Principle. Galactic cosmic rays (GCRs) are accelerated by high energy events in our galaxy and before they arrive at Earth, they are deflected multiple times during their propagation, and lose their initial directional information. Muons are produced in the Earth's atmosphere via the collision between these GCRs and the Earth’s atmospheric nuclei. Due to different atmospheric thicknesses and density gradients for different GCR's arrival angles, the muon energy spectrum varies according to the different zenith angles. As a consequence, the vertical muon flux is higher than the horizontal flux, but the average energy of vertical muons is lower than the horizontal ones. The HKMSDD-MSM tide monitor utilizes these near horizontal muons.
Figure 2 shows the principle of HKMSDD-MSM tide monitoring. In this scheme, HKMSDD-MSMs are placed at near-shore locations below sea level such as basements of commercial buildings, subway stations, underground parking lots etc. As shown in Figure 2, near horizontal muons would pass through seawater and land soil before arriving at the MSM. The total thickness of the materials that muons will traverse through before arriving at the MSM is:
L = D/cosθ +(d-H)/sinθ (m.w.e.) (1)
where D (m) is the distance between the MSM and the shoreline, H (m) is the land altitude measured from the lowest tide level, d (m) is the depth of the MSMs measured from ground level, and θ is the elevation angle. Here the average densities of the land soil (ρearth) and seawater (ρwater) were respectively assumed to be 2.0 gcm−3 and 1.0 gcm−3. Since the tide level variations Δh (m) only changes the second term of Eq. (1), as D increases, the MSM's sensitivity to the tide variations is degraded.
The muon flux observed at the MSM (N) can be calculated as follows. Once L is determined, the minimum muon energy (Ec) that arrives at the MSM can be derived from the muon's energy range relationship in H2O and SiO242. By integrating the open-sky muon energy spectrum43,44,45 over the energy range between Ec and infinity, we obtain the angular dependent integrated muon flux I (θ), where θ is elevation angle. By integrating I (θ) over the angular range between 0 and Θ, N is derived, where Θ holds the following relationship:
tanΘ = (d-H)/D (2)
Figure 3 shows I as a function of the elevation angle (θ < Θ) for different D. As long as θ < Θ, the soil portion in L relies only on D and θ. Therefore, as the distance between the MSM and the shoreline increases, the number of muons that arrives at the MSM will decrease. As a consequence, the time resolution of the HKMSDD-MSM tide monitor will be degraded as the length of D increases.
Case studies in Tokyo Bay. Urban underground spaces (UUSs) have various functions: storage, industry, transport, utilities and communications and public use. In Tokyo, most of the underground facilities in the city areas are for public use. Tokyo uses more than 50% of UUSs for transportation including subways, highway tunnels, and stations, and almost 40% of UUSs for public spaces, shopping areas, parking lots, storages and industrial use46. Throughout its historical development, UUSs in Tokyo have progressed from shallow to deep soil layers. Therefore, inside UUSs, the supply of stable utility (electricity, gas and water) is one of the most important factors. In Japan, the UUSs for public use are equipped with a three-step power failure prevention system. In particular, there is a regulation that a UUS with a floor area exceeding 1,000 m2 must be equipped with an independent emergency power generator by a UUS managing body. If the emergency power generator is shut down for some reason, it will be immediately replaced with a battery-operated system. Such a robust pre-installed infrastructure particularly designed for UUSs also offers an ideal space for stable and safe operations of muographic tide monitors even under extreme conditions such as severe storms and earthquakes.
The south-central Tokyo map in Figure 4 shows the distribution of Tokyo deep and large-scale UUSs (DLUUSs) located in the regions within 200 m from the shorelines. Here, the DLUUSs are defined as those having basement floors located below sea level with a floor size exceeding 1,000 m2. The south-central part of Tokyo consists of the main land and more than 15 islands in the north part of Tokyo Bay. Most of these islands are connected by bridges, but lines on the ocean in Figure 4 represent railway/motor underwater tunnels which connect these islands. A number of commercial sky scrapers were built on these islands, and some of them have UUSs reaching depths greater than 10 m from the ground surface. Since the elevation of these islands ranges between 1 m and 7 m, these floors are located below sea level.
HKMSDD-MSM. Figures 5 and 6 show close and vertical cross-sectional views of some representative UUSs indicated in Figure 4. As can be seen in this figure, other islands are located along the muon trajectories. These islands may degrade the quality of tide monitoring and thus this effect will be later discussed.
Figure 7 shows the proposed HKMSDD-MSM muograph design for the tide monitoring network. HKMSDD-MSM consists of two sets of scintillation detectors that consist of plastic scintillators and photodetectors. The length and the width of the scintillators are respectively 8 m and 15 cm, making a total detection area of 1.2 m2. There are a couple of options for photodetectors: photomultiplier tubes (PMT) or SiPM. In the former case, the PMTs are attached to the scintillators via acryl light guides. In the latter case, scintillation light is transported to SiPM via wave length shift (WLS) fibers. Since the Eljen's scintillators (EJ-208) and the Kuraray's WLS fibers (Y-11(200)) both have a long attenuation length of 4 m47 and 3.5 m48, respectively, one photodetector is sufficient for readout of each scintillator strip. Coincidence signals verified to be the same angle between these two detectors are recorded as muon signals. The current HKMSDD-MSM has a wide angular acceptance for the azimuthal angle (Figure 7B) and a narrow angular acceptance for the elevation angle (Figure 7C). The distance between two scintillator strips (x) is derived by dividing a double of the scintillator width (30 cm) by the observation geometry ((d-H)/D) (rad). In the cases shown in Figures 5 and 6, since (d-H)/D is 0.125 rad (7.1o), x is 2.4 m. As shown in Figure 7A, the scintillator strips are placed so that the HKMSDD-MSM does not receive the muons arriving from the direction opposite to the sea. However, some scattered upward-going muons could generate fake tracks.
Figure 8 shows the fraction of the fake tracks generated by the scattered upward-going muons as a function of the elevation angles. The number of events were normalized to the value observed at θ = 0±16.5 mrad, where θ is elevation angle. The observation conditions to produce this plot are summarized in the Method section. Since these data were taken in the open-sky environment, it is expected that this fraction will be somewhat lower than this in an underground environment. In conclusion, with the currently proposed setup, contamination by the near horizontal backward directed muons will be suppressed to a rate below 1%, and thus this effect will be neglected in the following discussions. Figures 7B and 7C respectively show azimuthal and elevation angular acceptance of HKMSDD-MSM in the cases shown in Figures 5 and 6. As shown in Figure 7C, HKMSDD-MSM does not have an acceptance for the angular region beyond 7.1o. This design helps to avoid recording muons that didn't pass though seawater, which would eventually degrade the sensitivity to Δh.
Figures 9 and 10 show the muon flux and detectable tide level variations Δh as a function of the distance between the MSM and the shoreline (D) for different depths (5 m and 15 m) from the mean sea level. Here the detectable Δh was derived from the standard deviation of the number of muons (ΔN) recorded with the proposed detector configuration (Figure 7). For longer D, muographs located at deeper locations would record more muons per unit time; hence would produce better resolutions for determining Δh since both the angular acceptance and the average elevation angle of incoming muons decrease. As the MSM depth (d) increases, the total solid angle required to accept muons at the MSM increases, however, since the ratio Δh/(d-H) decreases, sensitivity of the Δh detection or time resolution is degraded. These two factors are tradeoffs. The conclusion for dealing with this situation is as follows. For the purpose of real time monitoring (< 1hour), the distance between the MSM and the shoreline (D) has to be less than 50 m and 20 m to attain Δh < 50 cm and Δh < 10 cm, respectively. For the purpose monitoring with a longer time scale, if D is less than 20m, sub millimeter accuracy can be obtained per year. From this plot, we also can find that if the MSM depth is shallower, better Δh resolution is achievable for shorter D, but better Δh resolution is achievable for longer D if the MSM depth is deeper. This is because even the ground soil thickness along the muon path is thicker; hence degrading sensitivity to Δh, for longer D, the MSM's acceptance solid angle is larger if the MSM depth is deeper.
The current muographic tide monitor measures the tide height averaged over the shoreline to offshore, however, the muon's path length in seawater increases; hence the number of muons decreases as an elevation angle of incoming muons decreases and thus, the observed tide levels are representing those in the near-shore regions. Figure 11 shows the fraction of the number of muons out of the total number of muons (integrated over the entire angular region) as a function of the distance from the shore line for different distances between the MSM and the shoreline (D). As can be seen in this figure, the effect of the islands located further than 200 m from the MSM is negligible. In Cases (A) and (B) (Figures 5 and 6), since the depth of the MSM is 5 m from sea level, more than 95% of muons pass through the seawater located between the islands.