Muography. Группа авторов
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rock with a given thickness in units of meter water equivalent (mwe)."/>
Figure 1.1 Integrated muon flux after passing through rock with a given thickness in units of meter water equivalent (mwe). The angles are measured from the zenith.
1.2.7 Background Events in Muography
The background events that degrade the quality of muographic images can be originated from both outside (extrinsic background) and inside (intrinsic background) the observation system (a combination of detectors, radiation shields, and other related equipments). Primary GCRs produce not only muons but also cascades of protons, neutrons, mesons, and other electromagnetic particles. The extrinsic background is generated by these secondary particles. The number of these particles rapidly decreases as they travel in the atmosphere but some of them arrive at sea level. The number of protons, electrons, and pions above 1 GeV are, respectively, two orders, three orders, and four orders of magnitude lower than the number of muons in the same energy range at sea level (Particle Data Group, 2020). However, when kilometric objects are observed in which low muon rates are expected, these backgrounds substantially degrade the image contrast. In particular, the protons are heavier than muons; hence longer MFP is present within the material (~10 cm in Pb), and thus could be a serious source of the background. On the contrary, the electromagnetic components such as electrons and gammas can be rejected relatively simply by requesting a linear trajectory through multiple layers of detectors and radiation shields. The radiation length of electrons is less than 6 mm in Pb.
The intrinsic background is caused by the muons scattered inside the observation system. Increasing the thickness of the radiation shields to reduce more extrinsic background rates would result in more muons being scattered inside the detectors, and thus the resultant images would be blurred. The intrinsic background level can be reduced by improving the tracking quality of the observation system (Kusagaya, 2017).
In an extraterrestrial environment, the condition of the extrinsic background will be completely different from the terrestrial one. Unlike Earth, Mars and small solar system bodies (SSSB) either do not have their own atmosphere or, they have an extremely thin atmosphere. Therefore, GCRs and GCR‐originated gamma rays (continuum gamma rays) will tend to directly hit the ground surface. As a result, the level of the extrinsic background is much higher than that on the Earth’s surface, for example, the proton flux at the ground level of these SSSBs tends to be 100 times higher than the terrestrial muon flux of Earth at sea level (Prettyman et al., 2014). However, in outer space, it is difficult to reject these high‐rate extrinsic backgrounds by using radiation shields, since these shields would add too much weight to the overall payload of the spacecraft. Geometrical configuration of the detectors must be well‐designed when muographers plan extraterrestrial muography.
1.2.8 Required Measurement Times
A muographic image is represented as a function of elevation and azimuth angles (θ, ϕ). These angles of an incident particle can be computed as follows by connecting two points in a space S(x, y, z) with a straight line:
(1.3)
(1.4)
Figure 1.2 Principle of the muon tracking. The top view (a) and the side view (b) of the detectors are shown.
where L is the distance between the upstream (pointed towards the target object) and downstream detectors (pointed away from the target object). The subscripts of x and y indicate the first and second points (Fig. 1.2). The positioning resolution of the points (Δx, Δy) therefore gives the detector’s angular resolution (Δθ, Δϕ).
The maximum definition of the muographic image, R, will then be Φ/Δϕ × Θ/Δθ pixels, where Φ and Θ are, respectively, the horizontal and vertical viewing angles of the detector. Bin sizes (pixel size) of the image can be optimized to attain the sufficient statistics for muon counts recorded in each bin. Since the power to resolve the target volume depends on this pixel size and the distance between the target and detector, the measurement time required for attaining a given level of statistics for counts of muons arriving from a given section of the target volume is inversely proportional to the square of the distance between the target and detector. In muographic measurements, it is therefore ideal to get the detector as close to the target as possible. However, in most cases, accessibility and infrastructure availability (e.g., electricity) at geological sites limit the locations for measurements. Tanaka (2016) proposed airborne muography (placing the detector inside a helicopter) to practically remove these restrictions (Fig. 1.3). Tanaka (2013) and Kusagaya (2017) proposed another technique to observe dynamics within a shorter timescale than the time resolution of the observation system by integrating time‐sequential muographic images for the repetitionary processes.
1.2.9 Muographically Averaged Densimetric Thickness and Muographically Averaged Geometric Thickness
Since the detectors always have an angular resolution (Δθ, Δϕ), the transmitted muon flux measured in one image pixel is an integration of the flux of the muons that had passed through different regions in the target object. The transmitted flux averaged over the angle range θ ±Δθ and ϕ ±Δϕ, < N >, can be directly compared with the observed flux in the pixel of the muographic images. Inversely, if < N > is given, the muographically averaged densimetric thickness (MADT), < X >, can be uniquely determined by inserting < N > into equation 1.2. The muographically averaged geometric thickness (MAGT) is defined by <X>/ ρ. The MAGT is therefore different from the arithmetically averaged rock thickness (Tanaka, 2020a).
1.2.10 Limitations of Muography and Potential Geological Targets
The limitations of muography include the following: (i) As long as the target has a strong density contrast, this contrast will show upon a muographic image. However, muography only resolves the average density distribution along individual muon paths. Therefore, the user must end up making assumptions or interpretations about the more localized structure along these muon paths or must use more than one detector to resolve the three‐dimensional density structure. (ii) It is limited to near‐surface depths and results are only obtained for the volumes located at elevations higher than the detector. The measurements strongly depend on the nature of the local topography. The detector must be placed on a slope pointing towards a topographically prominent feature of interest. Otherwise, the detector has to be installed underneath the target of interest by utilizing tunnels, boreholes, etc. (iii) The method is in principle limited to ranges of 5–6 km (which limits the size of the potential targets), and (iv) the quality of the resultant muographic image depends on the heterogeneity of the geological environment, the density