Название: Muography
Автор: Группа авторов
Издательство: John Wiley & Sons Limited
Жанр: Физика
isbn: 9781119723066
isbn:
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29 Rosas‐Carbajal, M., Jourde, K., Marteau, J., Deroussi, S., Komorowski, J.‐C., & Gibert, D. (2017). Three‐dimensional density structure of La Soufrière de Guadeloupe lava dome from simultaneous muon radiographies and gravity data. Geophysical Research Letters, 44, 6743–6751. https://doi.org/10.1002/2017GL074285
30 Roy, M., Lewis, M., Johnson, A., George, N., Rowe, C., & Guardincerri, E. (2018). Inferring shallow subsurface density structure from surface and underground gravity measurements: Calibrating models for relatively undeformed volcanic strata at the Jemez Volcanic Field, New Mexico, USA. Pure Applied Geophysics 175, 1003–1018. https://doi.org/10.1007/s00024‐017‐1742‐4
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38 Tanaka, H. K. M., Nakano, T., Takahashi, S., Yoshida, J., Ohshima, H., Maekawa, T., et al. (2007). Imaging the conduit size of the dome with cosmic‐ray muons: The structure beneath Showa‐Shinzan Lava Dome, Japan. Geophysical Research Letters, 34, L22311. https://doi.org/10.1029/2007GL031389
39 Tanaka, H. K. M., Taira, H., Uchida, T., Tanaka, M., Takeo, M., Ohminato, T., et al. (2010). Three‐dimensional computational axial tomography scan of a volcano with cosmic ray muon radiography. Journal of Geophysical Research, 115, B12332. https://doi.org/10.1029/2010JB007677
40 Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9780898717921
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42 Tioukov, V., Giudicepietro, F., Macedonio, G., Calvari, S., Di Traglia, F., Fornaciai, A., et al. (2021). Structure of the shallow supply system at Stromboli Volcano through integration of muography, digital elevation models, seismicity, and ground deformation data. In: L. Oláh, H. K. M. Tanaka, D. Varga (Eds.), Muography: Exploring Earth's Subsurface with Elementary Particles, Geophysical Monograph Series 270. Washington, DC: American Geophysical Union. This volume.
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45 Yokoyama, I. & Ohkawa, S. (1986). The subsurface structure of the AIRA caldera and its vicinity in southern Kyushu, Japan. Journal of Volcanology and Geothermal Research, 30, 253–282. https://doi.org/10.1016/0377‐0273(86)90057‐0
SUPPLEMENTAL INFORMATION
S3.1. ANALYTICAL FORMULA FOR THE GRAVITATIONAL EFFECT
In the supplemental information, the analytical formula for the gravitational attraction of a rectangular prism is presented. They are necessary to calculate the gravity parts of the design matrix (equation 3.7) and the gravitational attraction by the topography (Δg terrain in equation 3.5).
The analytical integration of equation 3.7 is complicated. The problem is rather simplified by assuming that the observer is located at the origin of the Cartesian coordinate system (Figure S3.1). Equation 3.7 then is reduced to the form
(S3.1)
The analytical solution is provided by many authors (e.g., Nagy, 1966; Plouff, 1977). Especially among them, Plouff’s solution is rather simple:
(S3.2)