Three‐dimensional computational axial tomography scanof a volcano with cosmic ray muon radiography

Hiroyuki K. M. Tanaka,1 Hideaki Taira,2 Tomihisa Uchida,3 Manobu Tanaka,3

Minoru Takeo,1 Takao Ohminato,1 Yosuke Aoki,1 Ryuichi Nishitama,1 Daigo Shoji,1

and Hiroshi Tsuiji1

Received 30 April 2010; accepted 6 July 2010; published 30 December 2010.

[1] Cosmic ray muon radiography can measure the density distribution within a volcano.Unidirectional radiography shows a precise cross‐sectional view of a conduit and amagma body through a volcano parallel to the plane of the detector. However, it onlyresolves the average density distribution along individual muon paths. Precise size andshape of underground structure, such as a conduit or a magma body, provide clear andpervasive information on understanding dynamics of volcanic eruption. Here we show ahighly resolved three‐dimensional tomographic image of an active volcano Asama inJapan. Specifically, we developed a portable power‐effective muon radiography telescopethat can be operated stable with a realistically sized solar panel so as to place it around anactive volcano where commercial electric power is not available. The resulting imagebelow the crater floor shows that a local low‐density region accumulates sufficient gaspressure to cause Vulcanian eruption. The present muon computational axial tomographyscan has a resolving power with a resolution of 100 m, allowing it to see great detailin volcanoes.

Citation: Tanaka, H. K. M., H. Taira, T. Uchida, M. Tanaka, M. Takeo, T. Ohminato, Y. Aoki, R. Nishitama, D. Shoji, andH. Tsuiji (2010), Three‐dimensional computational axial tomography scan of a volcano with cosmic ray muon radiography,J. Geophys. Res., 115, B12332, doi:10.1029/2010JB007677.

1. Introduction

[2] In order to perform a numerical simulation of a magmainjection, the size and shape of the conduit near the surfaceare important factors. Small changes in chamber pressure,magma viscosity, and conduit diameter are known tostrongly amplify discharge rate. Muon radiography (muo-graphy) with cosmic ray muons has been used to image theinternal density structure of a volcano [Tanaka et al., 2003,2007a, 2007b, 2008, 2009; Tanaka and Yokoyama, 2008].When a muon is transmitted through a heterogeneous body,it is differentially absorbed, depending upon the varyingthickness and density distribution inside the mountain. Thistechnique is utterly independent of the geophysical modeland directly measures the density length (density times pathlength) [Groom, 2001]. Conventional two‐dimensionalmeasurements with unidirectional radiography generate two‐dimensional projection onto the plane, producing a latentimage of varying densities inside a volcano. The muographyhas higher resolving power than conventional geophysicaltechniques, with resolutions up to tens of meters, allowing it

to see smaller objects and greater detail in volcanoes.However, this technique only resolves the average densitydistribution along individual muon paths. Therefore, the usermust end up making assumptions or interpretations aboutmore localized structure along those muon paths. Otherwise,it is difficult for us to determine whether a vacant region islocalized or a relatively low density region is spread over alarger region along the muon path.[3] In general, volcanoes make good study targets because

they are usually axisymmetric, and it is reasonable toassume that the observed density variations are localized inthe vent or crater area. This is why the conventional two‐dimensional measurement with unidirectional radiography isuseful for volcanic observation. However, uncertainty stillremains over the exact position of the density anomaly, itsshape and its alignment. This uncertainty can be furtherconstrained with multiple observations with two or morecosmic ray muon detectors. Multidirectional muography caneliminate the superimposition of images of structures out-side the area of interest. In this work, we placed two muondetectors around Mount Asama in order to produce a three‐dimensional image to locate and size a low‐density regionnear the crater found in 2006 [Tanaka et al., 2007a].

2. Muon Computational Axial TomographySystem

[4] The experimental arrangement for a muon computa-tional axial tomography (CAT) (Mu‐CAT) system requires

1Earthquake Research Institute, University of Tokyo, Tokyo, Japan.2Department of Earth and Planetary Science, University of Tokyo,

Tokyo, Japan.3Institute of Particle and Nuclear Studies, High Energy Accelerator

Research Organization, Tsukuba, Japan.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2010JB007677

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a muon tracking device that (1) can be operated at a placewhere a commercial electric power is not available and (2) islight enough to be carried up to a mountain.[5] In order to satisfy these two requirements, we have

developed a light cosmic ray muon telescope module usinga Greinacher‐Cockcroft‐Walton photomultiplier tube (CW‐PMT) based on a Greinacher‐Cockcroft‐Walton voltageamplifier [Greinacher, 1920; Cockcroft and Walton, 1932;Goebel, 1969]. The CW‐PMT consists of a voltage multi-plier ladder network of capacitors and diodes used to gen-erate high voltages for accelerating photoelectrons producedat a photocathode of a photomultipler tube (PMT). Unliketransformers, this method eliminates the requirement for theheavy core and the bulk of insulation/potting required, andthus CW‐PMT can be far lighter and more energy efficientthan the conventional PMT using transformers. The relativesimplicity of the experimental method allows bringing thedetector up to the volcano where usually no external powersources are present. In comparison to the preexisting methodbased on the use of emulsion films, the CW‐PMT systemhas the following advantages and disadvantages. Onlinemuon monitoring is possible with the CW‐PMT systemwhereas the emulsion films have to be first developed whenwe analyze the muon data. However, the CW‐PMT systemrequires small but electric power whereas the emulsion filmsdo not. For this reason, the CW‐PMT system always re-quires an external power supply, e.g., solar panels andbatteries. In this respect a critical comparison with alterna-tive (and performing) methods based on the use of emulsionfilms should be mentioned for completeness.[6] Conventional PMT assembly (ASSY) consumes high

power because it uses resisters to distribute high voltage toits dynodes. The bleeder current in the resister also causes acertain restriction on the PMT output linearity. In this work,a high voltage supplier with a CW circuit is directly attached

to a Hamamatsu R7724 2‐inch PMT (R7724‐CW ASSY) toreduce the power consumption and to increase the outputlinearity. By employing the R7724‐CW ASSY, the powerconsumption of the whole system was improved by an orderof magnitude (from ∼100 W to 14 W) in comparison to theprior work [Tanaka et al., 2009]. The power consumption of14 W is for a single module for all 40 modules. R7724‐CWASSY also mitigates the problem on the PMT output line-arity by removing the resister chain across the dynodes. Ablock diagram of R7724‐CW ASSY is shown in Figure 1.By feeding a sinusoidal wave from an oscillator circuit tothe CW circuit, high voltage is applied to each dynode.[7] The size of one module is 130 × 10.4 × 10.4 cm3.

Each module consists of a polycarbonate case with a size of130 × 10.4 × 10.4 cm3 and a light shielded plastic scintil-lator with a size of 100 × 10 × 2 cm3, coupled with a R7724‐CW ASSY via an acryl light guide. The material of the casewas chosen to be resistant to impact and volcanic gas.Because density is 1 g/cm3 for a plastic scintillator, a vol-ume of 100 × 10 × 2 cm3 have a weight of 2 kg. Adding theweight for a PMT, a light guide, and a case to this, theweight of each module becomes ∼4 kg. At the observationsite, 40 modules are arranged to make two segmentedscintillation detector planes to track muon trails. They arearranged in 2 matrices with 10 X bars and 10 Y bars toobtain 100 pixels. The output from the CW‐PMT is fed to afield programmable gate array (FPGA)‐based muon readoutmodule [Uchida et al., 2010] in order to generate a histo-gram of muon events, representing the horizontal and ver-tical arriving angles of cosmic ray muons.[8] A newly developed detector was installed at a place

located 1.7 km north from the center of the crater of MountAsama, Japan (point N). The prior detector was alreadyinstalled to a place located 1.3 km east from the center of thecrater (point E). The Asama Mu‐CAT system consists of

Figure 1. (a) Block diagram of R7724‐CW assembly. By feeding a sinusoidal wave from an oscillatorcircuit to the CW circuit with a combination of diodes and condensers, high voltage is applied to eachdynode. (b) A photograph of the front end electronics directly attached to R7724 PMT.

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these two detectors (Figure 2). The distance between the twomatrices is 1.7 m at point N, and it is 1.28 m at point Ebecause the plastic scintillator with a size of 100 × 7 × 2 cm3

is used to achieve the same angular resolution as we use atpoint N, i.e., 60 mrad. The angular resolution and theacceptance of the telescope are ±30 mrad (75% CL) and±540 mrad, respectively. Because the size of the detectors isnegligible relative to the spatial scales of a volcano, eachpoint on a muograph plane is determined by an angle andthe distance between the detector and the object. Theangular resolution of each detector is 60 mrad. This angularresolution corresponds to the spatial resolution of 100 m atthe center of the crater from point N and of 80 m from pointE. At both of the sites, a wireless LAN antenna was installedso that the muon telescope system can be monitored on areal‐time network system. These data can be directly read bythe network processor when a remote PC access to theboard.

3. Analysis

[9] A grid is formed by discretizing a volume of Asamaabove 2170 m above sea level (asl) into ∼1000 cubicvoxels. The size of each voxel is 100 × 100 × 100 m3. Avoxel is a basic volumetric unit, and its size was deter-mined by the spatial resolution of the Mu‐CAT system.Average density in each voxel is estimated by fitting thedata with a damped least squares method.

[10] The conical ray pattern is accounted by the voxels bysolving the following equation: X = Lr (Figure 3), i.e.,

XA

XB

XC

0BBBB@

1CCCCA

¼

�����‘A1 ‘A2

‘B1 ‘B2

‘C1 ‘C2

0BBBBBB@

1CCCCCCA

�1

�2

0@

1A: ð1Þ

The density length data (X) in equation (1), as obtained withthe muon measurement, are fitted to the modeled data (r) in

Figure 2. Map of Asama volcano showing the location of the Mu‐CAT system. The dotted box showthe area where the value of Wm is reduced. Red lines show the location of the density distribution asshown in Figure 4.

Figure 3. Example of tomography. The density lengths XA,XB, and XC along muon paths A, B, and C are measuredwith muography. The data are fitted with the model densityr1 and r2.

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its least squares sense. The muon path length through themountain (L) can be measured from a topographical map.For the least squares fitting, here we employed a dampedleast squares method. The density length data are fitted tothe model data (r) by minimizing F(m) = E + "2N, where Eis the residual between the model and the data:

E ¼ X� Lrð ÞTWe X� Lrð Þ; ð2Þ

and N is a so‐called norm that is defined by

N ¼ r� hrið ÞTWm r� hriX� Lrð Þ; ð3Þ

and "2 is a parameter.We andWm are weight matrices to thedata and to the model, respectively. For simplicity in theanalysis, here we employed a diagonal matrix for We andWm. The density hri is empirically given. Bulk densitydeduced by the muon measurement is usually used for thisvalue.[11] In order to confirm the above tomography method,

we performed a model simulation in the case of (1 a modelof which a circular lower‐density region with a density of1 g/cm3 is added at the center of the mountain with adensity of 2 g/cm3 (Figure 4a), (2) a model of which acircular higher‐density region with a density of 2.4 g/cm3

is added around the lower‐density region (Figure 4b), and(3) a model of which an elliptic lower‐density region witha density of 1 g/cm3 is added at the center of the mountain(Figures 4c and 4d). Here we assume that the centralregion of the mountain can be deviated from the empiri-cally given density hri because it is reasonable to assumethat the density anomaly is localized near the vent area.Wm near the center is set to be 10% of that in the surroundedarea. The area where the diagonal component of Wm isreduced is here called “Wm window.” The results are shownin Figure 5 together with the diagonal component of Wm forthe model calculation.

4. Results and Discussions

[12] Asama Volcano on the Japanese island of Honshu islocated at the junction of the Izu‐Marianas and NE Japanvolcanic arcs. Asama erupted in 1783 (Tenmei 3), causingwidespread damage. The 3 month long Plinian eruption in1783 produced large lava flows toward the northwestdirection (Oni‐oshidashi) and large pyroclastic flows towardthe northeast direction (Azuma pyroclastic flow). Thepresent height is 2568 m, and there is a crater called Okamaon the top. Its crater floor is located at ∼2320 m asl.

Figure 4. Models used for the tomography simulation.(a) A circular lower‐density region with a density of 1 g/cm3

is added at the center of the mountain with a density of2 g/cm3, (b) a circular higher‐density region with a densityof 2.4 g/cm3 is added to Figure 4a, and (c) an ellipticlower‐density region with a density of 1 g/cm3 is added atthe center of the mountain. (d) The lower‐density region ofFigure 4c is rotated 135° clockwise.

Figure 5. Results of the model simulation. (a–d) Corresponding to the models in Figure 4. (e) Thediagonal component used for the present tomography simulation.

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[13] Each muon data as obtained at points N and E arecompared with the Geant4 [Agostinelli et al., 2003] MonteCarlo simulation results in order to deduce the averagedensity along the muon path. Observation time is 40 days atpoint N and 3 months at point E. The number of muonsnormalized to 1 month (30 days) is shown in Figure 6together with Monte Carlo simulation results as obtainedby assuming different uniform densities of Asama. Two datapoints in Figure 6d have long error bars because of a largesystematic error mainly from the detector configuration andare neglected in the following discussion. The observationtimes are quite different from point N and point E becausepoint E was constructed earlier than when point N wasconstructed. In general, the measurement time for telescopeE should be shorter to achieve the same signal‐to‐noiseratio. However, it is better for us to use data with a betterstatistic because it contributes to determining the densitydistribution with shorter error bars. Figures 7a and 7b showthe average density along the muon path from each obser-vation point. Assuming that the density changes smoothlywithin the detector resolution, we can interpolate the data to

produce Figures 7c and 7d. Figures 7c and 7d are essentiallycross sections through Asama parallel to each plane of thedetector at the different site, on which the average densityalong all the muon paths is projected. These two images areused to produce a Mu‐CAT image.[14] In this work, the size of each voxel was fixed to be

100 m, i.e., corresponding to the spatial resolution of 100 mat the center of the crater from point N. From the unidi-rectional muography [Tanaka et al., 2007a], the bulk densityof Asama was already measured to be ∼2.3 g/cm3. Thisvalue was used for determining hri in equation (3). Also,because it is highly expected that the density distributionnear the crater area is more heterogeneous than that in theother areas, we assume that the value of a part of thediagonal component of Wm in equation (3), which corre-sponds to the area around the crater, is smaller than otherpart of the component. This process means that the densitynear the crater can deviate more from the bulk density incomparison to the other area. The area where we reduce thevalue in the diagonal component of Wm is shown in Figure2 by dotted box. The amount of reduction is determined

Figure 6. Number of muons normalized to 1 month (30 days). Curves represent the muon events asobtained from the Monte Carlo simulation for the uniform density that ranges from 1.8 to 2.6 g/cm3 forthe elevation angle region between (a) 150 and 210 mrad, (b) 210 and 270 mrad, (c) 270 and 330 mrad,(d) 330 and 390 mrad, and (e) 390 and 450 mrad.

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empirically by considering the following two factors: (1) ifwe reduce the value of the component of Wm, a data fittingerror increases; (2) however, if we do not reduce it, theheterogeneity located near the crater area will be likely toappear near the detector where the muon path lines aredensely packed. We empirically determined the value to be0.25 whereas that for other component is 1.0.

[15] The analytical results are shown in Figure 8. Thededuced density in each voxel is plotted along the W–E andN–S directions at different elevations. Assuming the presentcrater is filled with the material, average density over fourvoxels around the crater center is determined to be 1.9 ±0.6 g/cm3 at an elevation between 2170 and 2270 m, 2.2 ±0.6 g/cm3 at an elevation between 2270 and 2370 m, and

Figure 7. Muographs as obtained from (a) point E and (b) point N, showing the average density alongthe muon path from each observation point. (c and d) Produced by interpolating Figures 7a and 7b,respectively, assuming the density changes smoothly within the detector resolution.

Figure 8. Density distribution along (a) the A–B line and (b) the C–D line in Figure 1. Because alongthe A–B and C–D lines voxels do not exist, the average density between two voxels across these lines isplotted.

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0.5 ± 0.6 g/cm3 at an elevation between 2370 m and 2470 m.The lower density observed at an elevation between 2170and 2270 m is probably due to fractured materials filledin a conduit. At an elevation between 2370 and 2470 m,where it is above the crater floor, a density below waterwas measured.[16] In the previous discussion, the size of the area where

the value of Wm is reduced is empirically determined. Inorder to evaluate this uncertainty, the data were fitted bychanging the size of the area where the value of Wm isreduced. The result is shown in Figure 9. The size depen-

dence is small for the density determined at elevationsbetween 2170 and 2270 m and between 2270 and 2370 m,whereas it is larger at the elevation between 2370 and2470 m. This can be explained by the following reason:Because there is a crater on the top, the low‐density regionis more localized at a higher elevation, whereas the frac-tured region is spread more below the crater floor. Con-sidering such a model uncertainty, the average densityover four voxels around the crater center is determined tobe 1.9 ± 0.7 g/cm3 at an elevation between 2170 m and2270 m, 2.2 ± 0.6 g/cm3 at an elevation between 2270 m

Figure 9. Average density over four voxels around the center of the crater at an elevation of (a) between2170 and 2270 m, (b) between 2270 and 2370 m, and (c) between 2370 and 2470 m for different size ofthe area where the value of the diagonal component of Wm is reduced.

Figure 10. Dumped least squares solution of two‐directional muography for (a) the region between2170 and 2270 m asl, (b) the region between 2270 and 2370 m asl, and (c) the region between 2370and 2470 m asl.

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and 2370 m, and 0.7 ± 0.9 g/cm3 at an elevation between2370 and 2470 m.[17] A dumped least squares solution of two‐directional

muography is shown in Figure 10. Assuming the densitychanges smoothly within the detector resolution, we canproduce the volumetric representation as shown in Figure 11.The size of the fractured region below the crater floor wasdetermined to be 300 ± 100 m for the W–E direction, and150 ± 50 m for the N–S direction. The fractured zone

below the crater floor seems to be extended toward the north.This might be related to the 1783 eruption that caused a largepyroclastic and lava flow toward the north direction.[18] The data presented here constitute evidence that we

have solved the problem that is inevitably encountered in theconventional unidirectional muography: “the technique onlyresolves the average density distribution along individualmuon paths.” However, there are still several limitations tothe present Mu‐CAT technique: in order to fit the data to themodel, (1) we have to assume the value for Wm; and (2) wehave to assume the size of the area where the value ofWm isreduced. This assumption increases the model uncertaintyand the error when determining the density. We have per-formed a model calculation and found that if we place eightor more muon observation points around the volcano, abovetwo assumptions will not be necessary. We anticipate thatthe Mu‐CAT will be a powerful tool to see smaller objectsand greater detail in volcanoes three dimensionally.

[19] Acknowledgments. Special funding arrangements by S. Okubo,K. Nakatsuka, and related people of ERI, JSPS (Japanese Society of Pro-motion of Science) and JST (Japan Science and Technology Agency) areacknowledged. T. Koyaguchi, J. Oikawa, Y. Aoki, E. Koyama of ERI;K. Nagamine of UCR; I. Yokoyama, member Japan Academy; andY. Yamashina, M. Seki, Y. Nagasaki, and S. Tanaka are also acknowledgedfor their valuable suggestions. This work greatly benefited from useful com-ments by two reviewers of this manuscript. This work is supported byGrants‐in‐Aid for Scientific Research (21200049).

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Figure 11. Volumetric representation inside Asama. Topof Asama is truncated at the elevation of 2470 m. Theimage is vertically sliced by a W–E plane including(a) the center of the crater, (b) 100 m north from the centerof the crater, and (c) 200 m north from the center of the cra-ter. (d) The image without cut. It can be visually seen thatthe low‐density area is extended toward the north directionin Figure 11c.

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power operation, Earth Planets Space, 62(2), 167–172, doi:10.5047/eps.2009.03.002.

Y. Aoki, R. Nishitama, T. Ohminato, D. Shoji, M. Takeo, H. K. M.Tanaka, and H. Tsuiji, Earthquake Research Institute, University ofTokyo, 1‐1‐1 Yayoi, Bunkyo, Tokyo 113‐0032, Japan. (ht@riken.jp)

H. Taira, Department of Earth and Planetary Science, University ofTokyo, 7‐3‐1 Hongo, Bunkyo, Tokyo 113‐0033, Japan.M. Tanaka and T. Uchida, Institute of Particle and Nuclear Studies, High

Energy Accelerator Research Organization, 1‐1 Oho, Tsukuba, Ibaraki305‐0801, Japan.

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