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Muography applied to archaeology: case study of a small size Macedonian Tumulus

Muographie appliquée à l’archéologie : étude de cas d’un tumulus macédonien de petite taille
Theodoros Avgitas, Sabine Elles, Corinne Goy, Yannis Karyotakis et Jacques Marteau
p. 7-15

Résumés

Une expérience de tomographie par des muons issus de rayons cosmiques a été conduite sur un site archéologique en Grèce, un tumulus. Cette contribution se propose de présenter les problématiques liées à la simulation de l’expérience et du site, par des outils communément utilisés en physique des particules. L’objectif scientifique est de comparer les résultats de la simulation avec les données enregistrées pour mettre en évidence des anomalies.

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Texte intégral

1. Introduction – Tumuli

1Tumuli were used in the ancient times to cover a funeral monument. Usually people were initially building the monument, whose size and decoration was testifying the importance of the buried people. Then the monument was covered by soil, transported from the neighborhood, forming a tumulus. Tumuli, of all sizes, can be found in many places around Earth and especially in Northern Greece. It is important for archaeologists to be aware of the existence of an underground funeral monument, before any excavation. Combining muon imaging or muography, with other techniques, can give an answer to this question without modifying and disturbing the site.

2In this paper, Section 2 introduces the general principles and issues of muography. Section 3 shortly describes simulation techniques used in high energy physics. Section 4 presents the experimental aspects of a muography application from the detector setup to the reconstruction of muon distributions. Section 5 compares data with the simulation before concluding and presenting some ideas for future developments.

2. Muography

3Muon imaging or muography has emerged as a powerful non-invasive method to complement standard tools in Earth Sciences and is nowadays applied to a growing number of fields such as industrial controls, homeland security, civil engineering (Kaiser, 2019; Bonomi et al., 2020). This technique relies on the detection of modifications – absorption or scattering – in the atmospheric muon flux when these particles cross a target.

4Atmospheric muons are secondary products of primary cosmic-rays, essentially protons and helium nuclei expelled by stars, interacting with nuclei encountered on the top of the atmosphere. In a simplified model, the particles cascades are: primary cosmic-rays + oxygen/nitrogen nuclei → parent mesons; (pions/kaons) → secondary muons.

5The rather low interaction cross-Section of muons with matter ensures that most of them reach the Earth’s ground level and that furthermore they may significantly penetrate large and dense structures. As suggested originally by Alvarez in 1970 (Alvarez et al., 1970) for the Chephren pyramid, this property may be exploited to perform density contrasts analysis of the interior of the target like X-rays do in medical imaging. Figure 1 shows the discovery by the ScanPyramids collaboration (Morishima et al., 2017) of a new void in the Khufu’s pyramid by multiple muon detectors outside and inside the pyramid.

6The range of applications of muography is very large since it may concern any large and dense structures, from volcanic domes to mountains, anthropic buildings, etc, which remain opaque to the standard investigation methods.

Figure 1: Discovery a new void in the Khufu’s pyramid by the ScanPyramids collaboration (Morishima et al., 2015).
Figure 1 : Découverte d’un nouveau vide dans la pyramide de Kheops par la collaboration ScanPyramids.

Figure 1: Discovery a new void in the Khufu’s pyramid by the ScanPyramids collaboration (Morishima et al., 2015).Figure 1 : Découverte d’un nouveau vide dans la pyramide de Kheops par la collaboration ScanPyramids.

Left: 3D reconstruction of the void by multiple muons imaging outside and inside the pyramid. Right: typical density map scatter plot – muon radiography – showing the large contrasts between different areas of the pyramid.
Gauche : Reconstruction 3D du vide par plusieurs imageurs à muons, placés à l’intérieur et à l’extérieur de la pyramide. Droite : carte de densité – radiographie par des muons – montrant de grands contrastes selon les différentes zones de la pyramide.

2.1. Underlying physics governing muography techniques

7Being charged leptonic particles, atmospheric muons undergo Coulomb electric interactions with the electrons and nuclei they cross along their journey inside matter. This results in a loss of a fraction of their energy by ionisation and radiation and also in a deviation of their trajectory. These properties, sensitive to the density and composition of the target are exploited in the two different modes of muography called “absorption muography” and “scattering muography”. The absorption mode is similar to X-ray medical imaging. One infers the mass distributions inside a given target from the measurement of the reduced muons flux due to their interaction with the matter of the target. The scattering mode allows the reconstruction of the mass distributions from the measurement of the muons trajectory deviation angles upstream and downstream the target. It is usually restricted to small targets while the absorption mode is well-suited for large volumes imaging.

2.2. Detection of atmospheric muons

8Detecting muons at the ground level exploits the same properties: charges resulting from the ionisation due to the muons when crossing plastic scintillators, silicone cells or gaseous systems of a detector are collected and shaped into an electric pulse. By recording this signal at several points along the trajectory, the direction of the muon track can be reconstructed: the muography detectors belong to the “trackers” category. Figure 2 illustrates two experimental implementations where the muon detector (pictures of the left column) is located either on the slope of an active dome (the Soufrière of Guadeloupe, Lesser Antilles, France) or in a gallery of the underground Mont-Terri laboratory (Jura, Switzerland). These trackers use plastic scintillators as detection medium. The sketches in the right column represent all muons trajectories falling into the detector’s acceptance.

9Tracking performance is measured in terms of spatial and angular resolution, usually driven by the size of the detector segmentation, and in terms of timing resolution. For a large structure muography, an important parameter is the detector acceptance (Sullivan, 1971), i.e. its capability of collecting the maximal number of muons for a given active surface. The background rejection is important for outdoor applications where one needs to eliminate, on one hand, random coincidences and requires fine timestamps of the order of the nanosecond or below, and on the other hand the small fraction of atmospheric electrons surviving at the ground level.

2.3. From data distributions to density maps

10The most difficult step in muography is the so-called “inverse problem”, i.e. going from raw data to reconstructed mass distributions. In absorption mode the detector measures the attenuation of the muon flux integrated all over the path of the muons L, inside the studied target of density ρ, i.e. its “opacity” defined as Image. Going from an opacity map to a density map requires therefore a model or more generally an “inversion technique” that provides the most probable mass distribution functions inside the target. The inverse problem needs to be constrained by the available “a priori” information but is also driven by the data quality which imposes strict requirements on the detector performance in terms of acceptance, resolution, stability in operation, duty cycle, etc.

Figure 2: Examples of muography applications.
Figure 2 : Exemple d’applications de muographie.

Figure 2: Examples of muography applications. Figure 2 : Exemple d’applications de muographie.

Upper row: open-air installation on the slope of the Soufrière of Guadeloupe (Lesser Antilles). Lower row: underground measurement in the Mont-Terri laboratory (Switzerland). The muon trackers are shown on the left while the muon trajectories falling into their acceptance are illustrated on the sketch on the right. The top left detector is similar to the one used for the data acquisition for the Tumulus.
Haut : Installation à l’air libre sur les versants de la Soufrière en Guadeloupe (Petites Antilles). Bas : Mesures souterraines dans le laboratoire du Mont-Terri (Suisse). Les détecteurs sont montrés sur la gauche, tandis que les schémas à droite illustrent les trajectoires de muons tombant dans les détecteurs.

11There are intrinsic limitations to the muography inverse problem, the major one being the limited statistics of the measurement: open sky muon flux is of the order of 1 muon per square centimeter per minute and may be reduced by several orders of magnitude after a large target. On top of the statistical limitation, there are intrinsic ambiguities for a single-point measurement since a muon deficit (negative anomaly) or a muon excess (positive anomaly) with respect to a given model leads to an infinite number of possibilities as to the precise location of this anomaly along the path.

12The approach reported in this paper to answer to the above problem is based on techniques developed in the field of high-energy physics; these are presented in the following section.

3. Monte-Carlo methods

13Monte-Carlo technique is the back-bone of the simulation program GEANT4 (Agostinelli et al., 2003) widely used in high-energy physics. GEANT4 is able to simulate the interactions of particles, including muons, with matter in any volumes. Monte-Carlo technique relies on the mathematical concept to approach numerical values by using random processes. This approach is particularly well-suited to describe interactions of particles as these interactions are governed by probability density functions.

14The main idea of a detailed tumulus simulation is to compare the real data – atmospheric muons crossing the tumulus with simulated data using a uniform density tumulus and with no internal structure or monument. Comparing the number of events observed in data and simulation, after a proper normalisation, should reveal in the tumulus any internal structure with a different density than the uniform one, used in the simulation. A complete simulation of muons crossing the tumulus and detected in the detector requires the following steps:

  • The energy and angular distributions of the incoming muons.

15The two-dimensional spectrum, energy versus direction taking into account their correlations, is obtained using a simulation package namely CORSIKA (Heck et al., 1998). This package tracks incident protons to the top of the atmosphere and follows the generated cascade and therefore muons to the ground. It is known to fit very well all existing data and is largely used by many cosmic ray experiments. However, precise measurements of the muon energy spectra on earth’s surface and close to the horizon do not exist and this is one source of systematic errors. The muon energy versus the zenith angle is shown in Figure 3, the zenith angle θz being defined with respect to the vertical and 0° representing down-going muons and 90° horizontal muons. In first approximation, the zenith angular distribution follows a cos2 θz differential distribution and the azimuthal distribution is isotropic. The CRY cosmic generator (Hagmann et al., 2007) was also tested, as well as the Reyna parametrization (Reyna, 2006).

  • Muon tracking through the tumulus and detection.

16Generated muons are propagated through the tumulus matter using the GEANT4 package. The tumulus geometry is introduced using precise geodesic measurements performed by geometers and takes into account the real shape of the tumulus. Typically, the tumulus base is 100 m wide and the height is 20 m. The muon interactions with matter are very well known and simulated. For the tumulus soil composition, a uniform composition of 1% C, 29% Si, 15% Al, 5% Fe and 50% O with a density of 2.2 g/cm3 is used. Figure 4-top displays a muon interacting with matter while crossing the tumulus.

  • Detector simulation.

17The experimental apparatus is completely simulated, starting from its exact geometry, its material and the detector response to an incident muon. For this paper a perfect detector, with no inefficiencies, is assumed in the simulation. Figure 4-bottom shows a muon going through the detector.

Figure 3: Muon energy versus the zenith angle as generated by CORSIKA.
Figure 3 : Énergie des muons en fonction de l’angle au zénith, générés par CORSIKA, et projections.

Figure 3: Muon energy versus the zenith angle as generated by CORSIKA. Figure 3 : Énergie des muons en fonction de l’angle au zénith, générés par CORSIKA, et projections.

The color code scales with the number of events: the red color materializes bins with the largest number of events. The step like behavior for the energy is an artifact of the ROOT (Brun & Rademakers, 1997) function used to draw random (theta, Energy) pairs from the initial flux distribution.
Le code couleur est proportionnel au nombre de muons : la couleur rouge représente les densités les plus fortes.

Figure 4: Top: Display of a simulated muon crossing the tumulus. Bottom: Representation of the detector and visualization of an incident muon crossing the detector.
Figure 4 : Haut : Illustration d’une trajectoire de muons traversant le tumulus. Bas : Représentation du détecteur avec un muon traversant le détecteur.

Figure 4: Top: Display of a simulated muon crossing the tumulus. Bottom: Representation of the detector and visualization of an incident muon crossing the detector. Figure 4 : Haut : Illustration d’une trajectoire de muons traversant le tumulus. Bas : Représentation du détecteur avec un muon traversant le détecteur.

The tumulus is seen from the top: the incident muon represented by the red line crosses the tumulus; the interaction with the tumulus matter generating secondary particles, is materialized by the green dots along the line.
Le tumulus est vu de dessus : le muon représenté par la ligne pointillée rouge traverse le tumulus ; les interactions avec la matière du tumulus, engendrant des particules secondaires, sont matérialisées par les points verts le long de la trajectoire.

4. Experimental setup

18A copy of the detector shown in Figure 2-TopLeft was deployed on an experimental site pointing toward a tumulus. Considering that the height of a tumulus, about 20 m high, the experimental context is less favorable than in the case pyramids presented in Section 2. Though, the application will serve as a full-scale exercise to deploy high-energy-physics methods in a muography experiment analysis.

4.1. Description of the detector

19The detector is composed of 3 stations spaced 60 cm apart, themselves made up by a double layer of scintillator bars. As shown on the drawing in Figure 5-top, the scintillator bars are aligned in orthogonal directions to form a stereo detection matrix, that in other words provides the (x,y) coordinates of a particle impact on its surface. Each layer is constituted of 32 (resp. 16) 80 cm long bars of plastic scintillator with a rectangular Section of 0.5 cm × 2.5 cm (resp 5 cm) for the top and bottom (resp. the central) station. It results in a 32 × 32 or 16 × 16 detection matrix. The transverse size of the bars defines the spatial and angular resolution of the detection system and the length of the detector, its geometrical acceptance: a muon going through the detector produces scintillating light in up to six planes. The scintillator bars are extruded with a central hole to host a wave-length shifter (WLS) fiber for the scintillation light collection. The WLS optical fibers used, (Kuraray Y11 or Bicron BCF 91A) have 1 mm diameter, collect the UV scintillation light and reemit the signal in the green range where the photosensors have the optimal response. A fiber-to-pixel connection in ensured by an optical system which is plugged, a pixelized photo-multiplier (PMT). Those PMTs (Hamamatsu 8804-300) have 8 × 8 pixels, a typical gain of 106 with a factor 1:3 dispersion on the pixels’ gains, that is the maximum inhomogeneity in gain between channels. The relatively high gain requires moderate amplification but the spread implies the necessity of a channel-to-channel gain correction, included in the present electronics of the detector. Each pixel with a sizeable signal is called a hit. The coordinate system for the reconstructed tracks of the particles crossing the detector is represented in Figure 2-TopLeft: ϕDet is measured in X-Y plane where 0° is aligned with the X axis. ΘDet is measured in the X-Z plane where 0° is also aligned with the X axis.

Figure 5: Top: Drawing of a double plane station illustrating the XY reading. The central fiber is also represented. Bottom: Monitoring of the data acquisition rate over three months.
Figure 5 : Haut : Schéma du double plan de détection, illustrant une lecture stéréo du signal. La fibre centrale est aussi représentée. Bas : Monitoring du taux d’acquisition sur trois mois. 

Figure 5: Top: Drawing of a double plane station illustrating the XY reading. The central fiber is also represented. Bottom: Monitoring of the data acquisition rate over three months. Figure 5 : Haut : Schéma du double plan de détection, illustrant une lecture stéréo du signal. La fibre centrale est aussi représentée. Bas : Monitoring du taux d’acquisition sur trois mois. 

4.2. Data taking and data preparation

20An initial data acquisition phase took place before the tomography data taking. The detector is oriented vertically so that the detector layers are horizontal: this position maximizes the acceptance to atmospheric muons. Data were acquired for 21.5 hours. This data set is used as calibration data to check the performance of the setup, such as the inefficiency due to the thresholds used at the level of the PMTs electronics. The detector acquisition was set in a two-fold coincidence between stations with a coincidence time window of 200 ns where a signal in a station corresponds to at least a double hit in X and Y planes. After this initial phase, the detector is rotated towards the tumulus with an inclination of 10° with respect to the ground. The entire data acquisition period lasted for ~90 days of uninterrupted data taking. The detector was monitored daily on site and remotely: Figure 5-bottom shows the stability of the system over the period.

21Data are pre-processed considering only the 3-fold coincidences events, and a minimum signal is required in the top and bottom station.

4.3. Reconstruction of tracks

22Following the data preselection described above, some additional quality cuts are applied to remove events on the edge of the detector. Then neighboring hits are clustered on each layer. Figure 6-top shows the distribution of the number of clusters on the first layer in the data and compared with the simulation. The significant larger multiplicity observed in data are due to electrons present in cosmic-rays: thanks to the simulation of electrons using GEANT4, their effect in the detector could be reproduced and studied. Their contribution was suppressed by a cut on the total energy deposited in the detector. The result of this cut can be observed in Figure 6-bottom: data and simulated muon data are in agreement. Next, events with at least one cluster on each layer are kept: using the maximum energy hit as the position of the cluster, a straight line is adjusted in each view providing the azimuthal and zenith angles, ϕDet and θDet. If there are more than one track in a view, the track with the best χ2 is kept and only events with one good track in each projection are selected. This selection results in around 4.2 million tracks.

Figure 6: Distribution of the number of clusters on the first layer.
Figure 6 : Distribution du nombre d’amas sur la première couche de détection.

Figure 6: Distribution of the number of clusters on the first layer. Figure 6 : Distribution du nombre d’amas sur la première couche de détection.

Top: before and Bottom: after electron suppression.
Haut : avant et Bas : après suppression des électrons.

23Figure 7 represents the distribution in θDet and ϕDet measured in the detector coordinates. On the projected θDet distribution, three features can be identified:

  • The inclination of the detector is visible at θDet ≈ -10°.
  • Tracks with θDet < -10° represent backward tracks entering the detector by the last station. These tracks can be used to normalize the simulation.
  • Finally, the deficit of tracks around θDet equals +10° to +20° highlights the absorption of muon tracks in the tumulus, with respect to open sky.
  • The segmentation and the geometry of the detector explain the empty bins in Figure 7: the position of the track at the top and bottom planes is given by the center of the hit scintillator bar, leading to forbidden directions.

Figure 7: Top: Data distribution of θDet versus ϕDet angles of reconstructed tracks. Bottom: Distribution of θDet in data and simulation; the uneven distribution is explained by the segmentation of the detector.
Figure 7 : Haut : Distribution de l’angle θDet versus l’angle ϕDet des traces reconstruites dans les données. Bas : Distribution de l’angle θDet dans les données et la simulation ; la distribution irrégulière est expliquée par la segmentation du détecteur.

Figure 7: Top: Data distribution of θDet versus ϕDet angles of reconstructed tracks. Bottom: Distribution of θDet in data and simulation; the uneven distribution is explained by the segmentation of the detector. Figure 7 : Haut : Distribution de l’angle θDet versus l’angle ϕDet des traces reconstruites dans les données. Bas : Distribution de l’angle θDet dans les données et la simulation ; la distribution irrégulière est expliquée par la segmentation du détecteur.

5. Data and Simulation comparison

24Using the angular and energy distributions, obtained with CORSIKA, a very large number of muon events reaching the detector volume was generated; low energy muons are absorbed by the tumulus as a muon loses in average 600 MeV per meter of crossed soil. Typically, horizontal muons with energy less than 60 GeV are stopped in the tumulus. In addition, incident muons will be scattered by the tumulus and will change direction.

25In order to allow a direct comparison between data and simulated data, it is important to get the right normalization between the two samples.

5.1. Normalization using open-sky data

26A large number of muons that reach the detector do not cross the tumulus and come from the open sky. This is the case for those with a polar angle θ > 32°. For practical reasons, the polar angle θ used in this Section is defined as θDet +10°, and the azimuthal angle, ϕ is equal to ϕDet. After checking that the angular distribution above 32° is well reproduced by the simulation, the normalization factor is obtained from the ratio between the number of observed events above 32° divided by the number of simulated events in the same angular range. Figure 8-top shows the θ and ϕ distributions of events in data and in simulation after normalizing the simulation with the factor defined above. In the open sky region, θ > 32°, a good agreement is observed. At θ = 25°, more events are observed in the data sample showing probably that the tumulus height in the simulation is higher than in reality, thus absorbing more muons with respect to the experimental data. For θ < 20°, which are tracks that in majority cross the tumulus the agreement is fair. The ratio Image is shown in Figure 8-bottom: the agreement between data and simulation is not better than 20% in average. Figure 9 shows the ratio Image in two dimensions, polar angle versus azimuthal angle, in bins of 2° allowing a fine image of the tumulus. Any hidden monument should absorb more muons resulting in a ratio Image < 1 at its position inside the tumulus. For ϕ > 25° and θ < 20°, we observe at least a factor 2 more experimental than simulated data, meaning that the tumulus shape or orientation in the simulation lack a precise description, whereas elsewhere Image stays within 20%. The precision of the simulation, as of today, does not allow to draw any relevant conclusions. The other two cosmic generator or parametrization mentioned in Section 3 exhibit a more severe disagreement with data than CORSIKA.

Figure 8: 1: θ distribution of events observed in data and simulation. 2: ϕ distribution of events in data and simulation. 3: Ratio R Data/Simulation versus θ. 4: Ratio R Data/Simulation versus ϕ.
Figure 8 : 1 : Distribution de l’angle θ dans les données et la simulation. 2 : Distribution de l’angle ϕ dans les données et la simulation. 3 : Rapport R Data/Simulation en fonction de θ. 4 : Rapport R Data/Simulation en fonction de ϕ.

Figure 8: 1: θ distribution of events observed in data and simulation. 2: ϕ distribution of events in data and simulation. 3: Ratio R Data/Simulation versus θ. 4: Ratio R Data/Simulation versus ϕ. Figure 8 : 1 : Distribution de l’angle θ dans les données et la simulation. 2 : Distribution de l’angle ϕ dans les données et la simulation. 3 : Rapport R Data/Simulation en fonction de θ. 4 : Rapport R Data/Simulation en fonction de ϕ.

Figure 9: Ratio R Data/Simulation versus azimuthal and polar angles. The colour scale represents the value of the ratio and is bounded at 2.
Figure 9 : Rapport R Data/Simulation représenté en fonction des angles polaire θ et azimuthal ϕ. L’échelle de couleur représente la valeur du rapport et est limitée à 2.

Figure 9: Ratio R Data/Simulation versus azimuthal and polar angles. The colour scale represents the value of the ratio and is bounded at 2. Figure 9 : Rapport R Data/Simulation représenté en fonction des angles polaire θ et azimuthal ϕ. L’échelle de couleur représente la valeur du rapport et est limitée à 2.

5.2. Normalization with the backward tracks

27Another possibility, expected to be less dependent on the precision of the simulation is to normalize the distribution using the backward tracks: these tracks are in an angular range which is similar to those crossing the tumulus contrary to open-sky tracks. To illustrate this alternative method, events were simulated isotropically in ϕ and following a pure cos2θ differential distribution, the energy correlation with θ being not taken into account; the simulated events were generated on 2 virtual planes placed symmetrically in front and behind the detector: these tracks do not cross the tumulus. The red line in Figure 7-bottom shows the simulated distribution normalized to the number of backward tracks. It can be seen that the open sky distribution is reasonably well reproduced (θDet > 20 deg): this observation reinforces the confidence in the more precise CORSIKA simulation used above. On the same figure, the deficit of tracks due to the absorption in the tumulus is clear. To use this normalization it is necessary in the future to generate backward tracks at the same time as forward tracks, using the full GEANT4 simulation.

6. Conclusions and outlook

28A proof of concept experiment was performed taking cosmic muons data with a 3-station muon detector pointing towards a tumulus. A full simulation package based on GEANT4, toolkit for high-energy physics, was developed in order to compare with the real data and to reveal internal structures of the tumulus. At this stage, the overall agreement between data and simulation is not better than 20%, insufficient for discovering a monument made by marble whom density, 2.5 g/cm3, is very close to the surrounding soil. The current simulation is limited by the lack of knowledge of the real density of the tumulus soil, of its precise geometry and of the exact detector position relative to the tumulus. The three items will be addressed in the future. In order to improve the precision, more data are needed, meaning a very long data taking time, given the low number of muons at the horizon. The use of two or three 4-layers detectors will enhance the discovery potential, allowing in addition for an online monitoring of the detector. Combining these data with those from other techniques used in geosciences is mandatory to confirm any discovery, and allow archaeologists to excavate the right position.

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Titre Figure 1: Discovery a new void in the Khufu’s pyramid by the ScanPyramids collaboration (Morishima et al., 2015).Figure 1 : Découverte d’un nouveau vide dans la pyramide de Kheops par la collaboration ScanPyramids.
Légende Left: 3D reconstruction of the void by multiple muons imaging outside and inside the pyramid. Right: typical density map scatter plot – muon radiography – showing the large contrasts between different areas of the pyramid. Gauche : Reconstruction 3D du vide par plusieurs imageurs à muons, placés à l’intérieur et à l’extérieur de la pyramide. Droite : carte de densité – radiographie par des muons – montrant de grands contrastes selon les différentes zones de la pyramide.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-1.jpg
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Titre Figure 2: Examples of muography applications. Figure 2 : Exemple d’applications de muographie.
Légende Upper row: open-air installation on the slope of the Soufrière of Guadeloupe (Lesser Antilles). Lower row: underground measurement in the Mont-Terri laboratory (Switzerland). The muon trackers are shown on the left while the muon trajectories falling into their acceptance are illustrated on the sketch on the right. The top left detector is similar to the one used for the data acquisition for the Tumulus. Haut : Installation à l’air libre sur les versants de la Soufrière en Guadeloupe (Petites Antilles). Bas : Mesures souterraines dans le laboratoire du Mont-Terri (Suisse). Les détecteurs sont montrés sur la gauche, tandis que les schémas à droite illustrent les trajectoires de muons tombant dans les détecteurs.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-3.jpg
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Titre Figure 3: Muon energy versus the zenith angle as generated by CORSIKA. Figure 3 : Énergie des muons en fonction de l’angle au zénith, générés par CORSIKA, et projections.
Légende The color code scales with the number of events: the red color materializes bins with the largest number of events. The step like behavior for the energy is an artifact of the ROOT (Brun & Rademakers, 1997) function used to draw random (theta, Energy) pairs from the initial flux distribution. Le code couleur est proportionnel au nombre de muons : la couleur rouge représente les densités les plus fortes.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-4.jpg
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Titre Figure 4: Top: Display of a simulated muon crossing the tumulus. Bottom: Representation of the detector and visualization of an incident muon crossing the detector. Figure 4 : Haut : Illustration d’une trajectoire de muons traversant le tumulus. Bas : Représentation du détecteur avec un muon traversant le détecteur.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-5.jpg
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Légende The tumulus is seen from the top: the incident muon represented by the red line crosses the tumulus; the interaction with the tumulus matter generating secondary particles, is materialized by the green dots along the line. Le tumulus est vu de dessus : le muon représenté par la ligne pointillée rouge traverse le tumulus ; les interactions avec la matière du tumulus, engendrant des particules secondaires, sont matérialisées par les points verts le long de la trajectoire.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-6.jpg
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Titre Figure 5: Top: Drawing of a double plane station illustrating the XY reading. The central fiber is also represented. Bottom: Monitoring of the data acquisition rate over three months. Figure 5 : Haut : Schéma du double plan de détection, illustrant une lecture stéréo du signal. La fibre centrale est aussi représentée. Bas : Monitoring du taux d’acquisition sur trois mois. 
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-7.jpg
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Légende Top: before and Bottom: after electron suppression. Haut : avant et Bas : après suppression des électrons.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-8.jpg
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Titre Figure 6: Distribution of the number of clusters on the first layer. Figure 6 : Distribution du nombre d’amas sur la première couche de détection.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-9.jpg
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Titre Figure 7: Top: Data distribution of θDet versus ϕDet angles of reconstructed tracks. Bottom: Distribution of θDet in data and simulation; the uneven distribution is explained by the segmentation of the detector. Figure 7 : Haut : Distribution de l’angle θDet versus l’angle ϕDet des traces reconstruites dans les données. Bas : Distribution de l’angle θDet dans les données et la simulation ; la distribution irrégulière est expliquée par la segmentation du détecteur.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-10.jpg
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URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-11.jpg
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Titre Figure 8: 1: θ distribution of events observed in data and simulation. 2: ϕ distribution of events in data and simulation. 3: Ratio R Data/Simulation versus θ. 4: Ratio R Data/Simulation versus ϕ. Figure 8 : 1 : Distribution de l’angle θ dans les données et la simulation. 2 : Distribution de l’angle ϕ dans les données et la simulation. 3 : Rapport R Data/Simulation en fonction de θ. 4 : Rapport R Data/Simulation en fonction de ϕ.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-13.jpg
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URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-14.jpg
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Titre Figure 9: Ratio R Data/Simulation versus azimuthal and polar angles. The colour scale represents the value of the ratio and is bounded at 2. Figure 9 : Rapport R Data/Simulation représenté en fonction des angles polaire θ et azimuthal ϕ. L’échelle de couleur représente la valeur du rapport et est limitée à 2.
URL http://journals.openedition.org/archeosciences/docannexe/image/12329/img-15.jpg
Fichier image/jpeg, 169k
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Theodoros Avgitas, Sabine Elles, Corinne Goy, Yannis Karyotakis et Jacques Marteau, « Muography applied to archaeology: case study of a small size Macedonian Tumulus »ArcheoSciences, 48-1 | 2024, 7-15.

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Theodoros Avgitas, Sabine Elles, Corinne Goy, Yannis Karyotakis et Jacques Marteau, « Muography applied to archaeology: case study of a small size Macedonian Tumulus »ArcheoSciences [En ligne], 48-1 | 2024, mis en ligne le 03 janvier 2026, consulté le 17 mai 2026. URL : http://journals.openedition.org/archeosciences/12329 ; DOI : https://doi.org/10.4000/12w34

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Auteurs

Theodoros Avgitas

Institut de Physique des 2 Infinis de Lyon (IP2I), IN2P3, CNRS, Université Lyon 1, UMR 5822, Lyon, France

Sabine Elles

Laboratoire d’Annecy de Physique des Particules (LAPP), Univ. Savoie Mont Blanc, CNRS/IN2P3, Annecy, France

Corinne Goy

Laboratoire de Physique Subatomique et Cosmologie (LPSC), Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France

Yannis Karyotakis

Laboratoire d’Annecy de Physique des Particules (LAPP), Univ. Savoie Mont Blanc, CNRS/IN2P3, Annecy, France

Jacques Marteau

Institut de Physique des 2 Infinis de Lyon (IP2I), IN2P3, CNRS, Université Lyon 1, UMR 5822, Lyon, France

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