ii) aggregates of mud clasts with sand grains and bioclasts intercalated; and (iii) discontinuous mudlines. As an example, the mudline sampled in core TK03-A is clearly not homogenous. Shades of grey underline variations of composition of the clayey matrix (Fig. 9). The mudline texture is an assemblage of sand and bioclasts with mud clasts that are more or less deformed and disaggregated (Fig. 10). This succession of more or less cohesive subunits shows evidence of post-tsunami deformation (Fig. 11).

In terms of fabric, subunits 2 and 4 do not share the same characteristics. In subunit 4, the AMS ellipsoid of sample TK03-23 has a high degree of anisotropy and an unusual oblate geometry; the K max dips at 50° towards the SSW and the K min is tilted 90° westward (Fig. 5C).

The fabric is visible on X-ray imagery as well and the imbrication of the coarsest clasts points to a current oriented towards the north-east (landward) at relatively high angles (type-a fabric), which is concordant with the results of AMS. The resolution of the scan does not allow the development of any fabric in the mudline to be characterised quantitatively (subunit 3). In subunit 2, the orientation and weak inclination (<15°) of the magnetic fabric suggests a current weakly directed seaward. Indeed, AMS samples TK03-16 and TK04-23 have K max that are oriented towards the south-west and west, respectively (Fig. 5C).

Hooumi trench

At Hooumi, the 2010 and 2011 tsunamis deposited fine patches of sand on the ground and there is no notable sedimentary unit related to these two events in the local stratigraphy.

However, coral boulders along the river (Fig. 2B) and a massive sand unit overlying soil (Fig. 12) attest to deposition from at least one larger-magnitude tsunami. There is almost no evidence of pedogenesis on top of this tsunami sand, suggesting that it corresponds to a recent event. The 1946 tsunami is a candidate but its runup at Hooumi was similar to the 2010 and 2011 runups (<3 m; [START_REF] Schindelé | L'aléa tsunami en Polynésie française : synthèse des observations et des mesures[END_REF].

The tsunami deposit is up to 40 cm thick (Fig. 12). Planar to oblique crude lamination is visible over its entire thickness. The thinnest laminae are enriched in silt-sized material.

Pebbles and roots at the base (43 to 32 cm depth) and in the central part of the deposit (23 to 18 cm depth) introduced gaps in the XRT sampling. However, the two cores retrieved (Ho01-A and Ho01-B) provide a high-resolution characterisation of grain size and fabric over two intervals of 10 cm (Figs 12 and 13). Subtle vertical variations of grain size and sorting are detected. Maximum grain size typically ranges between 0.4 mm and 0.6 mm, with three peaks higher than 0.8 mm. Sediment is poorly sorted, especially at the base of the two cores. There is no vertical grading except for a slight normal grading at the base of core Ho01-A (Fig. 12).

As in Tahauku, four types of clast fabric are distinguished (Fig. 13 23.5 cm depth). Core Ho01-A (Fig. 13) starts with a phase of poor organisation associated with normal grading. The sediment then adopts a clear high-angle fabric (type a) oriented south-east to SSW (i.e. rotation of the plunge from NNW to NNE between 16.5 cm and 14.5 cm depth on Fig. 13), before returning to a dispersed or weakly organised fabric (14.5 to 9.5 cm depth).

DISCUSSION

Types of sedimentary fabric

As demonstrated by the results presented above, X-ray tomography (XRT) is a powerful technique for characterising the fabric of unconsolidated sediments such as tsunami deposits.

The method used here allows a full 3D quantitative analysis of the fabric at a high-resolution (vertical step of 2.5 mm). The small-scale variations of fabric, together with grain size and sorting, would have been impossible to detect with other techniques, such as AMS. At both sites, four types of fabric were distinguished (Fig. 14):

(i) Type-a fabric represents moderate to high angle fabric (15 to 35° at Tahauku; 25 to 75° at Hooumi) with a well-defined orientation. Considering the funnel-shaped morphology of the Hoomi and Tahauku valleys, it can be assumed that the tsunami current was oriented parallel to the axis of the valley, i.e. directed towards the north-west at Hooumi and towards the northeast at Tahauku (Fig. 4). Thus, type-a fabric recorded in the lower part of core TK03-B is flow-parallel and directed landward (Fig. 8). Type-a fabric in the middle part of Ho01-B is characterised by high angles oscillating between flow-parallel and flow-oblique orientations (Fig. 13). In Ho01-A the interval of type-a fabric is parallel to oblique, with a notable seaward orientation. Flow-transverse orientations (i.e. perpendicular to the axis of the valley) are apparently rare in type-a fabric.

(ii) Type-b fabric is characterised by a low inclination of the grains (<15°) following two opposite orientations. Thus, the direction of the current cannot be determined if it is assumed that the fabric is parallel to the flow direction. At Tahauku, the type-b fabric is oriented parallel to the inferred flow direction (oriented south-west/north-east), except in a very short interval of flow-transverse fabric (south-east/north-west orientation at 38.5 cm depth on Fig. 8). The type-b fabric at Hooumi is parallel or slightly oblique to the flow (Fig. 13). Type-a and type-b fabrics have similar degrees of anisotropy and elongation of the ellipsoid of grain orientation (as defined by [START_REF] Benn | Fabric Shape and the Interpretation of Sedimentary Fabric Data[END_REF] but they are different in terms of angle of fabric (cf. plunge on fig. 14).

(iii) Type-c fabric is a low to high angle fabric with at least two different orientations. Both at Hooumi and Tahauku, type-c fabric is observed on short intervals (<1 cm thick) between other types of fabric. It is thus a transitional fabric: transition between type-a and type-d fabric in Ho1-A, short interval in a type-a fabric in Ho1-B (Fig. 13). More type-c fabric is present at Hooumi than at Tahauku. The mean degree of anisotropy is slightly higher than the other types of fabric (Fig. 14A), while the degree of elongation is notably lower than types a and b (Fig. 14B). 14). Type-d fabric is dominant in the upper part of core Ho01-A (Fig. 13).

It is found in alternation with type-b fabric in the lower part of core Ho01-B (Fig. 13) and in the upper part of core TK03-B (Fig. 8).

Influence of the grain-size distribution on sedimentary fabric

According to experimental data (e.g. [START_REF] Rees | Experiments on the production of transverse grain alignment in a sheared dispersion[END_REF][START_REF] Gupta | An experimental study of fabric development in plane-bed phases[END_REF], the development of a sedimentary fabric in sandy deposits does not necessarily relate to the strength of the current, because it also depends on sediment concentration and grain-size distribution. Studies of the magnetic fabric of tsunami deposits inferred from AMS reached similar conclusions [START_REF] Wassmer | Use of anisotropy of magnetic susceptibility (AMS) in the study of tsunami deposits: Application to the 2004 deposits on the eastern coast of Banda Aceh, North Sumatra, Indonesia[END_REF][START_REF] Schneider | Using Magnetic Fabric to Reconstruct the Dynamics of Tsunami Deposition on the Sendai Plain, Japan -The 2011 Tohoku-Oki Tsunami[END_REF].

High concentration and rapid deposition of sediment can even hinder the development of an anisotropic fabric because of significant interaction between touching grains and a lack of space for spatial organisation [START_REF] Hiscott | Fabric of coarse deep-water sandstones Tourelle Formation, Quebec, Canada[END_REF][START_REF] Falvard | X-ray tomography of tsunami deposits: towards a new depositional model of tsunami deposits[END_REF]. [START_REF] Schneider | Using Magnetic Fabric to Reconstruct the Dynamics of Tsunami Deposition on the Sendai Plain, Japan -The 2011 Tohoku-Oki Tsunami[END_REF] suggested that the primary fabric is better developed where fine-grained particles (silts and clays) are mixed with sands. The relationship between the preservation of a primary fabric and a finely-skewed grain-size distribution is particularly well-illustrated in the case of Tahauku (Fig. 15), where sand is mixed with finer sediments from a lagoon. In the lower part of core TK03-B, the onset of a type-a fabric with angles up to 35° is related to increased coarse sand fraction and high values of skewness. This is concordant with the observations of [START_REF] Capaccioni | Computer-assisted image analysis on clast shape fabric from the Orvieto-Bagnoregio ignimbrite (Vulsini District, central Italy): implications on the emplacement mechanisms[END_REF] who used XRT to characterise the vertical variations of the fabric of an ignimbrite. The degree of preferred orientation of the elongated grains of the ignimbrite is correlated with the percentage of matrix. At Hooumi, vertical variations of grainsize distribution are less pronounced (Fig. 12), but two of the three major peaks of skewness are found in sediments with a type-a fabric (Fig. 16). Thus, the development of type-a fabric in a tsunami deposit is probably controlled by interactions between medium to coarse sand and fine-grained fractions (silts, clays) and not only by the characteristics of the flow itself (current strength, flow regime, etc.).

However, finding relationships between sediment sorting and fabric is far from evident. Peaks of sorting index (i.e. very poor sorting) at the base of the two Hooumi cores coincide with a disperse fabric (Fig. 16). The short episode of normal grading identified in core Ho01-A (17.5 to 16.5 cm depth) is characterised by an upward increase of the sorting (cf. decreasing sorting index on Fig. 16), low skewness and poorly-defined fabric (dominant type-c fabric).

Flow-parallel versus flow-transverse fabric

The sedimentary fabric observed in the two tsunami deposits is oriented either parallel or oblique to the inferred flow direction. Studies on the magnetic fabric of tsunami deposits inferred from AMS reported both flow-parallel and flow-transverse orientations [START_REF] Wassmer | Use of anisotropy of magnetic susceptibility (AMS) in the study of tsunami deposits: Application to the 2004 deposits on the eastern coast of Banda Aceh, North Sumatra, Indonesia[END_REF][START_REF] Paris | Coupling eruption and tsunami records: the Krakatau 1883 case-study, Indonesia[END_REF][START_REF] Schneider | Using Magnetic Fabric to Reconstruct the Dynamics of Tsunami Deposition on the Sendai Plain, Japan -The 2011 Tohoku-Oki Tsunami[END_REF][START_REF] Falvard | X-ray tomography of tsunami deposits: towards a new depositional model of tsunami deposits[END_REF]. [START_REF] Falvard | X-ray tomography of tsunami deposits: towards a new depositional model of tsunami deposits[END_REF] combined AMS and XRT and found dominant low-angle flow-transverse fabrics in a tsunami deposit. However, the quality of the scans both in terms of resolution and contrast did not allow characterisation of the small-scale vertical variations of fabric.

Direct comparison between AMS and XRT data shows that the magnetic fabric broadly illustrates the flow-parallel fabric at the base of core TK03-B (Fig. 8). However, XRT data reveal more complex patterns of fabric with a transition from low-angle (type b) or disperse fabric (type d), to a well-defined moderate-angle fabric (type a) indicating a current oriented towards the north-east (landward). At Tahauku, the fabric is mainly parallel to the flow direction. Flow-transverse fabric between 38 cm and 40 cm depth (Fig. 8) coincides with low values of skewness and an upward decrease of the sorting (Fig. 15).

In core Ho01-B, the data here record a transition from high-angle flow-oblique fabric oriented north-east to flow-oblique fabric oriented SSW (29 to 26 cm depth on Fig. 13). Interestingly, the current reversal is marked by type-c fabric displaying the two opposite orientations. Typeb fabric at the top of Ho01-B is a typical example of flow-parallel fabric. Small-scale variations detected between 18.0 cm and 14.5 cm depth illustrate short-lived transitions from flow-parallel to flow-oblique fabric in a current directed seaward (backwash).

Flow-parallel fabric is common for sands transported at high sediment concentration and rapidly deposited (e.g. [START_REF] Rees | The production of preferred orientation in a concentrated dispersion of elongated and flattened grains[END_REF][START_REF] Rees | Experiments on the production of transverse grain alignment in a sheared dispersion[END_REF][START_REF] Hiscott | Fabric of coarse deep-water sandstones Tourelle Formation, Quebec, Canada[END_REF][START_REF] Gupta | An experimental study of fabric development in plane-bed phases[END_REF][START_REF] Deprez | Multiscale micro-CT imaging on sediment cores: unravelling the paleoflow directions in a megaturbidite[END_REF]. A high deposition rate is required for preserving this primary fabric. Such conditions are likely to be reproduced in tsunami waves transporting large amounts of sediment, especially during the inundation phase (e.g. [START_REF] Paris | Tsunamis as geomorphic crisis: lessons from the December 26, 2004 tsunami in Lhok Nga, west Banda Aceh (Sumatra, Indonesia)[END_REF][START_REF] Goto | Spatial thickness variability of the 2011 Tohoku-oki tsunami deposits along the coastline of Sendai Bay[END_REF]. [START_REF] Hiscott | Fabric of coarse deep-water sandstones Tourelle Formation, Quebec, Canada[END_REF] also observed flow-parallel fabric with angles commonly >20° in laminated sandstones formed by turbidity currents. [START_REF] Gupta | An experimental study of fabric development in plane-bed phases[END_REF] The onset of flow-oblique fabric indicates a reduction of the bed shear stress and a reorientation of the grains by rolling or sliding near the bed [START_REF] Gupta | An experimental study of fabric development in plane-bed phases[END_REF]. In the data herein, the ellipsoids of flow-parallel and flow-oblique fabrics are not significantly different in terms of angle of fabric, isotropy and elongation. The influence of parameters such as sediment concentration, grain size or flow regime on the production of fabric has been tested in experiments on sheared dispersions of sand. [START_REF] Allen | Sedimentary structures, their character and physical basis[END_REF] suggested that the vertical variability of fabric reflects variations of flow regime. Poorly-sorted sands deposited in the lower plane-bed phase show flow-parallel orientation patterns for the finer grains (<0.7 mm), and both flow-parallel and flow-transverse orientations for the coarser grains (>0.7 mm). [START_REF] Rees | Experiments on the production of transverse grain alignment in a sheared dispersion[END_REF] found that the flow-parallel fabric is preserved at low (1 to 2%) and high-sediment concentration (>11%), while the fabric becomes transverse for some intermediate concentrations (3 to 8%). At intermediate concentration, the production of a flow-parallel fabric is prevented by frequent 'grain to grain' collisions. At higher concentration, a reduction of the distance between colliding grains creates transfers of angular momentum and does not allow the development of a flow-oblique fabric [START_REF] Rees | Experiments on the production of transverse grain alignment in a sheared dispersion[END_REF], thus resulting in flow-parallel or disperse fabric. The vertical variations of fabric observed in tsunami deposits could reflect similar changes in sediment concentration (sediment pulses) and aggradation rate through time. Transitions from flow-parallel to flow-oblique fabric could be related to the deceleration of the flow and decrease of the sediment concentration, although local effects due to the topography (for example, wave reflection in the narrow valleys and bed roughness) should not be excluded.

Variations of the angle of fabric

Type-a fabric has imbrication angles of 15 to 35° at Tahauku and 25 to 75° at Hooumi. Angles of imbrication higher than 20° are common in sands rapidly deposited by sediment gravity flows (e.g. [START_REF] Hiscott | Fabric of coarse deep-water sandstones Tourelle Formation, Quebec, Canada[END_REF], and it is actually not surprising to have such highangle fabric in tsunami deposits. [START_REF] Cheel | Grain fabric in hummocky cross-stratified storm beds: genetic implications[END_REF] interpreted the bimodality and cyclic variations of the imbrication angle (from almost 0 to 35°) as variations of the strength of an oscillatory current during a storm. Deposits formed by unidirectional currents apparently display few variations of the orientation and angle of imbrication. Experimental upper plane beds have upcurrent imbrication angles ranging between 11° and 25°, whereas lower plane beds have angles lower than 15° both in upcurrent and downcurrent directions [START_REF] Gupta | An experimental study of fabric development in plane-bed phases[END_REF]. Lowangle type-b fabric (<15°) observed in the tsunami deposits displays similar bimodal orientation patterns. If the results of laboratory experiments are extrapolated, type-b and typea fabrics could correspond to phases of subcritical flow regime and near-supercritical flow regime, respectively. Indeed, the Froude number of a tsunami during its phase of inundation inland typically ranges between 0.7 and 2.0 [START_REF] Matsutomi | Inundation flow velocity of tsunami inland and its practical use[END_REF], i.e. at the transition between subcritical and supercritical conditions. However, the vertical variation of the angle of fabric is not an unequivocal proxy of the transport and deposition mechanisms, because it also depends on the grain-size distribution and shape of the grains. As discussed above, the grain-size distribution has an influence on the development of a sedimentary fabric. Moderate to high angle fabric (such as type-a fabric) is better preserved in sediments that have a finely-skewed grain-size distribution. There is a remarkable positive correlation between the skewness of the grain-size distribution and the angle of fabric, especially at Tahauku (Fig. 15). Higher values of skewness at Tahauku, compared with Hooumi, are due to larger inputs of fine sediments. Consequently, the fact that the angle of fabric is generally higher at Hooumi than at Tahauku (Figs 15 and 16), cannot be explained only by different sediment sources and grain-size distribution between the two sites.

A faster deposition rate at Hooumi is the most plausible explanation.

Two different scenarios of inundation

Detailed analysis of the vertical variations of grain size and fabric enable a scenario to be proposed for the two tsunamis. Core TK03-B, which was sampled in the lower part of the Tahauku tsunami deposit, represents the initial stage of inundation. The lowermost 4 cm (44 to 40 cm depth) are characterised by an inversely-graded sequence of poorly-defined laminae and a flow-parallel fabric. The progressive increase of the current strength and sediment concentration is illustrated by bimodal low-angle (type-b) fabric turning to disperse fabric (type-d). Type-a fabric represents the peak of aggradation of this first pulse (Fig. 8). The upper part of the core displays high-angle backset laminae associated with alternating type-b and type-d fabric. Both flow-parallel and flow-oblique trends are observed in type-b fabric, depending on the distribution of the shear stress in the boundary layer. The main inrush of inundation starts with a thick disorganised subunit of coarse sand with pebbles (Fig. 5) that is not suitable for a microtextural analysis. The pebbles are not preferentially oriented.

At this stage, the small beach is probably deeply eroded and sediment from other sources is incorporated into the deposit (sediment from the bay and from the riverbed). Indeed, the upper laminated sand sampled in core TK03-A is finer-grained (silty sand mixed with clay) than the underlying subunits (Fig. 6) and particularly rich in marine bioclasts. The heterogeneous texture of the mudlines (Fig. 10) confirms the conclusion of [START_REF] Falvard | X-ray tomography of tsunami deposits: towards a new depositional model of tsunami deposits[END_REF] who proposed that they represent the friction-dominated region of a high-energy erosive current rather than a calm settling of clay. The mudline corresponding to subunit 3 (Figs 5 to 10) marks the onset of the backwash, as confirmed by a seaward-oriented fabric in the laminated sand above the mudline (AMS samples TK04-23 and TK03-16 on Fig. 5c). The characteristics presented above (for example, different subunits separated by erosive discontinuities, a diversity of sediment sources and well-developed mudlines) point to a large event, i.e. larger than the effects reported for the 2010 and 2011 tsunamis in the Marquesas. At Tahauku, the 2011 tsunami had a maximum wave runup of 2.8 m at 90 m from the shoreline [START_REF] Reymond | The 2010 and 2011 Tsunamis in French Polynesia: Operational Aspects and Field Surveys[END_REF] and left a 15 cm thick deposit of coastal sand and pebbles (Fig. 5).

The 1946 and 1960 tsunamis are good candidates for the deposit studied here. The 1946 tsunami penetrated the Tahauku valley to a distance up to 830 m with a runup of 14.6 m [START_REF] Okal | A field survey of the 1946 Aleutian tsunami in the far field[END_REF] and the 1960 tsunami runup at Tahauku was 12 m [START_REF] Schindelé | L'aléa tsunami en Polynésie française : synthèse des observations et des mesures[END_REF].

At Hooumi, the 2 m high waves of the 1946 tsunami followed the Hooumi riverbed up to 660 m inland and deposited coral boulders up to 12 tons at 100 m from the shoreline [START_REF] Okal | A field survey of the 1946 Aleutian tsunami in the far field[END_REF]. The base of the boulders is buried in the tsunami deposit studied here, suggesting that it is the same event, which is consistent with the absence of pedogenesis on top of the deposit.

The coarse-grained basal subunit including pebbles (not sampled for XRT) is overlain by a 20 to 30 cm thick succession of laminated sand. This crude lamination indicates periodical variations of the aggradation rate due to successive sediment pulses that are associated with subtle variations in grain size, sorting and fabric. As observed in Tahauku, the common alternating type-b and type-d fabrics illustrate these variations of sediment concentration and deposition rate. There are no erosive discontinuities between each new pulse, even during the current reversals. A first reversal at 27 cm depth (Fig. 13) is characterised by type-a fabric oriented north-east to type-a fabric oriented SSW, with transitional type-c fabric in between.

Another phase of backwash is identified in the upper part of the tsunami deposit, with type-a fabric being notably directed seaward from 16.7 to 14.5 cm depth on core Ho01-A. The association between high-angle type-a fabric and backwash currents at Hooumi is in favour of a high deposition rate. The second backwash is preceded by a phase of suspension fallout, as evidenced by normally-graded sediments with poorly-defined, flow-oblique fabric (17.5 to 18.5 cm depth). This is consistent with a decreasing concentration and deposition rate at the end of the tsunami uprush. The fabric observed is not primary, as the grains settling down are reoriented oblique to the flow by rolling near the bed.

The two tsunami deposits differ in terms of composition, texture and structure, and they represent two different scenarios of inundation. Although the tsunami runup was considerably higher at Tahauku (14.0 m compared to 2.5 m at Hooumi during the 1946 tsunami), the two deposits have a similar thickness (30 to 40 cm). The Hooumi deposit was built by pure aggradation, while the Tahauku deposit is internally structured in several subunits separated by erosive discontinuities. The relatively thick deposit at Hooumi can be explained by: (i) a limited amount of sediment loss during backwash, resulting in a paucity of sediment being redeposited offshore (which is consistent with the type-a fabric and high deposition rate of the backwash deposits onshore); and/or (ii) more sediment availability when the tsunami occurred (for example, a beach-dune system more developed than today). This example illustrates the limitation of using the thickness of a palaeo-tsunami deposit as an indicator of its intensity, especially in the absence of information concerning the morpho-sedimentary setting prior to tsunami inundation.

CONCLUSION

Due to their central position in the Pacific Ocean, the Marquesas Islands represent a natural laboratory for studies on the sedimentary record of trans-Pacific tsunamis. The islands have a low-moist tropical climate and tsunami deposits are well-preserved. Only two sites were investigated here, but a regional study could provide a detailed reconstruction of the chronology of tsunamis generated by seismic mega-ruptures around the Pacific Ocean. The quality and relevance of the data obtained on the two tsunami deposits confirm that X-ray tomography (XRT) is a powerful technique for characterising the grain-size distribution and sedimentary fabric of tsunami deposits, as well as other types of sedimentary formations (for example, turbidites and pyroclastic flow deposits). Unlike other techniques such as anisotropy of magnetic susceptibility (AMS) or thin sections, XRT reveals the true three-dimensional fabric. Further investigations will help to better define relationships between the geometry of the fabric, the characteristics of the flow (current strength, flow regime and sediment concentration), the depositional processes, and the characteristics of the sediments at the source. Tahauku (southern coast of Hiva Oa Island), and observed tsunami runups since 1946 [START_REF] Schindelé | L'aléa tsunami en Polynésie française : synthèse des observations et des mesures[END_REF][START_REF] Reymond | The 2010 and 2011 Tsunamis in French Polynesia: Operational Aspects and Field Surveys[END_REF].

FIGURE CAPTIONS

  ): (a) high-angle (25 to 75°) fabric; (b) bimodal low-angle (<15°) fabric (two orientations with opposite angles); (c) low to high angle fabric with at least two orientations; and (d) dispersed fabric. From base to top, different trends of fabric are identified. The lower part of Ho01-B (33 to 30 cm depth) is poorly organised (type-d fabric), except at the level of a silty lamina (type-b fabric weakly oriented NNE or SSW). The lamina itself has a type-b fabric dominantly oriented NNE. From 30.0 to 26.5 cm depth, the data here record a progressive reversal from high-angle (type a) fabric oriented north-east (i.e. dipping towards the south-west) to bimodal high-angle fabric (type c), and finally high-angle fabric oriented SSW. After a short interval of disperse fabric (type d), clasts are weakly inclined (type b) with north-west or south-east orientations (25.0 to

(

  iv) Type-d fabric is a group of dispersed fabrics resulting from a random orientation of the grains. Type-d fabric usually displays low angles of inclination of individual grains, as for type-b fabric. Rare examples of moderate-angle disperse fabric correspond to transitional c-d fabrics. As for type c, type-d fabric has a low degree of elongation compared to type-a and type-b fabrics (Fig.

  obtained moderateangle (11 to 25°) flow-parallel fabric in sands deposited in the upper-stage plane-bed phase, with a minor flow-oblique mode, while Baumann et al. (2017) observed flow-parallel fabric turning to flow-oblique fabric in the distal part of a storm washover deposit.

Fig. 1 .

 1 Fig. 1. Marquesas Islands (French Polynesia) and study sites. (A) Main historical earthquake sources for tsunamis affecting the Marquesas Islands. (B) Map of the archipelago. (C) Study sites in Nuku Hiva Island. (D) Study sites in Hiva Oa and Tahuata islands. Black dots indicate sites where tsunami deposits were sampled for X-ray tomography (XRT).

Fig. 2 .

 2 Fig. 2. Field evidence of tsunami in the Marquesas Islands. (A) Erosional scars in sand ridges, driftwood at 9 m a.s.l., and a 12-cm-thick sandy laminated deposit overlying a soil at Haatuatua Bay (Nuku Hiva Island, June 2012). (B) Coral boulders scattered along the river banks near Hooumi (Nuku Hiva Island, June 2012); a-axis of the largest boulder on the right measures 1.7 m. (C) Washover fan of pebbles and boulders attached to an old dune up to 36 m a.s.l. at Hanateio (Tahuata Island, June 2012). (D) The washover fan is a clast-supported conglomerate with a bimodal composition of corals and basaltic rocks. Note the presence of abundant driftwood.

Fig. 3 .

 3 Fig. 3. Evolution of sand ridges and washover fans in Haatuatua Bay (Nuku Hiva Island) between June 2005 and April 2013 (DigitalGlobe imaging provided by Google Earth©).Erosion of the lower sand ridge and progression of the washover fans inland at altitudes up to 15 m a.s.l. is probably due to the impact of the 2010 (Chile) and/or 2011 (Japan) tsunamis.

Fig. 4 .

 4 Fig. 4. Location of the sampling sites at Hooumi (southern coast of Nuku Hiva Island) and

Fig. 5 .

 5 Fig. 5. Tahauku trench. (A) Shore-parallel section. Numbered circles and white squares correspond to bulk samples and anisotropy of magnetic susceptibility (AMS) samples, respectively. Two cores were sampled for X-ray tomography (TK03-A and TK03-B). (B)Shore-perpendicular section. (C) Results of AMS analyses: stereographic projection of the K max (K1), K int (K2) and K min (K3) axes, and graphs of P (degree of anisotropy) versus bulk susceptibility and T (shape parameter of the ellipsoid, with T > 0 for oblate ellipsoids and T < 0 for prolate ellipsoids).

Fig. 6 .

 6 Fig. 6. Grain-size distributions of the different subunits observed on the Tahauku trench (shore-parallel section). Vertical and horizontal scale of the graphs represent the number of

Fig. 7 .

 7 Fig. 7. Two-dimensional vertical slice, grain-size map and statistics (number of particles, maximum grain size and sorting index) obtained from X-ray tomography (XRT) at a vertical step of 2 mm down cores TK03-A and TK03-B (Tahauku). ND: no data (no reliable grain-size data could be obtained in clayey sediment such as mud lines and mud aggregates).

Fig. 8 .

 8 Fig. 8. Diagrams representing the sedimentary fabric characterised by X-ray tomography (XRT) at a vertical step of 2.5 mm down the TK03-B core. Four types of fabric are distinguished: (a) moderate-angle (15 to 35°); (b) bimodal low-angle (<15°); (c) moderateangle with at least two different orientations; and (d) dispersed.

Fig. 9 .

 9 Fig. 9. Structure and vertical variations of grain size in core TK03-A. From left to right: original X-ray image of the core, recontrasted negative of the original image, and detailed views of a mudline and a lens of coarse sand intercalated in the laminated silty sand. Note the presence of tests of gastropods and abundant shell fragments, and laminae of heavy minerals.

Fig. 10 .

 10 Fig. 10. Three-dimensional view of a mudline at ca 22 cm depth in core TK03-A. White dotted lines correspond to the zonation of the mudline, illustrating variations of texture and composition.

Fig. 11 .

 11 Fig. 11. Post-tsunami deformation structures in the Tahauku trench. Subunit 1 corresponds to the 2011 Tohoku-oki tsunami (Japan), and subunits 2 to 6 relate to a previous tsunami (the 1946 Aleutian tsunami or 1960 Chile tsunami).

Fig. 12 .

 12 Fig. 12. Two-dimensional vertical slice, grain size map and statistics (number of particles, maximum grain size and sorting index) obtained from X-ray tomography (XRT) at a vertical step of 2 mm down cores Ho01-A and Ho01-B (Hooumi).

Fig. 13 .

 13 Fig. 13. Diagrams representing the sedimentary fabric characterised by X-ray tomography (XRT) at a vertical step of 2.5 mm down cores Ho01-A and Ho01-B. Types of fabric: (a) highangle (up to 75°) fabric; (b) bimodal low-angle (<15°) fabric; (c) high-angle fabric with at least two different orientations; and (d) disperse fabric.

Fig. 14 .

 14 Fig. 14. (A) Anisotropy of the ellipsoids of grain orientation for different types of fabric (triangular diagram from Benn, 1994). S1: long axis of the ellipsoid (eigenvalue); S2: intermediate axis; S3: short axis. I: isotropy of the ellipsoid, with I = S3/S1. E: elongation of the ellipsoid, with E = 1-(S2/S1). The shape of the ellipsoid is represented at each end of the plot: isotropic (top), oblate (low left) and prolate (low right). (B) Elongation of the ellipsoid compared to its plunge.

Fig. 15 .

 15 Fig. 15. Grain-size distribution (in terms of sorting index and skewness) compared to the type of sedimentary fabric and its angle of plunge (Takauhu site). The angle of fabric is estimated from the plunge of the ellipsoid of orientation of the grains at a similar vertical step down the core.

Fig. 16 .

 16 Fig. 16. Grain-size distribution (in terms of sorting index and skewness) compared to the type of sedimentary fabric and its angle of plunge (Hooumi site). The angle of fabric is estimated from the plunge of the ellipsoid of orientation of the grains at a similar vertical step down the core.

ACKNOWLEDGEMENTS

This work was funded by the Contrat de Projet Etat -Polynésie française 2009-2013, project RINALPOF (Les risques naturels extrêmes sur les littoraux de la Polynésie française : archives géologiquesmodélisationréduction des risques) hosted by Université de la Polynésie Française (UPF). The authors are particularly grateful to Yannick Guéhenneux, Jérôme Bascou, and Krzysztof Suchorski (LMV). Philip Kempf, Paolo Marco de Martini, and Pedro Costa are thanked for their relevant and laudatory reviews. This is ClerVolc Laboratory of Excellence contribution number 324.


Erwan Lenormand

Thierry Goubier

Loïc Cudennec
email: loic.cudennec@intradef.gouv.fr

Henri-Pierre Charles
email: henri-pierre.charles@cea.fr

A combined fast/cycle accurate simulation tool for reconfigurable accelerator evaluation: application to distributed data management

Keywords: Hybrid simulation, Distributed systems, Reconfigurable Computing

Parallel computing systems based on reconfigurable accelerators are becoming (1) increasingly heterogeneous, (2) difficult to design and (3) complex to model. Such modeling of a parallel computing system helps to evaluate its performance and to improve its architecture before prototyping. This paper presents a simulation tool aiming to study the integration of reconfigurable accelerators in scalable distributed systems and runtimes, such as S-DSM systems, where S-DSM (softwaredistributed shared memory) is a paradigm to ease data management among distributed nodes. This tool allows us to simulate the execution of irregular compute kernels accessing distributed data. To deal with the complexity of modeling (3) the complete system we used a hybrid methodology. We integrated the simulation engine into the S-DSM. The distributed data management part is executed on the physical architecture allowing to generate precise and faithful latencies, and the accelerator simulation is cycle accurate. We used general sparse matrix-matrix multiplication (SpGEMM) as a case study.

We show that the use of this tool makes it possible to analyze the behavior of an heterogeneous system (1) with rapid prototyping and simulation. The analysis of the results allowed to determine the correct sizing of the architecture (2) to obtain the best performance. The tool allowed to identify the bottleneck of our architecture and confirmed the possibility of hiding data access latencies.

Our simulation platform allows to emulate a heterogeneous distributed system by introducing a slowdown between 1.2 and 3.7 times compared to the compute kernel simulation alone.

I. INTRODUCTION

Parallel computer systems are becoming increasingly heterogeneous. This trend can be observed at all scales from System-on-Chip (SoC) to supercomputers. Heterogeneity is a response to the power wall problem [START_REF] Eeckhout | Heterogeneity in response to the power wall[END_REF] by scheduling a task on the appropriate processing unit depending on its power and performance characteristics. However, as illustrated by the efficiency on the high performance conjugate gradient (HPCG) benchmark [START_REF]High-performance conjugate gradient (hpcg) benchmark results[END_REF], current systems are inefficient for applications with irregular data access and low arithmetic intensity. A good data management is critical to improve the performance of these systems. A runtime system can transparently provide developers with intelligence in data management. The increase in heterogeneity requires further research to improve the integration of new types of computing resources. In this context we want to study the integration of reconfigurable accelerators (Field-programmable gate array (FPGA)) in a software system unifying the distributed memories. Our goal is to allow accelerators to request access to distributed data. Designing this system is a complex task requiring to prototype a hardware IP and then to integrate this IP into a software system that is also complex. Finally we want to study the acceleration of irregular compute kernels with unpredictable (or hard to predict) memory accesses. To understand how to develop this system and to predict its performance, we need to model it. Thus, we need to model a compute kernel whose evolution depends on its memory accesses and induced latencies. The specificity of the system to model and the need to limit the prototyping time led us to develop our own simulation tool presented in this paper.

This tool should answer the following questions:

• What performance could the system achieve?

• Which configuration provides the best performance?

• What are the bottlenecks? Finally, this tool should enable rapid modeling and rapid simulation to facilitate the exploration work.

The paper is organized as follows: Section II describes the system to model, Section III gives some references on related work, Section IV presents our simulation tool, Section V describes the experiments conducted with the tool, finally, Section VI concludes this article.

II. INTEGRATION OF RECONFIGURABLE ACCELERATOR IN SOFTWARE-DISTRIBUTED SHARED MEMORY

A parallel programming model with shared memory is convenient to develop multi-threaded applications, which concurrently access data in a global memory space. In a single memory system, data sharing can be based on reliable hardware mechanisms. For distributed memory systems, the implementation of a shared memory is more complex and requires to minimize the processing and communication costs. The study of distributed shared memory (DSM) have started in the late eighties with systems such as Ivy [START_REF] Li | IVY: a shared virtual memory system for parallel computing[END_REF] and later adapted to clusters [START_REF] Amza | Treadmarks: shared memory computing on networks of workstations[END_REF], grids [START_REF] Antoniu | JuxMem: An Adaptive Supportive Platform for Data Sharing on the Grid[END_REF], many-core processors [START_REF] Ross | Implementing openshmem for the adapteva epiphany risc array processor[END_REF] and recent heterogeneous architectures [START_REF] Nelson | Latency-tolerant software distributed shared memory[END_REF], [START_REF] Kaxiras | Turning centralized coherence and distributed critical-section execution on their head: A new approach for scalable distributed shared memory[END_REF]. In this work we use a Software-DSM (S-DSM) [START_REF] Cudennec | Software-Distributed Shared Memory over heterogeneous micro-server architecture[END_REF] [10] allowing to federate the physical memories of heterogeneous architectures. We study the integration of reconfigurable accelerators in this S-DSM to accelerate compute kernels. The S-DSM allows tasks to allocate and access memory in a shared logical space. The S-DSM is organized as a semistructured super-peer network, as represented in Figure 1. A set of clients are connected to a peer-to-peer network of servers. Clients execute the user code and servers manage the shared data and metadata. Allocated data is split into chunks whose maximum size is defined by the user. Each chunk is under the control of a data coherence protocol. A chunk has a unique identifier (ID) and metadata indicating its size, state and location. The coherence protocol is in charge of the localization and the transfer of the chunk.

A. Software Distributed Shared Memory

Using accelerators within S-DSM-based applications follows the classical hybrid programming paradigm, widely adopted in HPC with MPI/CUDA or MPI/OpenMP applications for instance. In these software architectures, the user code is split into two parts: 1) a distributed overlay that manages communications between remote processes, schedules jobs and orchestrates data transfer between nodes and 2) a local proxy code on each node that locally exploits the computing resources using the provided application programming interface (API). This model results in a two-step procedure to retrieve data from the distributed overlay,. Firstly, manually converts this data into the accelerator format (potentially involving multiple copies in memory), then transfers data to the accelerator memory and offload the processing. The same applies for fetching the results from the accelerator back to the distributed overlay. Such hybrid-programming applications require from the user to manage data twice, both at the distributed overlay level and the accelerator level. One must note that one of the evolutions of systems with accelerators is shared memory at the node level, via solutions based on NVLink, OpenCAPI [START_REF] Stuecheli | IBM POWER9 opens up a new era of acceleration enablement: OpenCAPI[END_REF], CCIX [START_REF]An introduction to CCIX: white paper[END_REF] and others, clearly pointing out that this manual data management is a problem.

In this work, we propose a simulation tool that helps in modeling and exploring different configurations of a system in which data is transparently managed between computing kernels, either it is an FPGA IP or a software process.

B. Reconfigurable Accelerator Integration

All actors of the S-DSM (clients and servers) are basically software processes. To integrate a compute kernel implemented on an FPGA in the S-DSM, we need to create an interface between a software process and the programmable logic (PL) of the accelerator. As shown in Figure 2, this interface is based on the cooperation of a software process (FPGA-client) executed on a processing system (PS) and a hardware component (FPGA-server) implemented in the PL. The PS and the PL communicate through an on-chip (AXI) or off-chip (PCI Express) interconnect. The FPGA memory is segmented into chunk-sized locations. The FPGA-server operates as a cache directory. Each entry associates a location with a chunk and its metadata (ID, size, state). When a compute kernel requests access to a chunk, if it is present in memory, the transfer is directly initiated. Otherwise, the FPGA-server forwards the access request to the FPGA-client and the transfer will be initiated after the allocation of the chunk. Thus, the time required to access the data can be very variable and depends on the state of the memory. The FPGA-client is a S-DSM client process. It interprets the requests coming from the FPGA and translates them for the S-DSM server. In this way, the FPGA appears as a regular client for all S-DSM processes.

C. Compute Kernel

The compute kernel is based on the dataflow model. It receives data within streams, performs the processing function and generates the results within streams. This is the typical model of compute kernels generated by high level synthesis tools [START_REF] Cong | High-level synthesis for fpgas: From prototyping to deployment[END_REF]. In our system, data streams are associated with requests generated by the kernels. Thus, read requests result in an incoming data stream and write requests in a outgoing data stream. As shown in Figure 3, each stream is implemented by a FIFO and several signals. For read requests, the kernel communicates the chunk ID to the FPGA-server. Then, when the data is available, the FPGA-server transmits the chunk size and fills the FIFO with the data. The chunk size is required when coping with irregular compute kernels. For write requests, the kernel communicates the size and the chunk ID. Then the FPGA-server extracts data from the FIFO to write it back in memory. [START_REF] Liang | Paas: A system level simulator for heterogeneous computing architectures[END_REF], allow the simulation of a full heterogeneous CPU-FPGA platform to provide highly accurate performance estimates. These tools are based on the integration of a simulator, such as gem5 [START_REF] Binkert | The gem5 simulator[END_REF], Multi2Sim [START_REF] Ubal | Multi2sim: A simulation framework for cpu-gpu computing[END_REF] or Verilator [START_REF] Snyder | Verilator: the fast free verilog simulator[END_REF]. Each have various constraints and limitations. For example, HeteroSim [START_REF] Feng | Heterosim: A heterogeneous cpu-fpga simulator[END_REF] can not support the simulation of a runtime that controls the interactions between a CPU and an FPGA. PARADE [START_REF] Cong | Parade: A cycle-accurate full-system simulation platform for accelerator-rich architectural design and exploration[END_REF] only simulates programming models where all data must be copied to local scratchpad memory (SPM) before launching a compute kernel. gem5-Aladdin [START_REF] Shao | Codesigning accelerators and soc interfaces using gem5-aladdin[END_REF] represents the accelerator as a set of dynamic data-dependent graphs generated from the high-level language descriptions of algorithms. This approach, which is efficient for simulation, limits the reconfiguration of the accelerators. PAAS [START_REF] Liang | Paas: A system level simulator for heterogeneous computing architectures[END_REF] and PARADE are focused on simulating heterogeneous SoC.

Input data

Input

Full system simulation can be time consuming. One method to speed up simulation consists in associating a temporal dimension with an event. An automatic delay-annotated mechanism to replace the use of Instruction-Set-Simulation (ISS) in SystemC simulations is presented in [START_REF] Kirchsteiger | A software performance simulation methodology for rapid system architecture exploration[END_REF]. The contributions presented in [START_REF] Papamichael | Fist: A fast, lightweight, fpga-friendly packet latency estimator for noc modeling in full-system simulations[END_REF], are based on packet latency estimations to replace detailed Network-on-Chip models in full-system performance simulators. Latencies are estimated from an analytical model. With this method, the accuracy of the simulation depends on the reliability of the analytical model. Making a reliable model is not always simple.

FPGA Computer Aided Design (CAD) flow tools, such as Verilog-To-Routing (VTR) [START_REF] Murray | Vtr 8: High-performance cad and customizable fpga architecture modelling[END_REF], integrate simulation tools. These tools allow to ensure the correctness of the design and estimate the circuit-activity [START_REF] Seeley | Simulation-based circuit-activity estimation for fpgas containing hard blocks[END_REF]. However, these tools cannot simulate an entire distributed system.

Finally some methods are hybrid, such as [START_REF] Wicaksana | Hybrid prototyping methodology for rapid system validation in hw/sw codesign[END_REF]. To speed up the simulation of an HW/SW system, this work combines a virtual platform simulation for the software part with an FPGA-based physical prototype for the hardware part.

IV. HYBRID SIMULATION TOOL

The purpose that has led to the development of this simulation tool is the evaluation of the performance of compute kernels integrated into the system described in Section II. The kernels we want to study have two forms of irregularities: they perform unpredictable (or hard to predict) memory accesses and their arithmetic intensities are data dependent. The distributed nature of the system we are studying implies high and variable data access latencies. Thus, performance evaluation is based on the analysis of the compute kernel activity and the generation of data access latencies relating to this activity. A high-level view of kernel activity, based on a dataflow model, comes down to consume and produce data at different speeds. At a lower scale, the activity of the compute kernel is constrained by the resources allocated to it, access to shared resources and the data flow provided to it over time. Thus, our tool is based on (IV-B) the activity simulation of a compute kernel and (IV-A) the generation of latencies. It was developed in C++ as a library of modular components. This approach makes it possible to generate various compute kernels quickly. The simulation is executed by three processes (one S-DSM server and two S-DSM client), which communicate and synchronize through S-DSM requests. The first client reads the input matrices and writes the output matrix. The second client runs the simulation engine.

A. S-DSM Interface Simulation

The role of the S-DSM interface is to generate data access latencies. It reproduces the implementation of the directory by associating to each entry with a chunk. The number of locations is configurable. Thus, the size of the FPGA memory can be defined when launching the simulation. When a request is issued by the kernel four scenarios are possible, depending on whether the chunk is allocated or not in the FPGA and if there is a directory entry for this chunk in the FPGA or not:

1) the chunk is allocated, then the transfer is possible immediately; 2) the chunk is not allocated and a directory entry is available, then a latency is generated indicating the cycle number when the chunk will be allocated; 3) the chunk is not allocated, but a request is pending, then the chunk will be available at the cycle defined in scenario 2; 4) the chunk is not allocated and any directory entry is available.

In scenario 1, 2 and 3 the request sent by the kernel is acknowledged. In scenario 4, the request remains blocked until an entry becomes available.

To generate the latencies we use a S-DSM client, which performs the requests in the real environment and we measure the elapsed time. This elapsed time is converted into a number of FPGA cycles and is added to the current cycle counter. Finally cycles are added corresponding to the transfer time between the FPGA-server and the FPGA-client.

B. Compute Kernel Simulation

A compute kernel is developed as a pipeline, where each stage is separated by FIFOs. Each stage performs actions that can be 1) to interact with an external component or 2) to perform processing on data. A global clock is used to synchronize each stage. A stage can perform an action only if its input FIFOs are not empty and its output FIFOs are not full. Figure 4 is an example of a compute kernel architecture for a sparse matrix scalar multiplication. Data access patterns are generated by a finite state machine (FSM). These patterns are supplied to stages (Chunk read prefetch and chunk write prefetch), which perform chunk prefetch. It consists in sending a request to the S-DSM interface. When the request is accepted, the chunk ID is written to a virtual FIFO. We call it virtual FIFO, because, it does not correspond to a component implemented in a hardware design. However, in our study this FIFO allows to limit the number of prefetched elements by stream. Thus, this limit corresponds to the depth of the FIFO (prefetch depth). The memory access stages correspond to the transfer of data between the memory controller and each FIFO associated with a stream. To reproduce the real behavior of a memory controller, only one request can be accepted per cycle when the controller is idle. Each memory access is associated with a latency in order to reproduce behavior of DDR memories. The size of a memory transfer is limited according to a maximum burst length. At each cycle the number of data that can be read or written depends on the width of the bus. Finally, a read access can only be initiated if the FIFO Data has enough space to memorize all the data of a chunk. The size of a FIFO is configurable. The case study of our experiments is the general sparse matrix-matrix multiplication (SpGEMM) with matrices, which cannot be fully stored in the memory of the accelerator or the host node. This case requires the transfer of data between the distributed shared memory and the accelerator during execution. The study aims to determine the best configuration of the architecture to optimize the performance of the application.

Chunk

A. Case Study: Sparse General Matrix-Matrix Multiplication

SpGEMM is widely used to study acceleration methods for sparse linear algebra. This application has a well known behavior and generates irregular memory access patterns that makes it complex to optimize, with usually a low efficiency in terms of floating point operations per unit of time.

[i + 1] -RP [i]
is equal to the number of elements in the row. As shown in Figure 5c, We have adapted the CSR format to the use of chunks. We colocalize the value and the column index of an element to form a pair. The set of pairs representing a row is stored in a chunk, which makes it possible to use the chunks ID to browse the matrix row by row. Then we use chunks metadata to indicate the number of elements contained in the row. This structure reduces the number of memory accesses required to read or write a matrix row. It can be easily adapted to another compressed format (e.g. compressed sparse column format). To develop the compute kernel, we used the row-wise sparse matrix-matrix multiplication algorithm formulated by Gustavson [START_REF] Gustavson | Two fast algorithms for sparse matrices: Multiplication and permuted transposition[END_REF]. It limits random data access and is quite straightforward to parallelize. The kernel reads and distributes the non-zero elements of the first input matrix to several processing elements (PEs). Each PE multiplies the elements received by a row of the second input matrix. Finally the partial products are reduced and written. So, for a kernel with N P E, there are N + 2 streams of data between the memory and the kernel (one to read first input matrix, one to write the output matrix and one by PE to read the second input matrix). The kernel processes single precision floating point numbers. Gigabit Ethernet

B. Simulation Environment

Table I describes some characteristics of the platform used for the simulation. This platform is made up of two nodes. For both configurations the S-DSM server is executed on the Intel Core i7 local node. The Core i7 local node integrates an FPGA interconnected by a PCI Express bus. The Hikey 970 remote node integrates two Arm processors and is interconnected to the local node by a gigabit Ethernet network (Ethernet is implemented over USB 3.0 on the Hikey 970 development board). We use the remote node to model Xilinx FPGAs of the Zynq family, exploiting the fact that their host systems, made of big.LITTLE Cortex processors are similar.

We used a set of matrices (Table II) from the SuiteSparse Matrix Collection [START_REF] Davis | The university of florida sparse matrix collection[END_REF]. All matrices are derived from real applications. We chose matrices of variable sizes and densities because the performance of SpGEMM are data-dependent.

C. Results

We designed this simulation tool to explore different architecture configurations. We based our experiments on the ability of the tool to show the impact of different parameters on the performance of the architecture. For each experiment we limit the number of memory locations so that a matrix cannot be fully stored on the FPGA. In the first part of this subsection we present and analyze the results obtained. In the second part, we discuss the execution speed and the ins and outs of using this simulation tool. For the first test, we use a configuration with 8 processing elements. We vary the number of prefetched elements per stream of data. Intuitively, the higher the number, the less latency has effect. Figure 6 shows the results obtained. They partially confirm our intuition. We can observe that increasing the number of prefetched elements improves performance up to 1024 elements, after which we observe a decrease in performance. This phenomenon is explained by the fact that too early prefetching increases conflicts in the Fig. 6: Computation speed in GFLOP/s according to the number of prefetched elements by stream (higher is better) FPGA memory. This first experiment allows us to determine that the best parameter is 1024 prefetched elements. Fig. 7: Computation speed in GFLOP/s according to the number of processing elements (PEs) (higher is better)

For the second experiment, we vary the level of parallelism and we prefetch 1024 elements per stream. The objective is to observe the limits of the acceleration capacity of the compute kernel. Figure 7 illustrates the results. We can observe that the increase of processing elements allows a speedup, up to 16 PEs. Beyond, the increase in parallelism no longer speed up the execution. These results show that the processing elements are under-exploited due to an insufficient supply of data (data starvation). This phenomenon can be explained either by excessive data access latencies, or by a local bottleneck in the design. The integration of counters in the simulation tool allows us to monitor the activity of each element of the design. In Figure 8, we can see the memory controller occupancy rate. We can see that the bus is saturated for the 16 PEs configuration. This information highlights that the memory bandwidth is the bottleneck of our design. Also, it allows us to estimate the computation speed limit around 3 GFLOPS Fig. 8: Memory controller activity (occupancy percentage) according to the number of processing elements. Close to 100% means saturation For the last experiment, we studied three topologies, which generate different memory access latencies. The first corresponds to the ideal case where all the data is contained in memory at startup (i.e no latency for data access). For the second configuration, we consider an FPGA linked by a PCI Express bus to the node where the S-DSM server is located. Finally, the third configuration models a system where the server and the FPGA are not running on the same node and where the two nodes are interconnected by an Ethernet network. In this configuration the S-DSM client process is executed on the processor of the remote node. For this experiment we use a configuration with 16 processing elements and 1024 prefetched elements per stream. Figure 9 represents the results obtained. It shows Fig. 9: Computation speed in GFLOP/s according the system topology (higher is better) that it is possible to hide the latency of data access with our approach. For the consph and F2 matrices, the difference in performance is small between the configuration without latency and the configuration with the biggest latency. However for the matrices cop20k A, m t1 and s3dkt3m2 we can observe a degradation of performances. We can conclude that performances depend on the data set and that, to optimize the performances it is necessary to reorder the matrices to favor the temporal locality of data access.

The results previously presented show the ability of the tool to explore different architecture configurations. Our hybrid method makes this exploration work easier by using a real software-distributed shared memory system to run simulation on several nodes. We think that this tool has several advantages compared to a homogeneous method, where the whole architecture (processors, interconnects, accelerators) are simulated. The first is the use of physical architecture ensures the generation of accurate and faithful data. The second is to speed up modeling by concentrating all of the efforts on the compute kernel development. Finally, this method makes it possible to quickly simulate a complex system. Fig. 10: Simulation speed in thousands of cycles per second (higher is better) Figure 10 represents the execution times for the experiment shown in Figure 9. For red bars, as we do not simulate latency we do not use the S-DSM environment (i.e. only the simulation engine process is run). In this way, they represent the speed to simulate the compute kernel and the hardware S-DSM server only. The blue and purple bars represent respectively a local execution and a remote execution of the simulation engine. Thus, Figure allows to visualize the cost of modeling the environment of the S-DSM (which includes, a multicore processor and its memory system, a gigabit Ethernet network and at least 2 MPI processes). Obviously, we observe a decrease in the speed of simulation (between 1.2 and 2.3 times slower for local execution and 1.7 and 3.7 times slower for remote execution). However, considering the complexity of the simulated model we can say that our hybrid method still allows rapid simulation.

VI. CONCLUSION AND FUTURE WORK

In this article, we have presented a simulation tool, which aims to study the integration of reconfigurable accelerators in a software-distributed shared memory (S-DSM). Our objective was to simulate the execution of irregular compute kernels, which access to distributed data with variable latencies. To deal with the complexity of modeling this complete system we used a hybrid methodology. This approach consists in simulating only the compute kernel and integrating the simulation engine in the S-DSM. This method generates real latencies from physical architecture. We used sparse general matrix-matrix multiplication as a case study. We have shown, through the results of several experiments, that our simulation tool allows a correct sizing of the architecture to improve the performance of a compute kernel. The tool also allowed to determine that the memory bandwidth is the architecture bottleneck. Finally, the tool allowed to conclude that our approach could make it possible to hide the data access latencies, which is usually a limitation when coping with distributed systems.

To continue the exploration work, we plan to model new accelerator architectures with higher memory bandwidth. In particular we want to model cards that embed High Bandwidth Memory (HBM) technologies. Also, we want to develop other compute kernels with higher arithmetic intensities. Finally, we would like to estimate the energy consumption of the kernels.

To do this we plan to integrate the generation of traces to replay the execution with consumption estimation tools.

Fig. 1 :

 1 Fig. 1: S-DSM semi-structured super-peer topology

Fig. 2 :

 2 Fig. 2: Overview of the reconfigurable accelerator integration architecture

Fig. 3 :

 3 Fig. 3: Compute kernel interface

Fig. 4 :

 4 Fig. 4: Sparse matrix scalar multiplication kernel architecture overview

Fig. 5 :

 5 Fig. 5: Matrix representation

Processing System Host Memory Host CPU S-DSM server FPGA client MPI MPI FPGA FPGA Memory Programmable logic FPGA-server Compute Kernel 0 Compute Kernel 1 Compute Kernel n Interconnect

TABLE I :

 I Simulation platform setup

	Local node	Remote node (Hikey 970)
	Intel Core i7-6800k	Xilinx VC707	ARM Cortex-A73 / Cortex-A53
	3.6 GHz	200 MHz	2.36 GHz/ 1.8 GHz
	6 cores / 12 threads	2.8 k DSP	2 × 4 cores
	LLC: 15 MB	SPM: 5 MB	LLC: 8 MB / 2 MB
	RAM: 64 GB	RAM: 1 GB	RAM: 6 GB
	PCIe Gen2x8

TABLE II :

 II Square matrices used for simulations

	Name	Row	NNZ	Density (%)
	consph	83334	6010480	0.087
	cop20k A	121192	2624331	0.018
	F2	71505	5294285	0.10
	m t1	97578	9753570	0.10
	s3dkt3m2	90449	3753461	0.046

ACKNOWLEDGEMENTS

This work was supported by the LEXIS project, funded by the EU's Horizon 2020 research and innovation programme (2014-2020) under grant agreement no. 825532.