**3. Applications of the muon absorption technique**

The exploration of heavy structures requires penetrating probes, in order to convey information concerning the interior of the structure and its details. For objects having sizes of the order of 1 m or less, X-rays or neutrons may constitute a valid alternative. For instance, typical mass attenuation coefficients of X-rays (30 keV) are of the order of μ/ρ = 30 cm<sup>2</sup> /g for Lead, so that a nonnegligible fraction of X-ray photons may penetrate several cm of Lead. **Figure 2** shows a plot of the mass attenuation coefficient for photons of various energies (from about 0.1 to 10 MeV) in Lead, as derived from the NIST standard data [5].

For larger size objects, the attenuation of such probes would be too high, and more penetrating particles, such as high energy muons, are required to traverse larger thicknesses. The basic properties of muon interaction in matter are known since a long time. However, their potential as a penetrating probe to give information on the interior of large structures is more recent, and only in the last years the literature has seen a large body of applications in this field, also related to the corresponding development of appropriate detectors, electronics, reconstruction and simulation algorithms.

The muon energy loss is usually expressed through its average value

$$-\frac{dE}{dx} = a(E) + b(E)E\tag{4}$$

where *a*(*E*) takes into account the energy loss due to ionization, and *b*(*E*) the energy loss due to other processes (e+ e− pair production, Bremmstrahlung and photonuclear processes). The ionization term may be described by the Bethe-Bloch formula as a continuous process. At very high muon energies however, radiative processes become more important than the ionization processes. In case of muons, the value of the critical energy, where the two contributions are comparable, is of the order of several hundred GeV for medium-Z materials like the Iron. Radiative processes then dominate the energy loss of highly energetic cosmic muons, and should be taken into account when considering muons which have to traverse hundred metres solid rock. As an example, **Figure 3** shows the muon energy loss in Lead as a function of the muon energy [6]. The relative contribution of the individual terms due to pair production, Bremmstrahlung and photonuclear processes depends on the muon energy, with the last one being much smaller than the other two for increasing muon energies.

Considering a realistic momentum distribution of muons, GEANT simulations of the interaction of muons with solid rock may be performed. As an example, **Figure 4** shows the fraction of surviving muons after traversing a given thickness of volcano rock, modelled by a realistic chemical composition of the lava from Etna, mainly including SiO2 , Al2 O3 , FeO, MgO, and CaO. As it is seen from **Figure 4**, about 1% of the muon flux is still emerging after traversing 100 m thickness.

Due to the energy loss of muons in a solid material (such as the rock of a mountain), which for a thin layer is proportional to the quantity *ρ dx*, where *ρ* is the density of the material, the fraction of muons which survive after traversing a finite thickness x of material is given, to first order, by the integrated density over the path length *L*

∫

**3. Applications of the muon absorption technique**

**Figure 1.** Momentum spectrum of cosmic muons, parametrized by Eq. (2).

0.1 to 10 MeV) in Lead, as derived from the NIST standard data [5].

The muon energy loss is usually expressed through its average value

reconstruction and simulation algorithms.

−\_\_\_ *dE*

e−

to other processes (e+

44 Cosmic Rays

The exploration of heavy structures requires penetrating probes, in order to convey information concerning the interior of the structure and its details. For objects having sizes of the order of 1 m or less, X-rays or neutrons may constitute a valid alternative. For instance, typical

so that a nonnegligible fraction of X-ray photons may penetrate several cm of Lead. **Figure 2** shows a plot of the mass attenuation coefficient for photons of various energies (from about

For larger size objects, the attenuation of such probes would be too high, and more penetrating particles, such as high energy muons, are required to traverse larger thicknesses. The basic properties of muon interaction in matter are known since a long time. However, their potential as a penetrating probe to give information on the interior of large structures is more recent, and only in the last years the literature has seen a large body of applications in this field, also related to the corresponding development of appropriate detectors, electronics,

where *a*(*E*) takes into account the energy loss due to ionization, and *b*(*E*) the energy loss due

ionization term may be described by the Bethe-Bloch formula as a continuous process. At

*dx* <sup>=</sup> *<sup>a</sup>*(*E*) <sup>+</sup> *<sup>b</sup>*(*E*)*<sup>E</sup>* (4)

pair production, Bremmstrahlung and photonuclear processes). The

/g for Lead,

mass attenuation coefficients of X-rays (30 keV) are of the order of μ/ρ = 30 cm<sup>2</sup>

$$^0\_0\rho(\infty)d\infty \tag{5}$$

**Figure 2.** Mass attenuation coefficient of X- or γ-rays of various energies in lead, derived from the NIST standard data [5].

muon direction provides a density map, i.e. a map of the average density along that direction. A density map—once the actual traversed thickness is known and inserted for any specific orientation—may then reveal differences in the density evaluated along different directions. This is the basic principle of the muon absorption tomography. Although the muon absorption tomography may only provide two-dimensional density maps, in principle the combined use of several detectors, pointing to the object from different orientations may produce a 3D map of the object. The construction and use of a set of identical detectors, placed in different locations and working with comparable performance is not a trivial task and the real use of

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A standard setup for muon absorption experiments requires a muon tracking detector (telescope), usually employed in transmission mode (i.e. with the object being located between the open sky and the telescope). The reconstruction of a large number of tracks in the telescope allows for a 2D tomographic map, with a resolution which depends on the telescope tracking performance and on experimental disturbances such as multiple scattering effects in the material surrounding the object to be explored, as well as in the air. Many other aspects of the detector performance, such as its overall detection efficiency, response uniformity, sensitive area, alignment properties, duty cycle, cost and transportability, … influence the real capabil-

Considering the possibilities offered by muon absorption tomography, several applications have been proposed, with many experimental results obtained so far. Here a brief review of

A large interest in absorption muon tomography is related to the possibility of exploring the hidden part of mountains, especially active or potentially active volcanoes, by means of cosmic muons traversing part of their solid structure and being partially absorbed with respect to those coming from the open sky (**Figure 5**). This idea, exploited for the first time by Nagamine et al. in [7] and Tanaka et al. [8], has received an increasing attention in recent years, and a variety of projects, detector prototypes and operational activities have been reported. Important contributions to the field have been given by the Japanese collaboration leaded by H.K.M.Tanaka [8–12], which has employed a muon telescope made by several detection planes with scintillators with PMTs separated by Lead plates, by the Diaphane Collaboration [13–16], which carried out various measurement campaigns in several locations of the world (in France, Italy and Philippines) with scintillator-based muon telescopes, by the TOMUVOL Collaboration [17], employing resistive plate chambers detectors, and by the MU-RAY Project [18, 19], which has employed a muon telescope based on scintillator strips with SiPM photo-

A recent project has been developed also by our group in Catania, devoted to the study of the top craters of Mt. Etna, the highest active volcano in Europe, with a telescope equipped

installed since last year close to the top of the mountain. Preliminary tomographic images of such craters have been already obtained by a comparison between the map produced by

segmented planes of scintillator strips with multianode PMT readout, already

this opportunity is still to be exploited.

sensors for the exploration of Mt. Vesuvius in Italy.

ity of the instrument.

these fields is given.

**3.1. Vulcanology**

with three 1 m2

**Figure 3.** Muon energy loss in lead as a function of the muon energy, as derived from data reported in Ref. [6].

**Figure 4.** Transmission factor of cosmic muons as a function of the rock thickness traversed, as extracted from GEANT simulations for a realistic lava scenario from Mt. Etna.

Such quantity is sometimes called the opacity. A muon tracking detector, able to measure the number of muons arriving to it from any given direction, provides an experimental measurement of the opacity along different directions. The knowledge of the path length *L* for any muon direction provides a density map, i.e. a map of the average density along that direction. A density map—once the actual traversed thickness is known and inserted for any specific orientation—may then reveal differences in the density evaluated along different directions. This is the basic principle of the muon absorption tomography. Although the muon absorption tomography may only provide two-dimensional density maps, in principle the combined use of several detectors, pointing to the object from different orientations may produce a 3D map of the object. The construction and use of a set of identical detectors, placed in different locations and working with comparable performance is not a trivial task and the real use of this opportunity is still to be exploited.

A standard setup for muon absorption experiments requires a muon tracking detector (telescope), usually employed in transmission mode (i.e. with the object being located between the open sky and the telescope). The reconstruction of a large number of tracks in the telescope allows for a 2D tomographic map, with a resolution which depends on the telescope tracking performance and on experimental disturbances such as multiple scattering effects in the material surrounding the object to be explored, as well as in the air. Many other aspects of the detector performance, such as its overall detection efficiency, response uniformity, sensitive area, alignment properties, duty cycle, cost and transportability, … influence the real capability of the instrument.

Considering the possibilities offered by muon absorption tomography, several applications have been proposed, with many experimental results obtained so far. Here a brief review of these fields is given.

## **3.1. Vulcanology**

Such quantity is sometimes called the opacity. A muon tracking detector, able to measure the number of muons arriving to it from any given direction, provides an experimental measurement of the opacity along different directions. The knowledge of the path length *L* for any

**Figure 4.** Transmission factor of cosmic muons as a function of the rock thickness traversed, as extracted from GEANT

simulations for a realistic lava scenario from Mt. Etna.

46 Cosmic Rays

**Figure 3.** Muon energy loss in lead as a function of the muon energy, as derived from data reported in Ref. [6].

A large interest in absorption muon tomography is related to the possibility of exploring the hidden part of mountains, especially active or potentially active volcanoes, by means of cosmic muons traversing part of their solid structure and being partially absorbed with respect to those coming from the open sky (**Figure 5**). This idea, exploited for the first time by Nagamine et al. in [7] and Tanaka et al. [8], has received an increasing attention in recent years, and a variety of projects, detector prototypes and operational activities have been reported. Important contributions to the field have been given by the Japanese collaboration leaded by H.K.M.Tanaka [8–12], which has employed a muon telescope made by several detection planes with scintillators with PMTs separated by Lead plates, by the Diaphane Collaboration [13–16], which carried out various measurement campaigns in several locations of the world (in France, Italy and Philippines) with scintillator-based muon telescopes, by the TOMUVOL Collaboration [17], employing resistive plate chambers detectors, and by the MU-RAY Project [18, 19], which has employed a muon telescope based on scintillator strips with SiPM photosensors for the exploration of Mt. Vesuvius in Italy.

A recent project has been developed also by our group in Catania, devoted to the study of the top craters of Mt. Etna, the highest active volcano in Europe, with a telescope equipped with three 1 m2 segmented planes of scintillator strips with multianode PMT readout, already installed since last year close to the top of the mountain. Preliminary tomographic images of such craters have been already obtained by a comparison between the map produced by

**Figure 5.** A simple geometrical sketch showing the principle of muon tomography applied to the study of mountain structures. A tracking telescope is placed downstream of the structure being explored, reconstructing muon tracks which ideally have traversed a thickness of solid rock. A comparison with the tracks coming from the open sky or from the backside is used to provide a 2D density map of the structure. A nonnegligible background however may originate from muons which are scattered either from the solid rock or from the air.

muons originating from the front side and the corresponding map produced by the muons coming from the back side.

It must be remembered that other Projects [20, 21] are exploiting the possibility to employ the Cerenkov light produced by the muons in the air after traversing the large thickness of the rock by a Cerenkov detector prototype (ASTRI), originally devised for astrophysical investigation in view of the large Cerenkov Telescope Array (CTA) Project.

The interest in this field is twofold: from one side methods based on muon tomography may complement and sometimes even surpass the potential offered by traditional methods in the understanding the inner part of these structures, revealing empty spaces, or different density profiles inside the mountain. On the other side there is the hope to reach the resolution and capability to monitor in real time the time evolution of the subsurface structures, in order to control potential activities giving rise to explosions and lava eruptions. This last possibility at the moment is still far from being fully reached, while static investigations have offered beautiful pictures of the interior of mountains and volcanoes in several parts of the world.

An important aspect of the technique, which in some cases offers a better figure of merit in comparison to geological and geophysics methods, is the spatial resolution, which can be expressed as

$$
\Delta \mathbf{x} = L \, \Delta \theta \,\tag{6}
$$

**3.2. Underground measurements**

segmented into 32 scintillator strips.

environments.

**3.3. Archaeology**

The use of absorption muon tomography is of course not only limited to the study of large mountain structures, but proves much more useful for the investigation of smaller geological locations, underground cavities, caverns, mines and tunnels, due to the reduced thickness to be explored, hence to the large flux being measured. There are several examples of the use of this technique for these applications [21–25]. As a recent example, in one of these investigations [22], carried out to explore underground cavities in the Naples area, a muon detector similar to that employed for volcano muography was employed, with size 1 m x 1 m, and

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The vertical rock thickness above the detector was in the previous case about 40 m, which did not reduce too much the muon count rate, allowing for a significant result to be obtained in less than one month of data taking. Actually, for many of these applications, the range of rock thickness usually amounts to a few tens metres, which is a value much less than the values of interest for large volcanic structures. The possibility to install the detector in places which are not so prohibitive as for volcanic explorations gives larger opportunities to use this technique, which will likely be employed more and more in the near future to investigate underground

As recalled at the beginning of this Chapter, one of the first examples of muon absorption tomography is represented by the well-known work by Alvarez and collaborators [2], who employed a muon detector inside an Egyptian pyramid to search for possible hidden chambers. The interest in the study of these very old structures is still very large, and in 2017 a recent study [26] was reported by the ScanPyramid Project, supported by many Institutions, who succeeded to find a very large (~ 30 m) unknown chamber in the Great or Khufu's Pyramid. Such void was first explored by nuclear emulsions and then confirmed by measurements carried out with scintillation hodoscopes and gas detectors; hence, it represents a beautiful example of interrelations between different observation techniques pointing to the same body of evidence. Additional examples of the use of the muon absorption technique for archaeological studies have been reported over the last years [27–29], among which is a study

The first investigation concerned with the use of the muon scattering process to obtain a radiography of the hidden content in a volume dates back to the work by Borozdin et al. [30], who employed a set of drift chambers (60 × 60 cm) to get radiographic images of tungsten blocks. This technique proved to be very promising for several reasons: it does not introduce any additional radiation, as it is for instance for X-rays; moreover, most of the scattered muons contribute to build the image, contrary to absorption, where a large fraction of muons is absorbed by the material itself. In the scattering mode, the muon tomography technique

of the cavities in the Teotihuacan Pyramid of the Sun [27].

**4. Muon scattering and tomography**

where *L* is the distance between the detector and the structure being probed, and *∆θ* is the angular resolution of the tracking device. As an example, for a distance *L* = 500 m, and an angular resolution of *∆θ* = 1°, a spatial resolution of the order of 10 m is obtained, which is better than typical values of other geophysical methods.
