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Feasibility study of muon tomography application in a non-invasive representation of tumulus

Within the frame of the EKATϒ programme, whose purpose is the innovative imaging of the subsurface of archaeological sites and the interior of structural elements of monuments in “three” and “four” dimensions, the applicability of Muon Tomography technique in the representation of a tumulus is tested in the present work. The scanning of its internal structure is accomplished by measuring the flux deficit of cosmic muon tracks in the presence of an object inside the tumulus, compared to the muon flux when traversing a uniform tumulus (transmission muography). The feasibility study of the method is achieved with a simulation of the tumulus geometry and the structure under investigation. Following the simulation process, a tracking telescope, consisting of four MicroMegas detectors and two trigger plastic scintillators, will be placed near Apollonia’s tumulus to collect data. For the specific latitude where the Apollonia’s tumulus is located, the energy and angular muon distribution at sea level is studied. Implementing the dimensions of the telescope in the simulation, the back-projection method is examined for the localization of the hidden object and the estimation of its dimensions. The method is tested for the telescope optimal position, placed under the tumulus, and the realistic one, placed near the tumulus at the level of its base.


Introduction
Muon tomography (muography or muon radiography) is a technique that uses cosmic muons to generate three-dimensional images of volumes and define their density. It has been applied in various fields, such as geology, archaeology and security. After the discovery of a hidden chamber in the Great Pyramid of Cheops in November of 2017 [1], the idea of applying this technique in an archaeological structure of smaller scale occurred. Such structure would be a tumulus, which is a small man-made hill typically made of dirt with a base diameter of tens of meters. Tumuli found in Greece were built to cover Macedonian tombs and burial objects, which are expected to be located on the tumulus base at ground level. Imaging the interior of the tumulus using cosmic muons is a non-invasive and passive technique, since the particle source used for the scanning is not artificial. By measuring the deficit (or excess) of muon flux for a given direction it is possible to define the existence of an object of higher density (or a void) inside the tumulus.
Within the frame of the ΕΚΑΤΥ programme, funded by the National Strategic Reference Framework (ESPA), a cosmic muon telescope consisting of four MicroMegas detectors and two trigger plastic scintillators will be placed near Apollonia's tumulus to operate and collect data. The Appolonia's tumulus is located near the city of Thessaloniki and is partially excavated by the archaeological authority. Since there is evidence that further findings are possibly located inside the tumulus, it is an appropriate structure to examine the Muon Tomography technique. Prior to the telescope operation, the feasibility of the method has been studied by simulating the tumulus geometry and the possible structure inside, as well as the behaviour of the cosmic muons traversing them. Specifically, the back-projection method [6] was examined, as a possible effective method for the localization of the object inside the tumulus and the estimation of its dimensions.

Simulation
The simulation of the tumulus geometry was achieved using the Geant4 (version 10.06) simulation toolkit [2], developed to simulate detection systems and structures and the passage of particles through matter. The tumulus has the shape of a truncated cone with a bottom diameter of 92m, an upper diameter of 32m and a height of 17m, as shown in figure 1. The Cartesian coordinate system is placed in its centre. The material of the tumulus is dirt of density ρ = 1.2gr/cm 3 , the composition of which was defined according to the Engineering ToolBox [3], as shown in table 1.
To simulate the muon interactions with the tumulus, the Geant4 Standard Electromagnetic Physics constructor was implemented, where the processes of ionization, multiple scattering, Bremsstrahlung and pair production were included. The geometry of the MicroMegas telescope was also implemented, an apparatus consisting of four 45 × 45cm detection planes spaced by 20cm intervals. Each detection plane was constructed to be very thin and made of vacuum to ensure that muons will not further interact in it. The desideratum of the current analysis is to examine whether the behaviour of muons penetrating the tumulus will be observable by the detector and not to test the detector response and characteristics.  To simulate the cosmic muon distributions and implement them in the Geant4 simulation the Geant4-MATLAB muon generator was applied. The MATLAB code, developed in [5], produces muons with zenith angles in the range of 0-90°and energies in the range of 1-100 GeV and generates the necessary user-defined histograms for use with the Geant4 General Particle Source macro file. A detailed explanation of the Geant4-MATLAB muon generator is stated in [4]. The code generates three distributions; one of the cosmic muon energy and two of the muon zenith angle. The zenith angle is given for its normalised distribution following the approximate squared cosine law and for the correction for the solid angle effect. In figure 2, the three distributions are shown for muons with energies 1-60 GeV and 0 − 90 o zenith angle, obtained using the MATLAB code [5].

Back-projection method
To specify the size and the location of a potential hidden structure inside the tumulus, the backprojection method was examined, introduced in [6]. This method is proposed to be favorable for the imaging of hidden objects surrounded by a large amount of a material of different density. Furthermore, the method is applicable when the muon telescope is not point-like compared to the object under investigation, which is the case of a possible finding in a tumulus. A Macedonian tomb has typically the size of a few meters, which is comparable to the dimensions of the telescope. The distance of the investigated object from the detection apparatus has to not be very large with respect to the size of the instrument, as well. If these conditions are satisfied, not only the direction of motion of the detected muons, but also their impact point on 4 the detector carries useful information for the imaging, as different parts of the detector "see" the object along different directions.
The main concept of the method is to project backwards the muon tracks in vertical planes relative to the telescope axis. A bin size (pitch) is defined for every back-projected plane varying with the distance of the plane from the detector. The pitch p is chosen to be linearly dependent from that distance, as shown in equation 1 where p(x) is the pitch (bin size), which is a function of the distance x of the back-projected plane from the top detection plane, δ θ is the angular resolution of the muon telescope, defined as the accepted angle of each strip and p 0 is the pitch at x=0, which corresponds to the spacial resolution of the single detection plane. Following, the two-dimensional histograms of the ratio of the projected muon position to the corresponding pitch are plotted on every back-projected plane. Subtracting the histogram obtained for the case where the tumulus contains an object, from the corresponding one for the uniform-tumulus, an excess in the muon flux is observed in the region where the object is placed. The rms of the subtraction histogram will determine the width-to-pitch ratio. Plotting the width-to-pitch ratio as a function of the distance, the distribution is expected to reach a minimum at the distance where the front surface of the object is placed. The method proposes that the Full Width at Half Maximum of the subtraction at that distance corresponds to the object width. As a result, both the location and the dimensions of the object could be estimated. A description of the back-projection method is stated in detail in [6].
The muon telescope was firstly placed below the tumulus. This is the optimal position for the imaging of the object, because the maximal flux in the signal muon tracks is achieved and the structure under investigation is placed along the telescope axis. The muon telescope was oriented parallel to the xy plane, with its axis along the z direction, and it was placed so the top detection plane is at a distance of 3m from the tumulus base. Using the MATLAB code [5], a macro file with the muon energy ranging from 4 to 100GeV and the muon zenith angle ranging from 0 to 50 o was generated. The limits of the distributions were chosen as mentioned, so as not to generate tracks which will be lost anyway and consequently save computation time. Muons with energy less than 4GeV will be absorbed before reaching the detector even when crossing the minimum distance in the tumulus. Furthermore, muons with zenith angle greater than 50 o can not provide useful information (triple and quadruple coincidences) because of the telescope acceptance in this specific arrangement. The 34 × 34m muon generation plane was placed 1m above the tumulus top. A visualisation of cosmic ray beams hitting the tumulus in the above arrangement is shown in figure 3. As shown in the figure, muon tracks that will not end in an accepted area (dashed green box), surrounding the telescope within 3m from its centre, have been artificially killed.
Objects of various shapes, dimensions and orientations were examined. The materials that were tested were iron with density ρ = 7.874gr/cm 3 and marble (Calcium Carbonate CaCO 3 ) with ρ = 2.8gr/cm 3 . For a first test of the back-projection method, an iron compact cylinder of 1.5m diameter and height, which will be referred to as small cylinder, was placed inside the tumulus so its side touched the ground, as shown in figure 4a.
The spatial resolution of the single detection plane was chosen to be 0.5cm, which leads to an angular resolution of 8.3mrad. The back-projection of the muon tracks was calculated on xy planes, perpendicular to the z axis, spaced by a distance of half a meter. The two-dimensional histograms of the muon track position distribution were plotted on each plane, for the case of the uniform dirt tumulus and the addition of the object. The bin size on each plane was calculated using equation 1. The input in the histograms was the ratio of the x or y coordinate over the corresponding pitch of each plane. Three indicative back-projected planes of the subtraction histograms are shown in figure 5, for 1 billion initial generated muons. An excess in the muon flux is observed in the centre of the xy plane, where the object is placed, as expected.
(a) (b) (c) Figure 5: Back-Projection planes for small iron cylinder at a 3m distance from the detector.
The standard deviation of the x and y projections of the two-dimensional histograms were plotted as a function of the distance of the projected plane from the top detection plane, as shown in figure 6. These values correspond to the width-to-pitch ratio, the minimum of which will define the expected location of the hidden structure. Along with the ratio, the calculated width of the structure related to the distance of the back-projected plane is shown in figure 6. The width of the object was calculated as the product of the FWHM of each x and y projection distribution with the corresponding pitch value. The width-to-pitch ratio is minimised around the distance of 3m, which is the actual location of the object and seems to follow the expected distribution. However, observing the calculated width of the object using the FWHM value at the distance of 3m, it does not correspond to the expected value of 1.5m and the real width is underestimated. Figure 6: Width-to-pitch ratio (left) and FWHM (right) as a function of the back-projected plane distance for the small iron cylinder at 3m.
By further testing the effectiveness of the back-projection method for objects of different dimensions and placements, a larger cylinder of 3m diameter and height was examined. The cylinder was made of marble and was rotated by an angle of 90 o around the y axis. To be entirely visible by the telescope, the object was moved further away from the detector. It was placed with its base 2m above the tumulus bottom, meaning 5m away from the detector as shown in figure 4b. To test if a non-compact object would still be detectable, a hollow vertical cylinder was placed in a similar arrangement, as shown in figure 4c. Its outer radius was set to 1.5m and its inner to 1m.
By generating 2 billion initial muons, the two-dimensional histograms of the back-projected planes were plotted as shown in figure 7. The width-to-pitch ratio and the FWHM as a function of the distance are shown in figure 12. The circular projection of the object on the back-planes is distinct, especially in the plane where the cylinder base is located. The empty space in the case of the hollow cylinder is detectable as well. However, the width-to-pitch ratio is not minimised in the the expected distance of 5m and the FWHM does not correspond to the real size of the structure.
Continuing, the detection apparatus was placed in a realistic position, as the one of the upcoming experiment. The telescope was placed with its centre in the (48,0,-8)m point and it was rotated by 80 o around the y axis. A small elevation angle relative to the ground is needed, in order for the telescope to "observe" the tumulus base, where the hidden object is expected to be found. A more realistic representation of an object would be a 3 × 3m hollow box of 0.5m width, which resembles a hidden chamber in which the tomb could be placed. The hollow box was moved to the bottom of the tumulus, placed in the centre, which is expected to be the location of the possible hidden tomb chamber, as shown in figure 9a.
Constrains in the initial muon distributions were set, with the energy ranging from 15 to 50 GeV, the azimuthal angle from 85 o to 95 o and the zenith angle from 80 o to 90 o . Only almost horizontal muons carry useful information, as they are the ones that will cross the hidden structure and will be detected by the telescope, giving quadruple coincidence events. The 400 × 20m muon generation plane was parallel to the tumulus base and its centre was placed in the point (-400,0,9)m, 0.5m above the tumulus top. In the case of the side telescope, some more arrangements had to be made. The y and z component of each track were calculated in the x=46.5m position and the back-projection stared from this point. As the telescope is inclined, the x component of each track on the first detection plane is not the same for every quadruple coincidence. Hence, the tracks were projected at the x=46.5m, which is after the edge of the tumulus, so the back-projection began from the same point for every event.  interact with the tumulus material. As a result, the final z angle could be less than 90 o , so the corresponding track would be projected downwards. In this case, the track seems to reach the telescope from below, which of course does not reflect reality. Hence, only the tracks with momentum z angle in the range of 90 o − 100 o were taken into consideration. Iron was chosen as the box material and 4 billion initial muons were generated. A visualisation the cosmic beams with the above constrains in their energy, zenith and azimuthal angle is shown in figure 9b.
Starting from the yz plane at x=46.5m, the back-projection method was tested for 30 planes spaced by 2m, having 2-60m distance from the initial plane. The pitch of the initial plane was set to 1mm, giving an angular resolution of 1.67mrad. One indicative back-projected plane is shown in figure 10a. The scale is logarithmic for the z axis. An increased flux is observed in the centre of the projected image, however the projection does not reveal the box layout. The width-to-pitch ratio for this arrangement is shown in figure 10b. The front surface of the box is at 45m distance from the initial plane. However, the width-to-pitch ratio does not reach a minimum in this value. The corresponding width arisen from the FWHM of the y projection in the area of 45m is approximately 2.5m, which is close to the value of the real box width. Continuing, two boxes were examined. Along with the hollow box, a smaller compact box of 1.5m side was placed inside the tumulus. The two boxes were placed alternately at (34,0,-7)m and (39,0,-7)m, as shown in figure 11 (top). In this case the detector was placed at the point (48,0,-8.75)m, namely slightly under the ground level at -8.5m. Digging the ground slightly and placing the detector there would be possible in the real experiment. The initial kinetic energy of muons ranged from 15 to 30GeV and the zenith angle from 70 0 to 88 o . Two billion muons were generated at a 300 × 40m plane with its centre at (-150,0,9.55)m, approximately one metre above the tumulus top. The azimuthal angle was constrained between 78 0 and 102 o . The materials of the two boxes were iron and marble, which were also alternated. The initial pitch value was 3mm which corresponds to an angular resolution of 5mrad. In the case where the smaller box is closer to the telescope, its projection is distinctly observable and the layout of the larger box surrounding the smaller one is also detectable to e smaller extend, as shown in figure 11 (left). The two boxes are completely distinguishable in the case where the larger box is closer to the telescope and is made of iron (figure 10d). Only the top part of the objects is observable, because the detector does not totally "see" the boxes in the z coordinate, as no muon tracks reach it from the ground. In the y direction, the detector "observes" the whole object and the y coordinate is expected to provide more reliable results.
In the case where the smaller box was closer to the telescope and setting the initial pitch at 5mm (δ θ = 8.33mrad), the width-to-pitch ratio and the object width were plotted as a function of the distance, as shown in figure 12. In this case, instead of the FWHM the quadruple of the standard deviation 4σ was considered as the object width, which was observed that estimates more properly the real width. The width-to-pitch distribution for the y projection was fitted with a second order polynomial function (red curved line). The distribution for the case of the large marble box and the small iron one was fitted in the region from 3 to 10m. The width (4σ) distribution was fitted in the same region with a linear function. The corresponding distributions for the case of the large iron box and the small marble one were fitted in the region from 3 to 11m. The minimum value of the fitted function in the first case is 7.015m. This value is compatible with the real distance of the initial plane at x=46.5m from the small box front side at x=39.75m, giving a distance of 6.75m. The corresponding width obtained in this position by the linear fit is w=1.96024m, which is also compatible with the real box side of 1.5m. In the second case, the minimum value of the fitted function is 7.72488m, which is also compatible with the real distance of 6.75m. The corresponding width obtained in this position by the linear fit is w=1.59423m, which is very close to the box side of 1.5m. Consequently, the detector "observes" the closer object.

Conclusions and prospects
Muon tomography is a technique that could be applied in the scanning of tumuli and provide useful information for their internal structure. The need for this method is particularly important for an investigated structure of archaeological interest, due to its non-invasive nature. In the present work the feasibility of muon tomography, and specifically muon radiography, in the representation of a tumulus was examined with a simulation. By implementing the real cosmic muon distributions and the telescope geometry in the simulation, the object inside is not directly detectable. The back-projection method developed in [6] is applied, in order to specify the location and the size of the hidden object. The method is examined for two different placements of the muon telescope. Firstly, it is placed under the tumulus with its planes parallel to the tumulus base, which is the optimal placement to detect the hidden object. In this case, both  Figure 12: Width-to-pitch ratio and 4σ as a function of the back-projected plane distance with p=5mm for (a) large marble box and small iron box and (b) large iron box and small marble box.
the layout of the structure and the hollow space inside were distinctly observable in the backprojected planes. Secondly, the telescope is placed near the tumulus base having a small elevation angle, in order to face its base where the hidden object is expected to be found. This is the realistic placement of the telescope, as it will be the one during the real experiment. In this case a projection of the object would be detectable. The excess in muon tracks in the absence of the object is observable in the back-projected planes, so the object is detectable but its specific shape is not distinct. However, the object is properly localized and its size is correctly specified under certain conditions. Specifically, the object has to be comparable in size to the telescope, approximately being 3-4 times larger than the apparatus. Moreover, the distance between the object and the telescope has to not be very large, being of the order of some meters. As far as future work is concerned, more tests have to be applied to define the position and the width of the object with more accuracy. Considering setting up a second detection apparatus in the experiment would provide more information. Putting the second telescope in a similar placement facing the tumulus from a different side, a more spherical image of the object could be extracted. Another approach could be placing the second apparatus diametrically opposite facing the opposite side. By detecting the muon track before traversing the tumulus and comparing to the corresponding one after passing through it, the information of the multiple Coulomb scattering could be exploited. In this case, clearer conclusions concerning both the density and the width of the hidden object could be obtained.

Acknowledgment
This work has been accomplished on behalf of the project EKATY: Innovative imaging of the subsurface of archaeological sites and the interior of structural elements of monuments in 3 and 4 Dimensions. The project is running under the framework of the Operational Programme Competitiveness, Entrepreneurship and Innovation 2014-2020 (EPAnEK), Special Actions "Aquaculture" -"Industrial Materials" -"Open Innovation in Culture", Τ6ΥΒΠ-00211.