Muography. Группа авторов
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(Section 1.2.10) are discussed. In Section 1.3, after the brief introduction of early works in Section 1.3.1, we discuss the results of measurements in pioneering works by addressing two major topics: subsurface volcanism and tectonics (Sections 1.3.2, 1.3.3, and 1.3.4) and underground water (Section 1.3.5) and conclusions are given in Section 1.4. Various kinds of detectors used for muography will be introduced in the following chapters, and thus will not be described here.
1.2 PRINCIPLES OF MUOGRAPHY
1.2.1 Muon Energy Spectrum
Muons are produced during the interaction between primary GCRs and the nuclei in the planet’s atmosphere or within rocks if there is no atmosphere. These muons are called cosmic‐ray muons. An expression for the differential cosmic‐ray muon spectrum on Earth at various zenith angles has been derived by several authors in accordance with the hypothesis that the primary particles are isotropically incident at the top of the atmosphere, and that the mesons (pions and kaons) retain the directions of their producers (Bull et al., 1965; Bugaev et al., 1998; Gaisser & Stanev, 2008; Matsuno et al., 1984). These authors' analytical expressions have been validated and improved by comparison with the spectrum of muons taken from experiments performed at sea level (Achard et al., 2004; Allkofer et al., 1985; Haino et al., 2004; Jokisch et al., 1979; Matsuno et al., 1984), and the current expression is in good agreement with the observed muon flux. On Earth, the muon flux reaches its maximum (~200 1/m2/sr/s) at an atmospheric depth of approximately 300 g/cm2, depending on the latitude, and then slowly decreases as the muons pass through the additional atmospheric depth (Particle Data Group, 2020). The muon flux is ~90 1/m2/sr/s at sea level. The horizontal muon rate on Earth is suppressed compared to the vertical muons mainly due to the increased atmospheric path length and correspondingly higher energy cutoff. Furthermore, the average charged pion multiplicity is different. There is an appreciable probability that (higher energy) pions will collide with atmospheric nuclei before decaying into muons, and (lower energy) muons decay before reaching the Earth’s surface. However, the average muon energy becomes increasingly high as the direction traveled is more horizontal because pions decay before they re‐interact any further. While the decay constant of muons is 660 m, those of pions and kaons are much shorter, and respectively 7.8 m and 3.7 m.
On Mars, the surface atmospheric pressure is only ~1/100 that of the Earth, and thus, many of the primary particles reach the surface before undergoing a primary interaction. This results in both a lower meson production rate and a lower meson decay rate than in the Earth’s atmosphere. Tanaka (2007) indicated that based on the steep power law dependence in the early stages of the shower cascade, the meson flux would be strongly dependent on the atmospheric pressure, zenith angle, and muon energy. On Mars, the horizontal muon rate is higher than the vertical muon rate due to the additional atmospheric mass through which the muons transverse. The horizontal atmospheric depth of Mars is 100 g/cm2, a sufficient number of mesons. A sufficient number of muons to be practically detectable on the Martian surface are generated in the horizontal direction, and their energies are sufficiently high to practically perform muography on Mars. Muography can be performed because the probability of the decay of mesons before further interactions is higher than it would be on Earth; this is in stark contrast to the muon generation on Earth.
On small stellar bodies (SSB) such as asteroids or comets, there is no atmosphere. Primary GCRs directly collide with the stellar bodies and generate muons inside them. The average energy of these muons is much lower than the atmospheric muons because the secondary mesons are more copiously produced due to the short mean free path (MFP) inside solid‐state materials and thus, their energies are quickly dissipated. The resultant muon flux (> 50 GeV) is 103–104 times lower than the terrestrial muon flux, depending on the medium density (Prettyman et al., 2014). This flux has a tendency to decrease as a medium density increases because the meson’s MFP is further shortened. Currently, the application of muography to extraterrestrial objects is still in the conceptual phase.
1.2.2 Geomagnetic Effects in the Muon Flux
Muographic images are usually produced in the spherical coordinate system, and generally contain angular‐dependent background events that distort the images. In the following section, the possible sources of these backgrounds are examined. In the vicinity of Earth, due to positively charged primary GCRs and the geomagnetic field directed towards the geomagnetic North Pole, some eastern trajectories of the incoming cosmic rays are suppressed (East‐West effect). This geomagnetic cutoff is caused by the geomagnetic shielding that affects the charged cosmic rays arriving from outside the magnetosphere, and its threshold rigidities range from less than 109 V near the geomagnetic poles to about 1.6 × 1010 V for vertical particles near the equator (Smart & Shea, 1994). As a result, cosmic-ray muons from the east are found to have a weaker flux than those from the west. This East‐West geomagnetic effect is more pronounced at higher altitudes. In middle latitude regions at sea level, only primary GCRs having lower energies are more affected by the geomagnetic field, but they do not contribute to production of muons in the atmosphere. For this reason, there has been a long discussion about whether the East‐West effect is observable in the sea‐level muon flux (Hansen et al., 2005). The recent measurements with the Far detector used for the NOvA experiment showed the East‐West asymmetry of cosmic‐ray muons of ~1% (Petrova, 2019) within the zenith angular range between 30o and 70o at Ash River, MN, USA.
This East‐West geomagnetic effect strongly depends on the latitude where the cosmic‐ray muons are measured. First measured 70 years ago, the vertical flux of muons with momentum around 0.33 GeV/c at latitude 60° was 1.8 times higher with respect to the flux at the equator (Conversi, 1950). This latitudinal geomagnetic effect was more recently measured between the middle latitude region (the cutoff values of 2.7 × 109 V) and the region near the equator (the cutoff values of 1.4 × 1010 V), respectively, indicating variations by 20 and 10% in the flux of muons with energies of ~0.3 GeV/c and ~1 GeV/c and no significant variations could be seen in the muons above 3 GeV/c (Allkofer et al., 1975). In conclusion, this latitudinal effect is practically negligible in muography as long as the measurements are conducted within the mid‐latitude region. However, in the region near the equator, it can influence muons below ~5 GeV at sea level (Allkofer et al., 1975).
1.2.3 Altitudinal Atmospheric Effects in the Muon Flux
The muons that arrive at sea level are the last stage of a multi‐step cascade process. The average muon energy loss in the atmosphere is in the order of 2 GeV. Therefore, sub‐GeV muons originated in the upper atmosphere cannot reach sea level, and the muon energy spectrum varies at different atmospheric depths; in particular, in energy regions lower than 2 GeV. Based on the results of the CAPRICE 94 muon measurements (Boezio et al., 2000), the low‐energy (< 2 GeV) muon flux increases by a factor of 5 if the atmospheric depth is reduced by one half of the value at sea level (500 hPa) (Engel et al. 2001). On the contrary, the flux of muons with higher energies (3–20 GeV) increases only by a factor of 1.5 (Engel et al. 2001).
1.2.4 Seasonal Atmospheric Effect in the Muon Flux
When