1 Introduction

The Sirente crater field is situated in the Apennine mountains, specifically in the Prati del Sirente plain. This is found in Abruzzo, Central Italy (42°10'N, 13°35'E) (Fig. 1a, b). It features a ≈ 130 m wide, droplet-shaped depression, in plan view, with a rim elevated ≈ 2 m (i.e. the main crater). This is surrounded to the north and west by approximately thirty smaller depressions, some with elevated rims. Their diameters vary from 2 to 20 m (Fig. 1c). The outline, with a main crater at one end of a field of smaller craters, resembles that of known meteorite crater fields formed after the atmospheric break-up of the projectile (Ormö et al. 2002; cf. Torrese et al. 2019).

Fig. 1
figure 1

a Geographical setting of the Sirente main crater; b oblique aerial view (from E) of the Sirente plain (courtesy G. Fraternali), located on a listric block N of Sirente massif: the main crater is the black spot in the snow-covered plain; c map of the Sirente crater field showing the main dominant crater and the group of much smaller craters (adapted from Ormö et al. 2006); the elongated shape of the main crater suggests a relatively highly oblique impact with a flight direction of the projectile from the northwest; the size distribution of the smaller craters in the crater field suggests a trajectory from roughly north-northwest (Ormö et al. 2002; Torrese et al. 2019); d oblique view (from NW) of the Sirente main crater, showing a pronounced elevated rim. This figure was adapted from Fig. 1 published in Planetary and Space Science, Volume 168, Torrese, P., Rossi, A.P., Ormö, J., Rainone, M.L., Ori, G.G., Investigating the subsurface structure of the main crater of the proposed Sirente meteorite crater field (Central Italy): new clues from reflection seismics, Pages 27–39, Copyright Elsevier (2019), https://doi.org/10.1016/j.pss.2018.12.008

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Owing to the main crater’s elongated shape (droplet-shaped, in plan view), Ormö et al. (2002) considered that a relatively highly oblique impact was possible (Pierazzo and Melosh 2000). This would have a northwest flight direction of the projectile (which does not imply any collision of the projectile with the Sirente massif, which is south-southwest of the crater). However, its shape may also be due to an impact of two adjacent bodies. The size distribution of the smaller craters in the field would suggest a trajectory from a north-northwesterly direction (Ormö et al. 2002; Torrese et al. 2019).

No bedrock crops out in the Sirente plain. This seems to form the flat surface of an extremely thick valley infill in a half-graben north of the Sirente fault. The crater field is developed entirely in stiff but unlithified (i.e. unconsolidated) carbonate mud that is principally lacustrine in origin. This overlies a basement of Cretaceous and Miocene limestone (APAT 2005). Some larger limestone clasts (including boulders and blocks) can be found in the mud. Rock falls and avalanches from the steep north face of the Sirente massif, and occasional fluvial activity, contribute significantly to the valley’s coarse sediments (cf. Torrese et al. 2019).

A small lake is found in the main crater. This is flanked on all sides by a prominent saddle-shaped ridge, i.e. the topographic rim of the proposed crater (Fig. 1d) (cf. Torrese et al. 2019). The ridge measures approximately 10 m across. The rim wall slope and the lake’s flat floor result in a shallow bowl-shaped morphology (Ormö et al. 2002, 2006; cf. Torrese et al. 2019).

Ormö et al. (2002, 2006) discovered the crater field and proposed it to be of meteorite impact origin. They estimated it to have been formed in the 3rd to 5th centuries A.D., arriving at this based on 14C and thermoluminescence dating of heated material in the smaller craters and 14C dating of a paleo-soil layer from a core drilled through the outer flank of the main crater rim (B2 in Fig. 2). Radiocarbon dating of the target (impact) surface preserved below the rim dates the formation to 412 ± 40 A.D. (Ormö et al. 2002, 2003). The supposed event was soon linked to a late nineteenth century A.D. legend reported by the church sexton of Secinaro, a village nearby. This described how local pagans were suddenly converted to Christianity by the catastrophic impact of a falling star at Sirente (Santilli et al. 2003). The claimed finding created considerable ripples in the national and global press as the claimed meteoritic impact at Sirente was also related by the media to the celestial ‘Chi Rho’ sign said to have been spotted by Emperor Constantine prior to his victory against his rival Emperor Maxentius at Milvian Bridge, near Rome, in 312 A.D. It was even stated that the Sirente impact would have changed the path of both Roman and Christian history, so the affirmation of Christianity became linked to a celestial phenomenon (cf. Torrese et al. 2019). On the contrary, Weiss (2003) deems Constantine’s ‘vision’ to have been a solar halo phenomenon known as a ‘sun dog’, which may have preceded the Christian beliefs he later went on to express.

Fig. 2
figure 2

a Survey map showing the location of the 2D–3D ERT synthetic modelling along with other geophysical surveys and boreholes undertaken at the Sirente main crater; b digital elevation model (courtesy M. Marchetti, Istituto Nazionale di Geofisica e Vulcanologia) of the Sirente main crater (Universal Transverse Mercator (UTM) coordinate system, vertical exaggeration ×9.5) with the location of the 2D–3D ERT synthetic modeling and the other surveys. The elongated shape of the main crater suggests a relatively highly oblique impact with a flight direction of the projectile from the northwest (Ormö et al. 2002; Torrese et al. 2019). This figure was adapted from Fig. 2 published in Planetary and Space Science, Volume 168, Torrese, P., Rossi, A.P., Ormö, J., Rainone, M.L., Ori, G.G., Investigating the subsurface structure of the main crater of the proposed Sirente meteorite crater field (Central Italy): new clues from reflection seismics, Pages 27–39, Copyright Elsevier (2019), https://doi.org/10.1016/j.pss.2018.12.008

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However, in the years that followed, the meteoritic origin theory of the Sirente crater field was queried. It has been suggested that the main crater is a mud volcano due to trapped gas or a structure formed by the seepage of fluid (Stoppa 2006). Speranza et al. (2004, 2009) suggested that it was an anthropogenic cattle-pond in an area of karstic sags. This idea is backed by its supposed similarity to other structures found in the glacial and karst-alluvial uplands of the Abruzzo Apennines (cf. Torrese et al. 2019).

The principal problem with the impact origin theory is down to no meteoritic material and shock metamorphic features diagnostic of hypervelocity impact so far being identified (Speranza et al. 2004, 2009). Ormö et al. (2006, 2007) claim that no shock-metamorphic features or strong geochemical anomalies are expected at craters this size found in carbonate mud. Further, meteoritic fragments on the surface surrounding impact craters are rare in areas with an extensive history of iron-working (e.g. the Kaali crater field in Estonia), but areas in which iron-working spread relatively recently, such as in Australia and the Americas, commonly evidence such fragments at many of the known crater fields (Ormö et al. 2006). Furthermore, studies of recent Russian meteorite craters (e.g. Sterlitamak, Petaev 1992; Sikhote Alin, Svetsov 1998), as well as crater fields like Campo del Cielo that date back thousands of years (Cassidy and Renard 1996), have highlighted that most meteoritic fragments would be located several meters below ground, such as at the end of penetration tunnels or in true crater floor linings below the crater infill (i.e. the cavity floor formed by excavation and displacement during cratering) (cf. Torrese et al. 2019).

As the crater field is located within the Sirente-Velino Regional Park and is protected by park regulations that limit extensive drilling or excavation, non-destructive geophysical surveys are essential in the Sirente plain. A range of geophysical methods have been employed to investigate the internal structure of larger impact craters (e.g. Hildebrand et al. 1998; Pilkington and Grieve 1992), mud volcanoes (e.g. Rainone et al. 2015), sinkholes (Kaufmann 2014; Van Schoor 2002) other karst features (e.g. Benderitter 1997; Carrière et al. 2013; Guérin and Benderitter 1995; Torrese 2019; Zhu et al. 2011), and collapse pits (e.g. Torrese et al. 2021), however, literature concerning geophysical research of small meteorite crater fields is uncommon. Ormö et al (2007) investigated the Sirente crater field using a proton magnetometer and forward magnetic modelling; Speranza et al. (2009) conducted a similar magnetic survey also using Electric Resistivity Tomography (ERT); Torrese et al. (2019) carried out high-resolution seismic-reflection surveys across the main crater (cf. Torrese et al. 2019).

A significant difference between the formation of a crater due to a cosmic impact (exogenic) and that by endogenic processes such as mud volcanism or karst is the conspicuous ‘rootless’ nature of exogenic impacts. Speranza et al. (2009), in their ERT survey of the structure, noted a rootless morphology and upturned strata below the elevated rim at the Sirente main crater.

Torrese et al. (2019) found the subsurface structure of the Sirente main crater to be consistent with the impact hypothesis; they do not support other theories such as formation through karst or mud volcano. They propose a conceptual model based on seismic reflection profiles conducted across the main crater. The authors also found their seismic results to be consistent with ERT results produced by Speranza et al. (2009), suggesting an impact origin of the main crater. On the contrary, Speranza et al. (2009) stated that their ERT results do not support the impact theory and suggested the structure to be an anthropogenic cattle-pond (cf. Torrese et al. 2019).

In view of the scientific controversy involving the interpretation of such ERT data, this paper presents new results from synthetic modelling of ERT field data collected by Speranza et al. (2009), specifically PG1 profile. Synthetic model results aim at providing key indicators for objective and quantitative interpretation of the measured resistivity pattern, which is not always straightforward (Van Schoor 2002), and verifying the impact hypothesis proposed by Torrese et al. (2019). Detection of small sized structures such as slumps, compaction-fissures, upturning, down-warping and disruption of strata, or deep structures such as deep-seated central mound-like features or true crater floors, according to the impact hypothesis, is often challenging. Furthermore, shallow lateral heterogeneity and uneven topography such as the crater rim, may mask the true resistivity pattern of the subsoil model and generate artifacts and depth or lateral displacement of the geophysical targets (Torrese et al. 2021).

This study presents further insights on the subsurface structure of the Sirente main crater, which provide further clues around the controversy of its origin. Synthetic model results may result also useful at the survey designing stages of future ERT investigations aimed at detecting difficult geological targets that represent crucial elements for the definition of the mechanisms of formation of the Sirente main crater.

For our heavily populated world and highly interconnected society the impact of an asteroid or comet on the Earth today could produce a natural catastrophe far more damaging to civilization than any in recorded history. The current frequency of impacts of near-Earth objects (NEOs) on the Earth has been thoroughly researched in recent years (Harris et al. 2004). There is a considerable number of the works already published that deal with the problem of estimating the asteroid-comet hazards (e.g., Bland and Artemieva 2006; Chapman and Morrison 1994; Grieve and Shoemaker 1994; Ivanov et al. 2002; Morrison 2005; Morrison et al. 1994; Neukum and Ivanov 1994; Shoemaker 1983; Stewart 2011).

It should be noted that these estimates are of an approximate probabilistic sense and may differ from each other. This is primarily due to differences in the approaches used: when using methods based on the study of impact craters, the erosion processes of impact structures and incomplete data on the number of craters on some territories are of critical importance. As for the astronomical methods, difficulties are associated with the completeness of observations of small-diameter (50–250 m) asteroids (Amelin et al. 2013). In spite of all the efforts applied during the last years for the identification and tracing of potentially hazardous asteroids (NEO-asteroids), this task is still far from being completed. Also, it is important to estimate the rate of falling celestial bodies, depending on the physical properties of asteroids (Amelin et al. 2013).

Comparing the estimates of impact frequencies obtained with the help of different approaches, it seems that the crater formation rate is kept on almost a constant level during the last 3.5 billion years (Adushkin and Nemchinov 2007). Further work is needed on understanding the impact frequency of NEOs as a cosmic risk. Studies like this one, focused on recent impact craters, could play an important role in achieving this challenging task.

For simplicity, when analyzing the observed features in view of the proposed impact origin of the Sirente main crater, the terminology used throughout the paper follows the impact hypothesis, notwithstanding the fact that a consensus of the genesis is still pending.

2 Impact origin hypothesis based on seismic and ERT data

Torrese et al. (2019) suggested that the RFL2 seismic profile (Fig. 2 and their Figs. 3 and 5) allows a deep, rootless, bowl-shaped, sediment-filled crater structure to be defined. The crater has a weak, deep-seated central mound-like feature. Furthermore, the profile permits the recognition of potentially different seismic facies representing various crater infills, as well as strata beneath and close to the crater that are possibly affected.

Fig. 3
figure 3

a Near-crater structure of loose, stratiform layers above a more rigid substrate according to the “normal crater in a thin surficial layer” described by Quaide and Oberbeck (1968, Fig. 10b), which is an experimental reference to the observed structures of the Sirente main crater in the RFL2 seismic section (Torrese et al. 2019) and in the PG1 electrical section (Fig. 4). b Reconstruction (not to scale) of the subsurface structure of Sirente main crater based on PG1 (Fig. 4) electrical and RFL2 seismic data, according to the impact hypothesis. This figure was adapted from Fig. 10 published in Planetary and Space Science, Volume 168, Torrese, P., Rossi, A.P., Ormö, J., Rainone, M.L., Ori, G.G., Investigating the subsurface structure of the main crater of the proposed Sirente meteorite crater field (Central Italy): new clues from reflection seismics, Pages 27–39, Copyright Elsevier (2019), https://doi.org/10.1016/j.pss.2018.12.008

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Figure 3b includes a modelling of the subsurface structure of the main Sirente crater under the hypothesis. The sediment-filled structure depth, obtained by seismic imaging (the true crater floor is 53 m deep, on average, in RFL2), is in line with the resistivity imaging (Fig. 4) from the ERT surveys carried out by Speranza et al. (2009, their Fig. 4) across the main crater and with the bowl-shaped geometry of exogenic craters (i.e. impact and explosion craters, cf. Pike 1980). The depth to the limestone basement too (approximately 40–45 m), that underlies the unconsolidated carbonate mud just outside the crater, is consistent with the resistivity imaging depth (Figs. 3b, 4).

Fig. 4
figure 4

PG1 inverse resistivity section obtained from the field dataset by Speranza et al. (2009) across the main crater (used to design 2D and 3D synthetic models): overlay of the line-drawing interpretation from RFL2 seismic section (Torrese et al. 2019) and the resistivity pattern: a full-size PG1 models, b enlargement of a allowing a more detailed comparison focused on the main crater. The geometry of the crater bottom may be distorted due to the significant increase in seismic velocity occurring in the basement. This figure was adapted from Fig. 11 published in Planetary and Space Science, Volume 168, Torrese, P., Rossi, A.P., Ormö, J., Rainone, M.L., Ori, G.G., Investigating the subsurface structure of the main crater of the proposed Sirente meteorite crater field (Central Italy): new clues from reflection seismics, Pages 27–39, Copyright Elsevier (2019), https://doi.org/10.1016/j.pss.2018.12.008

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Torrese et al. (2019) found evidence of a deep-lying central uplift structure that is common in larger, complex impact craters (i.e. > 2–4 km diameter when formed in rock on Earth (cf. Pike 1980). These have also been identified in experimental craters as small as the Sirente main crater when developed in poorly consolidated targets (cf. Jones 1977; Roddy 1976). The model developed by Quaide and Oberbeck (1968) regarding the formation of “central-mound craters” seems plausible. Their study of strength-dominated lunar craters in targets with regolith overlying a more rigid substrate highlighted that “when a strong substrate is present at depths less than one crater radius beneath a normal crater”, above the interface to the stronger substrate there is an initiation of a centrally located “structural dome” of unexcavated weak material (Fig. 3b). At the Sirente site, this “structural dome” would be covered by the ongoing collapse of the weak upper layer during the early stage crater modification (i.e. the equivalent to the breccia lens in craters in rock) (cf. Torrese et al. 2019). However, PG1 ERT survey (Fig. 4) does not evidence any recognizable deepening of the limestone basement below the crater in the weak host (i.e., which encompass the crater, here underlying the crater) sediments, nor any distinct presence of a weak, deep-seated central mound-like feature as shown by profile RFL2. Torrese et al. (2019) suggested that this could be the result of a loss of lateral resolution in the ERT survey given the fairly significant depth as well as having relative high-conductive carbonate mud just below the surface, hampering penetration.

Just beyond the structure, at a depth of between 30 and 50 m, Torrese et al. (2019) discovered that strata are bent downwards and can be traced to a depth below what can be defined as the actual crater floor (“down-warping of strata” in Fig. 3b). The appearance of the target strata just outside the bowl-shaped structure is in line with observations at both experimental and natural impact craters (e.g. Figure 5.14 in Melosh 1989) and may be explained by something unusual and similar to the “camouflet”.

Similarly, the authors noted that strata up to a depth of 25 m below the NNE topographic crater rim are curved upwards before being crossed by the excavated crater floor (“upturned (overturned?) strata” in Fig. 3b). The visibly upturned strata displayed in profile RFL2 are also seen in profiles PG1 (Fig. 4) and PG2 in Speranza et al. (2009, their Fig. 4). This seemingly upwards movement of material is inconsistent with gravity-driven material movements during karst doline formation, and is, rather, extremely similar to the overturning of strata below impact crater rims (cf. Melosh 1989, his Fig. 5.14; Tancredi et al. 2009). The upward continuation of the deep-seated overturned strata observed in geophysical surveys is also seen in the overturned stratigraphy of the crater rim noted in the core drilling by Ormö et al. (2002, their Fig. 7). Torrese et al. (2019) claim that it is realistic to assume (and it also demonstrated in the seismics) that strata down-warping and overturning are also noticed down to approximately 20 m [compared with the central-mound crater model by Quaide and Oberbeck (1968, shown in Fig. 3a)]. The authors also found compaction-fissure-like characteristics, that is the down-warping of strata along with fracture features [“compaction features (down-warping of strata)” in Fig. 3b] below and just beyond the NNE rim (cf. Jones 1977; Ormö et al. 2002). Compaction rather than volume-expansion (i.e. down-warping and not structural uplift below the rim ejecta) characterizes explosion craters in porous, unconsolidated targets (see the discussion in Ormö et al. 2002). The resistivity pattern under the NNE elevated rim (Fig. 4) is consistent with the compaction zone (cf. Jones 1977). This is recognized by profile RFL2 and noted as strata “down-warping” by Ormö et al. (2002) (cf. Torrese et al. 2019).

Torrese et al. (2019) found that strata in the lower parts of the bowl-shaped, sediment-filled crater have an uneven look with dip angles unlike those of the surrounding plain, or lacking any clear structure (Fig. 3b). The authors separated this part into two facies that interpreted as material that has slumped down into the crater possibly still retaining some of its original stratification, or that has been completely disrupted and affected by the presence of the central mound-like feature. Above these deposits, lies a pack of continuous horizontal strata that was interpreted as post-impact lake sediment (Fig. 3b). These are confirmed by the core drilling (B1 in Fig. 2) conducted by Ormö et al. (2002) to circa 7 m below the floor of the lake. A general congruency between seismic and resistivity imaging of the crater infill is also displayed (Figs. 3b and 4). These especially regard the shallowest near continuous and parallel horizontal layers that represent the sediments of the lake floor and the SSW dipping layers that may be considered as slumps. In profile PG1 (Fig. 4), the lake floor sediments show no continuity beyond the crater. The fact that this facies drops to 15 m below the lake would rule out a purely anthropogenic origin of the pond. In fact, only an extensive but temporary excavation produced by an explosion would be able to create cavity of this size in the relatively unconsolidated material in which the Sirente structure is situated. A gradual excavation using machinery, or by hand, would not be able to reach such depths before the walls begin caving in due to the weight of the surrounding plain material. Any shallower and more conductive deposits (at 0–8 m) would represent more recent and finer lacustrine sediments while deeper and less conductive deposits (at 8–15 m) would be older and coarser lacustrine sediments or a breccia lens reworked by water and forming new layering (cf. Torrese et al. 2019).

Torrese et al. (2019) also discovered that seismic velocity (their Fig. 8) and resistivity boundaries (Fig. 4) are rather consistent. Deeper deposits of the structure infill show shallower and more conductive sediments (15–33 m) as well as deeper and less conductive deposits (33–55 m). The notable increase in velocity that appears to occur from 15 to 33 m in depth in profile RFL2 corresponds with the low resistivity body in profile PG1 (Fig. 4). It is significant that all probable blocks and boulders identified by seismic reflection (their Fig. 5 in Torrese et al. 2019) are localized within less conductive, probably coarser deposits (Fig. 4).

The preserved bedding in the unconsolidated host sediments (i.e., which surround the crater) situated beyond the crater versus the chaotic appearance inside the basin is noticeable in profile PG1 (Fig. 4), even if the resistivity range is quite similar. The lack of continuity and the quite different depth ranges would appear to suggest that these deposits have a different origin and age (pre-impact and post-impact). The interpretation of Torrese et al. (2019) contrasts here with that of Speranza et al. (2009), who suggest that the sediments inside and outside the crater have the same conductivity structure, ruling out different ages (pre-impact and post-impact) (cf. Torrese et al. 2019).

The depth of the sediment-filled, bowl-shaped crater seems to rule out a purely anthropogenic origin. Appearing to confirm that a cavity of these dimensions in such material could only have been created by an impactful, momentary explosion was the first-hand experience of Ormö et al. (2002, 2006). When carrying out machine excavations of the smaller C8 and C9 craters to a maximum depth of approximately 9 m (Ormö et al. 2002, 2006), much of the lower half of the excavated pit collapsed shortly after sampling. Nonetheless, the unstable target material would not prevent the formation of the elevated rim observed. Earth walls, for example those found in old fortification works, may be stable for thousands of years (cf. Torrese et al. 2019).

Torrese et al. (2019) highlighted, alternatively, that one could argue that the top section of the structure, i.e., near continuous and parallel horizontal layers interpreted as post-impact lake sediments, could be a shallow anthropogenic feature built on a pre-existing sag pond with karstic origins. A karstic origin seems, however, less probable as it is a gravitational process that is inconsistent with the upwards-direction of the strata deep below the rim, as well as the continuous strata below the structure. Further, no sign of a downwards continuation into the basement below the crater was seen in profile RFL2. This is in line with findings by Speranza et al. (2009), who also note the “rootless” appearance of the bowl-shaped structure in their ERT surveys.

3 Need for synthetic modelling

Synthetic modelling is a numerical simulation aimed at evaluating the capacity of the implemented model to detect and delineate predefined targets. This study arises from the need to verify whether the geophysical targets detected by ERT PG1 model (Fig. 4) are true underground features. This depends upon the response of the employed experimental setup to the degree of heterogeneity in the subsoil and the eventuality that the resistivity pattern obtained could be affected by measure and inversion artifacts.

The targets the study is focused on, identified by the joint interpretation of seismic profile RFL2 (their Figs. 3 and 5 in Torrese et al. 2019) and ERT PG1 profile (Fig. 4), were defined by Torrese et al. (2019) in their conceptual model shown in Fig. 3b. Among various geophysical surveys available at the site (Fig. 2), RFL2 and PG1 profiles had been selected by the authors because these are close, near-parallel profiles crossing the main crater rim-to-rim. Geophysical targets to be verified by synthetic modelling play a key role in defining the genesis of the Sirente main crater or in the ruling out of some mechanisms of formation such as meteorite impact, anthropogenic, karst or mud volcano origin.

The predefined targets the synthetic modelling has been focused on are:

  • upturned strata (“upturned (overturned?) strata” in Fig. 3b) that are displayed down to a depth of 25 m below the NNE topographic crater rim: this evidence would allow to rule out gravity-driven mechanisms and would highly suggest, instead, exogenic ones;

  • compaction-fissure-like features (“compaction features (down-warping of strata)” in Fig. 3b) below and just outside the NNE rim: this evidence would highly suggest exogenic mechanisms;

  • dipping layers (“slumps” in Fig. 3b) in the lower part sediment-filled crater: this evidence would allow to rule out a merely anthropogenic mechanism;

  • validation whether the presence of the elevated rim does affect the imaging of the structures detected below the crater rim (“upturned (overturned?) strata” and “compaction features (down-warping of strata)” in Fig. 3b); these geophysical targets play a key role in defining the genesis of the crater;

  • disrupted strata or strata affected by the presence of the central mound-like feature (“disrupted strata” in Fig. 3b) in the sediment-filled crater: this evidence would suggest exogenic mechanisms;

  • continuous horizontal strata (“post-impact lake sediments” in Fig. 3b, down to a depth of 8 m) above “slumps” and “disrupted strata” in the sediment-filled crater: this evidence would rule out a merely anthropogenic mechanism;

  • depth of the sediment-filled, bowl-shaped crater (53 m on average); this evidence would rule out a merely anthropogenic origin;

  • preserved bedding in the unconsolidated host sediments located outside the crater versus chaotic appearance inside the basin, as well as, lack of continuity and the rather different depth ranges; these evidences would suggest different origin and age of these deposits;

  • preserved bedding in the shallow strata located far from and outside the crater versus chaotic appearance in the shallow strata located near and outside the crater; this evidence would highly suggest exogenic mechanisms.

While two-dimensional (2D) synthetic modelling is aimed at replicating, simulating and verifying the entire section of subsoil investigated by PG1 model, three-dimensional (3D) modelling is focused on a localized and restricted volume of subsoil that crosses the northern rim of the crater: this portion of subsoil hosts shallow, target structures that play a key role in defining the genesis of the Sirente main crater.

4 Material and methods

4.1 Overview

Two-dimensional (2D) and three-dimensional (3D) synthetic modelling was performed along ERT PG1 model (Fig. 4), which crosses the main crater rim-to-rim to synthetically replicate the measured resistivity pattern. The steps involved in the modelling were:

  • designing of a conceptual model which simulates the measured resistivity pattern;

  • conversion of the conceptual model into a synthetic model;

  • generation of a synthetic dataset by forward modelling through the application of the synthetic model, according to the experimental setup involved in the field dataset collection;

  • inversion of the synthetic dataset to generate a realistic, synthetic, inverse resistivity model to be compared with PG1 model (field dataset).

4.2 Conceptual and synthetic model designing

The conceptual model (Fig. 5a) replicated the measured resistivity pattern revealed by PG1 model. It is an inhomogeneous model discretized in different units that represent the geometry of the bowl-shaped crater (basin), as well as the geometry of the features filling, underlying and surrounding the crater.

This model, which was designed according to that proposed by Torrese et al. (2019) (Fig. 3b) includes the geophysical targets that play a key role in defining the genesis of the Sirente main crater: upturned strata and down-warping of strata below the crater rim, compaction-fissure-like features below and just outside the crater rim, the weak, deep-seated central mound-like feature, dipping layers, disrupted strata and shallow continuous horizontal strata filling the crater, the preserved bedding in the host sediments located outside the crater and shallow strata located outside the crater affected by lower degree of chaotic appearance from the crater outwards. It also includes the true crater floor below the crater infill, the carbonate basement underlying the carbonate mud outside the crater, sporadic boulders located mainly at depth in the sediments filling the crater or located near the surface towards SSW, i.e., towards the steep north face of the Sirente massif.

Fig. 5
figure 5

2D synthetic modelling: a PG1-based conceptual model, b synthetic model derived from a, c synthetic inverse model derived from b of the Sirente main crater

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Conceptual model (Fig. 5a) was converted into a synthetic model (Fig. 5b) by assigning the measured electrical resistance value (Fig. 4) to each unit. The 3D synthetic model (Figs. 6 and 8a) was derived from the 2D synthetic model by giving each unit the third dimension, i.e., the lateral extension of the geological units.

Fig. 6
figure 6

2D synthetic modelling: different resistivity range extractions from the synthetic model (shown in Fig. 5b) of the Sirente main crater

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Fig. 7
figure 7

2D synthetic modelling: different resistivity range extractions from the synthetic inverse model (shown in Fig. 5c) of the Sirente main crater

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4.3 Forward and inverse modelling

Same electrode arrays (Wenner-Schlumberger and dipole–dipole) and experimental layout (72 electrodes spaced 5 m apart), which were used in the field dataset collection (2D) (Speranza et al. 2009), were used in 2D synthetic modelling. Same electrode arrays involved in the field dataset collection but a snake grid comprised of 12 × 4 electrodes spaced 10 m apart both along the X and Y axes was used in the 3D synthetic modelling. The merging of different arrays (Wenner-Schlumberger and dipole–dipole) differing in vertical and lateral resolution (Smith 1986) were employed to deliver better detectability and imaging and, therefore, provide more accurate inverse models according to Szalai et al. (2009), Torrese (2020) and Torrese and Pilla (2021).

The computational domain was discretized into tetrahedral cells in both forward and inverse modelling. A grid 355 m × 5 m in size, with a maximum depth of ≈ 50 m was designed for 2D modelling and a grid 110 m × 30 m in size, with a maximum depth of ≈ 20 m was designed for 3D modelling. Foreground region was discretized using a 0.5 m element size along the X, Y and Z direction. This domain discretization was necessary to prevent the occurrence of aliasing issues in applying the inhomogeneous synthetic model, which includes meter-sized structures (Figs. 6 and 8a). The background region was discretized using an increasing element size towards the outside of the domain, according to the sequence 1 × , 1 × , 2 × , 4 × and 8 × the foreground element size.

ERTLab Solver (by Multi-Phase Technologies LLC, Geostudi Astier srl), based on tetrahedral Finite Element Modelling (FEM), was used for both forward and inverse modelling. Two-dimensional and 3D synthetic datasets were generated by forward modelling through the application of the synthetic models.

The forward modelling was performed using mixed-boundary conditions (Dirichlet–Neumann) and a tolerance (stop criterion) of 1.0E-7 for a Symmetric Successive Over-Relaxation Conjugate Gradient (SSORCG) iterative solver. Among various algorithms [e.g., Sensitivity Conjugate Gradients (SCG), Incomplete Cholesky Conjugate Gradient (ICCG), Preconditioned Conjugate Gradient Method (CGPC)], some of which may be even more robust [e.g., Levenberg–Marquardt (Levenberg 1944; Marquardt 1963; Nelles 2001)], the SSORCG iterative solver was used as it provides fast convergence by decreasing the spectral condition number of the matrix (Bing and Greenhalgh 2001; Spitzer 1995) and is particularly efficient and accurate in the modelling of complex resistivity structures (meter-sized structures in this study) requiring a computational domain discretized in a large number of nodes (Spitzer 1995). Data inversion was based on a least squares smoothness constrained approach (LaBrecque et al. 1996). Noise was appropriately managed using a data-weighting algorithm (Morelli and LaBrecque 1996) that allows the adaptive changes of the variance matrix after each iteration for those data points that are poorly fit by the model: after each inversion iteration, the weights contained in the variance matrix are decreased for those data which are poorly fit by the reconstructed model; the weights of data with good fits are kept at their original values. In this algorithm, a variation of the least-absolute deviations method described by Mosteller and Tukey (1977) was implemented.

Since field data always contain noise in practice, the obtained synthetic datasets were corrupted with 1% random noise to provide realistic results and were inverted to generate inverse resistivity models. This value was considered appropriate to simulate the low level of field noise in the Sirente plain, also considering depth, volume and resistivity of the geophysical target (Liu et al. 2020). The inverse modelling was performed using a maximum number of internal inverse Preconditioned Conjugate Gradient (PCG) iterations of 15 and a tolerance (stop criterion) for inverse PCG iterations of 0.001. The amount of roughness from one iteration to the next was controlled in order to assess maximum layering along the X and Z directions for the 2D model and along the X, Y, and Z directions for the 3D model: a low value of reweight constant (0.1) was set with the objective of generating maximum heterogeneity.

Both 2D (Figs. 5c and 7) and 3D (Figs. 8b, c and 9) inverse resistivity models were chosen with a criterion based on the achievement of a minimum data residual (misfit error).

Fig. 8
figure 8

3D synthetic modelling: a synthetic model derived from the PG1-based conceptual model (shown in Fig. 5a), b, c synthetic inverse model derived from a of the Sirente main crater

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Fig. 9
figure 9

3D synthetic modelling: different resistivity range extractions from the synthetic inverse model (shown in Fig. 8b, c) of the Sirente main crater

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5 Results

5.1 2D synthetic inverse model

The resistivity pattern revealed by the 2D synthetic inverse model (Fig. 5c) is highly analogous with the resistivity pattern shown by the field inverse model (Fig. 4) and consistent with the presence of a deep, bowl-shaped, sediment-filled crater structure with a weak, deep-seated central mound-like feature. The synthetic inverse model allowed the recognition of structures consistent with the presence of (1) possible upturned strata (e in Fig. 5c), compaction-fissures (h in Fig. 5c) and down-warping of strata (j in Fig. 5c) below the rim, similar to what is known from explosion craters in porous, unconsolidated targets, (2) different facies representing a crater infill of disturbed material (i, g in Fig. 5c) resembling the breccia lens in craters formed in rock, as well as (3) preserved bedding in the shallow strata located far from and outside the crater (a in Fig. 5c) versus chaotic appearance in the shallow strata located near and outside the crater (b in Fig. 5c), similar to what is known from explosion craters in unconsolidated targets. The presence of the elevated rim (c in Fig. 5c) does not affect the imaging of the structures detected below the crater rim (e, h, j in Fig. 5c).

The synthetic inverse model is able to clearly recognize low to medium-resistivity deposits representing the crater infill: the shallowest, low-resistivity, continuous horizontal strata are consistent with post-impact lake sediments (d in Fig. 5c).

The lack of continuity between host sediments located outside the crater and crater infill is well exposed in the synthetic inverse model: pre and post-impact sediments are well expressed by the preserved bedding in the unconsolidated host sediments versus the chaotic appearance inside the crater (Fig. 5c).

It is also worth pointing out the difference between shallow strata located far from and outside the crater which still retain their original stratification (a in Fig. 5c) versus chaotic appearance in the shallow strata located near and outside the crater (b in Fig. 5c).

Possible, pre-impact, alluvial-lacustrine deposits (lacustrine deposits of the paleolake of the Sirente plain, not of the current small lake contained in the crater, for clarity) still retaining their original stratification show a roughly NNW-SSW depositional flow direction (“depositional flow direction for pre-impact carbonate mud” in Fig. 5).

Small sized high-resistivity bodies (f in Fig. 5c) may represent possible proximal ejecta and/or boulders that are likely derived from rock-falls and avalanches. These small sized high-resistivity bodies are consistent with some strong diffraction hyperbolas limiting the image resolution and interpretation of RFL2 stack section by Torrese et al. (2019) (their Figs. 3 and 5); their presence within shallow post-impact sediments is suggested by the occurrence of some small sized distortion affecting the resistivity pattern of PG1 model (120 m along the profile in Fig. 4); however no evidence of boulders included in the crater infill has been found in PG1 model.

The lack of continuity between host sediments located outside the crater and crater infill is also expressed by different depth ranges and resistivity structures: this is well exposed in the sections that report different resistivity range extractions from the synthetic inverse model (Fig. 7). The resistivity data can be divided into four resistivity units:

  1. 1.

    the low-resistivity unit, ranging from 51 to 80 Ω∙m (Fig. 7a), is associated with finest-grained deposits and is related to shallow, post-impact lake sediments inside the crater;

  2. 2.

    the middle-low resistivity unit, ranging from 80 to 100 Ω∙m (Fig. 7b), is associated to fine-grained deposits and is related to deep, post-impact lake sediments, part of post-impact disturbed material located inside the crater, possible upturned strata below the rim and part of pre-impact carbonate mud (outside the crater);

  3. 3.

    the middle-high resistivity unit, ranging from 100 to 145 Ω∙m (Fig. 7c), is associated to fine to medium grained deposits and is related to most of post-impact disturbed material located inside the crater and part of pre-impact carbonate mud (outside the crater);

  4. 4.

    the high resistivity unit, ranging from 145 to 290 Ω∙m (Fig. 7d), is associated to coarse grained deposits and is related to deep, post-impact disturbed material located inside the crater, part of pre-impact carbonate mud (outside the crater), possible, shallow, proximal ejecta and/or boulders (not exposed at the ground surface); this unit is also associated to the true crater floor and the limestone basement.

5.2 3D synthetic inverse model

The resistivity pattern revealed by the 3D synthetic inverse model (Fig. 8b, c) is highly analogous with the resistivity pattern shown for the same localized and restricted portion of subsoil by the field inverse model (Fig. 4) and the 2D synthetic inverse model (Fig. 5c). The 3D resistivity pattern is consistent with the presence of (1) possible upturned strata below the rim, similar to what is known from explosion craters in porous, unconsolidated targets, (2) possible impact ejecta in the close vicinity of the rim (Fig. 8b, c). As revealed by the 2D synthetic inverse model, the 3D model also suggests that the presence of the elevated rim does not affect the imaging of the structures detected below the crater rim (Fig. 8b, c).

The lack of continuity between host sediments located outside the crater and crater infill is also well exposed in the synthetic inverse model (Fig. 8b, c).

As revealed by the 2D synthetic inverse model, the 3D model also shows the difference between shallow strata located far from and outside the crater which still retain their original stratification (a in Fig. 8b, c) versus chaotic appearance in the shallow strata located near and outside the crater (b in Fig. 8b, c).

The 3D model shows resistivity values substantially consistent with the 2D model, but slightly higher values. This is due to the fact that the 3D model is focused on a shallower, localized and restricted volume of the subsoil portion investigated by the 2D model. The resistivity data can be divided into four resistivity units:

  1. 1.

    the low-resistivity unit, ranging from 45 to 80 Ω∙m (Fig. 9a), is associated with fine-grained deposits and is related to possible upturned strata below the rim, shallow, post-impact lake sediments and part of pre-impact carbonate mud;

  2. 2.

    the middle-low resistivity unit, ranging from 80 to 120 Ω∙m (Fig. 9b), is associated to fine to medium-grained deposits and is related to part of post-impact disturbed material located inside the crater and part of pre-impact carbonate mud;

  3. 3.

    the middle-high resistivity unit, ranging from 120 to 150 Ω∙m (Fig. 9c), is associated to medium-grained deposits and is related to part of pre-impact carbonate mud;

  4. 4.

    the high resistivity unit, ranging from 150 to 482 Ω∙m (Fig. 9d), is associated to coarse grained deposits and is related to possible, shallow, impact ejecta: these can be separated into large sized, proximal ejecta which are located in the close vicinity of the rim, and small sized, distal ejecta which are located 25–35 m away from the rim.

6 Discussion

Synthetic modelling allowed to verify that shallow and middle-depth (< 30 m below ground level) geophysical targets detected by the ERT field data model are true underground features. Modelling results allowed to rule out that factors such as uneven topography at the crater rim, electrode configuration and shallow vertical and lateral heterogeneities, have masked the true resistivity pattern of the subsoil and generated artifacts and/or depth or lateral displacement of the geophysical targets. The resistivity imaging derived from ERT field data appears unaffected by these disturbing factors.

Synthetic modelling allowed to recognize as true resistivity feature, target structures already been noted in ERT field data model and reflection seismic sections. These features, according to the conceptual model proposed by Torrese et al. (2019) (Fig. 3b) play a key role in defining the genesis of the Sirente main crater:

  • possible upturned strata below the crater rim,

  • possible compaction-fissure-like features below and just outside the rim,

  • chaotic appearance of strata in the lower parts of the crater infill with dip angles different to the surrounding plain, or without any obvious structure (material slumped down into the crater such as breccia lens-like features, or that has been completely disrupted),

  • shallow, continuous horizontal strata in the shallower part of the crater infill, interpreted as post-impact lake sediments, which show no continuity outside the crater,

  • deeper and less conductive deposits in the shallower part of the crater infill which would represent older and coarser lacustrine sediments or a water-reworked breccia lens providing new layering;

  • the lack of continuity between host sediments located outside the crater and crater infill that would suggest different origin and age (pre-impact and post-impact) of these deposits,

  • the presence of a shallow ejecta layer whose proximal areas to the crater would have been massively affected by the fall of fine grained deposits as it would expect for an impact in carbonate mud; the high resistivity values showed by ejecta could also indicate material (carbonate mud) that has undergone a certain thermal stress due to the impact; the thermal stress would have led to an increase in the resistivity value of the material.

The clearly upturned strata displayed in the synthetic inverse models are also revealed by profile PG2 (Fig. 1) by Speranza et al. (2009, their Fig. 4). These reach down to a depth of 10–15 m below the inner part of the elevated crater rim, especially on the NNE flank. This seemingly upwards movement of material is inconsistent with gravity-driven movements of material during karst doline formation, and is, instead, very similar to the overturning of strata below impact crater rims (cf. Melosh 1989, his Fig. 5.14; Tancredi et al. 2009). Evidence of deep-seated upturned strata is in line with the noted overturned stratigraphy of the crater rim encountered in the core drilling by Ormö et al. (2002, their Fig. 7). It could be argued that this core drilling does not reveal anything about what might happen at greater depths; however, Torrese et al. (2019) show in the seismics, down-warping and overturning of strata also are noticed down to approximately twenty meters [compare with the central-mound crater model by Quaide and Oberbeck (1968, shown in Fig. 3b)]. This evidence is not consistent with a purely anthropogenic origin of the crater (cf. Torrese et al. 2019).

The upturned strata below the crater rims had been noted by Speranza et al. (2009) in their ERT surveys of the main Sirente crater (profiles PG1–PG3, their Fig. 4). However, the proposed interpretation here conflicts with the interpretation by Speranza et al. (2009) although they too noted a difference in the conductivity and geometry of the carbonate mud below the crater rims. What was found was that the sedimentary packages become concave toward the rim and that the interface between them is lowered down to a depth of 25 m. They suggested that these characteristics probably represent a ‘‘geoelectric artefact’’ for data gathered at the rim, although they cannot rule out that they are related to the rim load above the soft carbonate mud. Whereas replication and validation of these structures represent one of the main objectives of this study, synthetic modeling excludes that these structures are related to measure or inversion artefacts for data gathered at the rim.

Similarly, 2D synthetic inverse models demonstrate how strata down to a depth of at least 15 m (25 m observed by Torrese et al. (2019) in their seismics, however) below the NNE topographic crater rim, are bent upwards before being cut by the excavated crater floor. It also shows compaction-fissure-like characteristics (h in Fig. 5c, to compare with “compaction features” in Fig. 3b, it is realistic to assume down-warping of strata as well as with fracture features) under and just beyond the NNE rim (cf. Jones 1977; Ormö et al. 2002). Compaction rather than volume-expansion (i.e. down-warping instead of structural uplift below the rim ejecta) is a recognised feature of explosion craters in porous, unconsolidated targets (see discussion in Ormö et al. 2002). The compaction evidence under and just beyond the crater rim would be consistent with the ≈ 1 m difference between the target surface and the plain, and the shallow depression that can be observed outside the rim flank, along the western edge of the crater rim, as seen by Ormö et al. (2002, their Figs. 6 and 7b, respectively). Compaction is also confirmed by core drilling B2 (Fig. 1), which shows strongly compressed materials below a paleosol, probably representing the target’s upper part (i.e., the impact surface, Ormö et al. 2002, their Fig. 8) (cf. Torrese et al. 2019).

The crater’s deeper section disrupts the generally horizontal strata, which are upturned at the structure’s rim but continuous below its floor. This is in line with the expected morphology of an impact crater of this size when developed in soft, porous sediments and has been confirmed by core drilling carried out previously (Ormö et al. 2002) (cf. Torrese et al. 2019).

Within the bowl-shaped structure, a well-developed chaotic infill can be interpreted as the “breccia lens”. This consists of material that relocated during the early collapse of the transient cavity during impact cratering. Above it is up to 5 m (however, up to 15 m observed by Torrese et al. (2019) in their seismics) of horizontally stratified sediments considered as post-impact lake deposits. The main alternative models regarding the Sirente main crater’s formation, i.e. mud volcano, anthropogenic cattle pond or karst doline, do not appear to be supported by the synthetic modelling as the structure is too deep to have been dug out by humans in what is relatively unconsolidated material. It also shows a deep-seated overturning of strata (cf. Torrese et al. 2019).

The lack of continuity between host sediments located outside the crater and crater infill is expressed in terms of both resistivity values and geometries. The crater appears filled with sediments having mostly resistivity values ranging from 100 to 145 Ω∙m at middle and great depths; host sediments located outside the crater show a wider range of values. This is well noticeable in Fig. 7. At shallow depths, continuous horizontal strata in the shallower part of the crater infill, interpreted as post-impact lake sediments, show no continuity near and outside the crater: here, the sediments show a chaotic appearance related to possible, shallow, impact ejecta. This is well noticeable in Figs. 7 and 8. The lack of continuity and the different geometry would suggest different origin and age (pre-impact and post-impact) of host sediments located outside the crater and crater infill.

Although synthetic modelling results are consistent with the presence of a deep, bowl-shaped, sediment-filled crater structure, synthetic modelling failed in replicating with suitable accuracy deeper structures (30 to 50 m below ground level). The synthetic inverse model appears too accurate at depth with respect to the field inverse model. The true crater floor, the weak, deep-seated central mound-like feature, the limestone basement, deep boulders appear too defined in the synthetic inverse model; differently, these features appear diffuse, not well defined by gradient outlines that extend beyond the true size of the body (Torrese et al. 2021) in the field inverse model. This is due to the underestimation of the loss of information (loss of detectability and resolution with depth, Torrese 2020) of the synthetic modelling, compared to the effective loss of information related to the natural materials investigated on the field. Therefore, no validation or further insight into these deep structures, such as the rootless morphology of the bowl-shaped crater, is provided by this study.

Despite the limitations inherent in synthetic modelling, the results from this study validate part of the structural features observed by ERT field data (Speranza et al. 2009) and consistent with seismic data (Torrese et al. 2019). These findings are consistent with the hypothesis of a small impact crater in a low-strength target, with a relatively shallow apparent crater. These features, which include possible upturned strata below the crater rim, possible compaction-fissure-like features below and just outside the rim, well-developed “breccia lens” consisting of material relocated during the early collapse of a cavity in incompetent material, as well as an ejecta layer showing an increase in the chaotic appearance towards the rim of the crater, are suggesting an impact origin of the Sirente main crater. Conversely, the structural features validated in this study do not support other proposed mechanisms of formation such as karst, mud volcano or merely anthropogenic origin.

Findings from 3D synthetic modelling will be also helpful in survey designing and interpreting stages of future 3-D ERT field surveys carried out at the Sirente main crater. Three-dimensional ERT field surveys would provide more accurate and complete geophysical models of the regions underlying and surrounding the crater rim and would allow to better define these shallow, small sized structural features that play a key role in defining the genesis of the Sirente main crater. This would provide further clues around the controversy of its origin.

7 Conclusions

The results from this study validate part of the structural features observed by ERT field data collected at the Sirente main crater. These structural features include possible upturned strata below the crater rim, possible compaction-fissure-like features below and just outside the rim, well-developed “breccia lens” consisting of material relocated during the early collapse of a cavity in incompetent material, as well as an ejecta layer showing an increase in the chaotic appearance towards the rim of the crater. Findings from this study are consistent with the hypothesis of a small impact crater in a low-strength target, with a relatively shallow apparent crater according to the conceptual model proposed by Torrese et al. (2019). Conversely, the structural features validated in this study do not support other proposed mechanisms of formation such as karst, mud volcano or merely anthropogenic origin.

Findings from 3D synthetic modelling will be also helpful in survey designing and interpreting stages of future 3-D ERT field surveys carried out at the Sirente main crater. Three-dimensional ERT field surveys would provide more accurate and complete geophysical models of the regions underlying and surrounding the crater rim, and would allow to better define these shallow, small sized structural features that play a key role in defining the genesis of the Sirente main crater. This would provide further clues around the controversy of its origin.