Three dimensional computational axial tomography scan of a volcano with cosmic ray muon radiography

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2010jb007677, 2010 Three dimensional computational axial tomography scan of 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 Tsuiji 1 Received 30 April 2010; accepted 6 July 2010; published 30 December [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 a magma body through a volcano parallel to the plane of the detector. However, it only resolves the average density distribution along individual muon paths. Precise size and shape of underground structure, such as a conduit or a magma body, provide clear and pervasive information on understanding dynamics of volcanic eruption. Here we show a highly resolved three dimensional tomographic image of an active volcano Asama in Japan. Specifically, we developed a portable power effective muon radiography telescope that can be operated stable with a realistically sized solar panel so as to place it around an active volcano where commercial electric power is not available. The resulting image below the crater floor shows that a local low density region accumulates sufficient gas pressure to cause Vulcanian eruption. The present muon computational axial tomography scan has a resolving power with a resolution of 100 m, allowing it to see great detail in volcanoes. Citation: Tanaka, H. K. M., H. Taira, T. Uchida, M. Tanaka, M. Takeo, T. Ohminato, Y. Aoki, R. Nishitama, D. Shoji, and H. Tsuiji (2010), Three dimensional computational axial tomography scan of a volcano with cosmic ray muon radiography, J. Geophys. Res., 115,, doi: /2010jb Introduction [2] In order to perform a numerical simulation of a magma injection, the size and shape of the conduit near the surface are important factors. Small changes in chamber pressure, magma viscosity, and conduit diameter are known to strongly amplify discharge rate. Muon radiography (muography) with cosmic ray muons has been used to image the internal 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 varying thickness and density distribution inside the mountain. This technique is utterly independent of the geophysical model and directly measures the density length (density times path length) [Groom, 2001]. Conventional two dimensional measurements with unidirectional radiography generate twodimensional projection onto the plane, producing a latent image of varying densities inside a volcano. The muography has higher resolving power than conventional geophysical techniques, with resolutions up to tens of meters, allowing it 1 Earthquake Research Institute, University of Tokyo, Tokyo, Japan. 2 Department of Earth and Planetary Science, University of Tokyo, Tokyo, Japan. 3 Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization, Tsukuba, Japan. Copyright 2010 by the American Geophysical Union /10/2010JB to see smaller objects and greater detail in volcanoes. However, this technique only resolves the average density distribution along individual muon paths. Therefore, the user must end up making assumptions or interpretations about more localized structure along those muon paths. Otherwise, it is difficult for us to determine whether a vacant region is localized or a relatively low density region is spread over a larger region along the muon path. [3] In general, volcanoes make good study targets because they are usually axisymmetric, and it is reasonable to assume that the observed density variations are localized in the vent or crater area. This is why the conventional twodimensional measurement with unidirectional radiography is useful for volcanic observation. However, uncertainty still remains over the exact position of the density anomaly, its shape and its alignment. This uncertainty can be further constrained with multiple observations with two or more cosmic ray muon detectors. Multidirectional muography can eliminate the superimposition of images of structures outside the area of interest. In this work, we placed two muon detectors around Mount Asama in order to produce a threedimensional image to locate and size a low density region near the crater found in 2006 [Tanaka et al., 2007a]. 2. Muon Computational Axial Tomography System [4] The experimental arrangement for a muon computational axial tomography (CAT) (Mu CAT) system requires 1of9

2 Figure 1. (a) Block diagram of R7724 CW assembly. By feeding a sinusoidal wave from an oscillator circuit to the CW circuit with a combination of diodes and condensers, high voltage is applied to each dynode. (b) A photograph of the front end electronics directly attached to R7724 PMT. a muon tracking device that (1) can be operated at a place where a commercial electric power is not available and (2) is light 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 using a Greinacher Cockcroft Walton photomultiplier tube (CW PMT) based on a Greinacher Cockcroft Walton voltage amplifier [Greinacher, 1920; Cockcroft and Walton, 1932; Goebel, 1969]. The CW PMT consists of a voltage multiplier ladder network of capacitors and diodes used to generate high voltages for accelerating photoelectrons produced at a photocathode of a photomultipler tube (PMT). Unlike transformers, this method eliminates the requirement for the heavy core and the bulk of insulation/potting required, and thus CW PMT can be far lighter and more energy efficient than the conventional PMT using transformers. The relative simplicity of the experimental method allows bringing the detector up to the volcano where usually no external power sources are present. In comparison to the preexisting method based on the use of emulsion films, the CW PMT system has the following advantages and disadvantages. Online muon monitoring is possible with the CW PMT system whereas the emulsion films have to be first developed when we analyze the muon data. However, the CW PMT system requires small but electric power whereas the emulsion films do not. For this reason, the CW PMT system always requires an external power supply, e.g., solar panels and batteries. In this respect a critical comparison with alternative (and performing) methods based on the use of emulsion films should be mentioned for completeness. [6] Conventional PMT assembly (ASSY) consumes high power because it uses resisters to distribute high voltage to its dynodes. The bleeder current in the resister also causes a certain restriction on the PMT output linearity. In this work, a high voltage supplier with a CW circuit is directly attached to a Hamamatsu R inch PMT (R7724 CW ASSY) to reduce the power consumption and to increase the output linearity. By employing the R7724 CW ASSY, the power consumption of the whole system was improved by an order of magnitude (from 100 W to 14 W) in comparison to the prior work [Tanaka et al., 2009]. The power consumption of 14 W is for a single module for all 40 modules. R7724 CW ASSY also mitigates the problem on the PMT output linearity by removing the resister chain across the dynodes. A block diagram of R7724 CW ASSY is shown in Figure 1. By feeding a sinusoidal wave from an oscillator circuit to the CW circuit, high voltage is applied to each dynode. [7] The size of one module is cm 3. Each module consists of a polycarbonate case with a size of cm 3 and a light shielded plastic scintillator with a size of cm 3, coupled with a R7724 CW ASSY via an acryl light guide. The material of the case was chosen to be resistant to impact and volcanic gas. Because density is 1 g/cm 3 for a plastic scintillator, a volume of cm 3 have a weight of 2 kg. Adding the weight for a PMT, a light guide, and a case to this, the weight of each module becomes 4 kg. At the observation site, 40 modules are arranged to make two segmented scintillation detector planes to track muon trails. They are arranged in 2 matrices with 10 X bars and 10 Y bars to obtain 100 pixels. The output from the CW PMT is fed to a field programmable gate array (FPGA) based muon readout module [Uchida et al., 2010] in order to generate a histogram of muon events, representing the horizontal and vertical 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 Mount Asama, Japan (point N). The prior detector was already installed to a place located 1.3 km east from the center of the crater (point E). The Asama Mu CAT system consists of 2of9

3 Figure 2. Map of Asama volcano showing the location of the Mu CAT system. The dotted box show theareawherethevalueofw m is reduced. Red lines show the location of the density distribution as shown in Figure 4. these two detectors (Figure 2). The distance between the two matrices is 1.7 m at point N, and it is 1.28 m at point E because the plastic scintillator with a size of cm 3 is used to achieve the same angular resolution as we use at point N, i.e., 60 mrad. The angular resolution and the acceptance of the telescope are ±30 mrad (75% CL) and ±540 mrad, respectively. Because the size of the detectors is negligible relative to the spatial scales of a volcano, each point on a muograph plane is determined by an angle and the distance between the detector and the object. The angular resolution of each detector is 60 mrad. This angular resolution corresponds to the spatial resolution of 100 m at the center of the crater from point N and of 80 m from point E. At both of the sites, a wireless LAN antenna was installed so that the muon telescope system can be monitored on a real time network system. These data can be directly read by the network processor when a remote PC access to the board. 3. Analysis [9] A grid is formed by discretizing a volume of Asama above 2170 m above sea level (asl) into 1000 cubic voxels. The size of each voxel is m 3.A voxel is a basic volumetric unit, and its size was determined by the spatial resolution of the Mu CAT system. Average density in each voxel is estimated by fitting the data with a damped least squares method. [10] The conical ray pattern is accounted by the voxels by solving the following equation: X = Lr (Figure 3), i.e., X A A1 A2 0 1 B X B A ¼ B B1 B2 A: ð1þ A 2 X C C1 C2 The density length data (X) in equation (1), as obtained with the muon measurement, are fitted to the modeled data (r) in Figure 3. Example of tomography. The density lengths X A, X B,andX C along muon paths A, B, and C are measured with muography. The data are fitted with the model density r 1 and r 2. 3of9

4 and N is a so called norm that is defined by N ¼ ðr hriþ T W m ðr hrix LrÞ; ð3þ Figure 4. Models used for the tomography simulation. (a) A circular lower density region with a density of 1 g/cm 3 is added at the center of the mountain with a density of 2 g/cm 3, (b) a circular higher density region with a density of 2.4 g/cm 3 is added to Figure 4a, and (c) an elliptic lower density region with a density of 1 g/cm 3 is added at the center of the mountain. (d) The lower density region of Figure 4c is rotated 135 clockwise. its least squares sense. The muon path length through the mountain (L) can be measured from a topographical map. For the least squares fitting, here we employed a damped least squares method. The density length data are fitted to the model data (r) by minimizing F(m) = E + " 2 N, where E is the residual between the model and the data: E ¼ ðx LrÞ T W e ðx LrÞ; ð2þ and " 2 is a parameter. W e and W m are weight matrices to the data and to the model, respectively. For simplicity in the analysis, here we employed a diagonal matrix for W e and W m. The density hri is empirically given. Bulk density deduced by the muon measurement is usually used for this value. [11] In order to confirm the above tomography method, we performed a model simulation in the case of (1 a model of which a circular lower density region with a density of 1 g/cm 3 is added at the center of the mountain with a density of 2 g/cm 3 (Figure 4a), (2) a model of which a circular higher density region with a density of 2.4 g/cm 3 is added around the lower density region (Figure 4b), and (3) a model of which an elliptic lower density region with a density of 1 g/cm 3 is added at the center of the mountain (Figures 4c and 4d). Here we assume that the central region of the mountain can be deviated from the empirically given density hri because it is reasonable to assume that the density anomaly is localized near the vent area. W m near the center is set to be 10% of that in the surrounded area. The area where the diagonal component of W m is reduced is here called W m window. The results are shown in Figure 5 together with the diagonal component of W m for the model calculation. 4. Results and Discussions [12] Asama Volcano on the Japanese island of Honshu is located at the junction of the Izu Marianas and NE Japan volcanic arcs. Asama erupted in 1783 (Tenmei 3), causing widespread damage. The 3 month long Plinian eruption in 1783 produced large lava flows toward the northwest direction (Oni oshidashi) and large pyroclastic flows toward the northeast direction (Azuma pyroclastic flow). The present height is 2568 m, and there is a crater called Okama on the top. Its crater floor is located at 2320 m asl. Figure 5. Results of the model simulation. (a d) Corresponding to the models in Figure 4. (e) The diagonal component used for the present tomography simulation. 4of9

5 Figure 6. Number of muons normalized to 1 month (30 days). Curves represent the muon events as obtained from the Monte Carlo simulation for the uniform density that ranges from 1.8 to 2.6 g/cm 3 for the 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. [13] Each muon data as obtained at points N and E are compared with the Geant4 [Agostinelli et al., 2003] Monte Carlo simulation results in order to deduce the average density along the muon path. Observation time is 40 days at point N and 3 months at point E. The number of muons normalized to 1 month (30 days) is shown in Figure 6 together with Monte Carlo simulation results as obtained by assuming different uniform densities of Asama. Two data points in Figure 6d have long error bars because of a large systematic error mainly from the detector configuration and are neglected in the following discussion. The observation times are quite different from point N and point E because point E was constructed earlier than when point N was constructed. In general, the measurement time for telescope E should be shorter to achieve the same signal to noise ratio. However, it is better for us to use data with a better statistic because it contributes to determining the density distribution with shorter error bars. Figures 7a and 7b show the average density along the muon path from each observation point. Assuming that the density changes smoothly within the detector resolution, we can interpolate the data to produce Figures 7c and 7d. Figures 7c and 7d are essentially cross sections through Asama parallel to each plane of the detector at the different site, on which the average density along all the muon paths is projected. These two images are used 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 m at the center of the crater from point N. From the unidirectional muography [Tanaka et al., 2007a], the bulk density of Asama was already measured to be 2.3 g/cm 3. This value was used for determining hri in equation (3). Also, because it is highly expected that the density distribution near the crater area is more heterogeneous than that in the other areas, we assume that the value of a part of the diagonal component of W m in equation (3), which corresponds to the area around the crater, is smaller than other part of the component. This process means that the density near the crater can deviate more from the bulk density in comparison to the other area. The area where we reduce the value in the diagonal component of W m is shown in Figure 2 by dotted box. The amount of reduction is determined 5of9

6 Figure 7. Muographs as obtained from (a) point E and (b) point N, showing the average density along the 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. empirically by considering the following two factors: (1) if we reduce the value of the component of W m, a data fitting error increases; (2) however, if we do not reduce it, the heterogeneity located near the crater area will be likely to appear near the detector where the muon path lines are densely packed. We empirically determined the value to be 0.25 whereas that for other component is 1.0. [15] The analytical results are shown in Figure 8. The deduced density in each voxel is plotted along the W E and N S directions at different elevations. Assuming the present crater is filled with the material, average density over four voxels around the crater center is determined to be 1.9 ± 0.6 g/cm 3 at an elevation between 2170 and 2270 m, 2.2 ± 0.6 g/cm 3 at an elevation between 2270 and 2370 m, and Figure 8. Density distribution along (a) the A B line and (b) the C D line in Figure 1. Because along the A B and C D lines voxels do not exist, the average density between two voxels across these lines is plotted. 6of9

7 Figure 9. Average density over four voxels around the center of the crater at an elevation of (a) between 2170 and 2270 m, (b) between 2270 and 2370 m, and (c) between 2370 and 2470 m for different size of the area where the value of the diagonal component of W m is reduced. 0.5 ± 0.6 g/cm 3 at an elevation between 2370 m and 2470 m. The lower density observed at an elevation between 2170 and 2270 m is probably due to fractured materials filled in a conduit. At an elevation between 2370 and 2470 m, where it is above the crater floor, a density below water was measured. [16] In the previous discussion, the size of the area where the value of W m is reduced is empirically determined. In order to evaluate this uncertainty, the data were fitted by changing the size of the area where the value of W m is reduced. The result is shown in Figure 9. The size dependence is small for the density determined at elevations between 2170 and 2270 m and between 2270 and 2370 m, whereas it is larger at the elevation between 2370 and 2470 m. This can be explained by the following reason: Because there is a crater on the top, the low density region is more localized at a higher elevation, whereas the fractured region is spread more below the crater floor. Considering such a model uncertainty, the average density over four voxels around the crater center is determined to be 1.9 ± 0.7 g/cm 3 at an elevation between 2170 m and 2270 m, 2.2 ± 0.6 g/cm 3 at an elevation between 2270 m Figure 10. Dumped least squares solution of two directional muography for (a) the region between 2170 and 2270 m asl, (b) the region between 2270 and 2370 m asl, and (c) the region between 2370 and 2470 m asl. 7of9

8 below the crater floor seems to be extended toward the north. This might be related to the 1783 eruption that caused a large pyroclastic 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 the conventional unidirectional muography: the technique only resolves the average density distribution along individual muon paths. However, there are still several limitations to the present Mu CAT technique: in order to fit the data to the model, (1) we have to assume the value for W m ; and (2) we have to assume the size of the area where the value of W m is reduced. This assumption increases the model uncertainty and the error when determining the density. We have performed a model calculation and found that if we place eight or more muon observation points around the volcano, above two assumptions will not be necessary. We anticipate that the Mu CAT will be a powerful tool to see smaller objects and 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 Promotion of Science) and JST (Japan Science and Technology Agency) are acknowledged. T. Koyaguchi, J. Oikawa, Y. Aoki, E. Koyama of ERI; K. Nagamine of UCR; I. Yokoyama, member Japan Academy; and Y. Yamashina, M. Seki, Y. Nagasaki, and S. Tanaka are also acknowledged for their valuable suggestions. This work greatly benefited from useful comments by two reviewers of this manuscript. This work is supported by Grants in Aid for Scientific Research ( ). Figure 11. Volumetric representation inside Asama. Top of Asama is truncated at the elevation of 2470 m. The image is vertically sliced by a W E plane including (a) the center of the crater, (b) 100 m north from the center of the crater, and (c) 200 m north from the center of the crater. (d) The image without cut. It can be visually seen that the low density area is extended toward the north direction in Figure 11c. and 2370 m, and 0.7 ± 0.9 g/cm 3 at an elevation between 2370 and 2470 m. [17] A dumped least squares solution of two directional muography is shown in Figure 10. Assuming the density changes smoothly within the detector resolution, we can produce the volumetric representation as shown in Figure 11. The size of the fractured region below the crater floor was determined to be 300 ± 100 m for the W E direction, and 150 ± 50 m for the N S direction. The fractured zone References Agostinelli, S., et al. (2003), Geant4: A simulation tool kit, Nucl. Instrum. Methods A, 506, , doi: /s (03) Cockcroft, J. D., and E. T. Walton (1932), Experiments with high velocity positive ions (II) The disintegration of elements by high velocity protons, Proc. R. Soc. London, Ser. A, 137, , doi: /rspa Goebel, W. (1969), A new modification of the Cockcroft Walton voltage multiplier circuit, Nucl. Instrum. Methods, 67, , doi: / X(69) Greinacher, N. (1920), High voltage DC generator, Bull. Schweiz. Elek. Ver., 11, 59. Groom, D. E. (2001), Muon stopping power and range tables 10 MeV 100 TeV, At. Data Nucl. Data Tables, 78, , doi: / adnd Tanaka, H. K. M., and I. Yokoyama (2008), Muon radiography and deformation analysis of the lava dome formed by the 1944 eruption of Usu, Hokkaido Contact between high energy physics and volcano physics, Proc. Jpn. Acad., Ser. B, 84, , doi: /pjab Tanaka, H., K. Nagamine, N. Kawamura, S. N. Nakamura, K. Ishida, and K. Shimomura (2003), Development of a two fold segmented detection system for near horizontally cosmic ray muons to probe the internal structure of a volcano, Nucl. Instrum. Methods A, 507, , doi: /s (03)01372-x. Tanaka, H. K. M., et al. (2007a), High resolution imaging in the inhomogeneous crust with cosmic ray muon radiography: The density structure below the volcanic crater floor of Mt. Asama, Japan, Earth Planet. Sci. Lett., 263, , doi: /j.epsl Tanaka, H. K. M., T. Nakano, S. Takahashi, J. Yoshida, H. Ohshima, T. Maekawa, H. Watanabe, and K. Niwa (2007b), Imaging the conduit size ofthedomewithcosmic ray muons: The structure beneath Showa Shinzan Lava Dome, Japan, Geophys. Res. Lett., 34, L22311, doi: / 2007GL Tanaka, H. K. M., et al. (2008), Radiographic imaging below a volcanic crater floor with cosmic ray muons, Am.J.Sci., 308, , doi: / Tanaka, H. K. M., T. Uchida, M. Tanaka, H. Shinohara, and H. Taira (2009), Cosmic ray muon imaging of magma in a conduit: Degassing process of Satsuma Iwojima Volcano, Japan, Geophys. Res. Lett., 36, L01304, doi: /2008gl Uchida, T., H. K. M. Tanaka, and M. Tanaka (2010), Development of a muon radiographic imaging electronic board system for a stable solar 8of9

9 power operation, Earth Planets Space, 62(2), , doi: / eps Y.Aoki,R.Nishitama,T.Ohminato, D. Shoji, M. Takeo, H. K. M. Tanaka, and H. Tsuiji, Earthquake Research Institute, University of Tokyo, Yayoi, Bunkyo, Tokyo , Japan. (ht@riken.jp) H. Taira, Department of Earth and Planetary Science, University of Tokyo, Hongo, Bunkyo, Tokyo , Japan. M. Tanaka and T. Uchida, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization, 1 1 Oho, Tsukuba, Ibaraki , Japan. 9of9