R. A. Millikan and G. H. Cameron, The Origin of the Cosmic Rays, Phys. Rev, vol.32, issue.533, 1928.

J. Clay, Penetrating radiation, Proc. R. Acad, pp.1115-1127, 1927.

L. Leprince-ringuet and P. Auger, Etude par la méthode des coïncidences de la variation du rayonnement cosmique suivant la latitude, J. Phys. Radium, vol.5, pp.193-198, 1934.

A. Compton, A Geographic Study of Cosmic Rays, Phys. Rev, issue.43, pp.387-403, 1933.

B. Rossi, Phys. Rev, vol.606, issue.36, 1930.

G. Lemaitre and M. S. Vallarta, On Compton's Latitude Effect of Cosmic Radiation, Physical Review, vol.43, issue.2, pp.87-91, 1933.

K. A. Olive, Review of Particle Physics. Chinese Physics C, vol.40, issue.10, p.100001, 2016.

T. Gaisser, T. Stanev, and ;. S. Eidelman, Cosmic Rays in the Review of Particle Properties, Physics Letters B, vol.592, pp.254-260, 2008.

, National Aeronautics and Space Administration

M. Spurio, Particles and Astrophysics A Multi-Messenger Approach. Astronomy and Astrophysics Library

X. Garrido, Étude de la composition des rayons cosmiques d'ultra-hautesénergies détectés par l'Observatoire Pierre Auger et analyse des processus hadroniques associés, 2008.

K. Greisen, End to the cosmic-ray Spectrum ?, Physical Review Letters, vol.16, issue.17, pp.748-750, 1966.

G. Zatsepin and . Vadem-kuzmin, Upper limit of the spectrum of cosmic rays, Journal of Experimental and Theoretical Physics Letters, vol.4, p.78, 1966.

J. Linsley, Evidence for a primary cosmic-ray particle with energy 10 20 eV, Physical Review Letters, vol.10, issue.4, p.146, 1963.

L. Leprince-ringuet, Les rayons cosmiques. Albin Michel, 1945.

L. N. Bogdanova, M. G. Gavrilov, V. N. Kornoukhov, and A. S. Starostin, Cosmic muon flux at shallow depths underground, Physics of Atomic Nuclei, vol.69, issue.8, pp.1293-1298, 2006.

S. Neddermeyer and C. Anderson, Cosmic-Ray Particles of Intermediate Mass, Physical Review, vol.54, issue.1, pp.88-89, 1938.

J. C. Street and E. C. Stevenson, New Evidence for the Existence of a Particle Intermediate Between the Proton and Electron, hys. Rev, vol.52, 1003.

E. J. Williams and G. E. Roberts, Evidence for Transformation of Mesotrons into Electrons, Nature, vol.145, issue.3664, pp.2-103, 1940.

H. A. Bethe, Molière's Theory of Multiple Scattering, Physical Review, vol.89, p.1953, 1256.

F. Bloch, Bremsvermögen von Atomen mit mehreren Elektronen, Z. Phys, vol.16, 1933.

A. Tang, G. Horton-smith, A. Vitaly, A. Kudryavtsev, and . Tonazzo, Muon Simulations for Super-Kamiokande, KamLAND and CHOOZ, Physical Review D, vol.74, issue.5, 2006.
URL : https://hal.archives-ouvertes.fr/in2p3-00109634

D. Chirkin, Fluxes of Atmospheric Leptons at 600 GeV -60 TeV, 2004.

K. A. Olive, Review of Particle Physics. Chinese Physics C, vol.40, issue.10, p.100001, 2016.

P. Shukla and S. Sankrith, Energy and angular distributions of atmospheric muons at the Earth, 2018.

D. Heck, J. Knapp, J. N. Capdevielle, G. Schatz, and T. Thouw, Report FZKA, vol.6019, 1998.

C. Hagmann, Cosmic-ray Shower Library (CRY), 2012.

L. Waters, MCNPX User's Manual, Version 2.5.0, 2005.

S. Agostinelli, J. Allison, K. Amako, J. Apostolakis, H. Araujo et al., , vol.506, pp.250-303, 2003.

E. P. George, Cosmic rays measure overburden of tunnel, Commonwealth Engineer, pp.455-457, 1955.

L. Alvarez, Search for hidden chambers in the pyramids, Science, vol.167, pp.832-839, 1970.

A. Menchaca-rocha, Search for cavities in the Teotihuacan Pyramid of the Sun using cosmic muons : preliminary results, Proceedings of the 32nd International Cosmic Ray Conference (ICRC2011), vol.4, p.325, 2011.

, Heritage Inovation Preservation, HIP ScanPyramids

K. Nagamine, Geo-tomographic observation of inner structure ofvolcano with cosmicray muons, Geography, vol.104, pp.995-1007, 1995.

H. Tanaka, Development of the cosmic-ray muon detection system for probing internal-structure of a volcano, Hyperfine Interact, vol.138, pp.521-526, 2001.

V. Tioukov, A. Alexandrov, C. Bozza, L. Consiglio, D. Nicola et al., First muography of Stromboli volcano. Scientific Reports, vol.9, issue.1, pp.1-11, 2019.

J. Marteau, J. De-bremond-d'ars, D. Gibert, K. Jourde, J. Ianigro et al., DIAPHANE : Muon tomography applied to volcanoes, civil engineering, archaelogy, Journal of Instrumentation, vol.12, issue.02, pp.2008-02008, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01554623

E. L. Menedeu, RPC application in muography and specific developments, Journal of Instrumentation, vol.11, issue.06, pp.6009-06009, 2016.

L. F. Thompson, J. P. Stowell, S. J. Fargher, C. A. Steer, K. L. Loughney et al., The application of muon tomography to the imaging of railway tunnels, 2019.

P. De-sloovere, Le télescopeà muons nouvel outil de la géophysique appliquée ?, 2016.

H. Jeffreys, An Invariant Form for the Prior Probability in Estimation Problems, Proceedings of the Royal Society of London. Series A, vol.186, pp.453-461, 1007.

F. Y. Edgeworth, On the Probable Errors of Frequency-Constants, Journal of the Royal Statistical Society, vol.71, issue.2-4, pp.651-678, 1908.

C. T. Wilson, On a Method of Making Visible the Paths of Ionising Particles through a Gas, Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, vol.85, issue.578, pp.285-288, 1911.

S. Neddermeyer and C. Anderson, Cosmic-Ray Particles of Intermediate Mass, Physical Review, vol.54, issue.1, pp.88-89, 1938.

D. A. Glaser, Some Effects of Ionizing Radiation on the Formation of Bubbles in Liquids, Physical Review, vol.87, issue.4, pp.665-665, 1952.

K. Kleinknecht, Detectors for Particle Radiation, 1998.

H. Wenninger, the tracks of the bubble chamber, 2004.

F. Sauli, Gaseous Radiation Detectors : Fundamentals and Applications, 2014.

J. S. Townsend and V. A. Bailey, The motion of electrons in gases, pp.873-891, 1921.

C. Ramsauer, Über den Wirkungsquerschnitt der Gasmoleküle gegenüber langsamen Elektronen, vol.369, pp.513-540, 1921.

C. Grupen and B. Shwartz, Particle Detectors, 2008.

L. A. Viehland, Gaseous Ion Mobility, Diffusion, and Reaction, Springer Series on Atomic, vol.105, 2018.

C. Sanborn and . Brown, Basic Data of Plasma Physics : The Fundamental Data on Electrical Discharges in Gases, 1967.

L. G. Christophorou and R. P. Blaunstein, Electron attachment in gases and liquids, Chemical Physics Letters, vol.12, issue.1, pp.173-179, 1971.

S. A. Korff, Electron And Nuclear Counters, 1955.

H. Genz, Single electron detection in proportional gas counters. Nuclear Instruments and Methods, vol.112, pp.83-90, 1973.

F. Thibaud, Développement de détecteurs Micromegas pixellisés pour les hauts flux de particules etévaluation de la contribution diffractiveà la leptoproduction de hadronsà COMPASS, p.195

H. Raether, Electron avalanches and breakdown in gases, Butterworths, 1964.

H. Geiger and W. Müller, Elektronenzählrohr zur messung schwäch-ster aktivitäten, pp.617-618, 1928.

S. Bouteille, Development and applications of micro-pattern gaseous detectors for muon tomography, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01759508

W. Shockley, Currents to conductors induced by a moving point charge, Journal of applied physics, vol.9, pp.635-636, 1938.

S. Ramo, Currents induced by electron motion, Proceedings of the IRE, vol.27, pp.584-585, 1939.

G. Charpak, The use of multiwire proportional counters to select and localize charged particles, Nuclear Instruments and Methods, vol.62, pp.262-268, 1968.

F. Sauli, Principles of operation of multiwire proportional and drift chambers, p.92, 1977.

A. Oed, Position-sensitive detector with microstrip anode for electron multiplication with gases, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, vol.263, issue.2, pp.351-359, 1988.

S. and D. Torre, MPGD developments : historical roadmap and recent progresses in consolidating MPGDs, Journal of Instrumentation, vol.8, issue.10, pp.10020-10020, 2013.

F. Sauli, GEM : A new concept for electron amplification in gas detectors, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, vol.386, issue.2, pp.531-534, 1997.

Y. Giomataris, . Ph, J. P. Rebourgeard, G. Robert, and . Charpak, MICROME-GAS : a high-granularity position-sensitive gaseous detector for high particle-flux environments, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, vol.376, issue.1, pp.29-35, 1996.

P. Serrano, Caliste-MM : a new spectro-polarimeter for soft X-ray astrophysics, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01723432

G. Charles, Mise au point de détecteurs Micromegas pour le spectromètre CLAS12 au laboratoire Jefferson, 2013.

I. Giomataris, Micromegas in a bulk, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, vol.560, pp.405-408, 2006.

M. S. Dixit and A. Rankin, Simulating the charge dispersion phenomena in micro pattern gas detectors with a resistive anode, Nucl. Instrum. Meth, vol.566, pp.281-285, 2006.

M. Dixit and . Others, Micromegas TPC studies at high magnetic fields using the charge dispersion signal. volume A581 of, Nucl. Instrum. Meth, pp.254-257, 2007.
URL : https://hal.archives-ouvertes.fr/in2p3-00141896

T. Alexopoulos, R. Oliveira, J. Wotschack, G. Tsipolitis, V. Polychronakos et al., A spark-resistant bulkmicromegas chamber for high-rate applications, Nucl.Instrum.Meth, vol.640, pp.110-118, 2011.

, LXCAT. Morgan database, www.lxcat.net, retrieved on, 2019.

D. Attié, TPC review. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, vol.598, pp.89-93, 2009.

. F-j-iguaz, . Ferrer-ribas, I. Giganon, and . Giomataris, Characterization of microbulk detectors in argon-and neon-based mixtures, Journal of Instrumentation, vol.7, issue.04, pp.4007-04007, 2012.

. Bibliographie,

S. Bouteille, Développement et applications de détecteurs gazeuxà micro-pistes pour la tomographie muonique. thesis, 2017.

T. Alexopoulos, R. Oliveira, J. Wotschack, G. Tsipolitis, V. Polychronakos et al., A spark-resistant bulkmicromegas chamber for high-rate applications, Nucl.Instrum.Meth, vol.640, pp.110-118, 2011.

S. Procureur, R. Dupré, and S. Aune, Genetic multiplexing and first results with a 50×50 cm2 Micromegas, Nuclear Instruments and Methods in Physics Research A, vol.729, pp.888-894, 2013.
URL : https://hal.archives-ouvertes.fr/in2p3-00907721

X. Yue, M. Zeng, Z. Zeng, Y. Wang, X. Wang et al., Mathematical modelling and study of the encoding readout scheme for position sensitive detectors, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, vol.816, pp.33-39, 2016.

D. Attie, S. Aune, P. Baron, D. Besin, H. Bervas et al., The readout system for the Clas12 Micromegas vertex tracker, 19th IEEE-NPSS Real Time Conference, pp.1-11, 2014.

D. Calvet, L'électronique de lecture de MINOS et autres développements récents, 2015.

S. Bouteille, D. Attié, P. Baron, D. Calvet, P. Magnier et al., Large resistive 2d Micromegas with genetic multiplexing and some imaging applications. Nuclear Instruments and Methods in, Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, vol.834, pp.187-191, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01467599

. Caen,

J. Galán, Signal propagation and spark mitigation in resistive strip read-outs, Journal of Instrumentation, vol.7, issue.04, pp.4009-04009, 2012.

Y. Tanaka, K. Miyake, and A. Saito, Diamond-like Carbon Film for Bearing Parts and Its Mass Production Technology, SEI Technical Review, p.5, 2019.

A. Ochi, Carbon Sputtering Technology for MPGD detectors. 3rd Academy-Industy Matching Event on Photon Detection and RD51 Mini-Week, vol.351, 2015.

M. Vanderbrouck, Production issues with Bulk Micromegas for the CLAS12 experiment, RD51 Mini-Week, 2016.

Y. , Capteur USB de données météo

, Air Liquide. Oxysorb, ref 123342

M. Frotin, P. Gros, D. Attié, D. Bernard, V. Dauvois et al., Sealed operation, and circulation and purification of gas in the HARPO TPC, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01719618

S. Procureur, New MPGD-based muon telescopes for ScanPyramids and associated R&D on gas consumption, 6th International Conference on Micro Pattern Gaseous Detectors, MPGD19 of 6th International Conference on Micro Pattern Gaseous Detectors, vol.19, 2019.

V. C. Paul and . Hough, Machine analysis of bubble chamber pictures, vol.73, p.2, 1959.

, Quand je viens vous voir, pour vous demander des trucs ; c'est l'enchanteur que je viens voir ; pour qu'il m'donne des solutions d'enchanteur : pas des combines a la noix ou des remèdes de bonne femme ! Vousêtes mon enchanteur, vousêtes pas ma grand-mère, Alexandre Astier

. .. Introduction, 147 6.2 Reconstruction de la carte de densité, p.151

. .. Résultats, 3.2 Influence du modèle du flux de muons

. .. Questions,

.. .. Conclusion,

.. .. Bibliographie,

, Dans les chapitres précédents, nous avons montré l'importance de la connaissance

, Système sur-contraint m ? n : le système n'admet en général pas de solutions

, Système sous-contraint m ? n : le système admet une infinité de solutions

, Les cas 2 et 3 sont des cas plus généraux et leur résolution reposent sur la décomposition de matrices. La méthode la plus générale 2 est la décomposition de matrices en valeurs singulières ou SVD (Singular Value Decomposition). La décomposition SVD n'impose aucune condition de rang ou de dimension sur la matrice considérée. Elle permet pour une matrice A de dimension m×n et de rang r

. U-?-r-m×m-et-v-?-r-n×n, unicité 4 d'une matrice diagonale ? ? R m×n nulle, excepté les r premierséléments diagonaux strictement positifs ? 1 ? ? 2 ?

L. , estimer quels sont les effets dans la manière de calculer les distances parcourues par les muons afin de remplir la matrice D, qui va par la suiteêtre décomposée par la méthode SVD. Deux choix s'offrentà nous et sont illustrés par la figure 6, p.12

, La première consisteà considérer une trajectoire moyenne pour le cône d'acceptance

, Cette trajectoire est calculée avec un angle ? c = (x c1 ? x c2

, N ? } et ? 1 et ? 2 les angles délimitant le cône d'acceptance, comme illustré sur la figure 6.12. Nous avons choisi 6 N ? = 10, sous-directions

T. K. Gaisser, Cosmic rays and particle physics, 1990.

P. Shukla and S. Sankrith, Energy and angular distributions of atmospheric muons at the Earth, 2018.

D. Heck, J. Knapp, J. N. Capdevielle, G. Schatz, and T. Thouw, Report FZKA, vol.6019, 1998.

I. Antcheva, M. Ballintijn, B. Bellenot, M. Biskup, R. Brun et al., ROOT -A C++ framework for petabyte data storage, statistical analysis and visualization, Computer Physics Communications, vol.180, issue.12, pp.2499-2512, 2009.