Christophe Matonti

J Bourget

F Fournier

E Håkansson

M Pellerin

F Hong

J Reijmer

Distinct petroacoustic signature in heterozoan and photozoan carbonates resulting from combined depositional and diagenetic processes

Keywords: carbonates, diagenesis, ultrasonic velocities, petroacoustic modelling, heterozoan, photozoan, Oligo-Miocene, NW-Australia, outcrop analogue

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

Introduction

Acoustic properties of carbonate reservoirs at core scale have been shown to be largely controlled by pore space architecture determined by depositional and diagenetic processes, including mineral transformations (e.g. [START_REF] Anselmetti | Controls on sonic velocity in carbonates[END_REF][START_REF] Eberli | Factors controlling elastic properties in carbonate sediments and rocks[END_REF][START_REF] Adelinet | Effective medium modeling of diagenesis impact on the petroacoustic properties of carbonate rocks[END_REF]Bailly et al., 2019a). In pure calcitic limestone reservoirs, porosity and pore geometry are the main factors controlling P and S-wave velocities (e.g. [START_REF] Weger | Quantification of pore structure and its effect on sonic velocity and permeability in carbonates[END_REF][START_REF] Hairabian | Depositional Facies, Pore Types and Elastic Properties of Deep-Water Gravity Flow Carbonates[END_REF][START_REF] Soete | Acoustic properties in travertines and their relation to porosity and pore types: Mar[END_REF][START_REF] Abdlmutalib | Factors influencing acoustic properties of carbonate rocks: Examples from middle Jurassic carbonates, Central Saudi Arabia[END_REF]. The variety of diagenetic processes (cementation, dissolution, neomorphism, etc) affecting carbonate rocks commonly result in a wide range of pore types, porosity and wave velocity as well as in a wide scattering of values in velocity-porosity relationships (e.g. [START_REF] Verwer | Acoustic properties of carbonates: Effects of rock texture and implications for fluid substitution[END_REF][START_REF] Brigaud | Acoustic Properties of Ancient Shallow-Marine Carbonates: Effects of Depositional Environments and Diagenetic Processes (Middle Jurassic, Paris Basin, France)[END_REF].

In carbonates rocks, pore type is an important factor controlling reservoir properties and fluid flow at the matrix scale (e.g. [START_REF] Blow | Petrophysics of lower cretaceous platform carbonate outcrops in provence (se france): implications for carbonate reservoir characterisation[END_REF]. In particular, this explains the significant scatter observed in porosity/permeability relationships existing in different geological contexts [START_REF] Ehrenberg | Porosity-permeability relationships in interlayered limestone-dolostone reservoirs[END_REF][START_REF] Lønøy | Making sense of carbonate pore systems[END_REF]. Because of the high chemical reactivity of carbonate minerals (e.g. [START_REF] Ehrenberg | Sandstone vs. carbonate petroleum reservoirs: A global perspective on porosity-depth and porosity-permeability relationships[END_REF][START_REF] Richard | Large-scale mass transfers related to pressure solution creep-faulting interactions in mudstones: Driving processes and impact of lithification degree[END_REF], the impact of diagenetic transformations on porosity and pore space architecture is considerable.

Assessing such an impact on velocity-porosity relationships is thus a major issue for the prediction of reservoir properties from remote data such as well logs and seismics [START_REF] Anselmetti | The Velocity-Deviation Log: A Tool to Predict Pore Type and Permeability Trends in Carbonate Drill Holes from Sonic and Porosity or Density Logs[END_REF][START_REF] Fournier | The equivalent pore aspect ratio as a tool for pore type prediction in carbonate reservoirs[END_REF][START_REF] Jafarian | Synthetic seismic model of a Permian biosiliceous carbonate-carbonate depositional system (Spitsbergen, Svalbard Archipelago)[END_REF][START_REF] Teillet | Origin of seismic reflections in a carbonate gas field, Lower Miocene, offshore Myanmar[END_REF] and to achieve valid porosity-permeability transforms, which are of prime importance in the modelling of carbonate hydrocarbon systems. Most of the published studies dealing with velocity-porosity relationships in purely calcitic (%CaCO3 > 95 %) marine carbonate reservoirs focused on tropical photozoan shallow-water carbonates (e.g. [START_REF] Anselmetti | Controls on sonic velocity in carbonates[END_REF][START_REF] Verwer | Acoustic properties of carbonates: Effects of rock texture and implications for fluid substitution[END_REF][START_REF] Brigaud | Acoustic Properties of Ancient Shallow-Marine Carbonates: Effects of Depositional Environments and Diagenetic Processes (Middle Jurassic, Paris Basin, France)[END_REF][START_REF] Fournier | Pore space evolution and elastic properties of platform carbonates (Urgonian limestone, Barremian-Aptian, SE France)[END_REF] or deep-water carbonates (Røgen et al., 2004;[START_REF] Hairabian | Depositional Facies, Pore Types and Elastic Properties of Deep-Water Gravity Flow Carbonates[END_REF]. However, shallow-water non-tropical heterozoan carbonates (sensu James, 1997) have received less attention, with regard to their petroacoustic properties. Heterozoan carbonates are different from photozoan carbonates in terms of the carbonate producing biota, mineralogy, depositional profile (lack of barrier reef, variable slope ramp, etc) and carbonate productivity (e.g. James, 1997;[START_REF] Wilson | Cenozoic carbonates in Southeast Asia: implications for equatorial carbonate development[END_REF][START_REF] Schlager | Benthic carbonate factories of the Phanerozoic#s3gt_translate_tooltip_mini { display: none !important[END_REF][START_REF] Michel | Heterozoan carbonates: When, where and why? A synthesis on parameters controlling carbonate production and occurrences[END_REF]. By considering the differential stability between aragonite, high Mg-and low Mg-calcite, distinct patterns of diagenetic evolutions and petroacoustic signatures are therefore expected between heterozoan and photozoan carbonates while interacting with similar fluids.

The present study is based on the sedimentological, petrographical, diagenetic and petroacoustic analysis of the Oligo-Miocene shallow-water heterozoan to photozoan carbonates from the Cape Range Group outcropping in the Northern Carnarvon Basin (NCB), in the most proximal part of the North West Shelf of Australia (Fig. 1A) [START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF][START_REF] Apthorpe | Cainozoic depositional history of the Northwest Shelf[END_REF][START_REF] Collins | Facies, outcrop gamma ray and C-O isotopic signature of exposed Miocene subtropical continental shelf carbonates, North West Cape,Western Australia[END_REF][START_REF] Riera | Stratigraphic Revision of the Miocene Trealla Limestone (cape Range, Western Australia): Implications For Australasian Foraminiferal Biostratigraphy[END_REF]. Offshore, age-equivalent carbonate sequences represent a thick part of the overburden, directly overlying the Mesozoic producing hydrocarbon reservoirs. They constitute a major target for regional hydrocarbon exploration and production [START_REF] Wallace | Geological controls on sonic velocity in the cenozoic carbonates of the northern carnarvon basin, north west shelf, western australia[END_REF]. The overburden exhibits strong vertical and lateral velocity variations believed to originate from depositional and diagenetic heterogeneities. It causes considerable seismic imaging and interpretation challenges, thus increasing uncertainties in regional reservoir and structural trap delineation, as well as major drilling hazards [START_REF] Wallace | Geological controls on sonic velocity in the cenozoic carbonates of the northern carnarvon basin, north west shelf, western australia[END_REF][START_REF] Shragge | The Western Australia Modeling project -Part 2: Seismic validation[END_REF]. However, the depositional architecture and diagenetic history of these Oligo-Miocene carbonates from the NCB remain poorly constrained, mostly due to the scarcity of rock samples available from offshore exploration wells (mainly cuttings). Detecting and quantifying the impact of depositional and diagenetic processes on acoustic properties is of paramount importance for correctly interpreting the seismic expression of carbonate systems and reservoirs (Fournier and Borgomano, 2007;[START_REF] Teillet | Origin of seismic reflections in a carbonate gas field, Lower Miocene, offshore Myanmar[END_REF]. In the present work, we therefore define a well-constrained depositional and diagenetic framework from nearby, age-equivalent outcrops, in order to assess the combined impact of carbonate production (heterozoan vs. photozoan) on the diagenetic evolution and acoustic properties of carbonate reservoirs (Fig. 2). The main goal of this study is thus to emphasize the interplay and feedbacks existing between primary sedimentary attributes, diagenetic paths and the resulting petroacoustic signature of distinct carbonates types. To achieve this objective, the integrated approach implemented in this work (sedimentology, diagenesis, laboratory petroacoustics and numerical modelling) aims at (i) constraining the sedimentological and diagenetic framework of the Oligo-Miocene carbonates sequences from the NCB, (ii) identifying the key parameters controlling the evolution of pore volume, pore network architecture and mineralogy in both heterozoan and photozoan carbonates, (iii) quantifying the relative impact of depositional features (texture, initial mineralogy) and diagenetic transformations on acoustic properties of reservoirs related to both carbonate associations.

Geological setting

This work primarily concerns carbonate outcrops of Oligo-Miocene age from the Northwest Shelf of Australia. The analysis focused on outcrops from the Cape Range peninsula, located in the onshore part of the Exmouth Sub-Basin (NCB, Western Australia, Fig. 1).

The NCB is the largest hydrocarbon province of Australia. Since the onset of hydrocarbon exploration in 1953, 145 GL of oil, 52 GL of condensate and 207 BCM of gas have been produced, mostly from Mesozoic age reservoirs. The sedimentary cover of the NCB, overlying the Jurassic and Cretaceous hydrocarbon-bearing reservoirs, is mainly composed of heterozoan ramp to photozoan carbonate platform deposits from Late Cretaceous to Quaternary ages (e.g. [START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF][START_REF] Cathro | Progradation along a deeply submerged Oligocene-Miocene heterozoan carbonate shelf: How sensitive are clinoforms to sea level variations[END_REF]. Onshore exposures of the Oligo-Miocene carbonate sequences of the NCB occur across the 20-30 km wide and 60 km long Cape Range peninsula, essentially within canyons and quarries (Fig. 1B). The Cape Range peninsula is located on the margin of the Exmouth sub-basin which is part of the NCB [START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF]. This basin evolved from a rifted margin (late Triassic to Early Cretaceous) to a passive margin (Early Cretaceous to present), and has been associated with a moderate and fairly constant subsidence during the Cenozoic [START_REF] Cathro | Cretaceous-Tertiary inversion history of the Dampier Sub-basin, northwest Australia: Insights from quantitative basin modelling[END_REF][START_REF] Czarnota | Spatial and temporal patterns of Cenozoic dynamic topography around Australia[END_REF]. The formation of the Cape Range peninsula topographic high resulted from the Exmouth sub-basin inversion which commenced during the Miocene. This tectonic inversion is characterized by the formation of several en-échelon SW-NE oriented open folds, such as the adjacent Rough Range and Giralia Anticlines, resulting from strike slip reactivation of enéchelon basement faults (e.g. [START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF]; Fig. 1B).

The Oligo-Miocene carbonate system of the NCB has been previously interpreted as a nontropical (temperate to sub-tropical carbonates) low-gradient, distally-steepened ramp prograding to the north-west. These results were obtained from the analysis of offshore wells and seismic [START_REF] Young | The middle cretaceous to recent sequence stratigraphic evolution of the exmouth-barrow margin, western australia[END_REF][START_REF] Cathro | Progradation along a deeply submerged Oligocene-Miocene heterozoan carbonate shelf: How sensitive are clinoforms to sea level variations[END_REF][START_REF] Moss | Sequence Biostratigraphy of Prograding Clinoforms, Northern Carnarvon Basin, Western Australia: A Proxy for Variations in Oligocene to Pliocene Global Sea Level?[END_REF] as well as from sedimentological studies of exposed sections in Cape Range (e.g. [START_REF] Condon | The cape range structure Western Australia; Pt 1: Stratigraphy and structure[END_REF][START_REF] Collins | Facies, outcrop gamma ray and C-O isotopic signature of exposed Miocene subtropical continental shelf carbonates, North West Cape,Western Australia[END_REF]. Regionally, the Oligo-Miocene carbonate have been subdivided into three distinct formations (Figs. 1B and3): the Late Oligocene to Early Miocene Mandu Limestone and Tulki Limestone and the Early to Middle Miocene Trealla Limestone (Fig. 3A) [START_REF] Condon | The cape range structure Western Australia; Pt 1: Stratigraphy and structure[END_REF][START_REF] Quilty | Sedimentation cycles in the cretaceous and cenozoic of Western Australia[END_REF][START_REF] Van Der Graaff | Explanatory Notes on the Yanrey-Ningaloo 1:250,000 Geological Series[END_REF][START_REF] Apthorpe | Cainozoic depositional history of the Northwest Shelf[END_REF][START_REF] Riera | Stratigraphic Revision of the Miocene Trealla Limestone (cape Range, Western Australia): Implications For Australasian Foraminiferal Biostratigraphy[END_REF] that, in the onshore part of the system, rest unconformably on the Tulki (Fig. 1C). The age of each of these formations has been established from foraminifer-based bio-stratigraphy [START_REF] Chaproniere | Palaeoecology of Oligo-Miocene larger Foraminiferida, Australia[END_REF][START_REF] Chaproniere | Oligocene and Miocene larger foraminiferida from Australia and New Zealand[END_REF][START_REF] Quilty | Cenozoic sedimentation cycles in Western Australia[END_REF]Apthrope 1988;[START_REF] Riera | Stratigraphic Revision of the Miocene Trealla Limestone (cape Range, Western Australia): Implications For Australasian Foraminiferal Biostratigraphy[END_REF]. The Mandu Limestone was deposited from the Late Oligocene to Early Miocene, including foraminifer zones P19-21 to N6 (Blow, 1969 nomenclature), which implies an age between 26 and 18 Ma. The age of the Tulki Limestone range from zones N6/7 and -possibly -up to the N8 zone on the eastern flank of Cape Range [START_REF] Chaproniere | Oligocene and Miocene larger foraminiferida from Australia and New Zealand[END_REF] [START_REF] Chaproniere | Oligocene and Miocene larger foraminiferida from Australia and New Zealand[END_REF], corresponding to an age from around 18 to 15 Myrs. Finally, the age of the basal Trealla Limestone ranges from upper Burdigalian in the southern Cape Range peninsula to the upper Langhian to the North [START_REF] Riera | Stratigraphic Revision of the Miocene Trealla Limestone (cape Range, Western Australia): Implications For Australasian Foraminiferal Biostratigraphy[END_REF]. The NCB is characterized by one of the most extensive open-access offshore 2D/3D high-resolution seismic data and well data coverage.

Such offshore datasets provide excellent insight into the stratigraphic architecture of the Oligo-Miocene carbonates [START_REF] Cathro | An early mid-Miocene, strike-parallel shelfal trough and possible karstification in the Northern Carnarvon Basin, northwest Australia[END_REF][START_REF] Schlager | Benthic carbonate factories of the Phanerozoic#s3gt_translate_tooltip_mini { display: none !important[END_REF][START_REF] Moss | Sequence Biostratigraphy of Prograding Clinoforms, Northern Carnarvon Basin, Western Australia: A Proxy for Variations in Oligocene to Pliocene Global Sea Level?[END_REF][START_REF] Ryan | A precursor extensive Miocene reef system to the Rowley Shoals reefs, Western Australia: evidence for structural control of reef growth or natural hydrocarbon seepage?[END_REF][START_REF] Rosleff-Soerensen | Seismic geomorphology and growth architecture of a Miocene barrier reef, Browse Basin, NW-Australia[END_REF]2016;Smith, 2014;[START_REF] Saqab | Seismic geomorphology and evolution of early-mid Miocene isolated carbonate build-ups in the Timor Sea, North West Shelf of Australia[END_REF], but only cover the more distal deposits (mid to outer ramp, slope and basin). The proximal parts of the basin are poorly penetrated by exploration wells and has almost no seismic coverage. However, onshore outcrops, along the anticline folds uplifted and exposed during the Middle-to-Late Miocene inversion of the margin [START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF][START_REF] Moss | Sequence Biostratigraphy of Prograding Clinoforms, Northern Carnarvon Basin, Western Australia: A Proxy for Variations in Oligocene to Pliocene Global Sea Level?[END_REF] allow to study the most proximal parts of the system. Unfortunately, onshore studies of the Oligo-Miocene sequences of the NCB are few, so that the current knowledge is limited to their broad age and a generalized facies and stratigraphic evolution model [START_REF] Collins | Facies, outcrop gamma ray and C-O isotopic signature of exposed Miocene subtropical continental shelf carbonates, North West Cape,Western Australia[END_REF].

In the studied outcrops, the Mandu Limestone (up to 300m thick; [START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF] exhibits an upward vertical change in facies from white to yellowish, fine grained marly and fine calcarenite (Lower Mandu) to fine-grained limestone with interbeds of larger foraminiferal packstone to floatstone (Upper Mandu) (Fig. 3A-C). The Tulki Limestone (up to 129m thick) consists of a hard, thick-bedded limestone interpreted as a proximal, proximal equivalent of the Mandu Limestone (Chaproniere, 1984, Fig. 3D). The Trealla Limestone is a diachronous carbonate formation [START_REF] Riera | Stratigraphic Revision of the Miocene Trealla Limestone (cape Range, Western Australia): Implications For Australasian Foraminiferal Biostratigraphy[END_REF] which overlies the Tulki Limestone unconformably [START_REF] Quilty | Cenozoic sedimentation cycles in Western Australia[END_REF][START_REF] Chaproniere | Oligocene and Miocene larger foraminiferida from Australia and New Zealand[END_REF][START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF]Fig. 1C). Locally, previous biostratigraphy dating suggests a time gap between Tulki and Trealla on the order of around 1 Myr, at least in the Giralia anticline [START_REF] Chaproniere | Oligocene and Miocene larger foraminiferida from Australia and New Zealand[END_REF]. The Trealla Limestone is a hard, white to cream crystalline limestone (Fig. 3F-G). A significant uplift (200-300m) and subsequent emersion of the Cape Range area occurred during the Late Miocene, as a result of deeper fault reactivation [START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF]. Outcropping thicknesses for the Mandu Tulki and Trealla formations in the Cape Range region average 80 m, 30 m and 20 m, respectively (Fig. 3A) [START_REF] Chaproniere | Oligocene and Miocene larger foraminiferida from Australia and New Zealand[END_REF][START_REF] Collins | Facies, outcrop gamma ray and C-O isotopic signature of exposed Miocene subtropical continental shelf carbonates, North West Cape,Western Australia[END_REF].

Database and Methods

This study is based on a multiscale (microscale to kilometre) and multidisciplinary approach, (Fig. 2), including field sedimentology, petrographic analysis of thin-section (microfacies, composition of the biota, diagenetic features), cathodoluminescence, carbon and oxygen stable isotope measurements, calcimetry, laboratory P and S-wave velocity measurements, helium porosity measurements and micro-CT scan imaging. The field-work focused on four main outcrops, located on the Cape Range peninsula (Fig. 1), Shothole Canyon (22.06319S;114.01199E, "1" in Fig. 1B), Charles Knife Road (22° 6'57.87"S;114° 2'20.10"E, "2" in Fig. 1B), Unnamed Quarry 1,(21°59'36.16"S;114° 5'37.98"E, "3" in Fig. 1B) Unnamed Quarry 2 (21°59'50.20"S;114° 04'54.50"E, "4" in Fig. 1B).

Carbonate petrography

During field-work, 47 rock samples were collected from the 4 sites studied, including 3 sites previously studied by [START_REF] Collins | Facies, outcrop gamma ray and C-O isotopic signature of exposed Miocene subtropical continental shelf carbonates, North West Cape,Western Australia[END_REF] as well as the previously unstudied Unnamed Quarry 2. The Mandu and Tulki limestones facies were described mainly from Shothole Canyon and Charles Knife Road, while expose facies descriptions of the Trealla formation were derived from all main localities. Trealla age-equivalent deposits also outcrop in Unnamed Quarry 2 (Fig. 1B), not previously described. Thin sections have been prepared from all 47 samples and subsequently inspected using optical microscope under polarized light as well as under cathodoluminescence in order to characterize both depositional and diagenetic features (Fig. 2).

High resolution scanning of each thin-section was carried out at UWA-CMCA using a Leica (Aperio) Scanscope XT that provided ×20 magnification digital slides. From these scans detailed point counting analyses has been performed using JMicroVision [START_REF] Roduit | JMicroVision : un logiciel d'analyse d'images pétrographiques polyvalent[END_REF] software in order to define the dominant pore type (DPT), as well as the relative proportion of macroporosity, the quartz content, and the micrite/sparite ratio of each sample. At least 400 points selected randomly on the image were required for each scan to obtain statistical relevance/mean stationarity of the considered classes (sparite, micrite, allochem, pore type, quartz). Micropores have been defined as pores with diameter smaller than 10 µm [START_REF] Cantrell | Microporosity in Arab Formation Carbonates[END_REF] while macropores have diameter higher than 10 µm. Vugs are defined as dissolution voids which cross-cut original grain boundaries and usually larger than the mean grain size. .

Laboratory measurements

Physical properties

Porosity and velocity measurements were performed on plugs at the Department of Earth Sciences of the Vrije Universiteit Amsterdam. The plugs (diameter: 3.8 cm; length: 6 cm) have been drilled on oriented samples, the same used for petrography, along their vertical direction. Porosity measurements have been performed using a helium pycnometer (AccuPyc 1330, Micrometritics). The pore volume is calculated from the ratio of the plug's bulk density on the grain density (following Kenter & Ivanov, 1995 methodology). Grain density is estimated from the volume of helium filling the pore space and bulk density is estimated from the volume and weight of the plug.

Among the 47 sample, only 39 allowed to obtain consistent P and S-waves velocity measurements. Velocities were measured using the Verde Geosciences High Pressure Measurement System (HPMS) under dry conditions with increasing isotropic confining stress of 2.5, 5; 10; 20 and 40 MPa, where most velocity values reach a plateau (see Fig. S1).

During measurements plugs are placed in an impermeable rubber jacket and immersed in a confining oil which pressure is gradually increased. Two piezoelectric transducers (emitter/receiver) generating ultrasonic source of 1 MHz frequency were used for the measurements performed along the plug axis. Measurements are based on the picking of wave first-break arrival, using a 3% of maximum amplitude threshold. 40 MPa is a classical value for confining pressure used in a majority of petrophysical studies. This value is greater than the highest burial stress experienced by the studied rocks, and has the advantage to make comparison of our data with other studies more valid.

Three-dimensional micro CT-scan acquisition (100 µm resolution and 0.1 mm section spacing: along the plug sample) have been performed in TOTAL CSTJF in Pau, in order to reassess the dominant pore-type of each sample with 3D data, detect the occurrence of possible plug scale heterogeneities and the presence of open discontinuities (fractures, stylolites).

Mineral geochemistry

CaCO3 content has been quantified by using an automated pressure calcimeter in the CEREGE laboratory (Aix-Marseille University) from rock-powder samples, drilled directly from the petrophysics plug samples. Measurements of stable isotopes ratio for Carbon and Oxygen (δ 13 C and δ 18 O) have been carried out on 42 powder samples acquired from millimeter-size drill bit and using an inductively coupled plasma mass-spectrometre (ICP-MS), at the Erlangen-Nürnberg University. Stable isotope data provide constraints in the interpretation of diagenetic environments and the paragenesis of the carbonates investigated.

Petroacoustic modelling: the EPAR approach

Effective property models, such as differential effective medium [START_REF] Norris | A differential scheme for the effective moduli of composites[END_REF]Zimmerman, 1991), have been shown to be a powerful tool in modelling velocity-porosity transforms and elastic moduli-velocity transforms, relating them to pore structure [START_REF] Xu | Modeling elastic properties in carbonate rocks[END_REF][START_REF] Fournier | Elastic properties of microporous cemented grainstones[END_REF][START_REF] Richard | Large-scale mass transfers related to pressure solution creep-faulting interactions in mudstones: Driving processes and impact of lithification degree[END_REF][START_REF] Cilli | The power-law relation between inclusion aspect ratio and porosity: implications for electrical and elastic modelling[END_REF][START_REF] Singh | Digital rock physics in four dimensions: simulating cementation and its effect on seismic velocity[END_REF]. The Equivalent Pore Aspect Ratio (EPAR) was defined by [START_REF] Fournier | Elastic properties of microporous cemented grainstones[END_REF] as the aspect ratio of pores from an equivalent elastic medium consisting of a non-porous calcitic host with spheroidal inclusions, which displays the same elastic moduli as the one measured on the actual rock. It is based on DEM (Differential Effective Medium) models and allows the combined effect of porosity, mineralogy and pore-type onto acoustic properties to be separated and quantified. The EPAR derived from the bulk modulus is named αK (Fig. 2).

The bulk modulus of the mineral phase, used in DEM computations, has been calculated by using the mean of the [START_REF] Hashin | A variational approach to the theory of the elastic behaviour of multiphase materials[END_REF] bounds and by considering the calcite and quartz fractions estimated from CaCO3 content (calcimetry) and point counting. The αK value of each sample is determined by matching the measured bulk moduli and porosity with the DEM models (Fig. 2 and Figure S1). Consequently, each of the 41 experimental couple of values (K; Φ) falls on one of these model curves, indicating its αK. It is worthy to mention that the αK value is not a direct estimate of the actual pore aspect ratio (which can be heterogeneous), but represents a proxy of the pore network stiffness [START_REF] Fournier | The equivalent pore aspect ratio as a tool for pore type prediction in carbonate reservoirs[END_REF], if all the pores were perfectly similar in shape.

Considering a source with a main frequency of 1MHz and the values of measured P-wave velocities, wavelengths should range from 3 to 6 mm. A few samples exhibit macropores which are of >5-10mm scale, which consequently don't fall into the effective medium domain regarding our measurements (these samples have been highlighted in Table 2).

Results

Depositional facies and paleoenvironments

Mandu Limestone formation (Facies association F1)

The Mandu Limestone is mainly composed of micritic wackestone to packstone facies (Facies association F1; Fig. 3B and Fig. 4A-B; Table 1A). In F1 grains are mainly Large Benthic Foraminifers (LBF, lower arrow in Fig. 4A), Planktonic Foraminifers (globigerinids), and scarce coralline algae and F1 can show a variable amount of quartz grain (upper arrow in

Tulki Limestone formation (Facies association F2)

The transition between the Mandu and Tulki Limestones successions is gradual and shows a decrease in matrix micrite content, terminating a long-term shift from > 80% in the lower Mandu to < 10% at the base of the Tulki (Fig. 4C and Fig. 5B, Table 1A). The Tulki Limestone is characterized by coarser bioclastic packstone to grainstone, locally crudely cross-bedded (Facies association F2, Table 1A), with the grains dominated by red algae, echinoderms, bryozoans, rodoliths (black arrow in Fig. 4C), reworked LBF (see Fig. S2) and shallow benthic foraminifers (see Appendix A). The foraminiferal assemblage and texture indicates that the Tulki Limestone accumulated in a comparatively shallow, high-energy environment, well within the euphotic zone.

Trealla Limestone formation (Facies association F3)

The Trealla Limestone records a marked change in terms of texture and grain composition as compared to the Mandu-Tulki succession, with high vertical and lateral variability. Two broadly defined facies have been recognized within Facies association 3 (F3): (i) Scleractinian-Halimeda floatstone with a red algal-foraminiferal (mainly represented by large miliolids) packstone matrix (Fig. 4D) and (ii) red and green algal-foraminiferal packstones to grainstones (Fig. 4E). The faunal and floral content (see Appendix A) of both facies indicates that Trealla Fm. limestones accumulated in a very shallow environment (< 10m), within the euphotic zone.

Diagenetic features and pore types

In carbonates rocks especially, pore volume and pore types are not only correlated to initial sedimentary processes but are strongly linked to the diagenetic transformations they have undergone from deposition to exhumation. The rocks studied in this work present a range of pore types including intercrystalline micropores (within matrix and allochems) to molds, intergranular, and vuggy macropores.

Mandu Limestone formation

Due to the dominantly mud-supported depositional texture of facies association F1, the Mandu Limestone show very scarce sparite cements, except in a few intraskeletal pores (Fig. 6A) and within mode-1 micro-fractures (SC) (Fig. 7A). Mandu is characterized by compaction markers such as stylolites/micro-stylolites, particularly in the micritic matrix (Fig. 6A showed that the micrite matrix and micritized allochems are luminescent (dull-orange luminescence), and revealed an additional phase of dark blue luminescent to nonluminescent, drusy to mosaic sparite cement (SC, Fig. 7B). This particular sparite cement is located mainly in the recrystallized micrite area (Fig. 7B) and in the mode-1 fractures.

Porosity in the Mandu Limestone is dominated by microporosity in micrite matrix and in micritized grains (mostly peloids and lepidocyclinids). Residual macroporosity in intraskeletal pores and mode-1 microfractures after partial occlusion by calcite cement is uncommon (Figs. 7A and6B).

Tulki Limestone formation

In the Tulki Limestone, pervasive compaction features such as large stylolites and concavo-convex grain contacts are observed (arrows in Figs. 6C and6F). As a result of such a compaction, few large blocky sparite cements have been able to develop in the reduced intergranular pore space. In most of the grainstone samples, the remaining intergranular pore space is entirely filled by two distinct phase of sparry calcite cement: (i) perigranular, isopachous fringes of prismatic sparry calcite cement (ISC) (Figs. 6D, 6E and 7C) displaying a dull-orange luminescence (Fig. 7D), and (ii) dark-blue luminescent to non-luminescent, drusy to mosaic, blocky calcite cement (SC) in intergranular position and inside the fractures (Figs. 7C and 7D), similar to those observed in the Mandu Limestone. Locally few anisopachous micritic and fibrous perigranular cements occur (arrows in Fig. 7D), suggesting an early diagenetic phase happening in a vadose and/or marine environment (e.g. [START_REF] Flügel | Microfacies of Carbonate Rocks: Analysis, Interpretation and Applications[END_REF].

In the Tulki Limestone, pore types are characterized by a dominance of various levels of intragranular microporosity within micritized grains which can lead to moldic/vuggy porosity (Figs. 6D and see 8A). In a few samples, where compaction features are less pronounced, intergranular porosity may dominate. Dissolution features affecting grains (vugs and moldic pores after bioclast leaching) or locally even matrix have been observed, particularly in the upper part of the Tulki Limestone (Figs. 8A and8B). Such dissolution pores (molds and vugs) are commonly filled by the non-luminescent blocky calcite cement (SC). Like in the Mandu Limestone, peloids and micritized bioclasts exhibit a dull-orange luminescence (Fig. 7D). In grainstones, especially where the perigranular fringe of prismatic calcite is lacking, concavo-convex contacts between grains are often observed (Fig. 6C). Additionally, stylolites are common, particularly in packstone intervals (Fig. 6F). No crosscutting relationship between SC and stylolites/concavo-convex grain contact has been observed, suggesting that SC calcite formed after development of the burial features.

At the macroscopic scale, another diagenetic feature is a rock pervasive oxidation resulting in a reddish colour (Figs. 3D and3E). It is important to note that this oxidation does not affect outcrops of the overlying Trealla rocks, at least in studied areas. From thin sections we established that iron oxide take place preferentially and mostly inside the intraskeletal spaces (Figs. 6C and6E). It is further found as fringes lining the boundary between perigranular prismatic cement (ISC) and the later non-luminescent blocky sparite cements (SC) (arrow in Fig. 6E). This suggests that iron oxide deposition took place relatively early in the diagenetic history, prior to the blocky sparite cementation and shows it is not related to a modern, telogenetic meteoric process. Iron oxides are also found lining the walls of the moldic pores and dissolution vugs (Fig. 8B), thus suggesting that they have circulated during or after this dissolution phase. Since the dissolution vugs have been filled by both ISC and SC, the dissolution phase is therefore interpreted to have occurred before sparry calcite cementation., thus at least prior to the final exhumation of these rocks (see section 4.7).

Trealla Limestone formation

The Trealla Limestone, contrary to Mandu and Tulki, is characterized by a widespread preservation of the primary intergranular porosity, especially in the grainstone facies. All samples show little-to-no intergranular cementation and a dominance of pointcontact between grain (Fig. 6G and see Fig. 13F), with no pressure-solution features. To a larger extent, no indication of mesogenetic diagenesis (sensu [START_REF] Choquette | Geologic Nomenclature and Classification of Porosity in Sedimentary Carbonates[END_REF] has been observed. Grains are generally rimmed by a thin isopachous fringe of equigranular sparry calcite cement (Fig. 6G red arrow), consistent with a formation within a meteoric phreatic lens (e.g. [START_REF] Tucker | Carbonate Sedimentology[END_REF]. Small areas of perigranular fibrous cement have also been observed. Aragonitic bioclasts (corals and green algae) are commonly leached, forming large moldic to vuggy pores lined by a similar fringe of equigranular calcite orrarely -completely filled by mosaic sparite (Fig. 6H).

Under cathodoluminescence the equigranular calcite is non-luminescent in its inner, early part and exhibits a dull-orange luminescence in its outer boundary ("ZSC" on Figs. 7E and7F). Such zoned sparry calcite cements (ZSC) should be therefore distinguished from the isopachous sparry calcite (ISC) observed in the Mandu and Tulki formations. Small areas of dark-blue luminescent to non-luminescent sparry cement developed in the intergranular pore spaces (Fig. 7F), is plausibly equivalent to the SC non-luminescent cement observed in the Tulki Limestone. As a result of limited cementation and lack of significant compaction features, some samples still preserved a large amount of initial intergranular porosity (see Fig. 13F).

Outcrop-scale structures and karstification analysis

The "Unnamed Quarry 2" (Fig. 1B) exposes a decametre scale outcrop displaying tectonic structures and karstic features at the top of the Tulki limestones (Fig. 8C). Although, it is difficult to precisely (bed to bed) correlate the stratigraphy, this quarry exhibits an uneven contact between LBF rich yellowish Tulki facies (F2) and white Trealla coral rich facies (F3) ("1" and "2" in Fig. 8C). The outcrop is affected by a N-S striking sub-vertical fault with a normal component (in yellow Fig. 8C). This fault shows vertical karst features (macro-scale dissolution) along its fractures in the associated damage-zone. A stratiform bed (of variable thickness) of pseudo-breccia embedded in a red "terra rossa" matrix is found (Fig. 8D) at the interface between the Tulki and Trealla formations, suggesting that a subaerial exposure and karstification phase occurred prior to Trealla deposition. Immediately below the karst-breccia bed, the limestone is affected by decimetre-to-meter scale dissolution voids, mostly horizontal and filled with calcite cement (Fig. 8E). Such diagenetic features as well as the pseudo-breccia bed are both cross-cut by the fault (and associated vertical karst) that postdates it, thus supporting the assumption that these karstic pseudo-breccias are not related to modern telogenetic processes, in contrast to the quaternary pisolitic material infilling voids within the Trealla, observed by [START_REF] Hocking | Geology of the Carnarvon Basin, Western Australia by R.M. Hocking[END_REF].

Carbon and oxygen stable isotopes ratios

The stable isotope signature of bulk-rock carbonates has been used to interpret the origin of the main diagenetic transformations (Fig. 9A). For all measured samples, the isotopic signatures are negative and depleted in both 18 O and 13 C as compared to the Miocene marine calcite values (e.g. [START_REF] Veizer | 87Sr/86Sr, δ13C and δ18O evolution of Phanerozoic seawater[END_REF]Fig. 9A). Isotope ratios exhibit a narrow δ 18 O range, averaging around -6 ‰VPDB, in combination with more scattered δ 13 C values, ranging from -1 to -9 ‰VPDB. This suggests that these rocks: (i) have undergone diagenetic transformations, resulting in a loss of their initial marine geochemical signature and (ii) that they underwent diagenetic transformations (neomorphism and/or cementation) in a meteoric environment influence, as suggested by low negative δ 13 C (e.g. [START_REF] Hudson | Stable isotopes and limestone lithification[END_REF][START_REF] Allan | Isotope signatures associated with early meteoric diagenesis[END_REF]. More particularly, the two measurements of the ZSC sparry calcite cements from the Trealla limestones revealing highly negative δ13C values, ranging from -7.07 to -8.67‰, while the corresponding δ18O values range from -5.53 to -6.05‰, thus strongly suggesting a meteoric origin for ZSC cements. One measurement made specifically from oxidized grain from the Tulki also display strongly negative value, suggesting that oxidation and its associated dissolution phase, also took place under strong meteoric influence.

Noteworthy, δ 13 C values from the Tulki and Mandu limestones shows decreasing upward values base to top (Fig. 9B). This strongly suggests that such a meteoric δ 13 C signature is not related to modern meteoric alteration, which would have uniformly all outcrops investigated, but rather to earlier processes occurring prior to the final exhumation of these rocks.

Furthermore, an abrupt negative shift in δ 13 C values occurs at the top of the Tulki Limestone (Fig. 9B), with δ 13 C values down to -8 ‰, which is consistent with the occurrence of a subaerial exposure at the top of Tulki formation (e.g. [START_REF] Quilty | Cenozoic sedimentation cycles in Western Australia[END_REF][START_REF] Chaproniere | Oligocene and Miocene larger foraminiferida from Australia and New Zealand[END_REF]Condon 1968; see also 5.1). Finally, low δ 13 C (-6 to -7 ‰) in the Trealla Limestone, are close to those of (ZSC) cements and fits well with its very shallow water deposition environment and are indicative of a later phase of meteoric diagenesis.

Pore type classification

A pore type classification has been developed based on a semi-quantitative analysis of thin-sections and CT-Scan images. In the studied samples, macropore space consists dominantly of intergranular, moldic and vuggy pores (Table 1B). Primary skeletal macropores are rare and do not represent a significant proportion of the macroporosity.

Intergranular pore spaces are mostly partially filled by calcite cements. Most of the samples display varying amounts of intercrystalline micropores located within micritized skeletal grains and/or within micritic matrix. The proportion of macropores has been semiquantitatively estimated from point-counting on thin-sections high-resolution scans.

Microporosity has been estimated by calculating the difference between measured total helium porosity and macroporosity determined by point counting. CT-Scan images of plugs have been used to assess possible pore type heterogeneities at the plug scale as well as to detect open discontinuities such as stylolites, fractures or vugs that have not been captured by thin-sections. Samples have been classified into 5 groups according to their dominant pore type (Table 1B): (i) DPT1: dominant intercrystalline microporosity with scarce or lacking macropores, (ii) DPT2: mixed microporosity and intergranular macroporosity, (iii) DPT3: dominant intergranular macroporosity, (iv) DPT4: dominant moldic and/or vuggy macroporosity. Samples with occurrences of open stylolites or micro-fractures, have been classified as above, with the addition of the suffix S (DPT1S, DPT2S and DPT3S).

Mineralogy, porosity and ultrasonic velocities

Measurements of CaCO3 content (calcimetry) performed on 20 samples from the Mandu and Tulki Formations (Fig. 5A) revealed that a significant amount of non-calcite material (up to 14%), may exist in the bulk rock, especially in the lower Mandu samples. This proportion rapidly decreases and become negligible at the transition with the Tulki Limestone. Considering the percentage of quartz estimated from point counting (Table 2), the non-calcitic fraction is assumed to be mainly composed of quartz grains.

Vp values at an effective stress of 40 MPa are highly scattered, ranging from 2351 m/s from to 6402 m/s. These velocities are mainly consistent, though slightly higher, than the wireline log data (performed at dm to m scale) from wells penetrating the age-equivalents limestones in the offshore part of the NCB (~ 2000-5000 m/s; [START_REF] Wallace | Geological controls on sonic velocity in the cenozoic carbonates of the northern carnarvon basin, north west shelf, western australia[END_REF][START_REF] Shragge | The Western Australia Modeling project -Part 2: Seismic validation[END_REF]. These offshore equivalents [START_REF] Cathro | Progradation along a deeply submerged Oligocene-Miocene heterozoan carbonate shelf: How sensitive are clinoforms to sea level variations[END_REF][START_REF] Wallace | Geological controls on sonic velocity in the cenozoic carbonates of the northern carnarvon basin, north west shelf, western australia[END_REF][START_REF] Moss | Sequence Biostratigraphy of Prograding Clinoforms, Northern Carnarvon Basin, Western Australia: A Proxy for Variations in Oligocene to Pliocene Global Sea Level?[END_REF] largely corresponds to the finer-grained facies F1A. Porosities values are also highly scattered between 0 and 35% (Table 2), with average porosities of 18% (Mandu Fm; F1), 2.8% (Tulki Fm; F2), and 8.3% (Trealla Fm; F3). The highest porosity values are found in the microporous samples from the Mandu Limestone (e.g. Msh-A15 27.5%). Ultrasonic velocities display a nearly linear decreasing trend with increasing porosity but with a strong scattering of values at a given porosity, averaging 1000 m/s for P-waves (Fig. 10A) and 500 m/s for S-waves (Fig. 10B). This variation in velocity values at a given porosity is not fully explained by the depositional texture or facies. Tight (porosity <1%) samples exhibit highest P-wave velocities, ranging from 6000 to 6500 m/s, which is consistent with values measured in pure calcite.

Dynamic bulk and shear moduli have been computed from Vp, Vs, and bulk density measurements (Table 2,). In tight samples, both moduli values range are within the magnitudes known for pure calcite (Kcalc=70 GPa, µcalc=30 GPa, e.g. Mavko et al., 2008).

They are found to be negatively correlated with porosity, but again with significant scattering for a given porosity value (Fig. 11). Depositional parameters along with pore types seem to control bulk moduli-porosity relationships. Indeed, the higher K values of the Trealla limestones, as compared to the Mandu and Tulki, is clearly correlated with dominant pore types, with a moldic to vuggy pore regime (DTP4) dominant in the Trealla and matrix and intragranular microporosity dominant in the Mandu and Tulki limestones (DTP1 to DTP2) (Fig. 11A and11B).

EPAR modelling and correlation with dominant pore type

In order to explain the cause of the observed scattering in velocity and bulk modulus at a given porosity and try to predict accurately pore type information from indirect measurements, we applied the EPAR approach, by implementing the so-called αK proxy [START_REF] Fournier | The equivalent pore aspect ratio as a tool for pore type prediction in carbonate reservoirs[END_REF]).

In the limestones studied, the obtained equivalent pore aspect ratio (αK) range from 0.03 to 0.53 (Fig. 12). It is interesting to point out that the αK-porosity plot shows that no correlation exists between αK and porosity, thus suggesting this parameter is not controlled directly by pore volume but more likely by pore network structure.

In contrast, dominant pore types, determined from quantitative point counting (Table 2; colours in It appears, therefore, that the αK variation is primarily related to the dominant pore type in each sample, i.e. related to depositional and diagenetic processes. However, it is important to note that for low porosity values (less than 5%) the dominant pore type show little correlation with the EPAR variation (grey zone in Fig. 12). This is explained by the fact that, DEM models tend to converge at low porosity (see Fig. S3) thus leading to increased uncertainty in αK computation and therefore inefficient discrimination of pore structures.

Paragenetic sequence influenced by subaerial exposure/erosion phase

Based on outcrop data, petrographic analysis and stable isotope results, a paragenetic evolution of the Oligo-Miocene carbonates from Cape Range is proposed (Fig. 13A-D). This paragenetic sequence and preceding sedimentological results reveals the major differences between the Mandu-Tulki and Trealla limestones in terms of both depositional features and diagenetic evolution. In particular, compaction and burial features, are prominent in the Mandu and Tulki formations, whereas they are completely lacking within the Trealla formation (Fig. 13E-F). In spite of their similar dominant depositional texture (packstonegrainstone), distinct patterns of diagenetic evolution led to dramatically different porosity, pore network and acoustic properties.

Due to their limited total thickness in the Cape Range (≤ 100m m), the Tulki and Trealla would be expected to have experienced comparable burial depth and thus display similar diagenetic processes and compaction features (Fig. 13A). Compaction features, such as stylolites observed in the Tulki (and Mandu) Limestone formed during burial, under lithostatic stress. Although no consensus exists regarding the minimum depth for their development, laboratory and in-situ studies suggest that stylolites do not require very high burial depth to form. Their nucleation has been estimated to occur at depths around 100m [START_REF] Koehn | Modelling of stylolite geometries and stress scaling[END_REF] whereas actual stylolite planes have been shown to develop at depths ranging from 200 to 1000m (e.g. [START_REF] Nicolaides | Pressure-Dissolution and Cementation in an Oligo-Miocene Non-Tropical Limestone (Clifton Formation), Otway Basin, Australia[END_REF]1997;[START_REF] Kroon | Multi-Scale State of Stress Analysis of the Potiguar Basin NE Brazil[END_REF]Bruna et al., 2018). The frequent and consistent occurrence of stylolites and concavo-convex grain contacts throughout the Tulki limestones, compared to the lack of any significant compaction features within the Trealla limestone, therefore suggest that an emersion occurred at top of the Tulki and led to the erosion of at least several 10s of meters of sediments, prior to deposition of the Trealla Limestone (Fig. 13A). Such an event has been suspected by [START_REF] Condon | The cape range structure Western Australia; Pt 1: Stratigraphy and structure[END_REF], [START_REF] Quilty | Sedimentation cycles in the cretaceous and cenozoic of Western Australia[END_REF] and [START_REF] Chaproniere | Oligocene and Miocene larger foraminiferida from Australia and New Zealand[END_REF], who noted thickness variations of the Tulki Limestone along Cape Range, the presence of an iron-rich layer associated at an erosional surface at the Top-Tulki and, furthermore, mentioned a possible slight angular unconformity between the Tulki and Trealla formations. From borehole date, they also noted an "intense alteration" of the Top-Tulki in onshore and proximal-offshore wells Muiron-1 and Ningaloo-1. Such an erosion, would have led to the erasure of the less-compacted part of the Tulki. The subsequent uplift of the Cape Range region during the Late Miocene did not allow for the deposition of thick sedimentary successions, thus explaining the scarcity of compaction features within the Trealla Limestone (even at its base). The occurrence of a major subaerial exposure event affecting the top of Tulki Limestones as proposed here is supported by: -(i) Karstic features affecting the top of Tulki limestones in the « Unnamed Quarry 2 » (Fig. 8) which are sealed by the Trealla Limestone.

-(ii) The occurrence of iron oxide deposits postdating both the perigranular (ISC) cement, and the dissolutions voids, (but predating both blocky SC cement, Figs. 6D and6E) and affecting the limestones below the top Tulki strongly supports that this oxidation takes place during this event.

It also explains why there is no such oxidation, in the Trealla Limestone, even in the currently open pore network.

-(iii) The highly negative δ 13 C shift between the at the Tukli-Trealla boundary.

The scenario outlined above implies a short-lived fall in relative sea level around the onset of the Middle Miocene. This relative drop may have been driven by an early stage of the North-Australian margin compression, which started with the collision with Timor during the Middle Miocene (e.g. [START_REF] Cathro | Progradation along a deeply submerged Oligocene-Miocene heterozoan carbonate shelf: How sensitive are clinoforms to sea level variations[END_REF][START_REF] James | Late Triassic -Mid-Jurassic to Neogene Extensional Fault Systems in the Exmouth Sub-Basin, Northern Carnarvon Basin, North West Shelf, Western Australia[END_REF] with modest transpression, even in the Cape Range area. Indeed, evidences of minor folding events during the Middle Miocene have been found offshore, North of Cape Range, in the Browse and Barcoo sub-basin (e.g. Rosleff-Soerensen et al. 2016, Wilson et al., unpublished data). Onshore Cape Range, where possible episodic deformations have been documented since the Mid-Miocene (e.g. [START_REF] Keep | Natural seismicity and tectonic geomorphology reveal regional transpressive strain in northwestern Australia[END_REF], Condon, 1968[START_REF] Quilty | Sedimentation cycles in the cretaceous and cenozoic of Western Australia[END_REF]. At the scale of Cape Range, even a slight overall tilt of 1° of the bedding could have led to the uplift up to 300°m, on the other (eastern) side of the peninsula. The actual main phase of the tectonic inversion of the North West Shelf basins starts latter (10-7 Ma; e.g. Keep et al., 2007;[START_REF] Rosleff-Soerensen | The response of a basinscale Miocene barrier reef system to long-term, strong subsidence on a passive continental margin, Barcoo Sub-basin, Australian North West Shelf[END_REF][START_REF] Saqab | New constraints on the timing of flexural deformation along the northern Australian margin: Implications for arccontinent collision and the development of the Timor Trough[END_REF]. It is thus likely that the final uplift of the Cape Range region initiated soon after the deposition of the Trealla limestones, explaining their lack of compaction features.

The influence Middle Miocene glacio-eustasy associated with the rapid growth of the East Antarctic Ice Sheet [START_REF] Miller | Unlocking the Ice House: Oligocene-Miocene oxygen isotopes, eustasy, and margin erosion[END_REF][START_REF] Zachos | A Turning Point in the Cenozoic Greenhouse to Icehouse Transition during the Late Middle Eocene[END_REF]John et al., 2011), resulting in sea level fluctuations in the amplitude of 20-60 m (John et al., 2011, Miller et al., 2013) cannot be excluded. Such eustatic variations could have resulted in repeated exposure of the low angle ramp system along which the Tulki limestone was deposited. However, the limited geographic extent of the subaerial exposure makes this explanation less probable. In both cases, significant erosion of the Tulki Limestone may have occurred during subaerial exposition and/or during the subsequent Trealla marine transgression.

Discussion

Impact of depositional and diagenetic processes on pore type evolution.

Microporosity development

The present work revealed that Mandu/Tulki and Trealla Limestones in the Cape Range anticline are characterized by distinct carbonate grain producers as well as different path in diagenetic evolution. (i) Together, the Mandu and Tulki formations constitute the proximal part of an extensive heterozoan ramp system whereas the Trealla limestones forms a sub-tropical to tropical, photozoan system (Fig. 14). (ii) While the Mandu and Tulki formations are characterized by significant microporosity and by the frequent pressuresolution features (Fig. 13E), the Trealla limestones are dominated by intergranular macroporosity associated with moldic and vuggy pores and little-to-no compaction (Fig. 13F).

The most prominent diagenetic feature affecting the Mandu limestone is the development of microporosity within carbonate matrix and grains. The significantly 13 C-depleted signature of the mud-supported carbonates from the Lower Mandu strongly suggests that microporosity developed as a result of neomorphic transformations of micrite within a meteoric diagenetic environment (Fig. 9A). Micrite neomorphism and associated microporosity in marine carbonates have been commonly assigned to meteoric diagenesis occurring during prolonged phases of subaerial exposures (e.g. [START_REF] Leonide | Diagenetic patterns and pore space distribution along a platform to outershelf transect (Urgonian limestone, Barremian-Aptian, SE France)[END_REF][START_REF] Deville De Periere | Influence of a major exposure surface on the development of microporous micritic limestones -Example of the Upper Mishrif Formation (Cenomanian) of the Middle East[END_REF]. Two distinct phases of cementation (ISC and SC) affect the Mandu and Tulki limestones. The ISC cement was most likely formed under a reducing marine or meteoric phreatic environment, whereas the SC phase is more indicative of an oxidizing meteoric environment, as suggested by the 13 C-depleted signature of the SC-rich Tulki grainstones facies (Fig. 9A). Furthermore, the precipitation of iron oxide postdating the ISC cements and but predating the SC infilling dissolution vugs (Fig. 6) below the karstified top of the Tulki unconformity allow the following inferences. (i) significant dissolution processes occurred during this exposure and (ii) SC formed during the same phase, prior to, or at the beginning of, the Trealla limestone deposition, where it may explain the same SC cement found in small amount in the Trealla intergranular pore space. As a consequence, the lack of significant microporosity within the Trealla limestone and the 13 C-depleted signature of microporous mud-supported limestones from the Mandu Limestone strongly suggest that microporosity development mainly occurred during the top Tulki during subaerial exposure.

Additionally, grainstone samples from the Tulki Limestones, whose intergranular pores have been occluded by SC cement, exhibit intragranular microporosity. This indicates that the SC cementation phase post-dates the development of microporosity (e.g. [START_REF] Fournier | Pore space evolution and elastic properties of platform carbonates (Urgonian limestone, Barremian-Aptian, SE France)[END_REF].

Finally, it is interesting to note that in contrast to the onshore Trealla facies studied here, the main diagenetic processes involved in the pore amount and pore type acquisition in offshore ageequivalent Trealla are essentially controlled by compaction and burial cementation, [START_REF] Wallace | Geological controls on sonic velocity in the cenozoic carbonates of the northern carnarvon basin, north west shelf, western australia[END_REF], largely similar to those described for the on-shore Mandu and Tulki formations described here. Indeed, these offshore deeper deposits are unlikely to have been exposed to meteoric processes, such as emersion-related diagenesis.

Although the impact of recent telogenetic processes on the acoustic signature of these rocks cannot be entirely ruled out, the present data support that such an impact is likely to be minimal. The preservation of a ddecreasing upward 13 C values below the top-Tulki subaerial exposure surface strongly suggests that no significant cementation and/or neomorphism occurred in recent telogenetic environments. Such processes would have implied a geochemical signature independent from the vertical position along the sedimentary succession. Moreover, no observations in the field, and more importantly on thin section, have shown indication of modern dissolution features. Only one significant dissolution phase has been observed (Fig. 8A-B) and has been shown to have occurred prior to the final exhumation of these rocks (cf. 4.7). As a consequence, modern exposure seems at least to not have significantly modified the microstructure of the limestones considered in this study.

Impact of the nature of carbonate production on the diagenetic evolution

A significant change in carbonate production occurred during the onset of the Trealla carbonate system, which have strongly impacted the dominant pore type acquisition. The dominant Low-to-High magnesian calcite heterozoan carbonate factory (LBF, red algae, etc, Fig. 14A) of the Mandu and Tulki limestones is replaced, in the Trealla limestone, by a photozoan carbonate production dominated by aragonitic biota (scleractinian and green algae, (ii) Local or regional modifications in nutrient content (from mesotrophic to oligotrophic conditions) in sea-water (e.g. [START_REF] Pomar | Ecological control of sedimentary accommodation: evolution from a carbonate ramp to rimmed shelf, Upper Miocene, Balearic Islands[END_REF] and its physicochemical properties. The fact that possible evaporitic minerals (anhydrite, dolomite) have been found both onshore and in offshore wells in the Trealla time-equivalents deposits [START_REF] Wallace | Geological controls on sonic velocity in the cenozoic carbonates of the northern carnarvon basin, north west shelf, western australia[END_REF][START_REF] Gallagher | The enigma of rare Quaternary oolites in the Indian and Pacific Oceans: A result of global oceanographic physicochemical conditions or a sampling bias?[END_REF]) also points to that hypothesis.

(iii) The subaerial exposure and erosion affecting the top-Tulki Limestone-including possible marine erosion during the Trealla transgression -could have led to a flattened topography at the proximal margin of the Exmouth basin, favoring the development of an extensive, euphotic, platform or-low-angle ramp carbonate system (Fig. 14B).

5.2 Impact of pore network and pore shape on the acoustic signature: physical and geological interpretation of the αK proxy 5.2.1 αK proxy variation in the light of pore stiffness

The αK values can be explained by the soft or stiff acoustic behaviour of each DPT class (Fig. 12). Indeed, EPAR modelling is based on the fact that different pore aspect ratios have different stiffness which can be separated in two domains, "soft" pores or "stiff" pores.

The boundary between stiff and soft pore domain usually corresponds to so-called referencepores whose aspect ratios range from 0.13 to 0.25, depending on the type and scale of acoustic data used [START_REF] Xu | Modeling elastic properties in carbonate rocks[END_REF][START_REF] Zhao | Quantitative geophysical pore-type classification and its geological implication in carbonate reservoirs[END_REF][START_REF] Hairabian | Depositional Facies, Pore Types and Elastic Properties of Deep-Water Gravity Flow Carbonates[END_REF]Fournier et al., 2018). In the Cape Range database, the threshold value between these two domains would be around 0.2, i.e. at the transition between dominant microporosity (DPT1) and dominant moldic/vuggy pores (DPT4). Interestingly, this value is very similar to the one obtained in slope and basinal tropical carbonates [START_REF] Hairabian | Depositional Facies, Pore Types and Elastic Properties of Deep-Water Gravity Flow Carbonates[END_REF], suggesting that this threshold might have actual physical significance for the pore network geometry/connectivity. The high αK values (>0.2) are associated with samples whose pore space is dominated by moldic and/or vuggy macropore (DPT 4), which match with the stiff pores domain (Fig. 12). This result is consistent with the low pore compressibility expected for such type of roundish and equant-shaped molds and vugs (Figs. 4 and6). The stiff nature of such pore types has been previously documented in a variety of published carbonate case studies (e.g. [START_REF] Anselmetti | The Velocity-Deviation Log: A Tool to Predict Pore Type and Permeability Trends in Carbonate Drill Holes from Sonic and Porosity or Density Logs[END_REF][START_REF] Saleh | Revisiting the Wyllie time average equation in the case of near-spherical pores[END_REF][START_REF] Fournier | Pore space evolution and elastic properties of platform carbonates (Urgonian limestone, Barremian-Aptian, SE France)[END_REF][START_REF] Hairabian | Depositional Facies, Pore Types and Elastic Properties of Deep-Water Gravity Flow Carbonates[END_REF].

The low αK values (<0.2) are associated with samples exhibiting dominant microporosity (DTP1), thus suggesting that micropore networks from Cape Range behave like soft or reference pores (sensu [START_REF] Xu | Modeling elastic properties in carbonate rocks[END_REF]. Indeed, such micropores, are located in between micrite calcite crystals, represent very flat pores and explain their low αK signature. The velocity-porosity relationships in carbonates with dominant microporosity have been commonly reported to be well modelled by the time average equation (Willy, 1951) and, as a consequence, micropore networks have been assumed to match with reference pores (Anselmetti andEberli, 1999, Eberli et al., 2003;[START_REF] Weger | Quantification of pore structure and its effect on sonic velocity and permeability in carbonates[END_REF]. However, the high diversity of micrite microfabrics described from various microporous reservoirs has been shown to result in a variety of acoustic behaviors, with pore networks ranging from soft (αK from 0.05 to 0.15) to stiff (αK from 0.15 to 0.25) domain [START_REF] Fournier | Elastic properties of microporous cemented grainstones[END_REF][START_REF] Hairabian | Depositional Facies, Pore Types and Elastic Properties of Deep-Water Gravity Flow Carbonates[END_REF], Fournier et al., 2018). In the present study, samples with dominant microporosity (DPT1) exhibit a similar scattering in αK with values ranging from 0.04 to 0.21. Such a scattering in αK values may therefore result from a polyphase evolution of micrites or from variable degrees of micrite transformation during diagenesis. Finally, the samples with dominant intergranular macropores (DPT 3) show intermediate αK values around 0.2-0.3, belonging to the stiff domain. This relative stiffness of the intergranular pore space in Cape Range samples is plausibly related to the partial occlusion of such intergranular pores by development of sparry calcite cementation around grains that, on one hand, stiffens the solid, mineral network and, on other hand, leads to the formation of relatively equant residual pores in the center of the intergranular space, thus behaving acoustically as an intermediate case between micropores and moldic pores.

Contribution of 3D CT Scan sections in underlining progressive diagenetic processes

A significant scattering of αK values is found within the distinct DPT classes (Fig. 12) with standard deviation for DPT4 and DTP1 classes at 0.15 and 0.06 respectively. To better understand the origin of such a αK variability, we used micro 3D CT-scan models (Fig. 15) in order to (i) detect the possible occurrence of pore type heterogeneities at the centimetre/plug scale, and (ii) to assess the possibility of subtler changes in the pore network. Thus, the CT images allow revealed why samples A10 and A8, in spite of the occurrence of molds and vugs of mm to cm scale, present very low αK values of 0.05 and 0.11 respectively (A10 and A14 in Fig. 15). Open fractures and/or open stylolites therefore results in significantly softened pore networks, shifting their αK value to shift into the soft-pore domain (αK<0.2, black arrows in Fig. 12). This acoustic behavior reflect the very flat shape and lowstiffness of such discontinuities, known to strongly reduce Vp and Vs (e.g. [START_REF] Pyrak-Nolte | Transmission of seismic waves across single natural fractures[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 samples exhibiting the highest or lowest αK values show very different pore network on CT-Scan. The samples with the lowest αK mostly display homogeneous micropore network (in grey, A8 in Fig. 15), with scarce macropores. In contrast, the samples with the highest αK values (around 0.5) contain only large and/or rounded molds and vugs (in black, Tr5 and Tr6 in Fig. 15D), making them even stiffer compared to lower αK samples in DPT4 class (i.e. αK ≈ 0.2; Fig. 15).

For samples located at the transition from the soft to the stiff pore domains (i.e. DTP1 and DTP4) (αK≈0.2), the CT-scan images exhibit similar patterns and proportions of micro and macropores, regardless of their DPT determined from thin section point counting (A12-13, Tr3-6 in Fig. 15). These patterns result from similar dissolution processes affecting especially the LBF in the Mandu (e.g. Fig. 6B) or grains and matrix in the Trealla (e.g. TR3 in Fig. 15), which formed a few small moldic/vuggy pores. These are better captured on the 3D CT-scan data (black box, A13 in Fig. 15) compared to the quasi-2D thin sections. Moldic pore from LBF leaching are flat, as a result of the original shape of these organisms, and may explain their relatively low stiffness, thus low αK signature (i.e. close to 0.2) for these DPT4 samples Additionally, the dissolution phase that led to the development of moldic pores and vugs could have also, in an early stage, deeply restructured the micropore space into a microvacuolar network) as evidenced in the Urgonian limestones from Provence [START_REF] Fournier | Pore space evolution and elastic properties of platform carbonates (Urgonian limestone, Barremian-Aptian, SE France)[END_REF][START_REF] Fournier | The equivalent pore aspect ratio as a tool for pore type prediction in carbonate reservoirs[END_REF]. These grains are thus still competent but may already behave acoustically as quasi-molds (blue arrow in Fig. 12). It is interesting to note that relatively low levels (less than 5-10%) of stiff macropores within a dominantly microporous pore network, as revealed by CT-scan analysis, are sufficient to induce a significant increase in αK. Therefore, in the perspective of pore type discrimination from acoustic properties, such threshold effects should be considered. Finally, it appears that αK variations are largely related to the dominant pore type in each sample and are able to capture pore network structures.

.

Combined effect of depositional and diagenetic processes on the evolution of acoustic properties of heterozoan and photozoan carbonates

Our research demonstrated significant differences in pore network architectures and petroacoustic responses (αK) between the heterozoan carbonates from the Mandu/Tulki Limestones, likely related to temperate to sub-tropical environments, and the overlying photozoan sub-tropical to tropical Trealla Limestone, probably deposited in sub-tropical to tropical setting.

Two main causes can be invoked to explain these differences. Firstly, the drastic change in mineralogy of the dominant primary carbonate producers (calcite in Mandu/Tulki formations, aragonite in the Trealla formation) has driven two distinct patterns of diagenetic evolution.

The dominance of calcite producing organisms (LBF, red algae, etc) favoured the development of microporosity, whereas the dominance of biota with less-stable aragonitic skeleton favoured the development of molds and vugs, during minor phases of subaerial exposure. As a consequence, moldic/vuggy photozoan limestones from the Trealla Limestone exhibit a stiffer acoustic signature, for a given porosity compared to microporous Mandu/Tulki heterozoan limestones.

Secondly, the emersion and subsequent marine transgression terminating the Tulki Formation led to significant erosion of the Tulki limestones. This may well explain the apparent higher burial depth indicated by the abrupt shift in compaction through pressure-solution (concavoconvex grain contacts and stylolites) between the Tulki and the overlying Trealla Limestone.

This is why the shallow-buried Trealla have been able to preserve a significant part of intergranular pores, which also prevented the development of stylolites and fractures after rock early embrittlement [START_REF] Bruna | Structural diagenesis of shallow platform carbonates: Role of early embrittlement on fracture setting and distribution, case study of Monte Alpi (Southern Apennines, Italy)[END_REF], therefore preserved from pore network softening. Additionally, higher burial, associated with little intergranular early cementation, characteristic of non-tropical ramp carbonates (e.g. James, 1997;[START_REF] Frank | Diagenetic pathways in deposits of cool-and cold-water carbonate factories[END_REF], favoured tight grain re-arrangement. This did not allow the preservation of large and intergranular pores in the Mandu/Tulki, increasing the relative amount of microporosity over macroporosity. These results therefore suggest that typical heterozoan, non-tropical carbonates, are likely to be less prone to develop high moldic macroporosity and stiff acoustic signature compared to the photozoan carbonates when subject to meteoric diagenesis.

Importance of integrative approaches for 3D modelling of carbonate systems and reservoirs

An important challenge of 3D modelling of carbonate systems and reservoirs is the integration of geological concepts making it possible to produce models that are more realistic than those that would be obtained only from well and seismic data. The use of forward modelling approaches revealed to be extremely relevant for building realistic models that can be shared by the various disciplines of carbonate exploration such as sedimentology, stratigraphy, diagenesis, seismic, geomodeling and reservoir geology [START_REF] Lanteaume | Testing geologic assumptions and scenarios in carbonate exploration: Insights from integrated stratigraphic, diagenetic, and seismic forward modeling[END_REF]. Moreover, such approaches allow sensitivity tests on stratigraphic and diagenetic scenarios, sequence stratigraphic concepts and controlling factors to be performed. The approach used in the present work allowed establishing and quantifying the link between carbonate producers, nature of dominant pore types and acoustic properties for a given diagenetic history controlled by subaerial exposure and subsequent erosion. The establishment of such links is fundamental in forward modeling since it makes it possible to convert depositional facies into acoustic properties according to different diagenetic scenarios.

Moreover, the 3D variability of the physical properties underlined at the plug scale from CTscan data have been shown to be significant, especially when microstructural discontinuities occurs. Capturing such a plug-scale variability has been shown to be of importance for the upscaling of acoustic properties at reservoir scale (Bailly et al., 2019b). In the future it would be interesting to perform full 3D analyses, trying to extract useful descriptors (such as continuity and tortuosity of the solid skeleton) from actual CT-scan 3D pore network in order to make direct linkage between acoustic and reservoir properties.

VI. Conclusions

The present work provides novel results which demonstrate the importance of the combined role of sedimentary attributes (depositional texture and mineralogy) and the diagenetic processes when assessing variability and specificity of the petroacoustic signature of heterozoan and photozoan carbonates. Our multidisciplinary and multiscale study of Oligo-Miocene carbonate deposits from the Cape Range peninsula revealed various issues concerning the link between the nature of carbonate production, the subsequent diagenetic and pore type evolution and acoustic properties:

-Heterozoan, non-tropical, carbonates from Mandu and Tulki formations, in the proximal part of a mainly Miocene carbonate ramp, are characterized by dominant microporosity and significant pressure-solution compaction features leading to reduced pore network stiffness and -consequently -decreased wave velocities.

-The sub-tropical to tropical carbonates from Trealla formation, displaying mainly moldic and partially cemented intergranular pores, display stiffer pore network leading to higher wave velocities.

-These petroacoustic signatures are influenced by other diagenetic features, such as fracture/stylolites and partial grain partial dissolution, which can be detected from combined thin-section and 3D-CT-scan data.

The variation in diagenetic evolution found for each of the three formations investigated is primarily related to: (i) differences in the initial intergranular cementation and compaction level, (ii) change in the skeletal mineralogy of the dominant carbonate producers.

Finally, the resulting dominant pore type information has been accurately retrieved from indirect petroacoustic data by using the Equivalent Pore Aspect Ratio proxy (αK). Additional CT-scan sections, revealed that αK is controlled, to some extent, by the transitional evolution of pores between soft to stiff pore network, reflecting increasing dissolution. The relevance of the αK proxy assessed in this geological context and others suggests promising applications to the abundant well log data in the offshore domain.

Figures captions:

Figure Average Vs is the average of the 2 perpendicular polarized S-wave velocities. Sample marked with a * are the one in which some macropore is larger than the average wavelength of Pwave used for the measurement.

Fig. 4A ;

 4A Fig. 4A; up to 14% based on calcimetry Fig. 5A). Mandu Limestone can be separated in two intervals (Lower and Upper Mandu Fm., Facies F1A and F1B; Fig. 3A-3B), based on texture, micrite proportion and the faunal content. Foraminiferal assemblage and other allochems indicates a depositional environment changing from the lower oligophotic zone (F1A) to mesophotic zone (F1B) (See Appendix A and Figure S2 for a more detailed facies description and depositional environment interpretations).

  red arrows) and compaction mode-1 micro-fractures affecting essentially the LBF (Fig. 6A black arrow). Micritisation and partial grain dissolution affects LBF skeleton, particularly the Lepydocyclinids (Fig. 6B red arrow). Cathodoluminescence observations

Figs.

  Figs. 11B and 12), are fairly well discriminated by the αK proxy, with: (i) samples characterized by a dominant intercrystalline microporosity (DPT1) showing αK values between 0.03 and ≤0.2, for a wide range of porosity value from 0.5 to 35% , (ii) samples characterized by dominant moldic to vuggy pores all display values >0.2 (DTP4); (iii) samples characterized by dominant intergranular pores show αK values mainly around 0.3; (iv) samples with mixed micro/intergranular porosity type show αK values mainly around 0.2 (DTP2). (v) samples affected by open discontinuities (DPT1S and DPT3S) exhibit αK values lower than their non-fractured counterpart, regardless of the initial DPT.

Fig

  Fig.14B.) known to be a less stable mineral than calcite (e.g.Tucker 1990), hence more prone to dissolution. Here, the shallow water environment of the Trealla limestone, particularly exposed to early meteoric diagenesis (cf. 4.2), favored the development of mainly

  Figure 1: A Location and latitude drift of the Cape Range area from the deposition of the Mandu formation (green contour) and the Trealla formation (blue contour) and present day location (black contour); B: Geological map showing the 4 main studied outcrops (blue-grey colour correspond to late Miocene Detrital/Eolian sandstone); (1: Shothole Canyon; 2: Charles Knife Road; 3: Unnamed quarry 1; 4: Unnamed quarry 2). C: Conceptual diagram illustrating the dynamo-stratigraphic relationships between the three Oligo-Miocene formations of the Cape Range region: The Mandu and Tulki Formations are partly coeval facies, separated from the overlying Trealla Formation by up-lift and erosion in the proximal part of the system.

Figure 2 :

 2 Figure 2: Diagram illustrating the multidisciplinary geological and petrophysical protocol.

Figure 3 :

 3 Figure 3: A: Synthetic log section of the Cape Range Oligo-Miocene deposits (modified from Collins et al., 2006). B-G: Outcrops photographs of the Mandu, Tulki and Trealla formations.

Figure 4 :

 4 Figure 4: Microphotographs of the 3 facies associations in Polarized light. A: Lower Mandu (F1A) peloidal, foraminiferal wackestone with large and disc-shaped benthic-foraminifera (Cycloclypeus); B: Quartz rich, peloidal and finely bioclastic packstone (F1B); C: Sharp erosive contact between foraminiferal packstone and sparitic grainstone in the Tulki Limestone (F2); D: Trealla packstone to grainstone dominated by recrystallized green algae skeleton (F3); E: Trealla packstone facies dominated by encrusting red algae and corals (F3).

Figure 5 :

 5 Figure 5: A: Matrix micrite content variation through the Mandu-Tulki limestone. B: Calcite content of whole-rock samples along the Mandu-Tulki part of the sedimentary succession.

Figure. 6 :

 6 Figure. 6: Microphotographs of the diagenetic features observed in the Mandu Fm (A-B), the Tulki Fm (C-F) and the Trealla Fm (G-H). A: compaction features: microstylolites (red arrow) and mode-1 fractures (black arrow); B: Partially dissolved LBF (lepidocyclinid); C:

Figure. 7 :

 7 Figure. 7: Microphotographs of thin-sections under polarized-light and cathodoluminescence showing the different cement phases. A-B: Mandu Fm, Dark blue (SC) calcite filling the recrystallized micrite area along with the burial fractures (Mandu); C-D: Tulki Fm, ISC and SC cements; E-F: Trealla Fm, showing ZSC and little developed SC cement.

Figure 8 :

 8 Figure 8: A: Outcrop photograph from the "unnamed quarry 2" outcrop. In yellow: the principal fault plane; in red: paleokarstic breccia at the boundary between the Tulki and the Trealla facies. B: Close-up on the paleokarst breccia presenting typical terra-rossa matrix. C: Close-up on the crosscutting relationship between vertical, fault related, karst deposits and the older horizontal karstic void filled with coarse calcite crystals, in the underlying Tulki Limestone; D-E: Microphotographs illustrating the pervasive dissolution phase affecting grains (D) and matrix (E) in the Tulki Limestone.

Figure 9 :

 9 Figure 9: Carbon and oxygen stable-isotopes: A: δ 13 C vs δ 18 O crossplot (dashed green box is the range of Miocene isotopic values; Veizer et al., 1999); B: Log of the vertical variations of δ 13 C through the entire sedimentary succession investigated.

Figure 10 :

 10 Figure 10: Vp -porosity (A) and Vs -porosity (B) crossplots with samples labelled as a function of the depositional facies association.

Figure 11 :

 11 Figure 11: Dynamic Bulk modulus vs. porosity crossplots with samples labelled with the depositional facies association (A), and dominant pore type (B).

Figure 12 :

 12 Figure 12: Crossplot of αK values as a function of porosity. Samples are labelled as a function of the dominant pore type (DPT) and facies association.

Figure 13 :

 13 Figure 13: Paragenetic sequences of the 3 formations highlighting the strong differences in diagenesis history between Mandu-Tulki and Trealla formations leading to different final petrophysical properties. Coloured arrows indicate the time of deposition for each formation along time. A: Schematic burial depth curve for the 3 formations (depth variations for the Tulki Fm is tentative, and based on minimal burial depth needed for compaction features observed); B-D: Individual paragenetic sequence presented in relative time scale. E-F: Comparison of microstructures and diagenetic features of the Tulki Fm (E) and Trealla Fm (F) formations showing the pronounced difference in terms of compaction and pore type.

Figure 14 :

 14 Figure 14: Conceptual block diagram models illustrating the difference in depositional systems between the Mandu-Tulki succession (A) and the Trealla succession (C).

Figure 15 :

 15 Figure 15: Micro CT-scans cross-sections showing variable αK values, highlighting the relationship between αK proxy and actual pore network structure.

Table 1 :

 1 A: Facies associations main characteristics B: Pore type classification

Table 2 :

 2 Table of laboratory petrophysical plugs measurements (and associated moduli and αk computed values), CaCO3 content and dominant pore type class from thin-sections scans.

Acknowledgments:

The present work is part of the project "Analogues rampes carbonatées funded" by TOTAL R&D CARBONATES, Pau, France. The authors would like to express their gratitude to the facilities, and the scientific and technical assistance of Microscopy Australia at the Centre for Microscopy, Characterisation & Analysis, The University of Western Australia, a facility funded by the University, State and Commonwealth Governments; especially Alysia Buckley and Paul Rigby for their valuable help in adapting the scanning device to rock thin sections. Koos de Jong for performing the petrophysical measurements in Department of Earth Sciences of the Vrije Universiteit Amsterdam. Baptiste Suchéras-Marx (CEREGE -AMU) for allowing using the calcimetry apparatus and his "faramineuse" help for the calcimetry measurements. Frank Nemeth for the production of the thin-sections at the UWA School of Earth Sciences laboratory. Stéphanie Vialle (Curtin University; Perth) and Claudio Delle Piane (CSIRO, Perth) for their welcome and help in accessing optical cathodoluminescence equipment. Lionel Marie (CEREGE -AMU), for helping in the sample preparation.

Michael Joachimski for the stable isotope measurements at GeoZentrum Nordbayern (University of Erlangen-Nuremberg). Pr. David Haig, for his valuable help during fieldwork, his helpful and interesting scientific discussions and knowledge on the regional Geology and its and for having been very welcoming. Anette George, Tony Allan and Victorien Paumard for their interesting scientific discussion on geochemistry and regional geology.