High-resolution synthetic seismic modelling: elucidating facies heterogeneity in carbonate ramp systems

With the aim of representing lithofacies in synthetic seismic facies in carbonate ramp systems, we used as a case study the Porto Badisco Calcarenite, which constitutes a carbonate ramp cropping out in the Salento Peninsula in southern Italy, on the southern margin of the Apula Carbonate Platform (ACP) (Fig. 1) (Bernoulli 2001; Tomassetti et al. 2018; Tancredi et al. 2022; Milli et al. 2024). The ACP is an extensive carbonate platform that has set and developed along the southern margin of the Tethys Ocean since the Mesozoic (Bernoulli 1972, 2001; D'Argenio 1974; Bosellini 2004). This platform extends from southeastern Abruzzi, from the Majella Massif representing the northernmost portion of the ACP, through Apulia and the Adriatic Sea between the Strait of Otranto, Albania and Greece (Eberli et al. 1993; Zappaterra 1994; Bosellini 2002, 2004). The ACP played a key role during the evolution of the Italian Peninsula following fragmentation of the Pangaea supercontinent at the end of the Jurassic and the collision between the African and Eurasian plates, with related subduction and formation of the Adria Plate (Carminati et al. 2012). The Adria Plate, towards the late Paleozoic, constituted a portion of the African Plate on which terrigenous–evaporitic sedimentation recorded in the Burano Formation was set. From the Upper Triassic to the Upper Cretaceous a massive carbonate platform, the ACP, was deposited (Ricchetti et al. 1988). In the Upper Cretaceous, the whole platform was affected by bending controlled by a new collision between the European and African palaeomargins, which resulted in the subduction of oceanic crust and gave the ACP a convex shape (Ricchetti et al. 1988; Ciaranfi et al. 1993). In the Cenozoic, with the progressive collision between the two palaeomargins, the ACP was increasingly bent until it reached emersion (Ricchetti et al. 1988; Milli et al. 2024). Carbonate production shifted to the platform margins between the Paleogene and the middle Miocene, in depositional environments of carbonate ramps (Bosellini et al. 1999). The Salento Peninsula is the southern portion of the ACP, on whose southeastern edge the study area crops out. Carbonate ramp systems have been preserved here, such as in the case of the Castro Formation and the Porto Badisco Formation attributed to the Chattian (Bosellini and Parente 1995; Bosellini et al. 1999; Brandano et al. 2020). The Porto Badisco Calcarenite (PBC), the object of this study, was deposited in the Upper Chattian and is a poorly cemented bioclastic calcarenite. This calcarenite has a maximum thickness of 60 m. Sedimentary structures often occur as ghosts as they have been erased by bioturbation, and lithofacies changes are most recognizable by rapid changes in skeletal components. The textures characterizing this formation span from packstone to grainstone but often the clasts are larger than 2 mm in size, producing rudstone and floatstone textures. In addition, coral-rich lithofacies occur in this formation, which are described in the Dunham, and the Embry and Klovan classifications, along with bioconstructed framestone textures (Dunham 1962; Embry and Klovan 1971). In this Chattian calcarenite, the major producers of calcium carbonate were large benthic foraminifera (LBF), with a large contribution from red algae and small colonies of corals arranged in several mounds a few metres in height (Pomar et al. 2014).

The PBC was analysed intensely by Pomar et al. (2014), identifying its ramp-shaped depositional model. Pomar et al. (2014) recognized six lithofacies belonging to this formation without, however, understanding which one was the oldest given the strong heterogeneity. For this reason, lithofacies will be described in this paper starting from the top of the depositional model and then from those deposited at lower bathymetries: (1) wackestone–packstone characterized by the abundance of small benthic foraminifera (SG); (2) coral mound framestone and floatstone–rudstone with coral fragments (CM); (3) packstone with large rotalids and nummulitids foraminifera (LR); (4) rhodolitic floatstone with LBF fragments (RF); (5) packstone to rudstone with large lepidocyclinids (LL); and (6) bioclastic packstone–wackestone fine calcarenite with well-graded skeletal fragments (FC).

In Porto Badisco, a runoff canal has created an excellent exposure of the PBC in a 1.5 km-long canyon. Here, nine stratigraphic logs were measured (Figs 1 and 2), spaced from each other by a minimum of 18 m to a maximum of 175 m apart, and correlated in the field thanks to the clear evidence of key horizons. The measured stratigraphic logs, which correspond to the sampling sites, were aligned almost parallel to the dip direction of the slightly inclined layers of the PBC. A total of 108 samples were collected from the nine measured outcrops. Samples at each site were collected from the bottom to the top, with an average interval of about 1 m at each lithofacies change.

The density and porosity of the PBC lithofacies were measured with an Anton Paar Ultrapyc 5000 helium pycnometer.

To carry out the petrophysical measurements, samples were shaped into parallelepipeds in order to calculate their geometrical volume, density and porosity but also so that they had flat geometrical faces in order to apply piezoelectric transducers and perform seismic velocity measurements (Tomassi et al. 2022; Trippetta et al. 2023).

The P-wave velocity (V_P) was measured with a four-channel digital memory oscilloscope connected to an ultrasonic generator pulser and two piezoelectric transducers. Samples were placed in a clamp with the transducers in contact with two parallel faces of the sample. One transducer acts as a transmitter and the other as a pulse receiver. Signals obtained were amplified and processed by the oscilloscope, and then exported to MATLAB in order to perform the manual picking of the first arrivals of the acoustic waves. All measurements were performed at the Rock Mechanics and Earthquake Physics Laboratory at the Sapienza University in Rome.

A set of 108 thin sections were produced, one from each sample collected in the field, in order to perform facies analysis and to discriminate the six different lithofacies of the PBC recognized by Pomar et al. (2014) (Fig. 3). To categorize lithofacies in terms of texture and size of skeletal components, the Dunham (1962) and Embry and Klovan (1971) classifications were used.

This is a heterometric packstone rich mainly in foraminifera and articulated red algae fragments, and to a lesser extent in bryozoans and corals fragments. Common among the foraminifera are large porcelain-shelled species that include the taxa Sorites and Austrotrillina, and large rotalids including Neorotalia. Spiroclypeus, Nephrolepidina and Amphistegina are present often as reworked fragments. Abundant among the smaller taxa are miliolides, textularids and rotalids. The presence of porcelain-shelled foraminifera is indicative of euphotic conditions in an area vegetated by seagrass meadows. Sediments trapped in the rhizomatic system of seagrass create a poorly graded texture with a large amount of matrix that has not been washed away by the hydrodynamic energy of the wave motion. The well-preserved amphisteginae and articulated red algae confirm a shallow-water environment. The large rotalids, nummulitids, Neorotalia, Spiroclypeus and lepidocyclinids, such as Nephrolepidina, dwelt more plausibly sheltered by dense leafage (leaf canopy) of seagrass in areas with mesophotic conditions, rather than at greater depths (Pomar et al. 2014; Tomassetti et al. 2018).

Coral colonies are often found in physiological positions in the field and create mounds 2–10 m high. On the sides of the mounds, overturned colonies and rudstones of coral fragments are present. The colonies are not in contact with each other. The major components of this lithofacies are coral fragments and LBF, often in fragments of nummulitids and large rotalids including Neorotalia. Among the macroforaminifera there are porcelain-shelled species, and among the microforaminifera there are miliolides. Fragments and encrustations of unarticulated red algae such as mastophoridae or Sporolithon are also common; as are fragments of brachiopods, bivalves and articulated red algae. In a zone at greater bathymetries than the SG lithofacies, there are photic and hydrodynamic conditions for the development of coral colonies. These are arranged in small mounds and do not form a framework resistant to wave motion, creating cluster reef structures and not a true frame reef (Insalaco 1998). Small benthic foraminifera, such as miliolids and cibicids, and porcelain-shelled fragments are allochthonous clasts derived from the seagrass. In situ sediments are represented by fragments of Nephrolepidina, nummulitids and coral fragments reworked during storm or high-energy events, which precipitated on the sides of the mounds, where the abundance of fine muddy matrix testifies that these were located below the limit of wave action (Pomar et al. 2014; Tomassetti et al. 2018).

The major components of this lithofacies are fragments of large rotalids, including Neorotalia, fragments of nummulitids, Operculina and Heterostegina. Fragments of Nephrolepidine and Amphistegina, large porcelain-shelled and smaller taxa including abundant miliolides are present. Unarticulated red algae in this lithofacies are melobesioids, mastoforoids and Sporolithon. Fragments of echinoderms and bivalves are also common. This lithofacies is characterized by the presence of in situ dweller components, such as the nummulitids and Nephrolepidina, and allochthonous fragments derived from more superficial lithofacies (CM and SG) such as Neorotalia, Amphistegina and miliolides. Moving towards deeper bathymetries increases the number of large rotalids, flattened-form nummulitids and unarticulated red algae. The presence of red algal associations, such as mastophoridae and the deeper dwelling melobesiodeae, confirm meso-oligophotic conditions. However, the fragmentation of large rotalids indicates the presence of hydrodynamic energy (Pomar et al. 2014; Tomassetti et al. 2018).

The rhodolites that characterize this lithofacies mainly have a laminar structure, produced by red algae such as Mesophyllum, Sporolithon and Lithothamnion. The matrix is a packstone with many rotalids, Eulepidina, nummulitids, Neorotalia, Nephrolepidina, Amphistegina and rare fragments of Miogypsinoides. Porcelain-shelled species are rare. Common, besides foraminifera, are bryozoans and fragments of echinids, bivalves, decapods and brachiopods. This lithofacies indicates sedimentation within the oligophotic zone characterized by the presence of mastoforoideae and melobesioideae red algae with a predominantly laminar structure. The former are found in the innermost portion of the oligophotic zone and form the core of rhodoliths; and the latter dwelt in the most distal portion of the oligophotic zone, forming encrustations surrounding the rhodolite core. This shows that transport has occurred from mesophotic conditions, which are colonized by mastophoideae, to oligophotic conditions, where melobesioideae dominate instead. Seagrass-associated and deeply transported sediments are still found. Confirmation of oligophotic conditions is also provided by the occurrence of Eulepidine in situ, with flat and thin forms (Pomar et al. 2015).

This lithofacies is characterized by a packstone–grainstone and sometimes rudstone rich in large lepidocylcinids such as Eulepidine and Nephrolepidine. In addition to lepidocyclinids, there are rotalids, abundant nummulitids, and well-preserved Amphistegina and Neorotalia. Encrusting and planktonic foraminifera are present. In addition to foraminifera, unarticulated red algae are common, forming branches and rhodolites. In the more distal portions of the oligophotic zone, beyond the rhodolytic cover, large, flattened-shaped Eulepidines are present in abundance. Deeper conditions are confirmed by the presence of planktonic foraminifera, and lower carbonate production by benthic foraminifera. Allochthonous components dismantled from the seagrass are miliolids, Amphistegina and Neorotalia. Other in situ foraminifera are nummulitids and Nephrolepidina. The decrease in limestone mud shows the presence of hydrodynamic energy caused by internal wave motion at the pycnocline (Fig. 4) (Munk 1981; Apel 2002; Pomar et al. 2012, 2014; Tomassetti et al. 2018).

This calcarenite is a fine bioclastic packstone–wackestone with well-graded and eroded fragments. Dominating among the components is a tritume of red algae, followed by plates of echinids, large rotalids and small benthic foraminifera. Among the LBF there are reworked fragments of Miogypsinoides, Neorotalia, lepidocyclinids, nummulitids and large Amphisteginae. This lithofacies shows components associated both with the euphotic zone, such as Amphistegina, Neorotalia, Miogypsina and small epiphytic taxa that proliferate in the area where seagrass grows, and components associated with the oligophotics, characterized by flat nummulitids and large lepidocyclinids. This fine, well-graded bioclastic deposit represents the distal accumulation of allochthonous components, dismantled by more superficial ramp sections, in a zone almost lacking in carbonate production in dysphotic or aphotic conditions (Pomar et al. 2014).

Through the facies analysis and their association, it was possible to reconstruct the depositional model recognized by Pomar et al. (2014). The depositional profile of the Porto Badisco Formation is a homoclinal carbonate ramp without a break in the slope angle (Fig. 4). The inner ramp in the euphotic zone is characterized by seagrass meadows with the SG lithofacies, followed by an area dominated by the presence of coral cluster reefs (CM lithofacies) at the flanks where large rotalids and nummulitids (LR lithofacies) dwelt. Moving towards the middle ramp, within the oligophotic zone, there is deposition of the rhodolitic floatstone lithofacies (RF), interdigitated with the large lepidocyclinid packstone lithofacies (LL). The outer ramp is characterized by the most distal lithofacies, the bioclastic fine calcarenite (FC) deposited within the aphotic zone, as demonstrated by the abundance of photo-independent biota.

The bulk density measurements presented in Table 1 show very heterogeneous values. The lithofacies with the highest densities are SG and CM, with values of 2390 and 2530 kg m⁻³, respectively. The lithofacies with intermediate density values are LR and RF, which show a bulk density of 2230 and 2110 kg m⁻³, respectively. The lithofacies with lower density values of the carbonate ramp of the PBC are LL and FC, which show a bulk density of 1710 and 1930 kg m⁻³, respectively. Despite the large heterogeneity, it can be observed that moving down the ramp in the depositional profile, the bulk density decreases. The standard deviations (2$σ$⁠) range from a minimum of 0.0006 g cm⁻³ for the FC lithofacies to a maximum of 0.0049 g cm⁻³ for the CM lithofacies. The standard deviation for the other lithofacies is between these two end members.

Averaged total and effective porosity values are reported in Table 1. Like the density values, porosity also reveals very heterogeneous values. The CM lithofacies is characterized by the lowest value of the whole lithofacies association (7.8%), followed by the SG lithofacies (12.99%). The LR lithofacies show a total porosity value of 18.8%. The RF and FC lithofacies slightly exceed 30% total porosity. The most porous lithofacies in the system is LL, with 38.12% total porosity. Effective porosities of lithofacies LR, RF, LL and FC are equal to the total porosity. Effective porosities of the SG and CM lithofacies are slightly lower than the total porosities, revealing a non-interconnected porosity of 0.88% for the SG lithofacies and 2% for the CM lithofacies. These values have been interpreted and explained by the presence of colonies or fragments of corals present in these lithofacies that are characterized by a primary porosity, mostly within the coral septa, which, however, has no interactions with the effective porosity. The complete porosity ranges measured through the PBC lithofacies are shown in Figure 5a. The standard error is less than 2%.

Table 1 shows the measured P-wave velocities (V_P) of the PBC lithofacies.

Averaged V_P velocities measured in the laboratory show a range of values: from a minimum of 3644 m s⁻¹ for the LL lithofacies to a maximum of 5573 m s⁻¹ for the CM lithofacies. Lithofacies SG show a high V_P value of 5183 m s⁻¹ that is typical of a medium compact carbonate. Slightly lower values characterize the LR (4599 m s⁻¹) and RF (4395 m s⁻¹) lithofacies. The FC lithofacies show a V_P value of 3633 m s⁻¹. These values were used to build the constant interval velocity model to run the synthetic seismic. The complete V_P ranges measured through the PBC lithofacies used to build the heterogeneous velocity model to run the synthetic seismic are shown in Figure 5b.

Comparing the averaged porosity and V_P of each lithofacies (Fig. 5c), we observed a classic inverse relation where lithofacies showing a higher porosity are characterized by lower V_P values (Ruggieri and Trippetta 2020; Trippetta et al. 2020; Tomassi et al. 2022).

As a first step in the model building, we correlated measured stratigraphic logs using key stratigraphic horizons observable in the field. We then produced a correlation panel following the depositional model that represented the stratigraphic architecture of the carbonate ramp (Fig. 6).

From the averaged petrophysical measurements and the stratigraphic log correlation panel, we built the velocity model needed to run the synthetic seismic in MATLAB (Fig. 7) (De Franco et al. 2019). The velocity model corresponds to a velocity values matrix characterized by 0.1 × 1 m sized cells (0.1 m in the depth direction and 1 m in the offset direction). The V_P values used to populate the matrix were those measured in the laboratory (Tomassi et al. 2022). The distribution of the V_P values through the matrix was performed using MATLAB's roipoly (polygonal region of interest) command. Roipoly allows a polygonal region of interest in the matrix to be selected and drawn by creating an interactive tool associated with the displayed velocity matrix. The roipoly command created a mask to be applied to the matrix as a binary image, setting a value for the pixels (matrix cells) inside the drawn polygonal region of 1 and a value for the pixels outside of 0. Multiplying the desired velocity value (i.e. the value measured in the laboratory for a given lithofacies) at the output of roipoly yields a mask with the required value to be added to the velocity matrix. By repeating this operation for each PBC lithofacies, a velocity values mask was generated for each individual lithofacies, represented as a polygon in the correlation panel. The velocity model was then produced as output by merging together the V_P masks. In order to complete the model, the Lower Chattian Castro Formation, below the Porto Badisco carbonate ramp, was also modelled (Pomar et al. 2014; Tomassetti et al. 2018). The Castro Formation shows coral-dominated lithofacies that in the PBC were those with higher V_P values but at a greater depth. We thus assigned a V_P value of 6000 m s⁻¹ to this formation due to the expected velocity increase at depth (Trippetta et al. 2021).

To represent the heterogeneities of petrophysical values (V_P), a Gaussian distribution algorithm was adopted for the velocity matrix in MATLAB with a different range of values for each lithofacies based on the data obtained in the laboratory (Tomassi et al. 2022). The V_P heterogeneity distribution through the matrix was performed using MATLAB's randn (normally distributed random numbers) command. Randn returns an array of normally distributed random numbers within a user-determined range that will be multiplied with the desired value, in our case the V_P ranges measured in laboratory for each lithofacies. A random-type distribution of V_P values was used as it represents well the real physical heterogeneities of carbonate rocks that do not follow any particular preferential direction but are indiscriminately and randomly distributed. In Table 2 are shown the V_P value ranges measured and reported in the box plot of Figure 5b, and used to build the heterogeneous velocity model (Fig. 8).

We can classify three main categories of methods used to perform seismic modelling: the integral equation method, the ray-tracing method and the direct method (Carcione et al. 2002). The finite-difference time-domain method is a direct method applicable to complex geological configuration (Moczo et al. 2007). It differs from the ray-tracing method in that the amount of scattered energy from the surfaces is not examined (Wang et al. 2002). Instead, the finite-difference time-domain method calculates the total wave field (Marfurt 1984; Carcione et al. 2002). In this paper we solve the wave equation using the finite-difference method, in which the geological model is discretized in a numerical mesh of a finite number of points. We chose this method as it is more convenient for the subsurface situation of the Porto Badisco area where a dense grid is needed due to the fine stratification and the large heterogeneity. With this method is possible to assign different acoustic properties to every grid point, simulating complex subsurface models and producing seismic images useful as a tool for the interpretation (Carcione et al. 2002).

In particular, here we present a 2D full-wave model that simulates the mechanical propagation of the wavefront through the modelled structure, achieved by simulating unmigrated stacked sections. Seismic processing and migration techniques leverage reflections to reconstruct the subsurface geometry, focusing on areas with continuous and significant reflectors (Khaidukov et al. 2004). Nonetheless, the process often overlooks certain geological features captured by diffractions, which are lost during processing and migration. The analysis of diffractions, however, can uncover structural information and enhance the details of the carbonate system (Moser and Howard 2008; Klokov et al. 2010). To address this issue, the current study employs unmigrated synthetic modelling.

In the context of pure 2D acoustic modelling, inherent constraints emerge from the employment of unmigrated stacked sections. This methodology results in imagery characterized by slight alterations in both the positions and geometries of the depicted features. However, it retains the diffraction signals induced by contrasts in acoustic impedance across subvertical reflectors. These signals manifest as dispersion points, facilitating the diffraction of the Ricker wavelet. This phenomenon is critical for interpreting the subsurface structures accurately, despite the spatial inaccuracies introduced by the 2D modelling approach.

From the velocity models shown in Figures 7 and 8, two unmigrated synthetic seismic stack sections were generated with the CREWES’ (Consortium for Research in Elastic Wave Exploration Seismology) toolbox, which suggests several numerical methods for exploration seismology with algorithms, including finite difference, for exploding reflectors. The function script afd_explode was chosen, which uses an input velocity matrix (the 10 × 10 m sized cells grid used as the velocity model) to calculate the exploding reflector directly from the velocity model if a normal incidence reflectivity is assumed (Margrave and Lamoureux 2019). This velocity model into afd_explode script creates an exploding reflector seismogram by inserting the correct variables into the script. The set variables are reported in Table 3.

Once the necessary parameters were entered, the script was run; and the unmigrated synthetic seismic stack sections of the Porto Badisco carbonate ramp were obtained. Synthetic seismic modelling starting from both a constant interval velocity model (Fig. 9a) and a heterogeneous velocity model (Fig. 9b) was performed for each lithofacies.

The seismic image derived from the constant interval velocity model (Fig. 9a) shows continuous and very pronounced seismic reflectors with large amplitudes, especially in the shallow layers of the model. Moreover, in the shallower portion of this model there is a strong disturbance caused by diffractions generated by the slight roughness of the topographical surface (from an offset of 500–1500 m). Due to the large amplitudes, the more proximal lithofacies of SG and CM are very confusing and difficult to differentiate but are still appreciable, especially CM, thanks to the diffraction hyperbolas generated by the top and flanks of the coral mounds (black arrows in Fig. 9a). The small lens-shaped stratifications of the LR, LL and FC lithofacies embedded in the RF lithofacies are not resolvable in the model in Figure 9a. The facies LR, RF, LL and FC are interpretable when they exhibit higher stratigraphic thicknesses, creating greater acoustic impedance contrasts: i.e. between offsets 1000 and 1500 m where they alternate with each other in a stratigraphic sequence (black arrows in Fig. 9a).

A multiple reflection is clearly marked (cyan dashed line in Fig. 9c) at twice the depth with respect the horizon of the bottom PBC to which it refers, tracing its topography and amplifying its inclination.

The seismic image derived from the heterogeneous velocities model (Fig. 9b) still shows multiple reflections, although less pronounced than in the previous model. Moreover, it shows a slight disturbance that could be mistaken for background noise but it is actually derived from lithology heterogeneities, as noted by Tomassi et al. (2022). This perturbation improves the visualization of the horizons, making the seismic image easier to interpret. Due to this disturbance, caused by constructive and destructive interference induced by the heterogeneities of seismic properties of rocks, the shallow layers of the model are characterized by lower amplitudes. This allows resolution of the most superficial horizons, which in the constant interval velocities model were hidden by the excessive signal amplitudes. In addition, the noise caused by diffractions produced by the topographical surface roughness is no longer appreciable. For instance, the SG lithofacies shows its characteristic seismic facies in which the coral mounds are embedded, while the marked and indecipherable parallel reflectors are no longer visible. The perturbation facilitates the recognition of the CM facies coral mounds by improving their visualization of the top and flanks (black arrows in Fig. 9b). The alternation of the LR, RF, LL and FC facies is clear, allowing visualization of thinner sedimentary lenses (black arrows in Fig. 9b).

The unmigrated synthetic seismic forward model performed with constant interval velocities (Fig. 9a) constitutes itself a very useful tool for studying the subsurface in the absence of data (Anselmetti et al. 1997; Duchesne et al. 2006; Falivene et al. 2010; Mascolo and Lecomte 2021; Tomassi et al. 2022) or for calibrating well data (Morozov and Ma 2009). However, this seismic forward model is affected by some artefacts such as multiple reflections (Claerbout 1971; Foster and Mosher 1992; Berkhout and Verschuur 2006), or the shallow high-amplitude reflectors or diffractions generated by topography that do not allow for clear interpretation. These signals are difficult to decode and interpret in geological horizons.

Conversely, the model generated with heterogeneous velocity (Fig. 9b) turned out to be clearer to interpret, despite modelling the heterogeneities of the physical system. This signal perturbation was not caused by instrumental drift or environmental noise because it is a synthetic model that cannot be affected by these biases (Tomassi et al. 2022, 2023, 2024c). The appreciable perturbation in the model in Figure 9b, on the other hand, represents the seismic signature of the lithofacies heterogeneities of carbonate rocks, providing supplementary insights into carbonate ramp systems (Falivene et al. 2010; Wang et al. 2020; Faleide et al. 2021; Tomassi et al. 2022). It is evident that by adding this natural feature of the system in the modelling, the geometries of the subsurface can be appreciated more effectively.

To quantify how visualization of the seismic image is improved by introducing the heterogeneity perturbation, we performed a difference between the two seismic outputs: i.e. Figure 9b has been numerically subtracted from Figure 9a (Fig. 10).

Figure 10 displays the diffractions generated by the topography and part of the large amplitudes of the shallower layers. Moreover, the difference between seismic outputs also shows a portion of the energy of the multiple reflections. These signals were greatly weakened by inserting a perturbation given by the heterogeneity, promoting the resolution of many horizons and facilitating seismic interpretation.

This is the evidence that adding a physical perturbation (not to be confused with background noise) characteristic of the carbonate system in synthetic seismic constitutes an improvement of the models to: (1) obtain more realistic seismic wavelets between different sedimentary layers (Pringle et al. 2008; Stanbrook et al. 2008); (2) enhance visualization (Zelt et al. 2013); and (3) obtain output closer to actual geophysical surveys (Calderón-Macías et al. 2000; Falivene et al. 2010; Wang et al. 2020), which typically have chaotic appearances, particularly in the carbonate systems domain (Eberli et al. 2004; Sun et al. 2013; Eloni et al. 2016).

Another advantage of using this type of workflow for unmigrated synthetic seismic forward modelling is improving the relation between lithofacies and seismic facies in the seismic imaging (Jafarian et al. 2018). This could be an excellent tool to indirectly identify lithofacies at depth in the absence of an adequate surface analogue (Iannace et al. 2014).

In the constant interval velocity model (Fig. 11a), the SG high-density and low-porosity wackestone–packstone seismic facies (1 in Fig. 11a) is characterized by low-amplitude and partially disrupted reflectors, despite this being one of the lithologies with a lower heterogeneity than the entire PBC. The CM lithofacies, a floatstone–rudstone to framestone with coral fragments, shows a light top reflector of the coral mound and within the mound presents a seismic facies characterized by small, continuous reflectors parallel to each other (2 in Fig. 11a). The LR, RF, LL and FC seismic facies are quite similar and are composed of continuous, poorly marked and parallel reflectors (3, 4, 5 and 6 in Fig. 11a). This similarity between seismic facies does not reflect the great differences from a lithological point of view as the lithofacies range from packstone with large rotalids (LR), red algae floatstone (RF) and large lepidocyclinids rudstone (LL) to a packstone–wackestone fine calcarenite. It is questionable that such assorted textures and skeletal components show similar seismic facies. This demonstrates that a classical synthetic seismic forward model performed from a constant interval velocity model is not adequate to match seismic facies with lithofacies.

The visualization of seismic facies is very different if a synthetic seismic forward model is performed by introducing a physical perturbation of the system that reflects the heterogeneity (Fig. 11b), providing more information on the lithofacies from the seismic output. As described in the Methods section, the petrophysical properties measured in the laboratory serve as direct inputs into the seismic modelling, reflecting the lithological characteristics of each modelled lithofacies. Consequently, the seismic output generated from the petrophysical data used as the model input mirrors these petrophysical attributes. Thus, our methodology could enable the indirect detection of geological peculiarities of the lithofacies within the seismic facies. Through meticulous laboratory measurements, we captured the essential petrophysical characteristics that dictate the behaviour of seismic waves within these lithologies. Embedding facies heterogeneity into the system, our model not only incorporates geological inputs but also provides from the seismic facies output a potential depiction of the complex geological characteristics of the underlying lithofacies. In this modelling we attempt to provide an additional element for the interpretation of seismic data in terms of lithological and petrophysical properties related to the seismic output, establishing a relationship between the lithological facies and the seismic facies. The seismic facies generated in the model rely primarily on the petrophysical characteristics of the lithology. In turn, the petrophysical characteristics reflect the geological processes that the lithology has undergone through mineralogy, sedimentation, diagenesis and erosion. This allows lithological information to potentially be derived from the petrophysical input of the model.

In the heterogeneous velocity model, the SG lithofacies is represented (1 in Fig. 11b) as a seismic facies characterized by disrupted, poorly continuous and barely marked (low-amplitude) reflectors. The CM seismic facies (2 in Fig. 11b) is separated from the adjacent lithofacies by a strong reflector of the coral mound top. Below this reflector, CM is characterized by a chaotic seismic facies formed by disrupted medium- to low-amplitude reflectors. This is a classic display in real reflection seismic outputs where tight carbonate rocks with high seismic velocity (such as CM) surrounded by other carbonates are characterized by chaotic and reduced seismic facies (Palaz and Marfurt 1997). In the seismic image in Figure 11b, the seismic facies of LR, RF, LL and FC are different from each other, which is in contrast to what was shown in the model in Figure 11a where they appeared very similar. The LR seismic facies (3 in Fig. 11b) presents appreciable medium-amplitude reflectors at its top and bottom. Within these is detected a seismic facies consisting of fairly continuous low-amplitude parallel reflectors. The RF seismic facies (4 in Fig. 11b) looks very chaotic with indiscernible very disrupted reflectors, however, with medium amplitudes. The LL seismic facies (5 in Fig. 11b) enclosed between two high-amplitude reflections at the top and bottom of the analysed layers show parallel and continuous low-amplitude reflectors. The FC seismic facies (6 in Fig. 11b) is characterized by low-amplitude, weakly continuous parallel reflectors.

The heterogeneity in the seismic facies, as revealed in Figure 11b, where distinct acoustic characteristics emerge for each lithofacies, underscores the critical impact of the V_P range variations that mirror the complex interplay between the lithological texture and seismic expression. This connection between textural and petrophysical variations, as detailed in the laboratory measurements of V_P ranges, is further elucidated when considering the broader implications of these findings. Even when lithofacies exhibit similar average V_P values, their respective V_P ranges provide unique seismic signatures due to differential acoustic impedance and scattering behaviours. These results not only reinforce the integral role of detailed petrophysical analysis in seismic interpretation but also highlight how such variations can complicate the seismic representation of lithological heterogeneities, requiring a detailed approach to integrating petrophysical data into seismic models. By examining the variability in V_P alongside density and porosity within each lithofacies, we gain deeper insights into their seismic manifestations, ultimately enhancing the ability to resolve complex geological structures within carbonate ramp systems.

Accordingly, in analysing the correlation between lithofacies and seismic facies, it is crucial to consider not only the absolute values but also the range of variations in the petrophysical properties used as inputs for the modelling (i.e. V_P). Table 2 and Figure 5b in our study clearly illustrate how different lithofacies exhibit distinct V_P ranges measured in the laboratory, which can be correlated to their sedimentological and textural characteristics. The SG lithofacies displays a moderately narrow V_P range (5158–5208 m s⁻¹), reflecting consolidated sedimentation and possibly a reduced presence of interconnected porosity. Despite the relatively uniform texture, the contained amplitude of the V_P range could indicate consistent sedimentation and stable depositional conditions that positively influence the clarity of seismic reflectors. The CM lithofacies presents the narrowest range of V_P values (5553–5593 m s⁻¹). This indicates a high uniformity in mineralogical and structural composition, typical of cemented coral constructions and framestones. This restricted range contributes to a well-defined seismic signal, with clear reflectors that facilitate the interpretation of the seismic facies. The LR lithofacies exhibits a broader range of V_P values (4549–4649 m s⁻¹), attributable to variations in compaction and sediment composition. The presence of large rotalids and other bioclastic fragments can introduce physical heterogeneity and greater acoustic energy scattering, resulting in a less predictable and more variable seismic signal. The RF lithofacies also shows a broad range of V_P values (4345–4445 m s⁻¹), indicative of the presence of rhodolithic structures with a matrix of variable granularity and differentiated porosity and density. Again, these characteristics can lead to scattering phenomena and discontinuous seismic reflectors, increasing interpretative complexity. The widest V_P range (3544–3744 m s⁻¹) for LL suggests a high degree of variability in physical and mechanical properties, which is likely to be due to variations in the size and distribution of the encompassing lepidocyclinids. This translates into a greater dispersion of the seismic signal and discontinuous reflectors. Finally, FC exhibits a V_P range (3593–3733 m s⁻¹) that reflects the heterogeneity of a lithofacies composed of fine calcarenite with a mixture of well-graded clasts. Variability in grain size and cementation can cause variations in the seismic response, making the correlation with seismic facies more challenging. The analysis of V_P ranges and petrophysical properties provides a more detailed picture of the connection between sedimentological and petrophysical characteristics and the seismic display influenced by varying degrees of acoustic energy scattering. Acoustic wave scattering is significantly influenced by V_P variations within different lithofacies. Analysing the V_P range highlights how variations in the petrophysical properties influence acoustic scattering, impacting the continuity of seismic reflectors and complicating interpretation. Integrating these phenomena into the seismic interpretation model not only enhances the resolution of seismic facies but also aids in a deeper understanding of the complex geological structures of carbonate ramp systems.

In the context of the results discussions, we delve into the phenomena that bridge lithological facies with seismic facies through petrophysical properties. Specifically, we interpret chaotic seismic facies as being generated by heterogeneous lithologies, characterized by clast-size diversity and mineralogical variation. This interpretation is grounded in the concept of seismic energy scattering, a phenomenon well documented in the existing literature. The dispersion of seismic waves represents a complex process influenced by a multitude of factors, including the stratification and heterogeneity within the geological structure. This is extensively discussed by Marion et al. (1994), Kennett (2009) and Sato et al. (2012), with Sato et al. (2012) focusing particularly on the scattering of seismic waves in random media (Marion et al. 1994; Kennett 2009; Sato and Fehler 2009). Moreover, Levander (1990) further explored the effects of dispersion, highlighting the impact of irregularities on wave propagation. Collectively, these studies underscore the significance of considering specific geological characteristics when understanding seismic wave scattering. The scattering of seismic energy is notably affected by irregularities within the geological media (Levander 1990). Numerical simulations have also played a crucial role in elucidating the behaviour of seismic wave propagation in complex velocity models, especially in the presence of lateral heterogeneities (Frankel 1989). In our work, we have extended the analysis of this phenomenon not only to interlithological but also to intralithological heterogeneity. Here, a highly heterogeneous lithofacies produces greater scattering at the transit of the seismic wave, introducing acoustic impedance disturbances that give rise to chaotic seismic facies characterized by disrupted or highly discontinuous and low-amplitude reflectors. Conversely, more homogeneous lithofacies tend to produce fewer scattering phenomena and more distinguishable reflectors within less chaotic seismic facies. This distinction underscores the intricate relationship between lithological composition, petrophysical properties and seismic facies, reinforcing the idea that seismic wave scattering and dispersion are critical to the interpretation of seismic data. Through our analysis, we aim to provide a deeper understanding of how lithological heterogeneities influence seismic reflections, thereby offering insights into the geological processes shaping the formations taken as our case study.

Incorporating heterogeneity into our forward seismic modelling enhances lithofacies and seismic facies correlation. By using realistic perturbations that mimic rock properties instead of traditional models with uniform velocities, we gain clearer insights into energy scattering and facies differentiation. This approach avoids the ambiguities of classical models and precisely matches seismic images to rock textures, improving our understanding of geological processes.

The model shown in this paper is built with a comprehensive workflow ranging from fieldwork, to petrophysical analysis in the laboratory, to modelling in MATLAB, addressing insights regarding the relationships linking lithofacies to their display in a seismic image.

By introducing a perturbation that reflects the heterogeneity of the physical system the disturbance observed in the synthetic seismic lines is not background noise given by instrumental drift but is an particular feature of the carbonate system caused by the heterogeneity.

By implementing the model with a disturbed signal, many artefacts such as topographical reverberation or excessive signal amplitude caused by excess acoustic impedance are removed or greatly attenuated, promoting the resolution of many horizons.

Our research has highlighted how the introduction of heterogeneities into unmigrated seismic models not only refines our understanding of the physical characteristics of carbonate ramp systems but also offers new approaches for interpreting seismic data. The importance of scattering phenomena in seismic visualization has emerged as a crucial aspect, leading to deeper interpretations of the underlying geological features:

• The implementation of heterogeneities has significantly improved accuracy in modelling seismic facies, demonstrating how variations in petrophysical properties affect resolution and seismic interpretation.

• Scattering phenomena, identified through the analysis of V_P ranges, have proven essential in understanding the complexity of seismic facies. The LL lithofacies, with a wider range of V_P values, has shown a higher frequency of scattering, resulting in a fragmented seismic signal that is difficult to interpret. Conversely, the narrower range of V_P values in the CM lithofacies has led to less scattering, resulting in more continuous reflectors and clearer interpretations.

• Integrating these phenomena into the seismic modelling and subsequent interpretation not only enhances the resolution of seismic facies but also deepens the understanding of the underlying geological structure.

The findings of this study recommend a paradigm shift in seismic interpretation practices, emphasizing the need to include scattering effects in modelling and analysis workflows to unlock a deeper understanding of carbonate systems. By embracing the complexity of the system, this work significantly contributes to the field of carbonate reservoir characterization, providing insights that could enhance global exploration and development strategies.

We sincerely appreciate the constructive feedback provided by the editor and the two anonymous reviewers, which has significantly enhanced the quality of our work. Marco Brandano and Laura Tomassetti are warmly thanked for their very precise suggestions, discussions and help provided during the fieldwork.

AT: conceptualization (lead), data curation (lead), formal analysis (lead), investigation (lead), methodology (lead), project administration (lead), resources (lead), software (lead), supervision (equal), validation (equal), visualization (lead), writing – original draft (lead), writing – review & editing (equal); RdF: conceptualization (equal), data curation (equal), formal analysis (equal), investigation (equal), methodology (equal), software (equal), supervision (equal), validation (equal), writing – review & editing (equal); FT: conceptualization (equal), data curation (equal), formal analysis (equal), investigation (equal), methodology (equal), project administration (lead), resources (equal), software (equal), supervision (lead), validation (equal), visualization (equal), writing – original draft (equal), writing – review & editing (equal).

This research was funded by the GreenSCENT project, part of the European Union's Horizon 2020 research and innovation programme, under grant agreement No. 101036480. This funding also enabled the publication of this paper as open access.

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 data will be made available upon request to the corresponding author.