Ground penetrating radar investigation and georeferencing without global satellite navigation systems: The case history of the amphitheatre of Lecce, Italy

In this work, we present a case history relative to ground penetrating radar measurements performed close to the Roman amphitheatre of Lecce, Italy. We have performed a classical data elaboration with focusing of the data and slicing putting into evidence hidden details of the structure of the monument. It will be shown that the interpretation of the ground penetrating radar data is meaningfully helped by the consultation of ancient documents, which makes the final result multidisciplinary. Finally, we have georeferenced the data matching the shape of the depth slices with the shape of the investigated roads. In fact, we did not have at disposal any differential global satellite navigation systems. Indeed, this can be a method exploitable in cases when satellite data are not available, either because the area is shadowed or because the user does not have a differential global satellite navigation system. The proposed geographical matching is achieved by means of the matching between the shape of the slices and those of the physical obstacles present in the field. Therefore, it is essentially based on a continuous of points, and so it is probably more precise than a method based on the only vertexes. In particular, the proposed procedure does not require any deformation of the shape of the slice.


INTRODUCTION
Investigation of monuments is a classical topic in geophysics. The results, in fact, can reveal hidden parts of the historical structures and can pre-advice about possible stability problems for the monument, that possibly involve safety issues for people. In particular, these investigations have allowed to identify graves Utsi & Colls, 2017), to characterize voids (Persico et al., 2014 or walled features (Gabellone et al., 2013;Geraldi et al., 2016), to highlight structural problems (Francisco et al., 2021) and so on. Thanks to the depth slices (Goodoman & Piro, 2013), maps This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. of an underground (or intra-wall) scenario, possibly at different depths, can be achieved. This has provided in some cases also the map of a previous building under the current one, making us appreciate how an original structure might have been enlarged or (more rarely but possibly) restricted or just reshaped over the centuries (Casas et al., 2018;Gabellone et al., 2013;Matera et al., 2016).
In July 2021, a ground penetrating radar (GPR) measurement campaign in two streets close to the Roman amphitheatre of Lecce, Italy, was performed. This monument is partially buried, because its memory had been lost and it was casually discovered due to building works performed F I G U R E 1 Left hand panel: geographical location of the monument. Right hand panel: the amphitheatre of Lecce. The two red lines roughly indicate the positions of two walls that limit the accessible parts of the ambulacrum (Source: Google).
at the beginning of the 20th century. In the meantime, buildings of subsequent periods (dating back up to the 15th century) had been constructed in this area, and they could not be demolished to bring to light the whole remains of the amphitheatre, being in their turn historical monuments. In Figure 1, we show a Google Earth image of the amphitheatre. It is relevant to outline that, under the visible steps of the amphitheatre, there is a corridor, originally running all around the arena. Such a corridor, common in all Roman amphitheatres, was called in Latin ambulacrum. Indeed, more concentric elliptical ambulacra were possible too and maybe this was the case also for this amphitheatre. However, only one is currently visible. Moreover, its circuit is interrupted and walled in two points, roughly represented by the two red lines in Figure 1. The amphitheatre had been investigated also in previous multidisciplinary measurement campaigns , and the conclusions retrieved was that quite probably there is a further part of the ambulacrum accessible beyond the walled termination, at least beyond the upper red line in Figure 1. We deem that this alleged further piece of ambulacrum is about 15 m long. However, it is not known whether the circuit of the ambulacrum is still nowadays complete or if the not accessible part has partially or totally collapsed in the past. It might have been also voluntarily filled up, completely or partially: We just don't know. Indeed, the hypothesis of a physical interruption of the original path is the most probable one, but it is not proved. It is also not known whether cavities corresponding to further external ambulacra (or more probably to part of them) may still exist.
Moreover, there is a point under the accessible part of the ambulacrum where a high degree of humidity is evident along the lateral walls, and this might pose a problem in the long period regarding the stability of the structure. In particular, currently (September 2022) it prevents the possibility to open to the large public this part of the ambulacrum.
In this paper, a GPR investigation on two pieces of the street adjacent to the amphitheatre will be presented.
As we had not at disposal a differential global satellite navigation system (GNSS), we have performed the georeferencing thanks to the shape of the depth slices (in a sense that will be better specified in the following) that have been matched with the shape of the footpath. This is equivalent to make use of a 'continuous' line of ground control points (Hackeloeer et al., 2014) instead of some isolated point chosen in the field. Moreover, the nominal size of the slices, as measured in the field, is preserved. In this way, a good precision can be reached, and in particular, no deformation of the image is needed in order to reconcile data conflicts. Indeed, the same adherence of the data to the bound of the footpath is an index of the precision (or not) of the relative positioning of the measurements as gathered in the field. It is worth mentioning that the same precision of the Google Earth map, commonly exploited for the georeferencing, might reach the order of 1 m or more (Wang & Wang, 2019). So, even if GNSS measurements were available, they might be more precise than the same Google Earth map, and this could generate some discrepancy in the local positioning, which cannot happen with the adopted method.
In the next section, some historical notes on the area of the amphitheatre of Lecce will be provided. Then, the GPR prospecting and data processing will be exposed. It is worth noting that historical maps of the area will help the interpretation of the results worked out from the GPR data. Subsequently, a specific section is devoted to the georeferencing procedure. Conclusions will follow.

THE ROMAN AMPHITHEATRE OF LECCE AND ITS SURROUNDINGS
The remains of the amphitheatre of the Roman city of Lupiae (nowadays Lecce) are located in the central St. Oronzo square (piazza Sant'Oronzo), up to the depth of 8 m under the current planking level. About one third of the ancient building has been completely uncovered during the last century, including the part of the arena and the cavea, whereas the remaining structures lay buried under the square and the surrounding buildings.
From the bas reliefs, we know that the amphitheatre hosted entertainments like venationes (hunts) and munera gladiatoria (gladiatorial games). Probably, it was constructed during the Augustan age (27 B.C.-14 A.C.) and restored and embellished during the reign of the Emperor Hadrian (117-138 A.C.). The elliptical building, measuring about 102 × 82 m, could host between 12,000 and 14,000 spectators. In particular, the cavea was higher than what it currently is, and there were of course more steps than those nowadays remained. The structure is partly excavated in the limestone, fully exploiting the mass of Lecce stone beneath to support the stepped seating, thus creating the arena, the lower ambulatory (ambulacrum) and the radial tunnels. The so-obtained carved stone blocks were used for the construction of load-bearing element like pillars, connected by opus reticulatum walls, made of small pyramid shaped stones (cubilia) embedded in a concrete core.
The structure's plan was subdivided into four sectors, marked by the four entrances that corresponded to the extreme points of the two main axes. A modular system of passages (vomitoria) and connecting stairs leads to the various sectors of the cavea (Amici, 1997(Amici, , 1999. The collapse of the Western Roman Empire led, among other things, to the end of the arena games and the consequent defunctionalization of the building, in a generalized process of de-urbanization. The historian Guidone describes the early medieval Lecce as a small city (parvum municipium) clustered around the theatrum, maybe referring to the area of the amphitheatre (Arthur, 2000). We have no other useful information to figure out the aspect of the area during the early Middle Ages, but it is possible to assume that the lack of maintenance and the spoliations of the decorative and structural elements led to the obliteration of the remaining parts of the building. Between the last part of the 14th century and the first half of the 15th century, new buildings rose up, reshaping the aspect of the so-called Piazza dei Mercadanti (Merchants Square, lately renamed with the current name piazza Sant'Oronzo), which remained almost unchanged until the beginning of the 20th century (Cazzato et al., 1984). In most cases, the late medieval and early modern buildings used the mighty pillars of the amphitheatre as foundations. In Figure 2, a map of the area surrounding St. Oronzo square (piazza Sant'Oronzo) dating back to 1882 is shown, whereas in Figure 3, a map zoomed on the area of square is proposed, dating back to 1907, that is during a period when the square was being transformed.
The rediscovery of the amphitheatre dates back to the first half of the 20th century, when the city of Lecce underwent radical transformations involving the widening and straightening of roads and the creation of new open spaces in its historical centre (Cazzato, 2000;Rossi, 2003). Pillars and walls of the amphitheatre started to come to light after the demolitions of the Sammarco house (1896) and of the forepart of the Russo Palace (1898) in Via degli Acaya (Of the Acaya Street), on the southeast side of St. Oronzo square. The archaeologist Cosimo De Giorgi in 1900 supervised the excavations after the demolition of the Isola del Governatore (the block including the Palace of the Governor) and the edification of the Banca d'Italia (Bank of Italy palace). From 1904, after the demolition of the Capone and Guerra palaces, up to 1911, he brought to light a first part of the amphitheatre (De Giorgi & Sotterranea, 1907).
A second phase of urban rearrangements, in the 1930s, led to the configuration of the square in his present shape. Isola delle Capande, the block located on the north side of the square, was demolished (Leucci et al., 2016), whereas massive excavation brought to light the arena and the cavea of the ancient amphitheatre (Bernardini, 1959;Martines, 1957).
The latest finding related to the amphitheatre is a pillar of the ambulacrum, discovered in 2007 in Via degli Acaya, during maintenance works regarding the sewerage network.

THE GROUND PENETRATING RADAR CAMPAIGN AND THE RESULTS
Ground penetrating radar (GPR) measurements were performed with a Ris Hi-Mode pulsed system, equipped with a dual antenna with central frequencies at 200 and 600 MHz, respectively. This means that two sets of data were simultaneously gathered along each measurement line. As well known, the data at lower frequency are expected to penetrate at deeper levels, whereas those at higher frequency are expected to provide a better resolution (Jol, 2009). In the following, we will show either data at 600 MHz or 200 MHz depending on which ones appeared heuristically better to us. A first area was prospected between the two streets Via Vito Fazzi and in Via Giuseppe Verdi. Here, 19 parallel measurement lines (Bscans) were gathered, spaced 50 cm from each other. The longest measurement line (Bscan) was about 48 m long, whereas the shortest one was about long 20 m. The in-line step of the data was 1.76 cm for the data at 600 MHz and 3.52 cm for the data at 200 MH. The time step was 0.125 ns for the data at 600 MHz and 0.25 ns for the data at 200 MHz. The time bottom scale was 128 ns for the data at 600 MHz and 265 ns for the data at 200 MHz.
The starting points of the Bscans were chosen at the passage between the asphalted part of the road and that covered F I G U R E 2 The area around St. Oronzo square (Piazza Sant'Oronzo) in 1882, before the demolitions of the 20th century (map done by M. Astuti). In particular, we have put into evidence a piece of palazzo Russo demolished in subsequent years.

F I G U R E 3
Transformation of Sant'Oronzo square at the beginning of the 20th century (Cazzato, 2000): The letter C indicates the demolished part of Russo palace (also put into evidence in Figure 2), and E indicates Sammarco house in the Isola del Governatore block.
with flagstones, whereas the final point was at the opposite footpath, which determined the different lengths of the Bscans and provided a geometrical indication useful for the georeferencing of the data. The processing was performed with the Reflexw code (https://www.sandmeier-geo.de/reflexw.html, last access on September 12, 2022) and consisted of zero timing (after 8 ns for the data at 600 MHz and after 15 ns for the data at 200 MHz), background removal on all the traces (Persico & Soldovieri, 2008), gain versus depth (with a linear coefficient equal to 0.5/1.5 and an exponential coefficient equal to 0.5/1.5 for the data at 600 MHz/200 MHz), 1D filtering (implemented through a Butterworth filtering  (Schneider, 1978) (performed on 65/50 traces for the data at 600 MHz/200 MHz) and slicing (Goodoman & Piro, 2013). The propagation velocity of the electromagnetic waves in the soil was evaluated on the basis of the diffraction hyperbolas to be equal to about 9 cm/ns, both for the data at 200 MHz and those at 600 MHz. The slices were created averaging the GPR signal along time intervals of 5 ns, about corresponding to 27.5 cm, both for the data at 600 and 200 MHz.
In Figure 4, a depth slice at about 73 cm is shown. The spot put into evidence by two black dotted lines is probably ascribable to a radial corridor connecting the ambulacrum (or the ambulacra, if further ones were originally present) with the arena, whereas the spot delimited by the dotted white line is probably associated to the remains of part of the Russo Palace, due to the geometrical coincidence of this spot with the map of this building in Figures 2 and 3. Several subservices can be identified too, as put into evidence by the solid lines. The slice is achieved from the data at 200 MHz. In Figure 5, we propose one of the Bscans with its displacement in the map. The Bscan is taken from the data at 600 MHz and is not migrated (whereas all the slices are based on migrated data) in order to put better into evidence the hyperbolical signature of some anomalies. In particular, we can see a quasi-horizontal discontinuity at the depth of about 45 cm (corresponding to 10 ns) in the first part of the Bscan plus some deeper reflections (see the right hand ellipsis) that are likely to be associated to the demolished Russo palace. It is also probable that the foundations of palazzo Russo were in their turn mounted in pre-existing ancient walls ascribable to the Roman amphitheatre. Instead, the left-hand ellipsis in Figure 5 corresponds to the alleged corridor between the ambulacrum and the arena: This is clear from the geometrical correspondence with the slice in Figure 4.
In Figure 6, we propose an image referring to the last Bscan on the opposite site of the street (similarly to Figure 5, the Bscan is not migrated). Several diffraction curves are visible, probably most of which referable to subservices that cross the street. The situation is anyway not simple to decipher, also due to the works done in this area when the amphitheatre was discovered and some overlying structures were demolished. In Figure 7, a depth slice at about 90 cm is shown, whereas in Figure 8, a depth slice ad about 135 cm is shown.
Some new anomalies appear, probably partially related to the amphitheatre and, in particular, a discontinuity is put into evidence by means of a curved dashed line. This discontinuity is probably related to the path of the ancient ambulacrum. Finally, in Figure 9, we arrive at a depth level about corresponding to 180 cm. The more intense reflections at 180 cm are probably caused by the ceiling of the ambulacrum, that is buried at about this depth level, as known by laser scanner measurements done in the past .
A second series parallel Bscans have been gathered in the final part of Via Giuseppe Verdi, when the street bends. In this case, 16 parallel Bscans were gathered, at distance 50 cm from each other. The Bscans were gathered in the same verse in order to be more precise with the georeferencing. The measurement parameters and the processing steps and processing parameters were the same as in the previous area. In Figures 10 and 11, two depth slices (calculated from the data at 600 MHz) are shown, respectively, at the depth levels of about 90 and 120 cm. In both cases, the main anomaly is a structure at the corner of the street. We estimate that this corresponds to structures analogous to those adjacently excavated, that is pillars of the lower porticus of the amphitheatre and a wall surrounding the arena. Of course, these structures used to support also the further part of the cavea that, as said, was higher than its current size. In this area, moreover, a presence of humidity is visible while walking within the ambulacrum.
Probably, the isolated anomalies visible in Figures 10 and 11 on the right hand side (in particular the anomaly surrounded with a dashed rectangle) of the images before the curve of the street are associated to this moisture.

THE GEOREFERENCING PROCEDURE
In the previous figures, the ground penetrating radar results have been georeferenced with the help of the open-source code QGIS (https://www.qgis.org/it/site/forusers/download. html, last access on September 12, 2022) within the 2D Cartesian reference system EPSG32633, associated to the WGS84 Earth ellipsoid and to the Gauss-Boaga cartographic projection. However, as said, we did not have at disposal differential global satellite navigation systems (GNSS) measurements, and so we adapted the position of the depth slices on the basis the size and shape of the retrieved depth slices. In fact, any slice in itself is intrinsically rectangular, but partially filled up with well recognizable no-fly zones, that is zones essentially zero padded. In particular, the actually measured areas were limited by unremovable obstacles, which modelled the shape of the really prospected area within each slice.
In order to implement this geometrical matching, the plugin 'Free Raster Georeferencer' was exploited. This plugin allows a controlled scaling, shift and rotation of a raster file imported in the QGIS map. In order to apply the algorithm, we pre-chose in the map four points depicting the vertexes of a rectangle with the same size as the slices to be imported. Then, we scaled and zoomed an imported slice up to when its vertexes coincided with the four prechosen points. In this way, we imposed in the Google Earth map the actual geometrical size of the slice. After doing this, subsequent translations and rotations to the imported and scaled slice were imposed up to when the bound of the no-fly zone of the slice was geometrically matched with bound of the footpath. In order to identify this geometrical matching, some transparency was imposed to the slice.
In Figure 12, a slice in the first area and a slice in the second area are shown together (there is a little overlap between the two areas as can be seen).
After reaching the desired displacement, we have picked the positions reached by the vertex of the slice and have used them for georeferencing all the slices representing the different depth levels. In order to perform the georeferencing based on these four points, we have not used any longer the 'Free Hand Georeferencer' plugin but the customary Georeferencer tool of QGIS. In other words, the Free Hand Georeferencer was exploited just for identifying the four vertexes of the slices in the map, so playing the role of the lacking GNSS. Then, the final georeferencing was performed by means of the classical Georeferencer of QGIS. Originally, also this tool was a plu-gin, but then it has been inserted in the default 'raster' curtain menu in the version 3.22 of QGIS, and then it has been moved under the 'layer' curtain menu in the subsequent version 3.28.
The reason of this apparently chaotic operation is twofold. First, the retrieved vertexes allow the georeferencing of several depth slices without any need to repeat the procedure of scaling translations and rotations, which avoids spurious geometrical discrepancies between the slices at different depth levels.
Moreover, after displacing the slice in its correct position, we had to make invisible the no-fly zones included in it. In QGIS, this operation can be performed depicting a polygonal shapefile on the really prospected area and then exploiting this polygon as a mask for making visible just the really measured data. The tool for this operation is the 'cut raster with mask'. However, this tool cannot be applied on the layer imported by means of the Free Hand Georeferencer, because the Free Hand Georeferencer produces a layer that syntactically is not a georeferenced raster.

CONCLUSIONS
In this paper, we have proposed some ground penetrating radar results achieved close to the Roman amphitheatre of Lecce, Italy. The amphitheatre is an important monument but is also a structure that might pose stability problems in the long period, in particular due to a humidity seeping visible at a certain point in the ambulacrum of the amphitheatre, probably due to some leak. In Figures 10 and 11 an anomaly possibly associated to this phenomenon has been outlined. Moreover, the data have put into evidence anomalies related to several subservices, to the buried remains of the amphitheatre and to a previous building partially demolished at the beginning of the 20th century.
It is relevant to outline how the knowledge of the history of the town and the availability of historical documents have helped the interpretation of the results.
We did not have at disposal a differential global satellite navigation system (GNSS) and so, as said, we have georeferenced the data thanks to the shape of the no-fly zones through a suitable procedure in QGIS, as described. In particular, looking at Figures 10 and 11, we can appreciate also how important a correct georeferencing can be for a correct interpretation of the results.
It is relevant to outline that, even in cases when a differential GNSS were available, it might work not properly. In particular, it cannot work indoor, it might become less precise in narrow street close to buildings and certainly does not work if the owners of the satellite constellation decide to make unavailable the signal for political or military reasons, which can happen (and indeed has happened, even if rarely) without any forewarning. So, a suitable spare method for the F I G U R E 1 2 Two semi-transparent depth slices in the two prospected areas, before the erasing of the no-fly zones.
georeferencing is well advised. In our case, the intrinsic shape of the prospected areas was probably more reliable than the gathering of the distances of the vertexes of the measured area form some marker targets identified the field, further than providing a faster and easier method.

A C K N O W L E D G E M E N T S
We are grateful to Institute for the Electromagnetic Sensing of the Environment IREA-CNR for putting at disposal their GPR system. We are also grateful to Dr Luca Furnari of the University of Calabria for his important suggestions about the QGIS software.
Open Access Funding provided by Universita della Calabria within the CRUI-CARE Agreement.

D A T A AVA I L A B I L I T Y S T A T E M E N T
The data are available on request.