© L. Murray-Bergquist et al., Published by EDP Sciences 2025

1 Introduction

Marine active refraction seismic experiments provide an important window into the small (∼10 km) scale structure of the crust and lithosphere offshore, but the expense and logistics of these experiments, especially access to stations and vessels equipped for refraction seismic experiments are a limiting factor in data collection. Offshore seismic experiments have become increasingly sophisticated, with technological advances in instrumentation and methods from improved processing of refraction seismic data with slope tomography to the use of Full Waveform Inversions (FWI) (Morgan et al., 2013; Rowe et al., 2022; Górszczyk and Operto, 2021; Górszczyk et al., 2024; Marjanović et al., 2019; Sambolian et al., 2021; Pipatprathanporn and Simons, 2021; Hovland, 2016). However, as FWI requires a very good starting model and dense station spacing, in most cases refraction tomography is used to either acquire the starting model, or as a final model if FWI is not possible, as is in most sparse academic experiments. In industry, streamer acquisition systems have been favoured as the most cost efficient survey method, however, the unique benefits of Ocean Bottom Nodes (OBNs) have spurred research into more automated and efficient systems of deploying and recovering OBNs. The added cost of maintaining a pool of OBNs, and the extra time required to deploy and recover them, must be weighted against the benefits which include better illumination of complex terrain, the addition of s-wave data, and added survey flexibility when there are obstacles (Vermeer, 2012; Hovland, 2016).

Most wide-angle refraction experiments are still predominantly executed along 2D profiles of Ocean Bottom Seismometers (OBS), providing high-resolution information along one line, but without volume information. This volumetric information is essential when attempting to understand the crustal heterogeneities in three dimensions. This lack of volumetric information can be filled in two ways:

1. Data mining by combining existing 2D refraction seismic lines into a dataset suitable for 3D tomography.

2. Designing future experiments for 2D and 3D tomography.

One of the challenges of 3D body wave tomography is achieving sufficient resolution to effectively image crustal-scale velocity anomalies. Although the theoretical resolution of a seismic experiment can be calculated based on the dominant wavelength of the seismic source and depth, the real resolution depends on the local geology. Widess (1973) found that the vertical resolution limit is one-eighth of the wavelength. The horizontal resolution limit is set by the width of the Fresnel zone, which is proportional to the wavelength and depth of the reflector. However, these theories only set the upper limit of the resolution, in practice the resolution is generally much lower depending on noise levels and the local geology. This is why we need methods for estimating the resolution of a refraction seismic experiment that are specific to the experimental design and the geologic setting. Work has been done on the problem of optimizing 3D experimental design, such as the subduction zone geomodel designed by Górszczyk and Operto (2021), that can be used for testing experimental designs and comparing tomographic methods, however, the model represents a subduction zone, and so would mainly be useful in testing station geometries for use in a subduction zone setting, whereas the workflow presented here could be used to determine a good station geometry for any offshore setting.

There are various ways of estimating the real world resolution of a 3D tomographic experiment. One common method is utilising the ray coverage or hit count as a proxy for resolution (Zelt, 1999), even though this is not always an accurate predictor as parallel rays do not contribute to resolution as much as crossing rays do (Zelt, 1998). A more reliable metric is the derivative weighted sum (DWS) which provides a relative measure of ray density at each node by weighting rays based on their distance from the node and summing the weighted rays (Toomey and Foulger, 1989). Checkerboard tests are commonly used to test the resolution power of the observed rays, or synthetic anomalies of other shapes that more closely resemble the aim of the study may be introduced to test the stability of a model (Zelt, 1999; McNutt, 2005). Some tomographic software includes calculations of the resolution matrix, DWS, or other metrics that can be used to assess the resolution more quantitatively (Meléndez et al., 2015; Simmons et al., 2019; Zelt, 1999; Meléndez et al., 2015). Zelt (1998) describes a method of calculating the lateral velocity resolution of an experiment using a more quantitative and robust extension of the commonly applied checkerboard test. The method calculates the semblance between input and recovered checkerboards for a range of checker sizes and then uses linear interpolation between the checker size and semblance at each node to find the smallest checker size that can still be reasonably well recovered, or in other words, the lateral resolution at each node.

In this study, we will apply Zelt’s (1998) method to test the potential of two existing refraction seismic experiments for 3D tomography, solution 1, and we will present a workflow that can be used to test the design of future refraction seismic experiments, solution 2. The workflow includes tests of synthetic data sets based on these two experiments but with the strategic addition of shots and stations to assess how they could be improved. This method was chosen because of its flexibility as it can be applied using any code and any starting model, and as it is more robust and less subjective than the classic checkerboard test. Both experiments examined in this paper are from the Liguro-Provençal Basin, which is a good candidate for data re-analysis because it has hosted multiple offshore seismic refraction experiments (Moulin et al., 2015; Afilhado et al., 2015; Merino et al., 2021; Dessa et al., 2011; Dessa et al., 2020; Gailler et al., 2009) as well as shoreline crossing experiments such as the AlpArray Experiment (Dannowski et al., 2020b). The main reason for the high scientific interest in this region is our poor understanding of the nature of the crust of the Ligurian Basin (Contrucci et al., 2001; Dessa et al., 2011; Dannowski et al., 2020b; Boschetti et al., 2023) that could benefit from the wider coverage provided by 3D tomography.

2 Geological setting of the liguro-provençal basin

The Liguro-Provençal Basin is located in a complex tectonic area, at the Western Alps–Northern Apennines junction at the northern extent of the Mediterranean Sea (Fig. 1). The Liguro-Provençal Basin formed as a back-arc basin in response to rollback of the Apulian slab and the retreat of the Ionian-Apulian subduction zone (Rollet et al., 2002). The basin opened from around 21 to 19–16 Ma with the counter-clockwise rotation of the Corsica-Sardinia block (Fig. 1) (Rehault et al., 1984; Gueguen et al., 1998; Jolivet and Faccenna, 2000). The basin ceased to open around 16–15 Ma (Rollet et al., 2002; Vigliotti and Langenheim, 1995), and while geodetic measurements suggest that the Ligurian-Provençal Basin and the Corsica-Sardinia block are now approximately stable with respect to the Eurasian plate (Nocquet and Calais, 2004), seismic data suggest that the basin is now under compression, with focal mechanisms of earthquakes from inside the basin showing thrust faulting which has been interpreted as the reactivation of old rift-related faults (Thorwart et al., 2021; Béthoux et al., 2008; Larroque et al., 2011).

The nature of the basin’s crust, whether atypical oceanic crust that is partially serpentinized mantle overlain by sediments (Contrucci et al., 2001; Dessa et al., 2011), or highly thinned continental crust (Dannowski et al., 2020b), has been investigated but is still debated as the basin’s crust has yet to be directly sampled with drilling. The thick sediment cover hinders direct sampling (Boschetti et al., 2023; Dessa et al., 2011).

The basin has a steep topography and a complex basin stratigraphy. The central part of the basin is covered by 6–8 km of sediment (Schettino and Turco, 2006) containing a layer of Messinian salt which varies in thickness, in some areas forming diapirs up to 2 km thick (Pautot et al., 1984; Dessa et al., 2011; Moulin et al., 2015; Bache et al., 2015). This evaporite layer is ascribed to deposition during the Messinian salinity crisis, (Bache et al., 2009; Contrucci et al., 2001; Jolivet et al., 2006) and complicates tomographic studies in the basin, by increasing the attenuation and scattering of the seismic signal due to the steep forms and strong differences in impedance and velocity between the evaporites and surrounding layers (Jones and Davison, 2014; Contrucci et al., 2001).

The Gulf of Lion, on the western side of the Liguro-Provençal Basin, is also covered in thick sediment (up to 6 km (Schettino and Turco, 2006)), however, near the southwestern coastline, areas of basement highs with relatively little sediment cover (1–2 km) have been observed (Moulin et al., 2015). Earlier studies interpreted these as volcanic in origin (Maillard and Mauffret, 1999; García et al., 2011), however, Moulin et al. (2015) suggest they are continental crustal features, related to rifting during the formation of the Liguro-Provençal and Valencia basins as their slower seismic velocities match that of typical continental crust. To the northeast and just south of Corsica there are some areas of volcanic origin (Rollet et al., 2002; Réhault et al., 2012).

Fig. 1 Bathymetry of the Liguro-Provençal Basin with the shot and station locations of the AlpArray–LOBSTER Experiment, including stations along the two shot profiles (yellow lines and green triangles respectively), and the SARDINIA Experiment (red lines and orange triangles respectively). The Alpine front and Ionian-Apulian subduction zone (S. Z.) are marked by red and black subduction lines respectively, and the Corsica-Sardinia block is labelled with Co on Corsica and Sa on Sardinia.

3 Data and methods

3.1 Data collection

3.1.1 The SARDINIA experiment

The SARDINIA Experiment consists of two sections of wide-angle seismic profiles with coincident multi-channel seismic data, three profiles in the Gulf of Lion and three profiles off the west coast of Sardinia (Aslanian and Olivet, 2006). Our work focuses on the profiles in the Gulf of Lion, acquired by the RV L’Atalante between November 25th and December 2nd, 2006, the study area is shown in Figure 2. The experiment used an air gun array with 8260 in3 volume towed between 18m and 28 m depth to shoot along the three profiles. All stations were deployed before shooting commenced and remained in place for the entire experiment (Moulin et al., 2015). The longest profile (AB) runs from the mouth of the basin in the southeast (40.02N, 7.04E) towards land in the northwest (43.00N, 3.48E), two profiles (CD (41.26N, 3.32E to 42.81N, 5.66E), EF (42.38N, 5.94E to 41.13N, 4.06E)) cross perpendicular to profile AB, oriented NE-SW with approximately 50 km between profiles, and about 13 km station spacing along the profiles. The northeastern extent of these profiles overlaps with the more recent AlpArray–LOBSTER Experiment (Fig. 1) (Aslanian and Olivet, 2006; Kopp et al., 2018) described in Section 3.1.2.

Fig. 2 Locations of the seismic stations of the 2006 SARDINIA Experiment: triangles mark the stations used in this study (green), planned stations that malfunctioned but are used in some synthetic tests (orange), and stations from the SARDINIA Experiment that were outside of this study (black). Black lines mark the shot profiles.

3.1.2 The AlpArray–LOBSTER Experiment

In June 2017 the French research vessel RV Pourquoi Pas? deployed 29 Ocean Bottom Seismometers (OBS) in a network with station spacing between 34 and 57 km across the Liguro-Provençal Basin (Fig. 3) (Crawford, 2017). These OBS recorded continuously for approximately eight months until the German research vessel RV Maria S. Merian returned to the area in February 2018 (Kopp et al., 2018). The vessel recovered one OBS (A412A) before deploying 35 short-period stations with around 7.5 km spacing along profile P01 (red lines, Fig. 3) which spans most of the basin. Two G-gun arrays were deployed on each side of the vessel to provide a total volume of 5126 in3. The profile was shot from the coast of Corsica westward towards the Gulf of Lion. At the end of the profile the vessel turned and continued shooting for an additional ∼83 km to the south to record shots in the larger OBS network. After shooting Profile P01, the OBS indicated by the light green triangles in Figure 3 remained on the seafloor while those marked by yellow triangles were recovered. After this, 15 short-period stations were deployed along Profile P02 with station spacing around 8 km (grey line, Fig. 3) and an airgun profile was shot, the southwest end of P02 crosses P01 and then runs roughly along the basin axis to the northeast.

Fig. 3 Map outlining the AlpArray–LOBSTER Experiment. Airgun shots are indicated in red for profile P01, and grey for profile P02. Triangles show land stations (blue), Ocean Bottom Seismometers (OBS) that recorded both profiles (green), OBS that recorded only profile P01 (yellow), the on-profile OBS (cyan), OBS that recorded passive data but no shots (orange), and OBS that were lost (black).

3.2 Data processing

3.2.1 The SARDINIA experiment

The geologic setting of the study area is characterized by thick sediment and, in the southwest, linear basement highs running roughly southeast from the coast into the gulf (Moulin et al., 2015). The high structural heterogeneity caused by these features meant that a 3D starting model that already included large-scale features was more suitable than a 1D starting model. A 3D starting model was created based on 2D velocity models along the seismic profiles published by Moulin et al. (2015).

The starting model includes water, sediment, upper crust, lower crust, and mantle layers. Each layer was assigned a constant velocity based on the forward modelling layers used by Moulin et al. (2015), and the layer interfaces were made by extrapolating the interfaces along the profiles to 3D. A slice of the starting model along profile CD is shown in Figure 4. The RMS of the real travel times compared with calculated ray paths through the starting model before any iterative adjustments is 0.87488 s.

The refracted and reflected arrivals were picked in the open-source software Pasteup (Fujie et al., 2008), a graphical user interface for seismic unix (Cohen and Stockwell, 2002). The on-profile picks were compared with the forward models published by Moulin et al. (2015) using the open source software Modelling (Fujie et al., 2008) that is a graphical user interface for rayinvr (Zelt and Smith, 1992).

All stations were deployed during the entire survey, meaning that each station was recording during the shooting of each profile. However, to focus on the area best suited to 3D tomography, between profiles CD and EF, only the stations along profile AB that were between the profiles and one to each side were used. Stations farther along AB to the north and south contributed less to the 3D resolution, and as the second station to the north along line AB was lost, one station to each side was deemed a suitable area of inclusion. All shots from profile AB that were recorded by one of the stations used were included. This resulted in 74,375 travel times in the real data set, see Table 2.

In general, the data quality was very good, with clear first arrivals for shot-station pairs from the same profiles, while the first arrivals from shot-station pairs from different profiles were sometimes difficult to distinguish, especially at long offsets (>40 km), or were obscured by the direct water wave arrival of previous shots. Three phase types were observed to cross between profiles CD and EF: basement reflections, refractions in the upper mantle (Pn), and Moho reflections (PmP) (Fig. 6b). In many cases, especially to the southwest, it was difficult to distinguish between the Pn and PmP phases, as they were very close in velocity. On all shot-station pairs from the same profile, the mantle phases were visible, with some exceptionally clear stations recording up to offsets of almost 100 km.

At long offsets, the water multiples were sometimes stronger and easier to identify (Fig. 6b), a phenomenon that is described by Meléndez et al. (2014) as resulting from constructive interference of the water multiple with its seafloor reflection. The root mean square (RMS) of the difference between the picked arrival times and model calculated arrival times can be used as an indication of pick and model quality. If the difference is large for all picks, then the starting model may be too far from reality, but if some picks are much farther from the calculated times than the rest of the model it can be an indication of miss-identified phases or wrong picks. To assess the overall pick quality and identify problematic picks the RMS was calculated for each station and phase type. All water multiples picked had higher RMS than the first arrivals, meaning that the water multiples are farther from the model and could be less reliable. Although the mean RMS of the first water multiples was within about 0.6ms of the first arrivals for each compared phase they were all higher, and for simplicity and to avoid adding unnecessary uncertainties to the model, only the first arrivals were used. The water multiples were, however, still useful as guides to identify the first arrivals at some cross-profile stations.

Picks that were marked as upper crustal refractions and inter-crustal reflections had the highest RMS difference between the picked data and model calculated arrivals compared to other phases. To include these reflections required an interface-reflector between the upper and lower crust, to test whether this interface should be included in the starting model the data were tested with a single layer crust and a two-layer crust. The two-layer crustal model which allowed for the inclusion of the inter-crustal reflections resulted in lower total pick RMS and Chi-squared values closer to 1 than the single crustal layer models, and so the two-layer crustal model was used for all tests in this area. The area covered by these tests is on the continental-oceanic transition zone, and the nature of the crust in this area is debated and possibly includes thinned continental crust underlain by intrusions of gabbro and serpentinised peridotites (Afilhado et al., 2008; Moulin et al., 2015).

Fig. 4 Slice of the starting model used for resolution tests of the SARDINIA Experiment. The slice runs SW-NE along profile CD, OBS are marked by red triangles and shots by thick black line.

Fig. 5 Slice of the starting model used for resolution tests of the AlpArray–LOBSTER Experiment. The slice runs mainly E-W along profile P01, OBS are marked by red triangles and shots by thick black line.

Fig. 6 Data examples from the hydrophone components of station CD25 of the SARDINIA Experiment: (a) shows an on-profile” example of shots from profile CD arriving at station CD25, colours indicate phase: water wave in yellow, sediment layer in red, basement reflection in light blue, upper crustal refractions in purple, inter-crustal reflection in fuchsia, lower crustal refraction in pink, PmP in orange, and Pn in mint green, the same colours are used to mark the first water multiple of the phases, and (b) shows an off-profile" example of shots from profile EF arriving at station CD25, only two phases are observed Pn (mint green) and PmP (orange) with the first, second, and third water multiples marked in teal.

3.2.2 The AlpArray–LOBSTER experiment

The refracted and reflected arrivals of the shots from profiles P01 and P02 were picked in Pasteup (Fujie et al., 2008) at on and off-profile stations, and the water wave arrivals were used to relocate the stations relative to the profiles. The data quality was generally good (Fig. 7), with 38,242 shots picked (Tab. 2). Shots were recorded at permanent land stations with up to 200 km offset in mainland France. However, some off-profile OBS close to the shot profiles, such as A417A, failed to record any usable reflections or refractions. There is a thick layer (1–2 km) of Messinian evaporites in the central portion of the Liguro-Provençal Basin (Dessa et al., 2020; Dannowski et al., 2020b; Moulin et al., 2015; Jolivet et al., 2006; Contrucci et al., 2001). The thickness and geometry of the evaporite layer is variable and may have caused higher scattering or soft sediments may have caused higher attenuation of the signal around this station. The water wave arrival was recorded which shows that the instrument was working, and as the hydrophone component was compared with the seismometer components, the problem was not with the instruments coupling to the seafloor, but rather with the signal arriving from the seafloor. Although refractions were recorded at some land stations, they provided limited ray coverage and as the steep topography along the shoreline can change the refractions and reflections of seismic waves (Khan et al., 2020) which can complicate phase identification and modelling, for the purposes of this study only the off-shore stations are used.

A three-layer 3D starting model consisting of water, sediment/crust, and upper mantle layers was created based on bathymetry data and the 2D seismic profile published by Dannowski et al. (2020b). A slice through the starting model along profile P01 is shown in Figure 5, the layers were each assigned a constant velocity and checkerboard perturbations were 5% of the velocity in each layer. With so much debate over the nature of the crust, and relative thickness of the sediments or crustal layers it was difficult to determine a suitable interface between sediments and crust and so the simplified solution of a combined layer was used to avoid adding a potentially wrong reflector. As a constant velocity was used, 5 km/s was assigned to the sediment/crust layer as a likely median velocity, and 7 km/s to the upper mantle layer, this does result in a large velocity step between layers, but as this did not noticeably effect the number of rays penetrating into the lower layer this was not seen as an issue. Likewise, a gradient was not necessary for rays to turn in the upper mantle, and so the constant velocities with 5% perturbations were kept as a simplified velocity model. The starting model has a starting RMS of 1.92933 s when the picked travel times are compared with the calculated ray paths through the starting model before any iterative adjustments.

Fig. 7 Data examples from the vertical seismometer components of stations from the AlpArray–LOBSTER Experiment: (a) on-profile station OBS210 recording shots from profile P02, and (b) off-profile station A414A recording shots from profile P01 from the inner corner where profile P01 turns to the south. Phase picks are marked by coloured dashes: yellow marks the direct water wave, red, purple, and pink mark refractions in the sediment and crustal layers, blue for basement reflections, mint green for Pn, and orange for PmP.

3.3 Synthetic tests

To compare the resolution of the actual available data with the theoretical resolution had all stations been functioning or with additional shots and stations, we designed a workflow using synthetic tests. Starting models were made for each area based on previous studies, as described in Sections 3.2.1 and 3.2.2, and then checkerboard perturbations of +/−5% of the velocity were added with cubic checkers in a range of sizes. The picked arrival times were used to determine the station-shot pairs to be used in testing the resolution of the real data. Synthetic tests were created with all planned stations, with extra shot profiles, and in the Gulf of Lion with the addition of stations as well. To reduce the over-estimation of the potential resolution of these setups, the minimum and maximum offsets at which each phase was observed in the basin were used to limit the potential ray paths to those within the observed offset range. The range of observed ray paths is shown in Table 1, and the number of rays used in each test is shown in Table 2.

The 3D traveltime tomography software FMTOMO was used for all tests (Rawlinson et al., 2006). FMTOMO uses a grid based eikonal solver with the main code written in FORTRAN. To initiate, a forward step using the Fast Marching Method (FMM) is first used to trace ray paths and calculate travel time predictions based on the starting model, then in each iteration an inversion step adjusts the model parameters such as the velocity model, interfaces, event locations, or some combination thereof, to match the observed travel times followed by another forward step to recalculate the travel times in the adjusted model (Rawlinson, 2007). In FMTOMO, checkerboard tests were carried out by adding the +/−5% perturbations, using the forward step to calculate travel times through the perturbed model, and then using these travel times as input with the unperturbed starting model to recreate the checkerboard by iteratively repeating the forward and inverse steps described above. After five iterations there was little change in the RMS. The semblance, the similarity between the recovered and input checkerboards, was computed as in Zelt (1998), using Eq. (1):

$$R=\frac{{{\displaystyle \sum }}_{j=1}^M{\left(D_{i_j}+D_{r_j}\right)}^2}{2{{\displaystyle \sum }}_{j=1}^M\left(D_{i_j}^2+D_{r_j}^2\right)}$$(1)

where D_ij is the input value at the jth node and D_rj is the recovered value at the same node. The resolvability, R, at each point in the model is calculated using a circular operator of M nodes, where the number of nodes depends on the grid spacing and radius of the operator. In this study, we tested a range of operator radii and a 5 km operator was chosen as a suitable compromise between providing smoothing while still showing local variations in resolvability.

For a more robust measurement, and to reduce the effect of the checker orientation on the resulting resolution, the input checkerboard was rotated by 45 degrees from 0 to 180 degrees, resulting in five different input models, and the average resolvability was calculated for each checker size. Resolvability contours between 0.6 and 0.8 were compared by plotting these contours over checkerboard tests and, as in Zelt (1998), it was found that areas with resolvability of 0.7 or higher were well resolved in all tests, while areas with resolvability below 0.7 were generally poorly recovered. This can be seen in Figures 8a and b, which show the 0.7 contour in green plotted on depth slices of the recovered 12 km checkerboard, unrotated and rotated 45⁰ respectively, at 9 km depth using the observed rays, the green 0.7 contour outlines the areas where the checkers are recovered. This figure also shows the effect of the checker orientation on the ray paths and resolution, which underlines the importance of taking the average of variously oriented starting models to gain a more robust representation of the resolution. The resolution was then estimated by linear interpolation at each node of the checker size versus the average semblance of all the rotated grids of that checker size to find the minimum resolvable checker size at each node. In other words, linear interpolation was used to find the minimum grid size at which a semblance of 0.7 was reached. This provides a clear map of the anomaly size that can be resolved in each area with the real data, or the scale that can potentially be resolved by a given geometry.

The SARDINIA Experiment in the Gulf of Lion uses a classic geometry for 2D seismic experiments. To test its potential for 3D tomography, and how this geometry could be made more suitable for 3D tomography we conducted four synthetic tests using:

1. The actual stations (green triangles in Fig. 9a) and observed rays.

2. The actual stations, (green triangles in Fig. 9a) but with rays estimated from the minimum and maximum offsets seen for each phase.

3. All planned stations (green and grey in Fig. 9a) with an additional shot profile (red line in Fig. 9a).

4. All planned stations (green and grey in Fig. 9a) with the addition of extra stations (red triangles in Fig. 9a).

The geometry used in the AlpArray–LOBSTER Experiment is typical of a passive seismic network with 2D seismic profiles, but this design could be improved for use in 3D tomography. In this case we tested the resolution provided by:

1. The actual stations (green triangles in Fig. 9b) and observed rays.

2. The estimated rays had all stations (green and orange in Fig. 9b) been functional and recording the entire time.

3. The addition of shot profiles in a grid through the basin (red lines in Fig. 9b) and all planned stations (green and orange triangles in Fig. 9b).

Fig. 8 Depth slice at 9 km depth of the recovered checkerboard using only observed rays and 12 km checkers rotated 45 degrees, the green contour marks the 0.7 resolvability contour. Stations are marked by red stars and shots by black lines.

Fig. 9 The study area for synthetic tests based on (a) the SARDINIA Experiment: triangles mark the real stations used (green), stations that malfunctioned (grey), and theoretical additional stations (red), black lines mark the airgun shot profiles, and a red line marks the theoretical additional shot profile, and (b) the AlpArray–LOBSTER Experiment: stations that recorded usable shots are marked by green triangles, and stations that were planned but did not record usable data or were collected before the shot profiles were complete are shown in orange, yellow lines denote the real shot profiles and red lines mark the suggested ideal shot profiles.

4 Results

4.1 The SARDINIA Experiment

The classical geometry of the SARDINIA Experiment, with two parallel profiles and one cross-cutting profile, showed that in this setting the two profiles were slightly too far apart (∼50 km) to provide well-constrained 3D resolution of the sediment and crustal layers without additional data. The actual observed rays (Fig. 10a) provided the lowest resolution with some well-resolved areas near profile AB, almost exclusively along the parallel profiles CD and EF and a small area of moderate resolution (15–30 km) in the southwestern area (3.8–4.2 deg E and 41.4–41.6 deg N) near the basement high. There is very little resolution in the outer corners along profile AB, north of profile CD or south of EF (Fig. 10a) and very poor resolution in between the two parallel profiles.

In addition, a W-E cross-cut of a checkerboard test using the observed rays shows that the ray coverage along this cross-cut is shaped in a semi-circle between the two parallel shot lines CD and EF (Fig. 11). Between profiles CD and EF a gap in the ray coverage is observed until a depth of almost 12 km. Along this cross-cut, the change in velocity is higher in the upper 5 km compared to the deeper parts.

All variations of the synthetic tests (Fig. 10b-d) show that the resolved area has high resolution along the profiles and between the parallel profiles CD and EF with lower resolution in the outer corners along profile AB, north of profile CD or south of EF. This is a much larger area of resolution compared with the observed rays (Fig. 10a) which were mainly resolved along the profiles.

The maximum ray range test shows an area of about 40 km² between profiles CD and EF close to the intersection with profile AB with resolution of 5 km or better (Fig. 10b). To the northeast and southwest the resolution is lower (5–15 km), for the area between stations on profiles CD and EF. The synthetic test with additional stations and the test with additional shots (Fig. 10c and d, respectively) show very similar results with a well resolved area of 8 km or better resolution between profiles CD and EF between latitudes 4 and 5.8 degrees. To the northwest and southeast of the parallel profiles there is some resolution (>10 km) along profile AB (Fig. 10c,d).

Fig. 10 The interpolated horizontal resolution at 12 km depth provided by (a) the observed rays, (b) the estimated rays using the minimum and maximum observed offsets for each phase, (c) an additional line of stations between profiles CD and EF, and (d) an additional shot profile between profiles CD and EF.

Fig. 11 Example W-E crosscut along Latitude 41.85 degrees, of the checkerboard test of the observed station-shot pairs from the SARDINIA Experiment using 12 km checkers rotated 45 degrees. The profiles are labelled where they cross this latitude, green triangles mark station locations projected onto this latitude.

4.2 The AlpArray–LOBSTER experiment

The network-setup of the AlpArray–LOBSTER experiment allows us to explore the potential of passive seismic networks for active seismic 3D tomography (Fig. 12). The results of the observed rays of the AlpArray–LOBSTER Experiment (Fig. 12a,d) show that there is only resolution along the profiles, and only at shallow depths. The resolution added by the off-profile stations was negligible, except for those very close (<6 km) to the shot lines. The synthetic test using maximum rays (Fig. 12b,e) produced a much larger area of 5–15 km resolution from around 42.0N to 43.0N degrees latitude and 5.0E to 8.5E degrees longitude. In this setup, the network stations generally contribute more to the resolution compared to the observed rays, but contribution from specifically the northern network stations (above 43.25N degrees latitude) and southern stations (at 41.8N degrees south) is limited, and the area of resolution is mainly within the shot lines. Similar to the observed rays, there is very little resolution at depth. The results of the synthetic test that adds a grid of shot lines vastly improves the resolution (Fig. 12c,f). The entire network area from 41.5N to 43.7N degrees latitude and 4.75E to 8.8E degrees longitude has a resolution <10 km. The resolution at depth is also improved, especially in the northern section, above 42.5N degrees latitude.

The synthetic case that estimates the rays had all stations been recording throughout the experiment shows a potential 10–20 km resolution in the middle section of the basin. This is still an optimistic estimation of the resolution as it takes the best case scenario, recording all rays within the maximum offset range shown in Table 1, and in the real case we have seen that some stations recorded a much more limited range. It can also be seen in Figure 12b and e that the off-profile stations do not significantly improve the resolution, the areas with reasonable resolution are generally in the corners between the shot profiles, such as between P01 and P02 or where P01 turns to the south providing shots from another angle. It can be seen in Figure 12 that off-profile stations alone and are not adequate for converting a 2D survey to a 3D survey without additional shots.

Fig. 12 The interpolated horizontal resolution at 10 km (a-c) and 17 km (d-f) depth provided by (a,d) the observed rays, (b,e) the maximum rays (see Tab. 1) had all stations been functional and recording during the entire experiment, and (c,f) all stations with the addition of a grid of shot profiles through the basin.

5 Discussion

5.1 Model resolution

Our results show that the parallel shot profiles of the SARDINIA Experiment alone (Fig. 10a) are not sufficient for 3D tomography in the Ligurian Basin, only the areas along the shot lines are well resolved. Likewise, the resolution provided by the observed rays in the AlpArray–LOBSTER Experiment (Fig. 12a,d) is too low to resolve crustal scale anomalies (<10 km) in 3D tomography anywhere except along the two seismic profiles. Comparing the shots that were actually recorded with the maximum number of shots that theoretically could have been recorded, shows that in both experiments a lower number of shots were recorded than anticipated. In the case of the AlpArray–LOBSTER Experiment, this difference is in part due to the maximum ray test assuming that all stations had been recording during the shooting of both profiles, while in reality many stations were collected before the second profile was shot. However, in the case of the SARDINIA Experiment, the same stations and shot lines were used in the observed and maximum ray tests, demonstrating that the method of estimating the ray coverage from the maximum offsets overestimates the actual coverage. This estimate is still closer to reality than using all shot-station pairs would be, but the results are skewed by the clearest arrivals, which in a structurally heterogeneous area such as the Liguro-Provençal Basin, is not negligible. In this case, using the median of each stations maximum range, or even the shortest maximum range of all stations could have been used to provide a more conservative estimate.

This variation in maximum recorded offsets between stations is in part due to the variable signal to noise ratio of the Liguro-Provençal Basin, which can be explained by the local geologic setting as heterogeneities in the sediment layer can cause increased scattering and attenuation in some areas compared with others. The Liguro-Provençal Basin hosts a thick sediment layer (6–8 km (Schettino and Turco, 2006; Moulin et al., 2015; Dannowski et al., 2020b)), which includes a variably thick layer of Messinian evaporites that in some places has formed salt diapirs (Bache et al., 2009; Jolivet et al., 2006; Schultz-Ela et al., 1993; Bellucci et al., 2024) resulting in a highly heterogeneous sediment layer. Such sedimentary heterogeneities likely caused increased scattering and higher attenuation of the seismic signal in some areas (Alaei, 2012) resulting in a low signal to noise ratio in those areas and limiting the recorded phases, as observed in these two experiments (Dannowski et al., 2020b; Moulin et al., 2015; Contrucci et al., 2001). Some areas, such as stations closer to the shore, might also have higher noise levels due to wave action or higher ship traffic. This means that while one station may be able to record longer offsets, another may be in an area with a much lower signal-to-noise ratio that causes only the closest shots to be recorded clearly, thus using the maximum offset of the first station would overestimate the coverage at the second station, for example in the case of AlpArray–LOBSTER station A417A which recorded only the water wave arrival despite other stations at similar offsets recording more phases.

One way to mitigate scattering and attenuation of the seismic signal, would be with denser sampling by decreasing the spacing of stations and shot profiles. Such changes in the experimental setup are required to constrain small (<10 km) scale anomalies such as areas with large salt diapirs in the sediment layer, and to avoid smearing such anomalies into deeper layers. Both experiments discussed in this paper would have ideally required a denser network and more shot lines to provide a high enough density of crossing rays to constrain a 3D tomographic model in this area. The reduced signal range in this geologic setting means that the network must be denser to produce the same sampling of the subsurface that can be achieved with fewer stations in an area with a higher signal to noise ratio where shots could be recorded at a longer offset at all stations. This means that in both research areas investigated, additional shots, and a denser network in the case of the AlpArray-LOBSTER Experiment, would be needed to resolve the geology of the subsurface to an adequate level of resolution (<10 km).

The addition of stations and shots generally improves the resolution because and the number of rays recorded will increase, however, not all rays are equal and the addition of crossing rays or rays in otherwise poorly constrained areas enhance the model resolution more than additional parallel rays would (Zelt, 1998). In the case of the SARDINIA Experiment, the addition of another shot profile or line of stations between profiles CD and EF provides a similar area of resolution, but the addition of the line of shots provides slightly higher resolution for the station and shot spacing tested (see the 0.7 resolvability contours from tests with the SARDINIA Experiment Fig. 13). As an additional shot profile is much cheaper and logistically easier to add (Vermeer, 2012; Hovland, 2016), the SARDINIA Experiment would have benefited greatly by an additional shot line between profiles CD and EF. Adding stations or shot profiles would increase the resolution because they not only add rays, but by adding sources or receivers between the profiles, the new profile spacing would be about 25 km. This distance is well within the range of the stations, and so the stations would be able to record not only the nearest shots, but a wide swath of the profile, thereby adding more crossing rays which would better constrain the model.

On the 0.7 resolvability contour (Fig. 13) the resolved area appears to increase with checker size until 20 km below which the 30 km checker resolution appears to decrease. This decrease in resolution is related to the vertical dimensions of the checkers: 9 km is near the vertical edge of the 30 km checkers where the velocity perturbation is weak, and so the results appear to show lower resolution. Checkers that change in both width and height are in principle desirable, because they allow some information on vertical resolution to be included in the analysis and they better reflect the mixture of velocity anomalies encountered. However, the difference in checkerboards makes it difficult to find a depth at which all checker sizes are at a comparable anomaly strength. The depth of 9 km was chosen as at this depth there is representative ray coverage in all tests, and the 6 km, 12 km, and 20 km checkers are at comparable strengths. However, the 30 km checkers are near the minimum anomaly strength at the edge of a checker, and so these results are less directly comparable.

Although larger maximum offsets were observed in the AlpArray data, Table 1, these were mainly due to a few very clear recordings near Corsica. The typical signal range was longer and clearer on the data from the SARDINIA Experiment and the median offsets were larger for most phases. As the OBS used were similar in both experiments this difference in signal range may be due to local differences in the signal to noise ratio or to the airgun arrays used, the SARDINIA Experiment used an airgun array with a larger volume. The lower signal range was an issue in the AlpArray–LOBSTER Experiment as most off-profile stations were too far from the shot profiles to record many shots and so contributed little to the resolution for 3D tomography (Figs. 10a and 12a). This is especially evident in the resolution of the AlpArray–LOBSTER Experiment around station A414A, situated in the inside corner of profile P01. Despite being surrounded by shots there is only a small area of low resolution next to the station to the northwest, followed by a gap, and then the better resolved (∼10 km) area in the corner of P01. The resolved area in the corner of P01 is comparable or even slightly smaller in area than the area resolved in the inner corners of the SARDINIA Experiment where profile AB crosses CD and EF, showing that the station A414A does not contribute much to the resolution. Although station A414A recorded shots from profile P01 both before and after its turn, these rays are unconstrained by crossing rays, and unfortunately the station did not record shots all the way into the corner where they would have constrained crossing rays from the turned profile. Ultimately, without additional station-shot combinations these unconstrained rays added little to the resolution, and the station would likely have been more effective if it were closer to the corner so as to record shots across those running from the turned profile to the stations on profile P01.

In the AlpArray data the off-profile stations recorded mainly mantle (Pn, PmP) phases and few sediment or crustal phases. This meant that in both experiments the upper 10 km or so were only constrained along the profiles where the station spacing was denser, and could not be resolved between the profiles or between off-profile stations. The resolution of the SARDINIA Experiment based on the actual observed rays is consistently higher in the southwest around the basement high than the thicker sediment layer to the northeast (Fig. 13). The very low levels of resolution between the off-profile stations and shot lines compared with the resolution along the shot lines where all phases were observed show a similar trend (Fig. 12a and b). From this experiment, off-profile stations are not recommended as the area between the station and profile will not be well-constrained without additional crossing rays, which could be provided by a shot line across the station. To achieve consistently high resolution throughout the model, the spacing of the stations and shots would need to be adjusted so that each station records at least some rays of all phases, thereby sampling all layers. Ideally each station should be within a few kilometres of crossing profiles so that the profiles can be used to relocate the station in latitude and longitude. The addition of shot profiles to the AlpArray–LOBSTER network (Fig. 12c and f) could potentially have reached 10 km resolution throughout the network, limited by the station spacing which varied in the range of 34 to 57 km. A more uniform distribution is therefore recommended, such as a grid of stations and shot lines, which is already becoming standard for 3D tomography.

Fig. 13 A comparison of the 0.7 resolvability contour at 9 km depth of the actual observed rays, the maximum ray coverage, and this geometry with the addition of a line of stations or shots between profiles CD and EF, calculated from the average semblance of the five starting grids for checker sizes (a) 6 km, (b) 12 km, and (c) 20 km. SARDINIA Experiment Phases

5.2 Comparison with previous studies

The synthetic tests based on the SARDINIA Experiment agree with what is expected from comparison with the 2005 Outer Rise Network. This is an experiment consisting of a network of 10 OBS (3-component seismometer and hydrophone) and 11 OBH (ocean bottom hydrophone) with 15–25 km station spacing conducted offshore Nicaragua (Lefeldt et al., 2012; Lefeldt et al., 2009). Similar to the SARDINIA Experiment, three airgun profiles were shot with two parallel profiles about 50 km apart and one crossing profile near the center 573 of the two parallel lines. The main differences between the experiments was that the Outer Rise Network included stations between the two parallel profiles, and used local and regional earthquakes in addition to shots. The success of the Outer Rise Network supports our synthetic results: the addition of stations between the parallel profiles of the SARDINIA Experiment would likely have made 3D tomography possible. The AlpArray–LOBSTER Experiment also used a passive network with airgun profiles through the network. There are however two main differences between the AlpArray-LOBSTER and Outer Rise Network experiments. The station spacing of the Outer Rise Network stations were 15–25 km apart whereas the AlpArray–LOBSTER stations were 34–57 km apart forming a less dense network. Also all off-profile stations of the Outer Rise Network were between the two parallel shot profiles thereby recording shots from two sides, whereas the off-profile stations of the AlpArray-Lobster Experiment are located outside the profiles, recording shots from just one side.

The 2008 GROSMarin Experiment deployed 21 OBS, each consisting of a 3-component geophone and a hydrophone, in a 37.5 by 50 km grid with 12.5 km station spacing as well 13 temporary land stations up to 30 km from the coast to achieve a matching density of stations on land (Dessa et al., 2011). Similar to the AlpArray–LOBSTER and Outer Rise networks, the GROSMarin Experiment recorded passive seismicity for almost six months in addition to the active shot profiles, however, only the active shots were used in the 3D tomography. Shot profiles crossed all stations and continued almost the same distance to each side of the OBS grid with continuous shots while turning for the next shot profile. The resulting coverage within the offshore grid achieved a resolution of 5–10 km above 5 km depth and 10–20 km deeper in the model based on checkerboard tests. Grids provide more uniform coverage, and when the station spacing is dense there is some built in redundancy meaning that a model can still be achieved even if some stations fail. In the GROSMarin Experiment 4 of the 21 OBS were lost, however, the dense grid meant that 3D tomography was still possible. Comparing this setup to the SARDINIA Experiment, this would be roughly equivalent to adding three shot profiles, with on-profile stations, between profiles CD and EF, which would likely have resulted in a similar resolution to that achieved in the GROSMarin Experiment.

Dunn et al. (2000) also favoured a grid-type geometry with two lines of 4 OBS with 5 km spacing about 40 km apart with a smaller grid of 7 OBS organized into three lines consisting of 2 OBS about 12 km apart, 3 OBS about 5 km apart and another line of 2 OBS about 12 km apart, all arranged symmetrically around the axis of the East Pacific Rise (Dunn et al., 2000). Airgun shot profiles were shot over the two outer lines of OBS and throughout the central grid of OBS. This geometry was able to resolve 3 km checkers above about 2 km depth and 4–5 km checkers at deeper depths within the entire area between the outer shot profiles, with higher resolution in the inner square of denser station and shot spacing. The ARAD Experiment also explored the East Pacific Rise just south of (Dunn et al., 2000), but with a network of 18 Ocean Bottom Hydrophones (OBH) and one OBS with variable spacing covered by a dense grid of 201 shot profiles covering a rectangular area of 20 by 23 km with 100m spacing between shot lines (Tong et al., 2003). This provided lateral resolution of 2.5–5 km between the surface and 1.2 km depth, with the resolution becoming poorer with depth. In both cases, the geologic setting is complex, but does not include the thick Messinian evaporite layer that complicates tomography in the Liguro-Provençal Basin, and both experiments use a much denser station and shot spacing with all stations within the shot network.

A study of the oceanic core complexes of the Mid-Atlantic Ridge around 13⁰ N was conducted using 3D tomography. A recent experiment focused on a 60 by 60 km area with a grid of 17 shot profiles (8 running N-S, 9 running E-W), over a dense network of 46 OBS, mainly deployed at the crossing points of the profiles with 6 OBS in a line between profiles to increase density over the main area of interest (Simão et al., 2020; Peirce et al., 2022). The resolution of the P-wave tomography was assessed using the method of Zelt 1998, also used in this paper. This grid was able to reach 2 km resolution in the area of dense OBS coverage, and 3 km resolution in the whole grid above 6 km depth. In the 6–7 km range a resolution of about 5 km was reached and below 7 km depth the resolution dropped to 10 km (Simão et al., 2020).

Although these are examples of different station-shot geometries, all these experiments involve shot profiles 631 over most of the stations, and in general the stations that are not crossed by profiles are between profiles so that they record shots from two sides to better constrain these stations. From comparison between these experiments and the synthetic tests presented in this paper, it appears that in both the SARDINIA and AlpArray–LOBSTER Experiments a denser network is recommended, and off-profile stations are not recommended, unless surrounded by shot profiles. 2D data sets may still hold potential for data mining, however, their applicability to 3D tomography depends on the density of the 2D shot lines and whether stations recorded continuously throughout the experiment. A more suitable application of 2D profiles may be as additional rays in local to regional scale earthquake tomography or later active experiments. In both cases this may require substantial down-sampling or weighting so as not to overpower the rays from natural sources.

5.3 Implications for the ligurian sea

The main benefit of 3D tomography over 2D tomography is the more holistic 3D view of the subsurface which takes into account out-of-plane wave propagation due to local heterogeneities which can cause errors in 2D models (Górszczyk et al., 2024). The natural trade-off of 3D experiments is that to obtain a similar level of resolution across a 3D area instead of a 2D line requires more stations and more ship time which can both be limiting factors. However, in highly heterogeneous areas such as the Ligurian Sea, the cost could be worthwhile to produce higher resolution volume information to fully understand the complex geology especially around the transition zones, even if only in a smaller area. An experiment with similar station spacing in all directions would by necessity not cover the same distance as a 2D line, but if well placed on an area of interest this could be a better way to examine the Ligurian Sea in more detail. The SARDINIA Experiment provided almost 900 km of linear data, however, it would have been interesting to relocate the OBS from the two extremities of the longest profile, AB, into a grid between the parallel profiles CD and EF, to provide a more detailed study of the crust at the continental-oceanic transition. This would have covered a smaller area, but an interesting area would be covered in more detail with the same number of instruments. Both the studies examined here would have benefited from additional shots, which are cheaper and easier to add than stations (Vermeer, 2012; Morgan et al., 2013). The Ligurian Sea still warrants exploration, especially as the debate on the nature of the crust in some areas of the Basin has not yet been settled (Contrucci et al., 2001; Dessa et al., 2011; Dannowski et al., 2020b; Boschetti et al., 2023), however, going forward it would be interesting to see experiments designed specifically for 3D tomography, and ideally with special attention paid to using a high number of shots and ensuring that shot lines cross each station, such as the grid used in the GROSMarin Experiment (Dessa et al., 2011). Ideally however, such an experiment could be coupled with streamer data to constrain the shallow sediment layers at least along the shot lines.

6 Conclusion

Offshore wide-angle seismic experiments provide a valuable window into the subsurface, however, collecting the data is difficult, time consuming, and expensive, and so data sets should be designed from the start to provide both the dense linear information of 2D tomography, and the volumetric information of 3D tomography. Care should be taken when designing an experiment to ensure that the target will be within the resolution power of the experimental design. The workflow developed in this study consists of the following steps that can be helpful in the planning stage: (1) creating a starting model using wide-angle refraction seismic data, (2) choosing a suitable set of station-shot ray paths based on a priori geological knowledge of the area, (3) running a series of synthetic tests with rotated checkerboards of the starting model, and (4) interpolating the lateral resolution as in Zelt (1998). This workflow is easy to apply, and limiting the expected phase range based on previous studies can help avoid over-estimating the ray coverage which is a common pitfall during the planning stage. It is important to take these steps to ensure that the goal of the experiment is within the resolution power of the chosen geometry. Likewise, this workflow can be applied after data collection to test that any anomalies in the resulting tomographic model are indeed within the resolution power of the experiment.

This workflow was applied to two offshore seismic experiments, the SARDINIA and AlpArray–LOBSTER Experiments in the Ligurian Sea. We found that in both cases the station-shot geometry provided too low resolution to be suitable for crustal scale 3D tomography, but could have been made more suitable by the addition of shot lines, or, by decreasing the station spacing. From the evaluation of these synthetic tests and comparison with similar experiments some general considerations emerged. 3D tomography of the Earth’s subsurface heavily depends on the ray coverage and especially the number of crossing rays. With this in mind, offshore networks should be designed so that stations are close enough to shot profiles that a wide swath of the profile can be recorded. As this distance depends on the local signal to noise ratio, which depends on the local geology of the area, the optimal station spacing should be determined for each experiment based on a priori knowledge. In general, off-profile stations are not recommended as the velocity of the area around the station is not well-constrained without additional crossing rays, and so a more uniform distribution such as a grid of stations and shot lines is recommended both for 2D and 3D tomography. While many 2D experiments are not sufficient for 3D tomography alone, they could be useful additions to later experiments or passive earthquake tomography.

Open research section

Data from off-profile stations in the AlpArray–LOBSTER Experiment are available through the AlpArray Seismic Network (2015), AlpArray Seismic Network (AASN) temporary component, AlpArray Working Group. https://doi.org/10.12686/alparray/z32015.

Data from profile P02 can be accessed through the German marine data archive PANGAEA from a previous publication here: https://doi.org/10.1594/PANGAEA.910561 (Dannowski et al., 2020a).

Data from profile P01 will soon be added to PANGEA in a new publication.

All data from the SARDINIA Experiment in the Gulf of Lion sections has already been published and can be accessed through Moulin et al., 2015.

Acknowledgements

This contribution is part of the German priority program “Mountain Building Processes in Four Dimensions (MB-4D)" SPP 2017 and of the international research initiative AlpArray supported by the Deutsche Forschungsgemeinschaft (grant no. LA 2970/3-1). HK was supported by ERC-SynGrant T-SECTOR-101071713. Many thanks to Prof. Rawlinson for technical help in using FMTOMO, and to Bruce Thomas and Séverine Furst for translating our abstract and title into French.

References

All Tables

All Figures

Fig. 1 Bathymetry of the Liguro-Provençal Basin with the shot and station locations of the AlpArray–LOBSTER Experiment, including stations along the two shot profiles (yellow lines and green triangles respectively), and the SARDINIA Experiment (red lines and orange triangles respectively). The Alpine front and Ionian-Apulian subduction zone (S. Z.) are marked by red and black subduction lines respectively, and the Corsica-Sardinia block is labelled with Co on Corsica and Sa on Sardinia.

In the text

	Fig. 2 Locations of the seismic stations of the 2006 SARDINIA Experiment: triangles mark the stations used in this study (green), planned stations that malfunctioned but are used in some synthetic tests (orange), and stations from the SARDINIA Experiment that were outside of this study (black). Black lines mark the shot profiles.
In the text

	Fig. 3 Map outlining the AlpArray–LOBSTER Experiment. Airgun shots are indicated in red for profile P01, and grey for profile P02. Triangles show land stations (blue), Ocean Bottom Seismometers (OBS) that recorded both profiles (green), OBS that recorded only profile P01 (yellow), the on-profile OBS (cyan), OBS that recorded passive data but no shots (orange), and OBS that were lost (black).
In the text

	Fig. 4 Slice of the starting model used for resolution tests of the SARDINIA Experiment. The slice runs SW-NE along profile CD, OBS are marked by red triangles and shots by thick black line.
In the text

	Fig. 5 Slice of the starting model used for resolution tests of the AlpArray–LOBSTER Experiment. The slice runs mainly E-W along profile P01, OBS are marked by red triangles and shots by thick black line.
In the text

Fig. 6 Data examples from the hydrophone components of station CD25 of the SARDINIA Experiment: (a) shows an on-profile” example of shots from profile CD arriving at station CD25, colours indicate phase: water wave in yellow, sediment layer in red, basement reflection in light blue, upper crustal refractions in purple, inter-crustal reflection in fuchsia, lower crustal refraction in pink, PmP in orange, and Pn in mint green, the same colours are used to mark the first water multiple of the phases, and (b) shows an off-profile" example of shots from profile EF arriving at station CD25, only two phases are observed Pn (mint green) and PmP (orange) with the first, second, and third water multiples marked in teal.

In the text

Fig. 7 Data examples from the vertical seismometer components of stations from the AlpArray–LOBSTER Experiment: (a) on-profile station OBS210 recording shots from profile P02, and (b) off-profile station A414A recording shots from profile P01 from the inner corner where profile P01 turns to the south. Phase picks are marked by coloured dashes: yellow marks the direct water wave, red, purple, and pink mark refractions in the sediment and crustal layers, blue for basement reflections, mint green for Pn, and orange for PmP.

In the text

	Fig. 8 Depth slice at 9 km depth of the recovered checkerboard using only observed rays and 12 km checkers rotated 45 degrees, the green contour marks the 0.7 resolvability contour. Stations are marked by red stars and shots by black lines.
In the text

Fig. 9 The study area for synthetic tests based on (a) the SARDINIA Experiment: triangles mark the real stations used (green), stations that malfunctioned (grey), and theoretical additional stations (red), black lines mark the airgun shot profiles, and a red line marks the theoretical additional shot profile, and (b) the AlpArray–LOBSTER Experiment: stations that recorded usable shots are marked by green triangles, and stations that were planned but did not record usable data or were collected before the shot profiles were complete are shown in orange, yellow lines denote the real shot profiles and red lines mark the suggested ideal shot profiles.

In the text

	Fig. 10 The interpolated horizontal resolution at 12 km depth provided by (a) the observed rays, (b) the estimated rays using the minimum and maximum observed offsets for each phase, (c) an additional line of stations between profiles CD and EF, and (d) an additional shot profile between profiles CD and EF.
In the text

	Fig. 11 Example W-E crosscut along Latitude 41.85 degrees, of the checkerboard test of the observed station-shot pairs from the SARDINIA Experiment using 12 km checkers rotated 45 degrees. The profiles are labelled where they cross this latitude, green triangles mark station locations projected onto this latitude.
In the text

	Fig. 12 The interpolated horizontal resolution at 10 km (a-c) and 17 km (d-f) depth provided by (a,d) the observed rays, (b,e) the maximum rays (see Tab. 1) had all stations been functional and recording during the entire experiment, and (c,f) all stations with the addition of a grid of shot profiles through the basin.
In the text

	Fig. 13 A comparison of the 0.7 resolvability contour at 9 km depth of the actual observed rays, the maximum ray coverage, and this geometry with the addition of a line of stations or shots between profiles CD and EF, calculated from the average semblance of the five starting grids for checker sizes (a) 6 km, (b) 12 km, and (c) 20 km. SARDINIA Experiment Phases
In the text