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 contrast of the structure being surveyed, and the period of data collection. Dynamics of geofluids such as magma, natural gas, underground water, and sea current will cause time‐dependent variations of the subterranean densimetric heterogeneity. These variations can be captured by time‐sequential muographic observations.
Figure 1.3 Photographs of airborne muography. Distant (a) and close‐up (b) views of the measurements are shown. The white inset in (a) indicates the region of the close‐up view in (b). The distance between the rotor blade and the cliff is a few meters. Exterior (c) and interior (d) views of the apparatus, an integrated form of an array of detectors and a helicopter, are shown. A highly qualified maneuvering skill is required for this operation.
1.3 PIONEERING WORKS
1.3.1 Early Works
In the early stage of cosmic ray studies, underground measurements were the most effective way to extend the energy range of the measured muon spectrum beyond 1 TeV. In these measurements, mine galleries located at various depths were utilized to measure the depth‐dependent muon flux since geological features of these mines were well studied. Inversely, if this depth‐dependent muon flux was used as a reference curve, the average density above the detector could be derived. The idea of using muons produced by cosmic rays as probes was first applied 75 years ago by E.P. George, who measured the thickness of the rock overburden above a tunnel of the hydroelectric plant in Snowy Mountain, Australia (George, 1955). George measured the reduction in the muon flux after passing through the rock. The apparatus consisted of Geiger counters but was unable to provide an image of any structure within the overlying rock.
The use of muography to reveal the internal structures of inaccessible objects in archeology was introduced in the late 1960s by a group led by Luis Alvarez to search for undiscovered chambers in the Pyramid of Chephern in Egypt (Alvarez et al., 1970). After the invention of a spark chamber with a digital readout, imaging became more realistic. The group recorded the trajectories of muons through the pyramid and studied their transmission to establish why the Pyramid of Chephren had only one burial chamber (the so‐called Belzoni chamber) while the pyramid made by his father Cheops had more complicated internal structures, including the King's and Queen's chambers and the Grand Gallery. This joint project between the United States and the United Arab Republic began in 1966. Calculations showed that if a hidden room was located above the Belzoni chamber, it could be observed in the same way that a void is highlighted by a darker area in an X‐ray image. However, no hidden rooms were found inside the pyramid. Instead, the group showed the potential of the technique by detecting the cap rock from the Belzoni chamber. This pioneering work paved the way for the application of muography in various fields.
Since TeV muons penetrate kilometric rock, the technique shown by Alvarez et al. (1970) was in principle applicable to mountains. This possibility was explored by focusing on detecting muons that traversed at angles almost parallel to the ground surface, which could be utilized to probe mountains by tracing the trajectories of muons emerging from the other side of the mountain (Nagamine et al., 1995). Muography cannot image the deep structure of a volcano such as the magma chamber; however, it can image shallow regions of the volcano, which can provide useful information for understanding how the eruption style might change. The first muographic image of the inside of a volcano suggested possible pathways for magma ejection by visualizing the shape and size of low‐density regions under a deposit of solidified magma (Tanaka et al., 2007). At the same time, the results showed visual evidence of the resolving power of muography, and its applicability to any targets smaller than volcanoes. The first time‐sequential muographic images that captured the motion of subterranean geofluid targeted the rainfall‐triggered permeation of water into the mechanical fracture zone of the active seismic fault (Tanaka et al., 2011). The results later motivated researchers to apply muography to monitoring underground water conditions (Tanaka & Sannomiya, 2012) and magmatic motion inside volcanoes (Oláh et al., 2019; Tanaka et al., 2014).
1.3.2 Magmatic Convection
By taking advantage of the resolving power of muography, we can
