Cédric Bailly
email: cedric.bailly@universite-paris-saclay.fr

T Kernif

Y Hamon

M Adelinet

J Fortin

Controlling factors of acoustic properties in continental carbonates: Implications for high-resolution seismic imaging

Keywords: Continental carbonates, Paludal tufa, Palustrine environment, Diagenesis, Multi-scale porosity, Acoustic properties, Synthetic seismic, Seismic interpretation

Highlights

 Investigation of palustrine and paludal tufa carbonates  Facies and diagenetic characterizations of heterogeneous porous carbonates  Multi-scale measurements of P-wave velocity in the laboratory and on outcrop  Geological significance of synthetic seismograms equivalent to crosswell seismic  Seismic imaging of continental carbonates is strongly controlled by diagenesis

Introduction

Seismic stratigraphy (sensu [START_REF] Vail | Seismic stratigraphy and global changes of sea level[END_REF], originally developed for marine, siliciclastic sediments and later applied to carbonate ones, is based on mapping of seismic reflectors that correspond to contrasts of acoustic impedances [START_REF] Sheriff | Limitations on resolution of seismic reflections and geological detail derivable from them[END_REF], thus geological contrasts having sedimentological and/or diagenetic origin (i.e., [START_REF] Fournier | Geological significance of seismic reflections and imaging of the reservoir architecture in the Malampaya gas field (Philippines)[END_REF][START_REF] Teillet | Origin of seismic reflections in a carbonate gas field, Lower Miocene, offshore Myanmar[END_REF][START_REF] Zampetti | Well log and seismic character of Liuhua 11-1 Field , South China Sea ; relationship between diagenesis and seismic reflections[END_REF].

In order to understand the stratigraphic value of seismic reflectors, several studies modelled 2D synthetic seismic sections, based on seismic-size well-exposed outcrop descriptions together with punctual ultrasonic measurements of samples (e.g., Anselmetti et al., 1997a;[START_REF] Jafarian | Synthetic seismic model of a Permian biosiliceous carbonatecarbonate depositional system (Spitsbergen, Svalbard Archipelago)[END_REF][START_REF] Janson | Seismic expressions of a Miocene prograding carbonate margin, Mut Basin[END_REF][START_REF] Kenter | Seismic models of a mixed carbonate siliciclastic shelf margin : Permian upper San Andres Formation, Last Chance Canyon, New Mexico[END_REF][START_REF] Kleipool | Variations in petrophysical properties along a mixed siliciclastic carbonate ramp (Upper Jurassic, Ricla, NE Spain)[END_REF][START_REF] Kleipool | Seismic characterization of switching platform geometries and dominant carbonate producers (Miocene, Las Negras, Spain)[END_REF][START_REF] Stafleu | Seismic models of a prograding carbonate platform: Vercors, south-east France[END_REF][START_REF] J O U R N A L P R E -P R O O F Stafleu | Seismic models of a shelf-margin depositional sequence: Upper San Andreas Formation, Last Chance Canyon, New Mexico[END_REF][START_REF] Zeller | Sequence architecture and heterogeneities of a field-Scale Vaca Muerta analog (Neuquén Basin, Argentina) -from outcrop to synthetic seismic[END_REF]. Assuming that plug-scale measurements are representative of decameter rock units, this approach is suitable for assessing the geological significance of reflectors representing large-scale geological heterogeneities within seismic resolution (size higher than 10 meters). Nevertheless, it is not accurate enough for discussing meter-scale heterogeneities, beyond seismic resolution, that are of crucial importance for the characterization of heterogeneous reservoirs. Fortunately, in order to better understand "sub-seismic" heterogeneities (i.e. meter-scale heterogeneities), crosswell seismic has been developed. Such method aims to image inter-well areas using high frequency acquisitions (between 100 and 2000 Hz), resulting in the imaging of reflectors representing meter-scale geological contrasts which bridge the gap between sonic log measurements and conventional seismic (e.g. [START_REF] Harris | High-resolution crosswell imaging of a Texas carbonate reservoir: Part I-Project summary and interpretation[END_REF][START_REF] Leiceaga | Crosswell seismic applications for improved reservoir understanding[END_REF][START_REF] Yu | Crosswell seismic imaging for deep gas reservoir characterization[END_REF]. For instance, [START_REF] Parra | Permeability and porosity images based on NMR, sonic and seismic reflectivity : Application to a carbonate aquifer[END_REF] used a combination of nuclear magnetic resonance, sonic and density well logs with inverted impedance section based on crosswell seismic for characterizing the geometry of heterogeneous vuggy carbonates. [START_REF] Antonelli | Integrated crosswell seismic: Case histories in advanced technology to improve reservoir description[END_REF] demonstrated the benefit of crosswell seismic for detecting sub-seismic heterogeneities in order to adapt their development strategy in regard to the lateral variation of the reservoir compartmentalization. More recently, [START_REF] Beavington-Penney | Integration of static and dynamic data and high-resolution sequence stratigraphy to define reservoir architecture and flow units within a 'super giant' gas condensate and oil field, Kazakhstan[END_REF] imaged the lateral continuity of fourth-order cycles within a carbonate reservoir using crosswell seismic to better understand the architecture of flow units. However, if we want to accurately interpret crosswell seismic, we must understand the links between meter-scale geological heterogeneities and their seismic imaging. Indeed, these links can help to integrate petrophysical heterogeneities within reservoir model and thus accurately predict the J o u r n a l P r e -p r o o f compartmentalization of carbonate reservoirs [START_REF] Brigaud | Characterization and origin of permeability-porosity heterogeneity in shallow-marine carbonates : From core scale to 3D reservoir dimension (Middle Jurassic, Paris Basin, France)[END_REF][START_REF] Herlinger | Influence of diagenesis on the quality of Lower Cretaceous pre-salt lacustrine carbonate reservoirs from northern Campos Basin, offshore Brazil[END_REF][START_REF] Thomas | Contribution of drone photogrammetry to 3D outcrop modeling of facies, porosity, and permeability heterogeneities in carbonate reservoirs (Paris Basin, Middle Jurassic)[END_REF][START_REF] Vincent | Unravelling the complexity of thin (subseismic) heterogeneous carbonate reservoirs: an integrated study of the Albian Mauddud Formation in the Greater Burgan Area, Kuwait[END_REF]. To be consistent, such an approach must be applied on several geological objects highlighting different kinds of heterogeneities, including sedimentary facies, diagenesis and pore types.

Continental carbonates may develop in a broad range of sedimentary environments, including lacustrine and palustrine, hydrothermal, paludal, fluvial and alluvial settings (Alonso-Zarza and Tanner, 2010a). Consequently, they present a wide variety of sedimentary facies that may be modified by early diagenetic processes (Alonso-Zarza and Tanner, 2010b; [START_REF] Armenteros | Diagenesis of Carbonates in Continental Settings[END_REF][START_REF] De Boever | What do we really know about early diagenesis of non-marine carbonates?[END_REF], thus creating complex porous networks embedded in mono-to polygenic mineralogical fabrics including carbonates and non-carbonates elements. This multi-scale geological heterogeneity should imply a large variability of their acoustic properties. However, only a few studies exist that document the elastic properties of these sedimentary rocks and compare them to an accurate geological description (Bailly et al., 2019a;[START_REF] Fournier | The equivalent pore aspect ratio as a tool for pore type prediction in carbonate reservoirs[END_REF]Garcia-del-Cura et al., 2012;Regnet et al., 2019a;[START_REF] Reijmer | Petrophysics and sediment variability in a mixed alluvial to lacustrine carbonate system (Miocene, Madrid Basin, Central Spain)[END_REF][START_REF] Soete | Acoustic properties in travertines and their relation to porosity and pore types[END_REF][START_REF] Vasquez | Petroacoustics and composition of presalt rocks from Santos Basin[END_REF]. In this context, we focus our study on palustrine and paludal tufa carbonates. Following the definition of [START_REF] Freytet | Les sédiments lacustres carbonatés et leur transformations par émersion et pédogenèse. Importance de leur identification pour les reconstructions paléogéographiques[END_REF], "a palustrine carbonate must present primary lacustrine depositional criteria (e.g. biota, sedimentary structures) together with evidences of subsequent exposure features (e.g. root traces, desiccation, …)". Consequently, these carbonates may develop in a wide range of lake environments. More specifically, paludal tufa carbonates accumulate exclusively in cool freshwater environments [START_REF] Pedley | Classification and environmental models of cool freshwater tufas[END_REF]. They correspond to calcite sediments accumulated under low depositional rates and ambient temperatures, forming poorly bedded and highly porous rocks (Capezzuoli et al., 2014). While the imaging of tufa carbonates was undertaken by [START_REF] Pedley | The recognition of barrage and paludal tufa systems by GPR: case studies in the geometry and correlation of hidden Quaternary freshwater carbonate facies[END_REF] with ground penetrating radar, there is a paucity of studies focusing on their petroacoustic properties and seismic imaging.

In this article, we investigated two study sites showing successions of heterogeneous paludal tufa and palustrine carbonates of Pliocene age belonging to the same geological formation (Kokkarion fm. of Samos Island, Greece;[START_REF] J O U R N A L P R E -P R O O F Weidmann | Neogene Stratigraphy of the Eastern Basin, Samos island, Greece[END_REF]. Sedimentary descriptions made at outcrop, as well as petrographic and petrophysical characterization of samples in the laboratory enabled us to build a sedimentary model and to define a paragenetic sequence. One of the main peculiarities of these J o u r n a l P r e -p r o o f deposits is the occurrence of cm-size moulds of macrophyte stems typical of paludal environment [START_REF] Pedley | Classification and environmental models of cool freshwater tufas[END_REF], which raises the question of plug measurement representativity [START_REF] J O U R N A L P R E -P R O O F Ehrenberg | Whole core versus plugs: Scale dependence of porosity and permeability measurements in platform carbonates[END_REF]. To characterize acoustic properties of such rocks that may have a Representative Elementary Volume (REV sensu [START_REF] Bear | Dynamics of Fluids in Porous Media[END_REF] higher than the length of regular plugs, we used in-situ measurements of P-wave velocity at outcrops (e.g. [START_REF] Matonti | Heterogeneities and diagenetic control on the spatial distribution of carbonate rocks acoustic properties at the outcrop scale[END_REF]. Based on these in-situ P-wave velocity and plug density measurements, we built seismic traces at a frequency equivalent to crosswell seismic. Such an approach coupling multi-scale acoustic measurements and geological descriptions finally aimed at discussing the geological controlling factors of the acoustic properties and seismic imaging of palustrine and paludal tufa carbonates.

Study framework

The two study sites are located on Samos, a Greek island in the eastern part of the Cyclades, in the Aegean-Anatolian area (Fig. 1a). Samos is characterized by different extensional regimes. Since the middle Eocene (~ 45 Ma), the Hellenic subduction induced a major back-arc extension which has led to the exhumation of metamorphic core complex [START_REF] Jolivet | Aegean tectonics: progressive strain localisation, slab tearing and trench retreat[END_REF]. During the middle Miocene, a slab tearing episode below the western margin of Anatolia induced a retreat of the western part of the slab. This led to a greater extension westward, thus splitting Cyclades and Menderes Massif areas [START_REF] Jolivet | Aegean tectonics: progressive strain localisation, slab tearing and trench retreat[END_REF]. According to [START_REF] Ring | Structural analysis of a complex nappe sequence and late orogenic basins from the Aegean Island of Samos, Greece[END_REF], this peculiar structural pattern generated a local ENE-WSW sinistral strike-slip faulting corridor, resulting in the formation of two pull-apart basins in Samos (Fig. 1a). In this study, we focused on the eastern basin, the Mytilini Basin which contains a more than one-thousand-meter-thick succession of Mio-Pliocene sedimentary rocks unconformably deposited on a metamorphic basement and distributed in five lithostratigraphic formations [START_REF] J O U R N A L P R E -P R O O F Weidmann | Neogene Stratigraphy of the Eastern Basin, Samos island, Greece[END_REF] Fig. 1a andb). The age of the sedimentary infill is well-known and is based on palynological study, mammal fauna description and radiochronological dating on volcanic rocks [START_REF] Ioakim | The Late Miocene Mammal Faunas of the Mytilinii Basin, Samos Island, Greece: New Collection[END_REF][START_REF] J O U R N A L P R E -P R O O F Koufos | A synopsis of the late Miocene Mammal Fauna of Samos Island, Aegean Sea, Greece[END_REF][START_REF] Pe-Piper | Late Miocene igneous rocks of Samos: the role of tectonism in petrogenesis in the southeastern Aegean[END_REF]Fig. 1b). Two sections were studied: the Marina and the Antenna sections, located 5 km apart (Fig. 1a). They cover the Kokkarion formation that succeeds to the siliciclastic facies of the Mytilini formation (Fig. 1a andb) and is capped by an erosional surface J o u r n a l P r e -p r o o f [START_REF] J O U R N A L P R E -P R O O F Weidmann | Neogene Stratigraphy of the Eastern Basin, Samos island, Greece[END_REF]. The Kokkarion Fm. is thus attributed to the Zanclean period. The Marina section consists of a well-exposed outcrop (Fig. 2a,b,c;37°41'24.96"N,26°56'55.98"E), composed of two carbonate intervals (Units 1 and 3), separated by a clay-dominated interval (Unit 2). The Antenna section is located on the topmost part of a hill, showing a succession of meter-scale layers of carbonates (Fig. 2d,e;37°44'20.98"N,26°56'45.39"E). J o u r n a l P r e -p r o o f

Material and methods

Field work

Sedimentary geology and sampling

Geological field work (facies description, logging, …) was carried out on two sedimentary sections in June 2017 and June 2018 (Fig. 1a, Fig. 2). Considering the vertical facies variations, 57 samples were collected for laboratory characterization purposes (~ one sample per meter). No samples were collected in the Unit 2 of the Marina section, mainly due to the low cohesiveness of the outcropping rocks (Fig. 2a,g).

Acoustic measurements

A high-resolution in-situ acoustic characterization was performed using a portable acoustic device (Pundit PL-200, PROCEQ) with 250 kHz transducers for measuring P-wave velocities. The traveling times of P-waves (first break) were picked on the digital oscillograph's touchscreen and divided by the path length for obtaining the P-wave velocities. The acquisitions were done horizontally, parallel to the stratification, with a distance of 20 cm between the sensors. We used a gel (Sonctec 54-T04) to ensure a good coupling between the outcrop surfaces and the transducers. The uncertainty on the velocity measurements is dependent on the first break picking and on the path length measurements (error < 5 %). Note that the horizontal measurements did not take into account the occurrence of bedding planes (080/30N). These measurements were done with a constant vertical sampling rateone measurement every 20 cmwhich allowed us to characterize the P-wave velocity of meter-thick as well-as decimeter-thick beds using the same approach (Fig. 2f,h,i). Furthermore, the acoustic acquisitions were done on rock surfaces' that do not exhibit any evidence of large cracks and fractures.

Therefore, the obtained results mainly reflect the properties of sedimentary rocks. Nevertheless, the impact of small scale structural heterogeneities can't be totally ruled out if the in-situ P-wave velocities variations are not comparable to the acoustic measurements performed in the lab [START_REF] Matonti | Heterogeneities and diagenetic control on the spatial distribution of carbonate rocks acoustic properties at the outcrop scale[END_REF]Bailly et al., 2019b). Note that fewer in-situ measurements were carried out on the Unit 2 of the Marina section (Fig. 2a) due to the weak rock cohesiveness (lack of signal on the oscillograph).

J o u r n a l P r e -p r o o f

Using in-situ P-wave velocity measurements aims to investigate sampling lengths higher than conventional plugs while characterizing centimeter-scale REV. Indeed, assuming a P-wave velocity in the range of 3000 m.s -1 and 6000 m.s -1 , the used frequency (250 kHz) implies the generation of wavelength sizes in the range of 1.2 and 2.4 cm (upper bound of the characterized REV). Conversely, by analogy with seismic, the lower bound of the REV is higher than the quarter wavelength size, a value in the range of 0.3 and 0.6 cm for in-situ P-wave velocity measurements [START_REF] Al-Chalabi | Principles of Seismic Velocities and Time-to-Depth Conversion[END_REF][START_REF] Sheriff | Exploration seismology[END_REF].

Laboratory analyses

Petrographic characterization

Fifty-seven thin sections were prepared, impregnated with blue epoxy to identify pore space.

They were studied using both conventional and cathodoluminescence microscopy (CL). We used the [START_REF] Dunham | Classification of Carbonate Rocks According to Depositional Textures[END_REF] and [START_REF] Choquette | Geologic Nomenclature and Classification of Porosity in Sedimentary Carbonates[END_REF] classifications for describing the limestone textures and the pore space. The main diagenetic phases were identified and organized chronologically according to their relative timing, mainly deduced from crosscutting relationships, as well as replacement and pseudomorphosis features. A visual quantification of the main diagenetic features was done (relative intensity from (0) absent to (5) pervasive). Additional SEM observations were performed for imaging the morphology of micrite and the microporous network of a few samples. We used the classification of Deville de [START_REF] Deville De Periere | Morphometry of micrite particles in cretaceous microporous limestones of the Middle East. Influence on reservoir properties[END_REF] for SEM observations.

Physical measurements

Depending on the sample size, horizontal plugs were cored with a diameter of 1 inch (25 mm) for 8 samples and 1.5 inch (40 mm) for 49 samples. The porosity and density were measured with the triple-weight method by assessing the plug mass under three different conditions: dried, fluid-saturated and fluid-saturated suspended in the saturating fluid. To ensure accurate measurements, we carefully followed this procedure:

-First, samples were dried in an oven during 48 hours at 60°C before measuring the dry-masses.

J o u r n a l P r e -p r o o f -Then, during a minimum timing of 24 hours, the dried-samples were placed in a desiccator connected to a vane pump to ensure the vacuum of the whole connected porosity (~ 10 Pa).

-A subsequent transfer of degassed and demineralised water within the desiccator was progressively done in order to ensure a fully saturation of the samples' connected porosity.

-Finally, saturated and apparent mass measurements were carried out and we calculated porosity and density. P-wave velocities were obtained on dry samples using 500 kHz transducers connected to a manually controlled ultrasonic pulser-receiver system (5072PR, Olympus) and a digital oscilloscope (DPO4034B, Tektronix). A gel (Sonctec 54-T04) was used to ensure a good coupling between the plug surfaces and the transducers. The first breaks were directly measured on an oscillograph and divided by the length of the sample to compute the P-wave velocity. A constant and very low axial pressure was applied on the samples using a clamping device (120 kPa for the 1 inch plugs and 40 kPa for the 1.5 inch plugs). Given that we wanted to compare the laboratory measurements with the in-situ P-wave measurements, we did not realize those measurements under confining pressure. The uncertainty of the velocity measurements was mainly dependent on the first break picking (error < 5 %). Assuming a Pwave velocity in the range of 3000 and 6000 m.s -1 , the transducer frequency (500 kHz) implies the generation of wavelength sizes in the range of 6 mm and 1.2 cm, equal to the upper limit of the REV.

Conversely, the lower limit of the REV is in the range of 1.5 mm and 3 mm (quarter wavelength criterion; [START_REF] Sheriff | Limitations on resolution of seismic reflections and geological detail derivable from them[END_REF]Geldart, 1995, Al-Chalabi, 2014).

Statistical analyses

Statistical analysis was conducted, consisting of: 1) normal law computation to compare the Pwave velocities acquired both in-situ and in the laboratory; 2) violin plots computation (combination of a boxplot and a probability density) to look at the in-situ P-wave velocities in the light of facies classification; and 3) Kernel regression computation to highlight the vertical trends of the in situ P-wave velocity (smooth curves with a 95 per cent confidence interval). We used the package ggplot2 of R, a free software environment for statistical computing and graphics.

J o u r n a l P r e -p r o o f

Synthetic seismic modelling

Based on the in-situ P-wave velocities and plug density measurements, synthetic seismic analyses were performed using EasyTrace TM Software (see [START_REF] Jafarian | Synthetic seismic model of a Permian biosiliceous carbonatecarbonate depositional system (Spitsbergen, Svalbard Archipelago)[END_REF] for the equations). We computed the acoustic impedance, the reflectivity coefficient (RC) and finally the 1D seismic trace (zero offset) using a convolution on the RC with an analytical Ricker wavelet. We chose a central frequency of 500 Hz based on resolutions calculation. Indeed, for a P-wave velocity in the range of 3000-6000 m.s -1 , this central frequency implied a limit of resolvability of 1.5-3 meters (quarter wavelength criterion, [START_REF] Sheriff | Exploration seismology[END_REF][START_REF] Al-Chalabi | Principles of Seismic Velocities and Time-to-Depth Conversion[END_REF]. This leads to characterize meterscale impedance contrasts, comparable to the crosswell seismic resolution (approximately 3 meters according to [START_REF] Harris | High-resolution crosswell imaging of a Texas carbonate reservoir: Part I-Project summary and interpretation[END_REF]. For Marina section, because of the absence of density measurements for unit 2, acoustic impedance was computed assuming a linear extrapolation of density between 15 and 29 meters.

Results

Facies definition

F1: Reddish to brownish clays

Facies F1 consists of centimeter to meter-scale levels of monotonous reddish to brownish clays (Fig. 2a, g, Fig. 3a). The thickest layers may contain a few floating sub-rounded cm-size quartz clasts.

Locally, isolated, nodular, whitish cm-size concretions are also observed and may be associated with root traces. This facies is only observed in the Marina section (Fig. 7a).

F2: Nodular and marly mudstone

Facies F2 corresponds to centimeter to decimeter layers of nodular and marly mudstone embedded in the reddish to brownish clays (Fig. 3b). It is not well-lithified, contains numerous root traces, cracks and rare sub-rounded to angular mm-size quartz clasts. F2 is only observed in the unit 2 of the Marina section, in association with F1 (Fig. 7a).

F3: Silty pedogenic mudstone/wackestone

J o u r n a l P r e -p r o o f At outcrop, the silty pedogenic mudstone/wackestone facies (F3) displays decimetre-scale beds with irregular surfaces (Fig. 2b). It corresponds to light beige limestones containing a few bioclasts (ostracods, gastropods), leaves and millimetric angular to sub-angular quartz (Fig. 3c) embedded in a microporous micrite (Fig. 3d). Macro-or microscopically, F3 shows numerous root moulds that point to a high pedogenic activity (Fig. 3c). This observation is strengthened by the occurrence of both curved cracks and calcified root cells (Fig. 3d). The silty pedogenic mudstone and wackestone are only observed in units 1 and 2 of the Marina section (Fig. 7a).

F4: Quartz-rich floatstone

Facies F4 corresponds to decimetre-thick beds showing an irregular base that may be of erosive origin. It contains sub-rounded to sub-angular, mm-scale quartz grains embedded in a light beige matrix.

Microscopically, F4 shows numerous infra-millimetric angular to sub-angular quartz within a microporous micrite (Fig. 3e). It displays locally a few carbonate clasts of millimeter size, mostly phytoclasts (Fig. 3e). The quartz-rich floatstone shows only two occurrences in the unit 1 of the Marina section (Fig. 7a).

F5: Peloidal and intraclastic floatstone/wackestone

This facies presents pluri-decimeter-to meter-thick tight beds often associated with exposure surfaces at their tops (Fig. 2b,d,e). Macroscopically, the peloidal and intraclastic floatstone/wackestone [START_REF] Alonso-Zarza | Palaeoenvironmental significance of palustrine carbonates and calcretes in the geological record[END_REF] presents a greyish matrix containing abundant root moulds. It displays also pseudomicrokarsts (sensu Freytet and Verrechia, 2002; see part 4.2.4. for explanations) infilled with millimeter rounded intraclasts embedded in a beige matrix. Microscopically, infra-millimeter rounded peloids are widely observed, commonly surrounded by a calcitic cement (Fig. 3f). Numerous root casts are also present (cemented root moulds sensu Klappa, 1980, Fig. 3f). Facies F5 is observed in both studied sections (Fig. 7).

F6: Bioclastic packstone/wackestone

J o u r n a l P r e -p r o o f Facies F6 corresponds to thick massive beds showing irregular bases and tops, related to exposure surfaces (Fig. 2b). Macroscopic view of the bioclastic packstones and wackestones shows a beige to greyish matrix with root structures (Fig. 3g). In thin section, peloids, ostracods and gastropods and non-recognizable clasts are observed (Fig. 3h). Locally, some charophyte oogones are present, as well as phytoclasts, oncoids and rare silt-sized quartz. All these different elements are embedded in a dark micritic matrix. The bioclastic packstone and wackestone are mainly observed in the units 1 and 3 of the Marina section, but also at the topmost part of the Antenna section (Fig. 7).

F7: Phytoherm framestone

At outcrop, the phytoherm framestone occurs as decimetre to meter-thick patches and beds with irregular boundaries (Fig. 2c,d,e, Fig. 4a). They show millimeter to centimeter stem-moulds acting as a framework of anchored macrophytes in life position (Fig. 4b). Facies F7 is spatially closely related with facies F8 (Fig. 2c, Fig. 4a). Macroscopically, facies F7 displays dark beige calcite fringes mimicking macrophyte stems, surrounded by a light beige matrix (Fig. 4c). Microscopically, these fringes consist of polycyclic calcite sheets (Fig. 4d). Millimeter-size macropores embedded in a microsparitic to sparitic framework were also observed (Fig. 4e). They are partially to completely cemented and/or filled by a micritic to peloidal matrix. A few levels present frameworks of charophyte thalli. Facies F7 does not contain any detrital fraction. The phytoherm framestones are observed in both studied sections (Fig. 7).

F8: Phytoclastic rudstone

Facies F8 shows pluri-decimeter to meter-thick beds with irregular stratification, locally erosive base and exposure features (Fig. 2c,d). Macroscopically, the phytoclastic rudstones present dark beige millimeter to pluri-centimeter clasts of macrophyte stem relics embedded in a beige matrix with local macroporosity (Fig. 4f). The petrographic observations highlight preserved and broken microsparitic to sparitic phytoclasts surrounded by a dark micritic matrix (Fig. 4g). Gastropods, oncoids, charophyte thalli and oogones are also present. The macropores may be partly to totally filled by a calcitic cement.

J o u r n a l P r e -p r o o f

A few beds of this facies contain a detrital fraction of silty quartz. The phytoclastic rudstone occurs in both studied sections (Fig. 7).

F9: Phytoclastic floatstone

The phytoclastic floatstone displays decimeter-to meter-thick massive beds associated with flat to irregular surfaces (Fig. 2b,c). Macroscopic observations show scattered dark beige oncoids and mmsized phytoclasts embedded in a beige matrix (Fig. 4h). Microscopic observations show rounded micritic to microsparitic oncoids and phytoclasts surrounded by a dark micritic matrix, occasionally pervasively and highly microporous (Fig. 4i). The macropores may remained unfilled or partly to totally filled by calcitic cement. Few beds of F9 contain a detrital fraction of silty quartz. This facies is present in both studied sections (Fig. 7).

J o u r n a l P r e -p r o o f

Diagenetic characterization

All the facies described above show evidence of early diagenetic modifications. The various diagenetic phases, including multiple types of cement, dissolution and recrystallization events are described. They are organized chronologically, according to their relative abundance and timing (Fig. 5), mainly deduced from crosscutting relationships, observed in the field and during petrographic analyses.

No microscopic characterization of facies F1 and F2 was done.

Micritization

J o u r n a l P r e -p r o o f

Micritization consists in the development of a micrite envelop around grains (gastropods, charophyte thalli, ostracods). It also occurs at the surface of the polycyclic fringe sparitic cements developed around the stem-moulds (Fig. 4d). Micritization is sporadically observed in facies F5, F6, F7, F8 and F9 in the Marina and Antenna sections (Fig. 5). [START_REF] Purser | Sédimentation et diagenèse des carbonates néritiques récents; les éléments de la sédimentation et de la diagenèse[END_REF] described such features in marine carbonates and associated them to a syndepositional process. [START_REF] Pedley | Freshwater (Phytoherm) reefs: the role of biofilms and their bearing on marine reef cementation[END_REF] also interpreted these "micrite fringes" as the earliest cements developing around the macrophyte stems. [START_REF] Lettéron | Multi-proxy paleoenvironmental reconstruction of saline lake carbonates: Paleoclimatic and paleogeographic implications (Priarbonian-Rupelian, Issirac Basin, SE France)[END_REF] observed micritized clasts in continental carbonates located under subaerial surfaces. According to [START_REF] Swirydczuk | The Pliocene Glenns Ferry Oolite: lake-margin carbonate deposition in the southwestern Snake river Plain[END_REF], micro-boring by endolithic algae around grains may be responsible of micritization.

Root moulds

Numerous root moulds are observed both at outcrop (vertical irregular tube-shaped root moulds, Fig. 6a) and in hand samples (branched rootlet network, Fig. 6b). These moulds can be solution enlarged, remained open or infilled by internal sediment, or various cements. They are commonly observed in facies F2, F3, F5 and more rarely observed in facies F4, F6 and F9, in both studied sections (Fig. 5).

These root traces and moulds are classically associated to a pedogenic activity occurring in palustrine setting [START_REF] J O U R N A L P R E -P R O O F Freytet | Lacustrine and palustrine carbonate petrography : an overview[END_REF].

Cracking

Circum-granular cracks are observed around oversized clasts (Fig. 6c). They are only identified in facies F2 and F3 of the Marina section, in close association with root moulds (Fig. 5a).

These curved cracks [START_REF] Freytet | Les sédiments lacustres carbonatés et leur transformations par émersion et pédogenèse. Importance de leur identification pour les reconstructions paléogéographiques[END_REF] outline desiccation episodes associated with the exposure of sediments (Alonso-Zarza, 2003).

Microkarstification

Microkarstification is observed below irregular surfaces, with decimeter-size reliefs infilled by a coarse brecciated material. Some of these structures still show enlarged root hollows, infilled by the same breccia or by a calcite cement. Microscopically, a complex irregular network of "vuggy" porosity J o u r n a l P r e -p r o o f is observed and infilled by vadose silt (geopetal structure) and granular to blocky calcite (Fig. 6d). These "pseudomicrokarsts" (in the sense of [START_REF] J O U R N A L P R E -P R O O F Freytet | Lacustrine and palustrine carbonate petrography : an overview[END_REF] are mainly observed in the Marina section (Fig. 5a) and occur occasionally in the Antenna section (Fig. 5b). They are abundant to pervasive in facies F5, common to abundant in facies F3 and F6 and F9, and rare in facies F4.

According to [START_REF] J O U R N A L P R E -P R O O F Freytet | Lacustrine and palustrine carbonate petrography : an overview[END_REF] "pseudomicrokarstification" is due to mechanical enlargement of root traces and not dissolution. This feature is common in palustrine and lacustrine environments and points to early diagenesis occurring in vadose environment.

Vadose silt and dripstone cements

Pseudomicrokarsts, root hollows, or other macropores may be partially affected by geopetal infills composed of crystalline and vadose silts (Fig. 6d andf). Additionally, dripstone cements (sensu Flügel, 2010, Fig. 6e andf) may also occur in the primary inter-framework voids of the phytoherm framestone (F7) and in pseudomicrokarsts. The vadose silts are rarely to commonly observed in both sections (Fig. 5). The dripstone cements are mainly observed within the Antenna section (Fig. 5b) in facies F5, F7, F8 and F9. These cements are non-luminescent in CL. The timing of the vadose silt infill with respect to other processes may vary between Marina and Antenna sections (Fig. 5). For the Marina section, vadose silts occur before a subsequent pore-lining cement (Fig. 6d) while in the Antenna section, they occur after pore-lining cement (Fig. 6f).

The pendant morphology generally indicates vadose conditions [START_REF] Flügel | Microfacies of Carbonate Rocks. Analysis, Interpretation and Application[END_REF], while the nonluminescence suggests oxidizing conditions, also in line with a vadose environment [START_REF] Meyers | Calcite cement stratigraphy : an overview[END_REF].

The specific distribution of these silts cements associated to roots and pseudomicrokarsts suggests an early meteoric diagenesis in a vadose setting.

Pore-lining cement fringe

A pore-lining cement fringe may partially occlude the porosity of the studied carbonates. It mostly consists of a granular calcite with crystal size comprised between 50 µm and 150 µm. Note that one occurrence of early pore lining cement corresponds to an acicular cement (white arrow, Fig. 6f). This phase succeeds dripstone cements (Fig. 6e) and occurs before or after vadose silt deposition J o u r n a l P r e -p r o o f (Fig. 6d, f) It is mainly observed in facies F5 and F7, occasionally in facies F8 and F9, and more rarely in facies F3 and F6. The pore-lining cement is more common in the Antenna section than in the Marina section (Fig. 5a,b).

The cross-cutting relationships with dripstones and vadose silts indicate an early cement phase, probably associated to a meteoric phreatic setting.

Aggrading recrystallization

The subsequent diagenetic phase consists in aggrading recrystallization, implying an increase of the micrite crystal size. It occurs as patches within matrix (Fig. 6c) or affect intensely to pervasively the whole fabric of the studied carbonates (Fig. 6e,f,g). SEM observations within a recrystallized sample associated to root casts (Fig. 6g) show the presence of a serrate micrite with subrounded crystals surrounded by larger crystals with euhedral overgrowths (Fig. 6h). The intensity of this recrystallization process is higher in the Antenna section than in the Marina section. It is rare in facies F3 (Fig. 5a) and affects facies F5, F6, F7, F8 and F9 with different intensities (Fig. 5a,b). Such a recrystallization process has already been described by [START_REF] Volery | Lacustrine microporous micrites of the Madrid Basin (Late Miocene, Spain) as analogues for shallow-marine carbonates of the Mishrif reservoir Formation (Cenomanian-early Turonian, Middle East)[END_REF]. These authors argued that these crystal morphologies are due to an LMC-LMC recrystallization within a phreatic lens, a hypothesis that can be advanced here, based on the crystal morphology and LMC mineralogy. Even if the timing of this phase is unclear, it seems coeval with the pore-lining and blocky cementation that occur early after deposition, in a meteoric phreatic setting.

Blocky calcite cement

Following the previous phases, a blocky calcite cementation occurs (Fig. 5). It consists of calcite crystals with sizes up to 500 µm (Fig. 6i). It totally fills the porosity (Fig. 6 d,f,g,i). As highlighted by the CL pictures, different stages of calcite are identified (Fig. 6j). In most of the cases, it is nonluminescent with a few thin bright orange bands. Blocky calcite cement is mostly observed in the Antenna section, like the pore-lining cement and the recrystallization (Fig. 5b). It affects all the facies, except facies F4.

J o u r n a l P r e -p r o o f

The crystal morphology and the luminescence pattern, similar to the older banded cement (OBC) of [START_REF] Meyers | Calcite cement stratigraphy : an overview[END_REF], suggest precipitation in an active freshwater phreatic zone [START_REF] Dickson | Identification of subaerial exposure surfaces and porosity preservation in Pennsylvanian and Lower Permian shelf limestones, eastern Central basin platform, Texas[END_REF].

Description of the vertical evolution of facies and diagenesis

Marina section

The Marina section is divided in three main lithostratigraphic units (Fig. 7a). The first one consists of a 15 m thick succession of carbonate facies (F4, F5, F6, F7, F8 and F9) that alternate with reddish to brownish clays (F1) or silty pedogenic mudstone (F3). Whereas F1 and F3 are dominantly affected by root moulds and pseudomicrokarsts, carbonate beds show abundant recrystallization, and phreatic cement occluding the macroporosity. In a lesser extent, these carbonate beds also show root traces and erosive base. The topmost three meters of the unit 1 show the most intense diagenesis, with the highest occurrences of diagenetic phases.

The second unit, between 15 and 29.5 m, mainly consists of reddish to brownish clays (F1)

showing occasional decimeter-to meter-scale beds of nodular and marly mudstone with numerous root traces (F2). A decimeter-thick tight bed of silty pedogenic mudstone (F3) capped by a 20 centimeterthick bed of sandstone is also observed between 20 and 21 m.

The third unit (between 29.5 and 38 m) is dominated by pure carbonate rocks (F5, F6, F7 and F9). The base of the unit is highly affected by pedogenesis and shows numerous root traces and an upward increasing intensity of recrystallization and cementation. The second part of the unit is mainly dominated by decimeter-to meter-thick beds of heterogeneous tufa carbonates (F8 and F9). These beds show evidence of a common to intense recrystallization as well as a relatively rare cementation.

Antenna section

The Antenna section exclusively consists in pure carbonate facies F5, F6, F7, F8 and F9 (Fig. 7b). Between 0 m and 11.4 m, tufa-related facies occur (F7, F8, F9) showing intense to pervasive J o u r n a l P r e -p r o o f recrystallization, with rare to common vadose features and a moderate to intense phreatic cementation.

In these levels, numerous pedogenic exposure surfaces occur, associated with decimeter-thick beds of peloidal and intraclastic packstones. These beds show a common to intense recrystallization and phreatic cementation and some vadose features together with rarely preserved root moulds. The section is covered (not exposed) between 11,4 and 17 m.

Between 17 and 18.5 meters, several decimeter to meter-thick beds of tufa-related facies (F7, F8, F9) are observed, showing evidence of intense recrystallization and phreatic cementation. The P-wave velocity-porosity data is compared to the empirical Raymer-Hunt-Gardner equation (RHG, Raymer et al., 1980) computed for a pure calcite medium in atmospheric conditions, indicating J o u r n a l P r e -p r o o f a decrease of P-wave velocity with increasing porosity: VpRHG = (1-Φ) 2 *VpCalcite + Φ*VpFluid (VpCalcite = 6400 m.s -1 ; VpAir = 340 m.s -1 ; [START_REF] Mavko | The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media[END_REF]. This equation assumes that the rocks are isotropic and monomineralic, well cemented and do not contain any crack-like or mould-like pores. Note that this equation is used to discriminate samples in the light of their pore geometries and mineralogical content.

Here, we use the term "fitting with RHG" when our data are comprised within the +/-5% of the RHG trend.

Table 1 summarizes the whole laboratory dataset, including petrographic characterization and petrophysical measurements. The statistical distribution of petrophysical properties are indicated in table 3. The Marina samples present scattered P-wave velocities (ranging between 2500 m.s -1 and 6200 m.s -1 ; median = 5226 m.s -1 ), associated with a large variation of porosity, from 3 % up to 29 % (Fig. 8a). A part of this dataset fits with RHG while a few samples exhibit higher (n =4) and lower (n = 8) P-wave velocity values than expected. The dataset exhibits normal law distributions for both Pwave velocity and porosity data (Fig. 8b andc). The Antenna samples shows high P-wave velocity values (from 5000 m.s -1 up to 6200 m.s -1 ; median = 5880 m.s -1 ) with porosity values lower than 8 % (Fig. 8a). Most of this dataset follows the RHG equation, except a few data that exhibit lower P-wave velocity than expected (P-wave velocity values lower than 5500 m.s -1 ). Moreover, the dataset exhibits normal law distributions for both P-wave velocity and porosity data (Fig. 8b andc). 9a), facies F3 presents porosity higher than 14 % and the lowest P-wave velocities of the dataset, even lower than the one expected by RHG (lowest values of the dataset). The only value available for the facies F4 is also lower than RHG. Facies F5 and F6 display values fitting with RHG, with porosity between 4 % and 16 % and P-wave velocity between 6000 m.s -1 and 4700 m.s -1 . Data corresponding to facies F7 shows porosity between 10 % and 22 % and P-wave velocity ranging between 6000 m.s -1 and 4500 m.s -1 , higher than expected with RHG. Facies F8 shows porosity between 3 % and 12 % and P-wave velocity ranging between 6200 m.s -1 and 5100 m.s -1 mostly fitting with RHG.

Facies F9 displays porosity between 5 % and 17 % and P-wave velocity ranging between 5400 m.s -1 and 4100 m.s -1 , mostly lower than RHG except for one sample that is fitting with RHG. For the Antenna section (Fig. 9b), a few samples display lower P-wave velocity than expected with RHG (around 500 J o u r n a l P r e -p r o o f m.s -1 and 1000 m.s -1 lower), mainly corresponding to facies F5 and F7. Nevertheless, all other samples are fitting with RHG prediction and no clear distinction can be made based on facies description.

In-situ P-wave velocity dataset

Table 2 summarizes the whole field dataset, including facies classification and in-situ acoustic measurements. Statistical distribution of field dataset is also indicated in table 3. Fig. 8d shows the unimodal distributions for the in-situ P-wave velocity measurements (Vpin-situ) acquired on both sites.

The Marina in-situ P-wave velocities range between 800 m.s -1 and 6300 m.s -1 with a median of 3911 m.s - 1 . For the Antenna section, the Vpin-situ range between 2100 m.s -1 and 6600 m.s -1 with a median equal to 5618 m.s -1 . As for the plug P-wave velocities (Vpplug), the Vpin-situ of the Antenna section are higher than the ones measured in the Marina section (Fig. 8d). The Vpin-situ acquired on the Marina section present a higher variability than the one measured on Antenna section.

We can describe the P-wave velocity signature according to the facies classification using violin plots (Fig. 9c andd). For the Marina section (Fig. 9c), data obtained on facies F1 and F2 presents low Vpin-situ values, lower than 1500 m.s -1 for the reddish to brownish clays and mainly comprised between 2000 m.s -1 and 3000 m.s -1 for the nodular and marly mudstone. Most of facies F3 and F4 presents Vpinsitu lower than 3000 m.s -1 . Then, two groups of carbonate facies can be defined: i) a first group with high Vpin-situ (higher than 4000 m.s -1 , low dispersion of data around the median) corresponding to facies F5 and F6; and ii) a second group with scattered Vpin-situ (from 2000 m.s -1 up to 6000 m.s -1 , high dispersion with flattened probability density) corresponding to facies F7, F8 and F9. Concerning the Antenna dataset (Fig. 9d), most of the identified facies present high Vpin-situ, ranging between 4000 m.s -1 and 6500 m.s -1 (facies F5, F7, F8 and F9), while facies F6 presents Vpin-situ lower than 4500 m.s -1 . For facies F7, F8 and F9, a distinction should be done between the two sections. We observe a flattened probability density associated with large interquartile values for the Marina section (Fig. 9c), while the probability density mimics a normal distribution associated with lower interquartile values for the Antenna section (Fig. 9d).

J o u r n a l P r e -p r o o f 4.5. Vertical evolution of the physical properties and associated high resolution seismic

Marina section

In Fig. 10, the geological descriptions of the Marina section are compared with physical properties acquired in laboratory and on outcrop, together with the resulting synthetic seismic trace.

Generally, when the plug porosity increases, the in-situ P-wave velocity decreases, and vice versa. The plug (Vpplug) and in-situ (Vpin-situ) P-wave velocity measurements show the same vertical trends.

In the first unit, the vertical evolution of P-wave velocity shows a rough correlation with facies:

detrital-rich facies (F1 to F4) are associated with relatively high to moderate porosity (15 to 30 %) and low P-wave velocity (1500 to 3000 m.s -1 ), whereas pure carbonate facies (F5 to F9) rather show low to moderate porosity (3 to 15 %) and high P-wave velocity (4000 to 6000 m.s -1 ). The first half of the unit (up to 8m) is therefore characterized by abrupt vertical changes of Vpin-situ, and the second one by more homogeneous and blocky patterns.

Only few data are available for the second unit and mainly correspond to hard layers made of facies F2 and F3. They display relatively low Vpin-situ, varying mainly between 1000 m.s -1 and 3000 m.s - J o u r n a l P r e -p r o o f

1 . An unique level shows moderate to high values of Vpin-situ between 20 and 21 meters (between 3000 m.s -1 and 5000 m.s -1 ).

The third unit displays abrupt vertical changes of Vpin-situ, but no obvious correlations with facies are observed. The first half of the unit (facies F6, F1 and F5) is characterized by a blocky pattern of high P-wave velocity (5000 to 6000 m.s -1 ), whereas the second one, dominated by heterogeneous carbonate facies (F7, F8, F9) shows important vertical variations or porosity (7 to 22 %) and velocity (from 2000 m.s -1 up to 6000 m.s -1 ).

The acoustic impedance obviously displays the same vertical trends as the one of Vpin-situ. The resulting reflection coefficient is used to build a synthetic seismic trace that shows a succession of 14 soft-kicks (negative amplitude reflectors in blue) and 15 hard-kicks (positive amplitude reflectors in red). Following the SEG normal convention, the soft kicks correspond to downward decreases of acoustic impedance and negative reflection coefficients, while the hard kicks correspond to downward increases of acoustic impedance and positive reflection coefficients. Indeed, most of the soft kicks are related to downward decreases of Vpin-situ (S2, S3, S5, S12, S13 and S14; Fig. 10) and several hard kicks are related to downward increases of Vpin-situ (H1, H2, H3 and H13; Fig. 10). Rapid alternations in acoustic impedance imply a cancellation of the reflection coefficients, resulting in abnormal and attenuated seismic reflectors (e.g., S4, H14, S14; Fig. 10). Furthermore, note that meter-scale levels of Vpin-situ with homogeneous and blocky pattern may also correspond to attenuated and obliterated seismic reflectors (H4, H5, H6; Fig. 10).

J o u r n a l P r e -p r o o f

Antenna section

In the Antenna section, the plug porosity evolution does not show huge vertical variations, being always centred around 2 % to 4 %, with only rare levels of porosity higher than 6 % (e.g., at 6 m, 9 m and 18.6 m; Fig. 11). Most of the plug P-wave velocities fit with the in-situ measurements, despite a few levels that show discrepancies between high Vpplug (centred around 5500 m.s -1 ) and lower Vpin-situ (down to 3000 m.s -1 ).

In the first part of the Antenna section (between 0 m and 11.4 m), Vpin-situ is globally high (between 5000 m.s -1 and 6400 m.s -1 ). It shows only one interval with lower Vpin-situ values (down to 3000 m.s -1 ) between 6 m and 6.6 m, corresponding to a more porous bed (6,5 % of porosity, facies F5).

In the second part of the Antenna section, Vpin-situ is high between 17 m and 20.2 m, showing values between 5000 m.s -1 and 6200 m.s -1 with punctual low Vpin-situ levels at 17. The synthetic seismic trace of Fig. 11 shows a succession of 6 soft kicks and 6 hard kicks with a much lower amplitude than the one observed on the Marina section (Fig. 10). Indeed, most of the section presents homogeneous and high values of AI without any contrasts of Vpin-situ, implying an attenuation of the reflectors (S1, H1, S2, H3, S4, H4, S6, H6; Fig. 11). Only four reflectors show noticeable amplitude corresponding to high-resolution facies changes (H2, S3, S5 and H5; Fig. 11). J o u r n a l P r e -p r o o f

Discussion

Depositional model

Based on the facies definition together with the description of their vertical evolution, a depositional model is proposed (Fig. 12). This model follows partially the studies of [START_REF] Pedley | Classification and environmental models of cool freshwater tufas[END_REF] and [START_REF] Arenas | Sedimentology of tufa facies and continental microbialites from the Palaeogene of Mallorca Island (Spain)[END_REF]. It is characterized by three coeval domains: alluvial plain (dominated by siliciclastic facies), palustrine (mixed sedimentation) and paludal (pure carbonate sedimentation). The Marina section covers the entire depositional model while the Antenna section mainly represents the paludal domain.

The association of homogeneous reddish to brownish clays (F1) with occasional beds of nodular and marly mudstone (F2) observed in the unit 2 of the Marina section (Fig. 7a) are characteristic of an alluvial plain domain with local ephemeral ponds showing a strong pedogenesis (Fig. 12).

Laterally to this terrestrial domain, a shallow lake is expected (Fig. 12). On its margins, silty pedogenic mudstones to wackestones (F3) dominate, together with peloidal and intraclastic floatstones to packstones (F5). They both show strong evidence of pedogenesis and are grouped into a palustrine domain (Fig. 12). As outlined by [START_REF] Alonso-Zarza | Palaeoenvironmental significance of palustrine carbonates and calcretes in the geological record[END_REF], the intraclastic limestones (F5) are the most widespread facies of these environments. Facies F4 (quartz-rich floatstone) is the result of the mixing of quartz-rich sediments coming from the terrestrial domain (fluvial inputs) and reworked carbonate allochems (phytoclasts). Facies F6 (bioclastic packstones and wackestones), characterized by lacustrine biota (e.g., ostracods and gastropods) as well as charophytes, strongly suggests a shallow depositional environment. Indeed, as shown by [START_REF] J O U R N A L P R E -P R O O F Asaeda | Morphological and reproductive acclimations to growth of two charophyte species in shallow and deep water[END_REF], the optimum development depth of charophytes is comprised between 2 m and 4 m deep. The high occurrence of root traces and exposure surfaces in this facies also point to shallow conditions with episodic exposure and pedogenesis.

The meter-thick levels of phytoherm framestone (F7) correspond to the "vertical tube facies" of Ordóñez and Garcia del Cura (1983), the "phytoherm cushions" of [START_REF] Pedley | Classification and environmental models of cool freshwater tufas[END_REF], or the "phytotravertine" of [START_REF] Claes | Sedimentology, three-dimensional geobody reconstruction and carbon dioxide origin of Pleistocene travertine deposits in the Ballık area (south-west Turkey)[END_REF]. According to [START_REF] Pedley | Freshwater (Phytoherm) reefs: the role of biofilms and their bearing on marine reef cementation[END_REF], the polycyclic calcitic fringes of phytoherm tufa (Fig. 4d) are due to biomediation processes that allow the phytoherm construction by the in-situ growing of low-magnesian calcite cements on the periphery of macrophytes. These coatings allow the preservation of moulds related to macrophytes after the plant decay. Phytoherm framestone J o u r n a l P r e -p r o o f accumulate in a paludal domain (Fig. 12). It follows the definition of [START_REF] Pedley | Classification and environmental models of cool freshwater tufas[END_REF], corresponding to a shallow environment with slow hydrodynamic processes. These deposits are organic-poor as the paludal tufa succession described by [START_REF] Pedley | Sedimentology of Quaternary perched springline and paludal tufas : criteria for recognition, with examples from Guadalajara Province, Spain[END_REF]. They settle within a freshwater marsh, with depth ranging from a few decimeters to a few meters [START_REF] Pedley | Sedimentology of Quaternary perched springline and paludal tufas : criteria for recognition, with examples from Guadalajara Province, Spain[END_REF]. They are associated with phytoclastic rudstones (F8) that correspond to the "cross-tube facies" of Ordóñez and Garcia del Cura (1983). This latter facies can have two origins: i) the plant decay, implying a collapse of the phytoherm framestones [START_REF] Pedley | Sedimentology of Quaternary perched springline and paludal tufas : criteria for recognition, with examples from Guadalajara Province, Spain[END_REF][START_REF] Pedley | Tufas and travertines of the Mediterranean region: A testing ground for freshwater carbonate concepts and developments[END_REF]; or ii) a reworking of the phytoherm framestones by flood episodes ("macro detrital tufa" of [START_REF] Ford | A review of the tufa and travertine deposits of the World[END_REF]. Here, the occurrence of erosive bases, oncoids, and reworked phytoclasts within the phytoclastic floatstones (F9) clearly points to episodic higher hydrodynamic conditions in this paludal environment.

As outlined by Heimann and Sass (1996), the paleotopographic setting exerts an important control on the accumulation of such deposits. The succession of palustrine and paludal carbonates of Samos may have accumulated within a low gradient valley fed by freshwaters coming from the neighbouring marble massif (Ampelos nappe of [START_REF] Ring | Structural analysis of a complex nappe sequence and late orogenic basins from the Aegean Island of Samos, Greece[END_REF], equivalent of the metamorphic basement shown in Fig. 1a). Such a carbonate source may explain the high degree of saturation with respect to CaCO3 that was necessary for the widespread development of paludal and palustrine facies.

The depositional model proposed for the Kokkarion formation of Samos is in part analogous to the "lowgradient, non-stepped fluvial and fluvio-lacustrine" sedimentary facies model of [START_REF] Arenas-Abad | Fluvial and Associated Carbonate Deposits[END_REF].

J o u r n a l P r e -p r o o f

Relevance of multi-scale acoustic characterization

Multi-scale characterization of acoustic properties is of importance to understand the geological controlling factors of elasticity in sedimentary rocks and therefore their seismic imaging. In this context, the Pliocene outcropping carbonates from Samos are an ideal target. They show a low amount of burial -in the range of few hundreds of meters -equivalent to the Mio-Pliocene sedimentary systems from SW Turkey (e.g. Çiftçi et al., 2010). Nevertheless, the results acquired on Samos are based on dry acoustic measurements, whereas subsurface reservoirs are fluid saturated (e.g. [START_REF] Fournier | The equivalent pore aspect ratio as a tool for pore type prediction in carbonate reservoirs[END_REF]. Thus, they are valid in gas saturated reservoirs. In the case of water or oil saturated reservoirs, the velocities obtained in this study should be adjusted by i) correcting the densities and ii) correcting the bulk moduli using Gassmann equation ( 1951). Note that Gassmann correction is only valid on specific range of frequency, as seismic dispersion and attenuation may occur (e.g. [START_REF] Borgomano | Seismic Dispersion and Attenuation in Fluid-Saturated Carbonate Rocks : Effect of Microstructure and Pressure[END_REF][START_REF] Fortin | Porous and cracked rocks elasticity: Macroscopic poroelasticity and effective media theory[END_REF].

Furthermore, results of this work show punctual occurrences of Vpin-situ lower than Vpplug that may be due outcropping root-moulds (Fig. 6a), stem moulds (Fig. 4b) or cracks/fractures. Indeed, as mentioned by [START_REF] J O U R N A L P R E -P R O O F Nelson | Geologic analysis of naturally fractured reservoirs[END_REF], fractures are pervasively distributed in almost all geological contexts and J o u r n a l P r e -p r o o f may decrease the P-wave velocity of rocks (e.g. [START_REF] Boadu | Effects of fractures on seismic-wave velocity and attenuation[END_REF][START_REF] Matonti | Heterogeneities and diagenetic control on the spatial distribution of carbonate rocks acoustic properties at the outcrop scale[END_REF][START_REF] Matonti | P-wave velocity anisotropy related to sealed fractures reactivation tracing the structural diagenesis in carbonates[END_REF]. The differences between in-situ and plug velocities can be used to infer a crack/fracture density (Bailly et al. 2019b). However, as highlighted by the Kernel regressions (Figs 10 and 11), the overall vertical evolution of Vpin-situ mostly mimics the Vpplug evolution. In the case of the Antenna section, the occurrence of punctual lower Vpin-situ has no effect on the reflection coefficient and thus on the reflectors (Fig. 11). In the case of the Marina section, it is not so straightforward, but most of the reflectors are obtained in domains where the Vpin-situ are equal to the Vpplug (H1, S2, H2, S3, H3, H4, S5, H5, H6, H12, S12, H13, S13; Fig. 10); i.e. domains without cracks/fractures. Therefore, at the first order, the seismic reflectors obtained in this work are not controlled by structural heterogeneities.

Sedimentary control of acoustic properties

Facies control on the velocity-porosity relationship at plug scale

As stated by [START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF], the velocity-porosity relationship is crucial for inferring reservoir properties from seismic data. Since the 1950s, several empirical relationships linking these properties have been established (e.g., [START_REF] Wyllie | Elastic wave velocities in heterogeneous and porous media[END_REF][START_REF] Anselmetti | Controls on Sonic Velocity in Carbonates[END_REF]. Here, the RHG equation (Raymer et al., 1980, Fig. 8a) is used to compare the facies description to a standard petrophysical trend (Fig. 9a andb). Furthermore, the potential impact of facies changes on the seismic reflection are discussed using curves of constant impedances on the velocity-porosity cross-plots as previously proposed in the literature [START_REF] Anselmetti | Physical properties and seismic response of carbonate sediments and rocks[END_REF]Anselmetti et al., 1997aAnselmetti et al., , 1997b;;[START_REF] Anselmetti | Physical properties and seismic response of carbonate sediments and rocks[END_REF]Eberli, 2001, Bailly et al., 2019a).

The Marina section offers the opportunity to investigate a huge range of P-wave velocity and porosity. In Fig. 9a, three groups of data can be identified: i) a first group corresponding to high and medium P-wave velocity and porosity fitting with RHG predictions; ii) a second group showing a higher velocity-porosity trend than RHG; and iii) a third group displaying a lower velocity-porosity trend than RHG.

The first group corresponds to intraclastic and peloidal floatstone (F5), bioclastic packstone (F6) and phytoclastic rudstone and floatstone (F8 and F9). These facies mainly deposited in palustrine and paludal J o u r n a l P r e -p r o o f domain, they rarely contain a detrital fraction (Fig. 12). They mostly present a homogeneous texture without any microcracks or heterogeneous macroporosity (Fig. 3f, g, h, Fig. 4h,i), thus explaining the fit with RHG predictions.

The second group is only represented by phytoherm framestones (F7). According to several authors (e.g., [START_REF] Anselmetti | Physical properties and seismic response of carbonate sediments and rocks[END_REF][START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF][START_REF] Fortin | Effects of pore collapse and grain crushing on ultrasonic velocities and Vp/Vs[END_REF][START_REF] Fournier | Pore space evolution and elastic properties of platform carbonates (Urgonian limestone, Barremian-Aptian, SE France)[END_REF], 2018, Regnet et al., 2019a, 2019b), microstructures with spherical pores might explain these higher values of P-wave velocities. Indeed, the petrographic description showed framework-related macropores inside these samples (Fig. 4e), explaining these peculiar acoustic velocities not predicted by the RHG equation.

The third group of samples corresponds to silty pedogenic mudstones (F3), quartz-rich floatstones (F4)

and phytoclastic floatstones (F9). Most of these samples contain abundant siliciclastic material (Fig. 3c,d,e) and were deposited within the palustrine domain, at the transition between the alluvial plain domain and the paludal domain (Fig. 12). According to several authors (Anselmetti et al., 1997b;[START_REF] Kenter | Parameters controlling sonic velocities in a mixed carbonate-siliciclastics Permian shelf margin (upper San Andres formation, Last Chance Canyon, New Mexico)[END_REF][START_REF] Kenter | Acoustic behavior of sedimentary rocks: Geologic properties versus Poisson's ratios[END_REF], more than 5 % of siliciclastic content within carbonates decreases the P-wave velocity, thus resulting in a lower velocity-porosity trend than the one predicted by RHG for pure carbonates.

The comparison of the velocity-porosity plot with the facies descriptions helps to understand the scattering of data and distinguish pure versus impure carbonate facies. This point is of importance for seismic modelling because these two sets of data present respectively high and low values of acoustic impedances with a threshold around 10.10 6 g.cm 3 .m.s -1 (Fig. 9a), that may control the generation of seismic reflectors (Fig. 10). Nevertheless, it does not allow to make distinction between pure carbonate facies (F5, F6, F8 and F9) that do not exhibit peculiar acoustic signatures.

Unlike the Marina section, most of the phytoherm framestones (F7) of the Antenna section fit with the RHG prediction (Fig. 9b). No peculiar distribution of acoustic properties is observed in the light of facies classification. The whole dataset presents low porosity values (< 8 %) and corresponds to pure carbonate facies (F5, F6, F7, F8, F9). This lack of facies control was previously observed for pure carbonate samples [START_REF] Fournier | Pore space evolution and elastic properties of platform carbonates (Urgonian limestone, Barremian-Aptian, SE France)[END_REF][START_REF] Regnet | Acoustic and reservoir properties of microporous carbonate rocks: Implication of micrite particle size and morphology[END_REF]. Here, it results from an absence of detrital content, microcracks or heterogeneous macroporosity. Furthermore, the curves of constant impedance J o u r n a l P r e -p r o o f only correspond to high values of AI (between 13.10 6 g.cm 3 .m.s -1 and 17.10 6 g.cm 3 .m.s -1 ), thus questioning the implication of facies changes in the seismic modelling of this section (Fig. 11).

Facies control of in-situ acoustic measurements

Based on Vpin-situ and the sedimentary description, a statistical view of the data is provided per facies, using violin plots (Fig. 9c andd). Such in-situ acoustic measurements have already been proposed

to characterize fractured outcrops [START_REF] J O U R N A L P R E -P R O O F Jeanne | Multiscale seismic signature of a small fault zone in a carbonate reservoir: Relationships between VP imaging, fault zone architecture and cohesion[END_REF][START_REF] Matonti | Heterogeneities and diagenetic control on the spatial distribution of carbonate rocks acoustic properties at the outcrop scale[END_REF] and for upscaling purposes (Bailly et al., 2019b). Here, this approach aims to obtain a large set of data representative of a scale higher than the conventional plug scale while discussing about the facies control.

In the Marina section, the low values of P-wave velocities observed for F1, F2, F3 or F4 are analogous to literature data for such detrital-rich facies [START_REF] Bourbié | Acoustics of Porous Media[END_REF]. These results are similar to the laboratory dataset (Fig. 9a), outlining again the impact of detrital content on the acoustic properties. The acoustic contrast between F1 values (lower than 1500 m.s-1) and F2, F3 or F4 values (from 2000 to 3000 m.s-1) may imply possible seismic reflection. As previously presented, two groups of carbonate facies can be defined, based on their P-wave velocities. The higher velocities observed for facies F5 and F6 can be explained by a rather homogeneous composition (Fig. 3f, g, h), without any large-scale heterogeneities (i.e. absence of macroporosity). On the opposite, the lower values and the important scattering of the P-wave velocities for the carbonate facies F7, F8 and F9 suggest outcropscale heterogeneities, such as macropores related to phytoherm and phytoclastic facies (Fig. 4a, b, e, g).

Consequently, the lower P-wave velocity values (< 4000 m.s -1 , Fig. 9c) of phytoherm framestones (F7)

and phytoclastic floatstones and rudstones (F8 and F9) may create contrasts with higher P-wave velocities (> 4000 m.s -1 , Fig. 9c) of pure carbonate facies (F5, F6, and to a lower extent F7, F8 and F9).

This point is not observed with the laboratory dataset, where the pure carbonate facies (F5, F6, F7, F8 and F9) are always associated with high P-wave velocities (> 4000 m.s -1 ; Fig. 9a).

For the facies F5, F7, F8 and F9 of the Antenna section, the median values of the in-situ P-wave velocities are all comprised between 5000 and 6000 m.s -1 (Fig. 9d), in line with the laboratory dataset values (Fig. 9b). This observation suggests a lack of facies control on the acoustic properties, except for the bioclastic packstone where the median of the in-situ P-wave velocity is lower than 4000 m.s -1 (F6, J o u r n a l P r e -p r o o f Fig. 9d).This points to a possible scale effect and a potential impact of heterogeneities that are not characterized at the laboratory scale [START_REF] Matonti | Heterogeneities and diagenetic control on the spatial distribution of carbonate rocks acoustic properties at the outcrop scale[END_REF]Bailly et al., 2019b), here most probably related to the occurrences of root networks that are highly developed at the top of the Antenna section (Figs 6b,7b and 11).

To summarize, the facies variation can explain the wide range of acoustic velocities acquired on the Marina section. However, similar facies occurring in the Antenna section show very small variations of P-wave velocity. As a consequence, the sole sedimentological description is not enough to understand the distribution of acoustic properties in these carbonates.

Impact of early diagenesis on acoustic and seismic properties

We compare the velocity-porosity datasets with diagenesis for palustrine and paludal carbonates (Figs 13 and 14). Four main diagenetic overprints and related pore types are defined, describing the velocity-porosity data: i) pervasive recrystallization and blocky cementation (Figs 13a,b and 14a,b,d);

ii) preserved root moulds showing a pore-lining cement (Figs 13a, c and 14a, f); iii) preserved heterogeneous macroporosity (Fig. 14a,c); iv) microporous host containing cemented root-moulds (Fig. 13a,d) and showing evidence of recrystallization (Fig. 14a,e). Following the allochem content (ostracods, polycyclic calcite sheets of tufas…), and the crystal morphology of micrite, we assume that the primary mineralogy of the carbonate mostly corresponds to low magnesian calcite (e.g. Capezzuolli et al., 2014).

The paragenetic sequences (Fig. 5) show that an intense to pervasive phase of recrystallization together with a subsequent phase of granular to blocky calcite cementation (Fig. 6f-j) affect some pure carbonate samples (F5, F6, F7, F8, F9), especially for the Antenna section (Figs 5b,7b,11). Conversely, in the Marina section, these diagenetic processes are less intense and occur more sporadically (Figs 5a, 7a and 10). The SEM investigations of some recrystallized samples from the Antenna section display a fused micrite associated with P-wave velocity matching the RHG prediction (Fig. 14a,d). Other samples show a preserved microporosity, with a subrounded micrite showing small, rounded crystals (<2 µm) embedded within larger overgrowth crystals (>4 µm), associated with a P-wave velocity slightly lower J o u r n a l P r e -p r o o f than RHG prediction (Fig. 14a,e). Such morphologies are a typical result of the Ostwald ripening process that occurs during meteoric diagenesis in a phreatic setting [START_REF] Volery | Lacustrine microporous micrites of the Madrid Basin (Late Miocene, Spain) as analogues for shallow-marine carbonates of the Mishrif reservoir Formation (Cenomanian-early Turonian, Middle East)[END_REF]. This process allows the dissolution of the smallest and most unstable crystals, thus favouring the overgrowth of the larger crystals (Fig. 14e). The different process intensities between fully recrystallized samples (fused micrite, Fig. 14d) and partially microporous samples (subrounded micrite, Fig 13e) can be explained by the residence time of the rocks in a phreatic meteoric environment oversaturated with respect to CaCO3:

the longer the time is, the stronger the recrystallization and cementation are. Furthermore, given the described depositional textures (especially F7 and F8), the relatively high primary porosity of the studied palustrine and paludal tufa carbonates would have provided a good primary permeability allowing fluid infiltration [START_REF] De Boever | What do we really know about early diagenesis of non-marine carbonates?[END_REF] and a high diagenetic precipitation potential.

Pervasive recrystallization and cementation are thus proposed to be the main drivers of the porosity/velocity signatures in the Kokkarion formation. These diagenetic processes built a rigid framework and occluded pore space, which results in P-wave velocities averaging 6000 m.s -1 , porosity values comprised between 2 to 5% and very high acoustic impedance values (mostly higher than 14.10 6 g.cm 3 .m.s -1 (Figs 13a and14a). In the Antenna section, samples only partially recrystallized (subrounded micrite, partial preservation of microporosity, Fig. 14a,e) show slightly higher porosity (6%) and lower velocity (5300 m.s -1 ), with still high acoustic impedance (13.10 6 g.cm 3 .m.s -1 ). However, they are not associated with a large range of porosity and velocity, as observed in the Marina section (low AI values, down to 5.10 6 g.cm 3 .m.s -1 , Fig. 13a). Indeed, some samples of the Marina section present root-related moulds (Fig. 13c) and high microporosity (Fig. 13d), resulting in P-wave velocity values lower than 5500 m.s -1 and porosities higher than 10 % (Fig. 13a). Hence, the occurrence of microporosity may imply P-wave velocities lower than non-microporous rocks, thus obstructing wave propagation in carbonates ("softening effect" sensu [START_REF] Xu | Modeling elastic properties in carbonate rocks[END_REF]Payne, 2009, Zhao et al., 2013, see also [START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF][START_REF] Baechle | Effect of microporosity on sonic velocity in carbonate rocks[END_REF][START_REF] Fournier | Elastic properties of microporous cemented grainstones[END_REF]. We can also notice the occurrence of pore-lining cement filling root moulds of some microporous samples (Figs. 13c and14f). Such a cement rigidifies the microporous samples ("stiffening effect" sensu [START_REF] Xu | Modeling elastic properties in carbonate rocks[END_REF]Payne, 2009, Zhao et al., 2013), inducing P-wave velocities matching the RHG prediction and resulting in intermediate AI values centred around 12.10 6 g.cm 3 .m.s -1 (Figs 13a and14a). Finally, for the phytoherm framestone (F7) and J o u r n a l P r e -p r o o f phytoclastic rudstone (F8), even if the preserved macropores result in medium to high porosities (between 6 % and 23 %), high to moderate values of P-wave velocities are observed (between 6000 m.s - 1 and 4500 m.s -1 ), higher than RHG prediction (Fig. 14a,c). Indeed, the preservation of heterogeneous macropores, due to the absence of blocky cementation, induces a stiffening of the microstructure and controls the acoustic properties of phytoherm framestone and phytoclastic rudstone (Fig. 14a,c), mimicking the acoustic behaviour of mould-rich carbonates (e.g. [START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF][START_REF] Soete | Acoustic properties in travertines and their relation to porosity and pore types[END_REF].

The variation of this porosity is responsible of the high fluctuation of in-situ P-wave velocity in the Marina section (Fig. 10).

In summary, the Marina section displays large differences in the diagenetic processes overprinting the facies heterogeneities, resulting in a large range of acoustic impedance. In contrast, the Antenna section only shows high values (with minor variations) of acoustic impedance, due to a pervasive recrystallization and cementation of the whole sedimentary section.

J o u r n a l P r e -p r o o f

Impact of diagenetic homogenization

Diagenetic homogenization can obliterate the seismic signal, resulting in reflection free zones (sensu [START_REF] Mitchum | Seismic stratigraphy and global changes of sea level, Part 1: glossary of terms used in seismic stratigraphy[END_REF], as exemplified on the Antenna section where the acoustic impedance is rather homogeneous (Fig. 11). This is entirely due to an overall high intensity of recrystallization and cementation (Fig. 14a,b) that erased all the potential contrasts associated to vertical facies variations (red box on Fig. 15b), resulting only in high AI. Following our dataset, such erasing of geological contrasts may also be due to a pervasive pedogenesis and a low meteoric phreatic cementation (Marina section, reflector H4 on Fig. 10). It results in the preservation of root moulds within meter-thick succession of microporous silty pedogenic mudstone (F3) and bioclastic packstone (F6). In these contexts, the absence of seismic reflectors is thus related to the vertical homogeneity of the porosity J o u r n a l P r e -p r o o f values inducing a blocky pattern of the P-wave velocity variation, itself explained by: i) a cemented and recrystallized succession of pure carbonates or ii) a pedogenic microporous succession of pure and impure carbonates. Such high-resolution reflection free-zone in continental carbonates (here up to 20 meters-thick, Antenna section, Fig. 11) is analogous to the "seismodiagenetic units" defined by [START_REF] Fournier | Geological significance of seismic reflections and imaging of the reservoir architecture in the Malampaya gas field (Philippines)[END_REF] or the "petroacoustic groups" of [START_REF] Teillet | Origin of seismic reflections in a carbonate gas field, Lower Miocene, offshore Myanmar[END_REF] for marine carbonates.

Indeed, these "units" or "groups" correspond to decameter-thick successions of various facies overprinted by a given diagenetic signature, equivalent to the diagenetic homogenization of the Antenna section responsible of the reflection free-zone's formation. Consequently, those findings are likely suggesting a crucial diagenetic control on seismic reflection in paludal and palustrine carbonates.

Heterogeneous facies and low diagenetic contrasts

As highlighted by the blue box in the Fig. 15a, low amplitude seismic reflectors occur within the heterogeneous facies succession (F7 and F8, H14 and S14 of Fig. 10). Such a signal is explained by the high vertical contrast of acoustic impedance induced by the rapid succession of beds with high contrasts of P-wave velocity signature (as outlined by the violin plots of F7, F8 and F9, Fig. 9d). It is analogous to the "destructive interfering waves" phenomena proposed by [START_REF] Jafarian | Synthetic seismic model of a Permian biosiliceous carbonatecarbonate depositional system (Spitsbergen, Svalbard Archipelago)[END_REF].

Furthermore, the diagenetic characterization of these heterogeneous carbonates shows a high intensity of recrystallization together with a moderate cementation, pointing to a lack of diagenetic contrast (blue box on Fig. 15a). These beds show a preserved macroporosity, resulting from a combined control of sedimentological heterogeneity (genesis of primary macroporosity) and diagenetic evolution (low cementation). As a consequence, succession of low amplitude seismic reflectors amongst high amplitude reflectors may point to heterogeneous and macroporous carbonates. Additionally, other low amplitude seismic reflectors occur within the Antenna section, (H2, S5 and H5 on the Fig. 11). In these cases, they are rather associated to vertical facies variations with low diagenetic contrasts (blue box of Fig. 15b) occurring amongst a global reflection free zone. Therefore, the interpretation of low amplitude seismic reflectors in paludal and palustrine tufa carbonates need to be done with care given that they may correspond either to a heterogeneous porous succession (blue box of Fig. 15a) or to a low porous succession (blue box of Fig. 15b).

J o u r n a l P r e -p r o o f carbonates from Madrid Basin, Central Spain (Reijmer et al., 2021, Fig. 16b); iv) outcropping and subsurface analogs of presalt carbonates (Regnet et al., 2019a, Fig. 16b); and v) subsurface Lower Cretaceous presalt carbonates from Santos Basin, offshore Brazil (Vasquez et al., 2019, Fig. 16b). Note that all the data of the Fig. 16 were acquired under dry conditions, therefore solely controlled by microstructural heterogeneities and not influenced by fluid-induced velocity dispersion (e.g. [START_REF] Borgomano | Seismic Dispersion and Attenuation in Fluid-Saturated Carbonate Rocks : Effect of Microstructure and Pressure[END_REF]. Furthermore, the acoustic data of samples from Samos are fairly consistent with other acoustic datasets, although the pressure conditions of the measurements are not similar (~0.1 MPa for Fig. 16a ; 27.6 MPa to 40 MPa for Fig. 16b).

A first striking feature from the Fig. 16 is the well-known impact of siliciclastic content on the acoustic properties that greatly reduce the P-wave velocity for a given porosity (Anselmetti et al., 1997b[START_REF] Kenter | Parameters controlling sonic velocities in a mixed carbonate-siliciclastics Permian shelf margin (upper San Andres formation, Last Chance Canyon, New Mexico)[END_REF][START_REF] J O U R N A L P R E -P R O O F Ehrenberg | Whole core versus plugs: Scale dependence of porosity and permeability measurements in platform carbonates[END_REF], Reijmer et al., 2021). On the opposite, the occurrence of stiff pores within pure carbonate hosts (e.g. stem-moulds, ooid-moulds, bio-moulds, vugs and framework porosity, Fig.

J o u r n a l P r e -p r o o f 16) significantly increase the P-wave velocity for a given porosity (e.g. [START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF][START_REF] Fournier | The equivalent pore aspect ratio as a tool for pore type prediction in carbonate reservoirs[END_REF], Bailly et al., 2019a[START_REF] Jaballah | Physical properties of Cretaceous to Eocene platform-to-basin carbonates from Albania[END_REF][START_REF] Matonti | Distinct petroacoustic signature in heterozoan and photozoan carbonates resulting from combined depositional and diagenetic processes[END_REF], Salih et al., 2021). Consequently, the heterogeneities of both mineralogy and porous networks strongly control the acoustic impedance (AI) of continental carbonates and therefore seismic. As an example, for a porosity of 10 %, AI contrasts between stem mould-rich tufa carbonates (15.10 6 g.cm 3 .m.s -1 ; Fig. 16a) and siliciclastic-rich carbonates (9.10 6 g.cm 3 .m.s -1 ; Fig. 16b) can create seismic reflectors, reflecting the depositional environment control. Conversely, for pure calcite rocks, AI contrasts between highly cemented and recrystallized carbonates (16.10 6 g.cm 3 .m.s -1 ; Fig. 16a) and ooid mould-rich or vug-rich carbonates (8.10 6 g.cm 3 .m.s - 1; ; Fig. 16a,b) can also create reflectors, outlining here a diagenetic control. However, for AI in the range of 8-10.10 6 g.cm 3 .m.s -1 , seismic cannot depict contrasts between poorly porous siliciclastic-rich carbonates and highly porous carbonates with moulds, vugs and framework porosity (Fig. 16b), making difficult the imaging of such a continental carbonate succession.

Another essential controlling parameter of acoustic and seismic properties of continental carbonates is their primary mineralogy. Indeed, continental depositional environments can induce the precipitation of i) stable LMC (e.g. paludal tufa of Kokkarion Formation of Samos) and ii) unstable HMC and/or aragonite (e.g. oolitic grainstones of Hora formation of Samos, Bailly et al., 2019a). Such mineralogical heterogeneities are responsible of two distinct diagenetic trends controlling the acoustic and seismic properties: i) the stable mineralogy of paludal tufa carbonates inhibited subsequent dissolution processes while cementation and recrystallization processes induced a decrease of the primary porosity and an increasing P-wave velocity (Fig. 16a). On the opposite: ii) the unstable mineralogy of lacustrine oolitic grainstones controlled their dissolution potential, resulting in high secondary porosity and low P-wave velocity (Fig. 16a). Such considerations are analogous to the findings of [START_REF] Anselmetti | Controls on Sonic Velocity in Carbonates[END_REF] and [START_REF] Matonti | Distinct petroacoustic signature in heterozoan and photozoan carbonates resulting from combined depositional and diagenetic processes[END_REF] who also point out the control of initial mineralogy on the diagenetic potential of marine carbonates and their resulting acoustic properties.

J o u r n a l P r e -p r o o f

Conclusions

In this work, the acoustic and seismic properties of two sedimentary successions of palustrine and paludal carbonates are discussed. An extensive petrographic characterization enabled to define nine facies affected by several diagenetic processes acting in a meteoric realm. According to the vertical facies variations, a depositional model corresponding to a low gradient valley fed by freshwaters is proposed. Combining geological observations with i) a field and laboratory investigation of acoustic properties, and ii) 1D synthetic seismic modelling of two studied sections lead to the following conclusions. At the plug scale, facies and early diagenetic overprint control the acoustic properties. At the outcrop scale, the sole facies variation does not explain the acoustic properties evolution. Indeed, despite the two studied section display similar sedimentary facies, their seismic responses are distinctive, mostly due to a diagenetic control:

J o u r n a l P r e -p r o o f

(1) Geological contrasts corresponding to vertical changes of facies combined with diagenetic contrasts lead to the development of high amplitude seismic reflectors;

(2) Vertical facies variations overprinted by an extensive diagenetic homogenization correspond to reflection free zones;

(3) Vertical facies variations combined with low diagenetic contrasts and vertical succession of heterogeneous porous facies are associated with low amplitude seismic reflectors.

These conclusions demonstrate the sedimentary and diagenetic controls of seismic properties in palustrine and paludal tufa. Such geological controlling factors are of primary importance to understand the reservoir compartmentalization of heterogeneous carbonates using crosswell seismic imaging.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Geological framework: (a) Map of Samos Island (Greece) showing the two sedimentary basins and the two study sites, with a focus on the Mytilini basin; (b) Stratigraphic column of the Mytilini basin (modified after Weidmannet al., 1984; Bailly et al., 2019a). Studied sections are part of the Kokkarion Formation.

Fig. 3 .

 3 Fig. 3. Overview of the different facies (part 1). Color code used for each facies is the same throughout the manuscript. (a) F1: Macroscopic view, reddish to brownish clays (unsampled); (b) F2: Macroscopic view, nodular and marly mudstone (unsampled); (c) F3: Macroscopic view, silty pedogenic mudstone with root moulds (white arrow) and millimetric quartz (black arrow) ; (d) F3: PPL view, silty pedogenic mudstone with calcified root cells (white arrow) and microporous matrix (bluish brown colour of the matrix); (e) F4: PPL view, quartz-rich floatstone containing millimeter-size phytoclasts (black arrow); (f) F5 : PPL view, peloidal and intraclastic floatstone with root casts (white arrow); (g) F6: Macroscopic view, bioclastic packstone showing root casts (white arrows). (h) F6: PPL view, bioclastic packstone.

Fig. 4 .

 4 Fig. 4. Overview of the different facies (part 2). Color code used for each facies is the same throughout the manuscript. (a) Outcrop view, phytoherm framestone beds and patches (F7) showing local centimeter-size moulds of phragmite stems (black arrows), alternating with phytoclastic rudstones (F8); (b) F7: Macroscopic view, phytoherm framestone with a framework of anchored macrophytes in life position (black arrows); (c) F7: Macroscopic view, preserved stem-mould (black arrow) encrusted by a cement fringe (white arrow); (d) PPL view, polycyclic cement fringes (white arrows); (e) F7: PPL view, phytoherm framestone showing a huge macroporous framework (blue epoxy); (f) F8: Macroscopic view, phytoclastic rudstone composed of numerous reworked tufa clasts (black arrows); (g) F8: Microscopic view, phytoclastic rudstone with a significant interparticular

Fig. 5 .

 5 Fig. 5. Paragenetic sequences of the studied sections showing the relative intensity of each process sorted per facies: (a) Paragenesis for Marina section; (b) Paragenesis for Antenna Section. The legend explains the color code for porosity development or reduction and the relative intensity scale of the diagenetic processes.

Fig. 6 .

 6 Fig. 6. Overview of the diagenetic processes: (a) Macroscopic view, root hollows (moulds; white arrows); (b)

  From

  18.5 m to 20.8 m, meter-thick beds of peloidal and intraclastic packstone (F5) occur, dominated by root moulds, pseudomicrokarsts and phreatic cements. They are capped by decimeter-thick beds of recrystallized tufa-reworked facies (F8 and F9) up to 23 m. Finally, up to 24.5 m, bioclastic packstone (F6) occurs, showing numerous root traces at its top and an upward increasing recrystallization together with an abundant phreatic cementation.J o u r n a l P r e -p r o o f

Fig. 7 .

 7 Fig. 7. Sedimentology and diagenesis of (a) Marina section and (b) Antenna section.

4. 4 .

 4 Multi-scale acoustic characterization 4.4.1. Laboratory dataset

Fig

  Fig. 9a, b presents the laboratory dataset sorted in the light of facies description. Concerning the

Fig. 8 .

 8 Fig. 8. Overview of the P-wave velocity and porosity datasets: (a) P-wave velocity acquired on plugs (500 kHz)

Fig. 9 .

 9 Fig. 9. Facies control of P-wave velocity: (a) P-wave velocity versus porosity at plug scale for Marina section and (b) Antenna section; (c) Violin plots of P-wave velocities acquired at outcrop scale for Marina section and (d) Antenna section.

Fig. 10 .

 10 Fig. 10. High resolution seismic stratigraphy of the Marina section. From left to right: Sedimentary log and relative intensity of diagenetic processes (see Fig. 7 for the legend); Plug porosity; P-wave velocity in situ (green colour) and plug (blue colour); Plug density; Acoustic impedance; Reflection coefficient; Synthetic seismic. Smooth curves with 95 per cent confidence intervals are indicated for Vpin-situ. The asymmetric shape of reflectors is due to the time-depth conversion.

  4 and 18.2 m (values around J o u r n a l P r e -p r o o f alternating low (down to 3500 m.s -1 ) and high (up to 5500 m.s -1 ) values.

Fig. 11 .

 11 Fig. 11. High resolution seismic stratigraphy of the Antenna section. From left to right: Sedimentary log and relative intensity of diagenetic processes (see Fig. 7 for the legend); Plug porosity; P-wave velocity outcrop (green colour) and plug (blue colour); Plug density; Acoustic impedance; Reflection coefficient; Synthetic seismic. Smooth curves with 95 per cent confidence intervals are indicated for Vpin-situ. The asymmetric shape of reflectors is due to the time-depth conversion.

Fig. 12

 12 Fig. 12 Depositional model proposed for the Kokkarion fm. of Samos Island.

Fig. 13 .Fig. 14 .

 1314 Fig. 13. Diagenetic control of acoustic and seismic properties in palustrine carbonates. The colors used to frame the pictures refers to the colors used in the crossplot. (a) P-wave velocity versus porosity sorted per facies and diagenesis; (b) PPL view of a recrystallized (R) bioclastic packstone showing primary intragranular porosity filled by a blocky cement (B); (c) PPL view of a microporous (µPhi) intraclastic wackestone showing a pore-lining cementation (C) in residual root-moulds; (d) PPL view of a microporous (µPhi) micritic matrix of a silty pedogenic wackestone.

Fig. 15 .

 15 Fig. 15. Geological significance of high-resolution reflectors in palustrine and paludal tufa carbonates: (a) Examples of well-developed seismic reflectors (green box) and low amplitude seismic reflectors (blue box) in the Marina section; (b) Examples of obliterated seismic reflectors (red box) and low amplitude seismic reflectors (blue box) in the Antenna section. The facies stacking and diagenetic overprint are simplified from Figs 10 and 11.

Fig. 16 .

 16 Fig. 16. Compilation of P-wave velocity and porosity data of continental carbonates. The vertical red arrows point to samples showing a distinctive porous network explaining the positive deviation from the RHG equation. (a) Comparison of our dataset with the data of Bailly et al. (2019a). The acoustic measurements were acquired under dry conditions with a very low pressure. (b) Comparison of the datasets provided by Soete et al. (2015), Reijmer et al. (2021), Regnet et al. (2019a), and Vasquez et al. (2019). The acoustic measurements were acquired under dry conditions with a high confining pressure (40 MPa, 27.6 MPa). Note that our samples and the one of Bailly et al. (2019a) and Soete et al. (2015) are quasi-pure carbonates, containing only calcite with a small siliciclastic amount. Samples of Regnet et al. (2019a) are composed of calcite, dolomite and a variable siliciclastic content (quartz and clays). Samples of Vasquez et al. (2019) are composed of calcite, dolomite, quartz and a variable amount of clays. Samples of Reijmer et al. (2021) are composed of calcite and a variable siliciclastic content (quartz, clays and plagioclase).

Table 1 .

 1 Dataset of petrographic characterization and petrophysical measurements acquired on samples.

	569
	Section	Thickness (m)	Sample Facies	Diagenetic typing	Vp (m.s -1 )	Phi (%)	Density (g.cm3)
	Marina	0,6	MA01	F6	Recristallization + Cementation		9,00	2,46
	Marina	1,2	MA02	F6	Recristallization + Cementation		6,88	2,51
	Marina	2,2	MA03	F3	Root mold, no cement + Microphi		17,58	2,21
	Marina	2,8	MA04	F3	Root mold, no cement + Microphi		14,99	2,29
	Marina	4,6	MA05	F8	Recristallization + Cementation		2,82	2,61
	Marina	5,4	MA06	F3	Microcracks + Microporous matrix		14,29	2,30
	Marina	6,2	MA07	F9	Recristallization + Cementation		5,29	2,56
	Marina	7,4	MA08	F8	Recristallization + Cementation		4,86	2,57
	Marina	8,4	MA09	F6	Root mold, cement + Microphi mx.		16,11	2,26
	Marina	9,4	MA10	F3	Microcracks + Microporous matrix		29,00	1,89
	Marina	10,6	MA11	F4	Microporous matrix		19,53	2,12
	Marina	12,2	MA12	F6	Recristallization + Cementation		7,62	2,50
	Marina	13	MA13	F9	Root mold, cement + Microphi mx.		15,60	2,29
	Marina	14	MA14	F7	Heterogeneous macroporosity		12,82	2,36
	Marina	15	MA15	F5	Root mold, cement + Microphi mx.		11,14	2,41
	Marina	29,1	MA16	F3	Microporous matrix		25,81	2,00
	Marina	30,1	MA17	F6	Recristallization + Cementation		4,17	2,60
	Marina	30,9	MA18	F6	Recristallization + Cementation		4,07	2,60
	Marina	32,5	MA19	F5	Root mold, cement + Microphi mx.		13,06	2,35
	Marina	33,1	MA20	F9	Microcracks + Microporous matrix		13,99	2,30
	Marina	33,5	MA21a	F8	Heterogeneous macroporosity		9,89	2,43
	Marina	33,5	MA21b	F8	Heterogeneous macroporosity		11,39	2,39
	Marina	35,1	MA22	F8	Heterogeneous macroporosity		6,37	2,49
	Marina	35,3	MA24	F7	Heterogeneous macroporosity		22,27	2,08
	Marina	35,7	MA25	F7	Heterogeneous macroporosity		17,37	2,22

J o u r n a l P r e -p r o o f

Table 2 .

 2 Dataset of field characterization and in situ acoustic measurements.

571 Section Thickness (m) Facies Vp (m.s -1 ) Section Thickness (m) Facies Vp (m.s -1 )

		Marina Marina	4 15	F9 F5	4292 5128	Marina Antenna	37.1 11.2	F8 F9
		Marina Marina	4.2 15.2	F7 F2	4950 2532	Marina Antenna	37.3 11.4	F9 F9
		Marina Marina	4.4 15.4	F7 F2	3333 3909	Antenna Antenna	0 11.6	F7 F9
		Marina Marina	4.6 16.2	F7 F2	3415 2317	Antenna Antenna	0.2 17	F7 F7
		Marina Marina	4.8 16.4	F1 F2	1485 2083	Antenna Antenna	0.4 17.2	F7 F7
		Marina Marina	5 16.6	F9 F2	2857 2128	Antenna Antenna	0.6 17.4	F7 F9
		Marina Marina	5.2 20	F9 F3	4444 2947	Antenna Antenna	0.8 17.6	F5 F8
		Marina Marina	5.4 20.2	F3 F3	3145 4282	Antenna Antenna	1 17.8	F9 F8
		Marina Marina	5.6 20.4	F3 F3	4415 3913	Antenna Antenna	1.2 18	F7 F8
		Marina Marina	5.8 20.6	F3 F3	2257 5000	Antenna Antenna	1.4 18.2	F7 F7
		Marina Marina	6 23	F7 F2	5464 778	Antenna Antenna	1.6 18.4	F5 F7
		Marina Marina	6.2 23.2	F7 F2	5464 1370	Antenna Antenna	1.8 18.6	F9 F5
		Marina Marina	6.4 25.4	F9 F2	5587 2679	Antenna Antenna	2 18.8	F9 F5
		Marina Marina	6.6 25.6	F9 F2	5747 2882	Antenna Antenna	2.2 19	F9 F5
		Marina Marina	6.8 25.8	F1 F2	1172 3297	Antenna Antenna	2.4 19.2	F9 F5
		Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina Marina	0 0.2 J o u r n a l P r e -p r o o f F6 5181 Marina 32.9 F9 F6 5348 Marina 33.1 F9 7 F9 2286 Antenna 2.6 F7 7.2 F9 2954 Antenna 2.8 F8 7.4 F8 5864 Antenna 3 F8 7.6 F8 3571 Antenna 3.2 F8 7.8 F8 2387 Antenna 3.4 F8 8 F6 2778 Antenna 3.6 F8 8.2 F6 1786 Antenna 3.8 F8 8.4 F6 3442 Antenna 4 F8 8.6 F6 2581 Antenna 4.2 F8 8.8 F6 2293 Antenna 4.4 F8 9 F6 2425 Antenna 4.6 F8 9.2 F3 1916 Antenna 4.8 F5 9.4 F3 2233 Antenna 5 F7 9.6 F3 1972 Antenna 5.2 F7 9.8 F3 1954 Antenna 5.4 F7 10 F3 1754 Antenna 5.6 F7 10.2 F3 2230 Antenna 5.8 F8 10.6 F4 1798 Antenna 6 F5 10.8 F4 2653 Antenna 6.2 F5 11 F5 1864 Antenna 6.4 F9 11.2 F5 3935 Antenna 6.6 F7 26 F2 1771 Antenna 19.4 F8 28.3 F2 2444 Antenna 20.2 F5 28.5 F2 2538 Antenna 20.4 F5 28.7 F1 1014 Antenna 20.6 F5 28.9 F1 1433 Antenna 20.8 F9 29.1 F3 2109 Antenna 21 F8 29.5 F3 2151 Antenna 21.2 F8 29.7 F6 3668 Antenna 21.4 F8 29.9 F6 5143 Antenna 22 F8 30.1 F6 6333 Antenna 22.2 F8 30.3 F6 5337 Antenna 22.4 F8 30.5 F6 5865 Antenna 22.6 F9 30.7 F6 5525 Antenna 22.8 F8 30.9 F6 5602 Antenna 23 F6 31.1 F6 5970 Antenna 23.2 F6 31.3 F6 5970 Antenna 23.4 F6 31.9 F5 5102 Antenna 23.6 F6 32.1 F5 4878 Antenna 23.8 F6 32.3 F5 5222 Antenna 24 F6 32.5 F5 4717 Antenna 24.2 F6 J o u r n a l P r e -p r o o f 32.7 F5 2252 Antenna 24.4 F6	2005 1550
	572	Marina Marina	0.4 11.4	F6 F5	4831 5249	Marina Antenna	33.3 6.8	F9 F7	2712
		Marina Marina	0.6 11.6	F6 F6	4831 5013	Marina Antenna	33.5 7.8	F8 F7	5195
		Marina Marina	0.8 11.8	F6 F6	4963 6079	Marina Antenna	33.7 8	F8 F7	4640
		Marina Marina	1 12	F6 F6	4396 5775	Marina Antenna	33.9 8.2	F7 F7	5666
		Marina Marina	1.2 12.2	F6 F6	5405 5775	Marina Antenna	34.1 8.4	F7 F7	5666
		Marina Marina	1.4 12.4	F6 F6	5571 5607	Marina Antenna	34.3 8.6	F7 F7	4444
		Marina Marina	1.6 12.6	F5 F9	5362 5296	Marina Antenna	34.5 8.8	F8 F7	4863
		Marina Marina	1.8 12.8	F5 F9	5405 4167	Marina Antenna	34.7 9	F8 F5	3279
		Marina Marina	2 13	F3 F9	2333 5751	Marina Antenna	34.9 9.2	F8 F5	3257
		Marina Marina	2.2 13.2	F3 F9	3231 5263	Marina Antenna	35.1 9.4	F8 F7	2469
		Marina Marina	2.4 13.4	F3 F9	2133 4902	Marina Antenna	35.3 9.6	F7 F9	3106
		Marina Marina	2.6 13.6	F3 F9	2676 5530	Marina Antenna	35.5 9.8	F7 F9	3431
		Marina Marina	2.8 13.8	F3 F9	1818 5075	Marina Antenna	35.7 10	F7 F8	5115
		Marina Marina	3 14	F3 F7	2532 4545	Marina Antenna	36.1 10.2	F7 F8	2326
		Marina Marina	3.2 14.2	F3 F7	2139 5333	Marina Antenna	36.3 10.4	F7 F8	2397
		Marina Marina	3.4 14.4	F4 F7	1963 4751	Marina Antenna	36.5 10.6	F8 F7	5291
		Marina Marina	3.6 14.6	F9 F5	3976 4267	Marina Antenna	36.7 10.8	F8 F8	4515
		Marina Marina	3.8 14.8	F9 F5	4320 5075	Marina Antenna	36.9 11	F8 F8	2778

Table 3 .

 3 Statistical distribution of petrophysical properties.

	573
	Statistical		Marina section			Antenna section
	distribution	Vp plug	Porosity	Density	Vp in situ	Vp plug	Porosity	Density	Vp in situ
	Median	5226	13	2.36	3911	5880	4	2.57	5618
	Mean	4930	13	2.35	3757	5785	4	2.57	5138
	Std. dev.	954	7	0.19	1487	297	2	0.05	1153
	Min	2611	3	1.89	778	5110	1	2.43	2128
	Max	6156	29	2.61	6333	6201	8	2.65	6711

J o u r n a l P r e -p r o o f

m.s -1 ). Then, Vpin-situ presents a more scattered pattern toward the top of the section, with

Acknowledgments

This work was supported by IFP Energies Nouvelles (grant XFP32/001). It is a part of the PhD project of the first author, at IFP Energies Nouvelles and Laboratoire de Géologie of Ecole normale supérieure, as well as the master thesis of the second author. We thank Phillippe Blanc (society Lithologie Bourgogne) for the preparation of the thin sections, Damien Deldicque (ENS) for the SEM observations and Nicholas Badullovich for the English proofreading of this article. We acknowledge John J. G.

Reijmer and two anonymous reviewers for their constructive comments which helped to improve this manuscript. We also thank the associate editor Telm Bover-Arnal.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: