**5. Other applications**

In principle, dense structures may be explored by muon tomography, either by using the muon absorption or the scattering process, even if they are placed on the Earth surface. As an example, water towers were imaged by muon telescopes [52, 53], calibrating the response of the detector as a function of the water content inside the tower. Post-injection monitoring of CO2 stored in subsurface locations was investigated by several authors [54–56] by means of muon tomography. Industrial applications have also seen contribution from muon tomography [57, 58]. Finally, another application for the monitoring of civil buildings and structures which employs cosmic muons as a useful probe is the study of the angular distribution of muons detected in coincidence between a tracking detector on the ground and a set of additional detectors mechanically linked to the structure being monitored. Any movement of the structure with respect to the ground will result in a small modification of the distribution of the orientations of cosmic muons detected in coincidence, provided a good reconstruction of tracks and stable working conditions are achieved during long measurements [59, 60].

understand and analyze the experimental data being collected, improve the reconstruction and imaging techniques and help to design new apparatus and evaluate their performance. One of the items that has been long discussed in the muon scattering technique is the reconstruction of the distribution of the scattering centres, leading to a 2D or 3D tomographic image. While the simplest approach employs the POCA method, as discussed in Section 4, better algorithms and methods have been introduced, especially to deal with situations where multiple scattering centres exist. The Maximum Likelihood/Expectation Maximization (EL/ EM) iterative method [64] is employed as a valid alternative for processing muon scattering

Cosmic Ray Muons as Penetrating Probes to Explore the World around Us

http://dx.doi.org/10.5772/intechopen.75426

53

Clustering algorithms, which are a set of multivariate data analysis techniques, have been also used to group homogeneous items in a dataset. One of the most known clustering algorithms is the Friends-of-Friends. Applied to muon tomography, clustering analysis helps to detect

Another important aspect of the development of numerical methods in muon tomography is concerned with physics simulations. The importance of numerical simulations in the design of an experimental setup, as well as in the correct interpretation of the effects observed, has been long recognized in nuclear and particle physics and it is nowadays a routine aspect of any quantitative experimental investigation. This is also the case for any tomographic study carried out with cosmic muons. Very frequently, reconstruction and imaging algorithms are tested against simulated data, to compare the merits of different approaches and evaluate their inherent performance. In other cases, only a detailed simulation of the physics processes taking place in the experimental setup and in the surrounding environment may help to understand important aspects of the problem. As an example, the study of the background contribution to the direct flux of muons arriving to the detector through the rock is very important, since in some cases this contribution may be even larger than the direct flux [66], thus leading to an overestimation. In many cases a detailed simulation of the initial energy and angular cosmic particle distributions, coupled to a transport study of these particles along the mountain profile may help to disentangle some of these aspects and provide a quantita-

tive estimate of the role of the background in the corresponding measurements.

The list of possible applications provided by this short review is not at all exhaustive, and many other examples of the use of cosmic-ray muons to explore various aspects of our environment are available in the literature [67]. Since the first quantitative investigations at the end of 1990s, in about 20 years, the use of cosmic-ray muons for imaging has grown in interest and this technique is now enough consolidated to be proposed even for commercial use. The variety of possible applications in the field has promoted interdisciplinary studies, with the contribution of experts from different areas, and has already given interesting results in many practical situations. The number of papers, articles, technical reports and conference contributions is more and more large, and specialized conferences and workshop have been organized in the last few years to promote exchange of opinions and results, new collaborations and

data and reconstruct tomographic images.

objects within a spatial domain [65].

**8. Conclusions**

## **6. Muon tomography outside the Earth?**

Since cosmic rays originate from any direction and permeate all the known Universe, the question whether the same concepts discussed so far apply also to other places outside our terrestrial environment is intriguing. Limiting ourselves to the nearest environment outside the Earth, namely the Solar System, the interaction of the primary cosmics with other planets and celestial bodies produces different results depending on the presence of an atmosphere around the solid structure of the body. For planets or satellites where no atmosphere at all exists, such for instance the Moon, energetic primary particles interact with the surface without producing an extensive air shower. In other situations, where a massive atmosphere exists, much deeper and dense than the Earth atmosphere, as for instance on Venus or Jupiter, air showers may be created but most of the secondary particles are subsequently absorbed by the atmosphere itself, so that only a very small fraction of particles is able to arrive to the surface. Monte Carlo calculations of the interaction of energetic particles with the detailed structure of these bodies should be carried out for any specific situation in order to understand their peculiarities. In case of Mars, where the atmospheric pressure near the surface is only 1/100 with respect to Earth, the development of air showers has been studied in some detail by Tanaka [61], allowing to understand how the proportion between primary protons and secondary pions or muons is very much different than on Earth. In particular, due to the reduced thickness of the Martian atmosphere, the vertical flux of muons is much smaller with respect to the values obtained on the Earth; however, for inclined muons, close to the horizontal, the situation is reversed, and a larger flux of muons would be observed. In any case, contamination from the primary protons is a challenge, and some way to discriminate between the two species should be devised. It is interesting that such concepts have been discussed with relation to realistic Martian exploration missions, trying to understand even the practical aspects and problems which would be required to solve to carry out tomographic measurements on the Red Planet [62, 63].

#### **7. Imaging and simulation methods and algorithms**

Muon tomography has offered over the last years also a good environment for the development of mathematical and statistical algorithms, numerical simulation and procedures, to understand and analyze the experimental data being collected, improve the reconstruction and imaging techniques and help to design new apparatus and evaluate their performance.

One of the items that has been long discussed in the muon scattering technique is the reconstruction of the distribution of the scattering centres, leading to a 2D or 3D tomographic image. While the simplest approach employs the POCA method, as discussed in Section 4, better algorithms and methods have been introduced, especially to deal with situations where multiple scattering centres exist. The Maximum Likelihood/Expectation Maximization (EL/ EM) iterative method [64] is employed as a valid alternative for processing muon scattering data and reconstruct tomographic images.

Clustering algorithms, which are a set of multivariate data analysis techniques, have been also used to group homogeneous items in a dataset. One of the most known clustering algorithms is the Friends-of-Friends. Applied to muon tomography, clustering analysis helps to detect objects within a spatial domain [65].

Another important aspect of the development of numerical methods in muon tomography is concerned with physics simulations. The importance of numerical simulations in the design of an experimental setup, as well as in the correct interpretation of the effects observed, has been long recognized in nuclear and particle physics and it is nowadays a routine aspect of any quantitative experimental investigation. This is also the case for any tomographic study carried out with cosmic muons. Very frequently, reconstruction and imaging algorithms are tested against simulated data, to compare the merits of different approaches and evaluate their inherent performance. In other cases, only a detailed simulation of the physics processes taking place in the experimental setup and in the surrounding environment may help to understand important aspects of the problem. As an example, the study of the background contribution to the direct flux of muons arriving to the detector through the rock is very important, since in some cases this contribution may be even larger than the direct flux [66], thus leading to an overestimation. In many cases a detailed simulation of the initial energy and angular cosmic particle distributions, coupled to a transport study of these particles along the mountain profile may help to disentangle some of these aspects and provide a quantitative estimate of the role of the background in the corresponding measurements.
