We developed a radiographic technique to image a subsurface conduit shape using cosmic-ray muons. The test measurement was performed in Showa-Shinzan lava dome located in Hokkaido, Japan as an example. A muon detector with an area of 6000 cm2 was set up at the foot of the lava dome. Muon tracks recorded in nuclear emulsion films in the detector were analyzed to determine the level of energy absorption along different ray paths through subsurface beneath the lava dome. A typical angular resolution of the muon detector of 10 mrad corresponds to a spatial resolution of 10 m at a distance of 1 km, which is difficult to be addressed with seismological technique. We mapped differentially absorbed cosmic-ray muons, which depend upon the varying thickness and density beneath the dome. We successfully imaged the conduit shape and determined a conduit diameter of 102 ± 15 m, assuming the observed high absorption region beneath the dome is localized in the vent area.
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 The exact size and shape of the conduit beneath a volcano is not known. To perform a numerical simulation of a magma injection, the size and shape of the conduit near the surface is an important factor. Small changes in chamber pressure, magma viscosity and conduit diameter are known to strongly amplify discharge rate. However, usually the conduit diameter makes a significant difference in eruption modeling studies [e.g., Barmin et al., 2002; Gonnermann and Manga, 2003; Mangan et al., 2004].
 Radiography with x-rays is commonly used in both medical and industrial applications. When a beam of radiation is transmitted through any heterogeneous object, it is differentially absorbed, depending upon the varying thickness and density of this object. The image registered on a photographic film adjacent to the specimen under examination constitutes a shadowgraph or radiograph of its interior. Industrial radiography has been used for detection of internal physical imperfections such as voids, cracks, flaws, and porosities. It is frequently used for visualization of inaccessible internal parts in order to check their location or condition. This technique can be applied to view volcanoes [Tanaka et al., 2003, 2005, 2007a, 2007b] except for substituting penetrating muons to serve in place of X-rays.
 The cosmic-ray muon imaging method is, in principle, the same as medical usage X-ray radiography. We use muon attenuation and absorption for materials of geological interest. A photographic film can be used to produce images of the internal volcanoes. However, since normal photographic films are not generally sensitive to muons, a special photographic film coated by nuclear emulsion [Tanaka et al., 2007a, 2007b] is used. The part of the volcano to be “mu-rayed” is placed between the cosmic-ray muon source and the photographic receptor to produce what is a shadow of all the internal structure of that particular part of the volcano being mu-rayed. Since cosmic-ray muons are particles generated in the atmosphere that continuously bombard the earth's surface from above, we can perform radiography everywhere at anytime on the earth.
 The muons are blocked or strongly attenuated by dense part such as magma and pass through surrounding less-dense part. Those areas where the muons strike the photographic receptor turn black when it is developed. So where the muons pass through less-dense parts of the volcano such as surrounding areas, vacant regions, etc, the film turns black.
 Cosmic-ray muons arrive at angles ranging from vertical to horizontal [Thompson et al., 1975]. It is also well known that muons are arriving in the horizontal direction with a smaller average intensity, but with a higher intensity at energies above a few 100 GeV. Because muons become highly penetrative as their energy becomes higher, these horizontal muons can be used for the purpose of radiography of the volcano. The attenuation is directly proportional to the density of the material with minimal uncertainty due to chemical composition [Particle Data Group, 1998]. Thus, the result is a two-dimensional projection onto the film, producing a latent image of varying densities inside a volcano.
2. Muon Mapping
 On the earth, all naturally occurring muons are created by cosmic rays. The muons from these cosmic rays generally arrive at angles ranging from vertical to horizontal (The overall angular distribution of muons at the ground is ∞cos2θ (in unit of zenith angle)). Thus, the cosmic-ray muon imaging technique is limited to near-surface depths and strongly depends on the nature of the local topography (the detector must be placed on a slope pointing toward a topographically prominent feature of interest, and there will only be results for the volume located above the detector).
 Since muons are unusually penetrative of ordinary matter, they are also detectable deep underground. Figure 1 shows the vertical muon intensity versus depth in unit of km water equivalent (symbol: km.w.e) [Ambrosio et al., 1995]. Thus, the cosmic-ray muon imaging technique can be applied to km scale geological materials. The way in which high energy muons are stopped when travelling through matter has been studied well and is summarized in various articles [Particle Data Group, 1998; Adair and Kasha, 1976; Groom, 2001]. Figure 2 shows the integrated flux of cosmic-ray muons at various zenith angles penetrating through a given thickness of rock, X, in unit of km water equivalent [Tanaka et al., 2007a, 2007b]. The intensity of an image pixel in the detector is determined by the attenuation of incident muons caused by absorption in the Earth's crust. By determining the path lengths from topographic information, the measurement gives us the average density along the path lines of cosmic-ray muons through the Earth. Among the measured properties of the crust's interior, density plays a special role because it is most readily interpreted in terms of composition and state. These could represent local-scale geological processes, such as the movements of magma in the conduit of a volcano. Thus, independent measurements of density would be of considerable value. Because muons are the most numerous charged particles at sea level, we can use a relatively simple particle detector (radiation detector) to detect, track and identify muons.
 Because the size of the detector is negligible relative to the length scales of a volcano, the coordinate system used in this measurement is a coordinate system in which each point on a plane is determined by an angle and a distance (the distance between the detector and the object: R) (Figure 3). The transmission image is therefore mapped in the angular coordinate. The angular coordinate (also known as the zenith angle or the azimuth angle denoted by θ or ϕ) denotes the positive or anticlockwise angle required to reach the point from the 0° ray. Therefore, minimum resolvable distance (spatial resolution: ΔX, ΔY) at an object is defined by minimum resolvable angle of the detector. (angular resolution: Δθ, Δϕ) and the distance between the object and the detector (R); (ΔX, ΔY) = R x (Δθ, Δϕ).
 A nuclear emulsion photographic film was used in order to perform cosmic-ray muon imaging of Showa-shinzan lava dome. A nuclear emulsion film consists of a number of emulsion layers. The receptor elements of these emulsion layers are the same as photographic film, i.e. micro-crystals of AgBr. Micro-crystals of AgBr are incorporated in the emulsion layers. When a muon passes through this layer, part of the micro-crystals on the particle trajectory records the path and these trails can be analyzed when the emulsion is later developed, somewhat like photographic film. Because the setting angle of the film can be precisely measured, we can determine the incident angle of the muon. The trails are read through a microscope as 16 tomographic CCD images and transferred to a computer automatically. For various arriving angles, we can count the number of these trajectories for muons which either stop within the object or, if they have enough energy, escape from the object. Because film is cumulative, relatively weak radiation can be detected by prolonging the exposure until the film can record an image that will be visible after development.
 The muon flux arriving from the backward direction, mainly transmitted through air can be used to confirm whether or not the muon flux recorded in the film is azimuthally isotropic at the observation point. Since cosmic-ray muons do not arrive from the downward, we can distinguish “forward-directed” from “backward-directed” muon trails by choosing either positive (+θ) or negative arriving angles (−θ) (Figure 3). The horizontal viewing angle of our detector is ±500 mrad (±28.7°). The vertical viewing angles are 500 mrad for “forward-directed” muons and 300 mrad (17.2°) for “backward-directed” muons.
3. Results and Discussion
 Showa-Shinzan is a lava dome on the east flank of Usu volcano. The area was uplifted steadily from January 1944 to November 1944. In November, lava broke through to the surface. By September of 1945, the dome and central plug had grown 407 m above ground level. The peak is now 398 m tall, and still actively smoking. Fumarole temperature ranges from 130°C to 230°C (November 2004).
 A cosmic-ray muon detector with a relatively small area (6000 cm2) was placed at a foot (alt. 187 m) of Showa-shinzan lava dome with the aim of imaging the conduit shape beneath the dome that is higher in elevation adjacent to the detector. Figure 4 shows the topography of Showa-shinzan lava dome (see the photograph in Figure 5a) and the surrounding area with the location of the cosmic-ray muon detector. The film was exposed for 3 months. Figure 5d shows a transmission image as a result of that cosmic-ray muons are transmitted through Showa-shinzan lava dome. For reference, the muons arriving from the backward directions mainly transmitted through air are also plotted in the same angular region in Figure 5b. We can confirm azimuthally isotropic cosmic-ray flux in Figure 5b. For subsurface of Showa-shinzan lava dome, this image shows three relatively weak transmission zones (the dark red zones beneath the dome in Figure 5d). The transmission of muons depends on the local density structure of the volcanoes. A dense material such as magma more interacts with the muons by absorption. However, the intensity of the transmitted muon is still affected by the volume (geometry) of the material through which it passes. The weaker (or stronger) muon transmissions come from: a longer (shorter) path length and a higher (lower) average density along the path. From the raw transmission projection (Figure 5d), three strong density-length anomalies are observed. One is due to long path (position (θ, ϕ) = (60–160, 170–400) and (60–160, 600–900)), the other due to high density (position (θ, ϕ) = (60–160, 400–600)). In order to remove this effect, we reconstructed the subsurface crustal density structure (Figure 5e) by comparing the transmission image (Figure 5d) with the local topographic structure (Figure 5c) by referring to the integrated flux of muons at various zenith angles penetrating through a given thickness of rock (Figure 1) [Tanaka et al., 2007b]. Figure 5e is essentially a cross section through the dome parallel to the plane of the detector, on which the average density along all the muon paths is projected. Figure 5e is drawn with a vertical spatial resolution of ±15 m and a horizontal resolution of ±15 m. High density region can be seen beneath the dome.
 In our measurements, we have confirmed the following important properties of this technique, which will be useful for future imaging:
 (1) With three months of observations, an average density determination within a thickness of a few hundred meters can be made with an accuracy of a few % and with a vertical resolution of ±15m and a horizontal resolution of ±15 m at 500 m distance. The spatial resolution and density contrast of the internal structure that is resolved depends on the number of detected muons that pass through the region or feature of interest, and thus they can be improved simply by using a larger detector.
 (2) We found that the bulk density of the lava dome was 2.71–2.91 g/cm3 (the error at each data point is 0.17g/cm3) and the density of the surrounding area was 1.90–2.35 g/cm3 (the error at each data point is 0.13g/cm3). These values are consistent with the density of rock samples of lava in Usu volcano (2.51–2.92 g/cm3) and the gravimetric density of the surrounding area (2.30–2.37 g/cm3) [Nemoto et al., 1957].
 (3) Because the density variations beneath the dome are very smooth, the data points were fitted by a polynomial function. Here it was assumed that the rising point of the fitted curve was the border of the conduit. Assuming the observed high density region beneath the dome is localized in the vent area, this region is explained by a conduit diameter of 102 ± 15 m. The image is consistent with the Yokoyama's model of the growth mechanism of the 1944 lava dome of Usu volcano [Yokoyama, 2002, 2004].
 The imaging is relatively simple and inexpensive  and provides information for geologic interpretations of various near surface phenomena. There are several limitations to the cosmic-ray muon imaging technique: (a) it is limited to near-surface depths; (b) the method is limited to horizontal ranges of 2–3 km (which also limits the potential targets); (c) this technique only resolves the average density distribution along individual muon paths. However, the cosmic-ray muon imaging technique has much higher resolving power than conventional geophysical techniques, with resolutions up to several meters, allowing it to see smaller objects and greater detail in volcanoes.
 The authors are deeply indebted to K. Kodama of Aichi University of Education and M. Komatsu of Nagoya University for their valuable contributions. Special funding arrangements by S. Okubo and related people of ERI and JSPS (Japan Society for the Promotion of Science) are acknowledged. M. Takeo and T. Koyaguchi of ERI, K. Nagamine of UCR and I. Yokoyama, M.J.A. are also acknowledged for their valuable suggestions. This work will greatly benefited from useful comments by two reviewers of this manuscript.