Green functions of the earth at borehole sensor installation depths for surface point load
Green functions of the earth at borehole sensor installation depths (0 to 962.5m, at each 68.75m) for the surface vertical point load were calculated using spherical earth model 1066A. Correct calculation requires both eigen functions and Legendre functions whose order n exceeds 1 million. Green fun...
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| Published in | Papers in Meteorology and Geophysics Vol. 48; no. 4; pp. 89 - 100 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Japan Meteorological Agency / Meteorological Research Institute
1998
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| Subjects | |
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| Abstract | Green functions of the earth at borehole sensor installation depths (0 to 962.5m, at each 68.75m) for the surface vertical point load were calculated using spherical earth model 1066A. Correct calculation requires both eigen functions and Legendre functions whose order n exceeds 1 million. Green function behavior at depth=0 and depth≠0 are significantly different, especially at a short distance from the loading point. In the θ (angular distance) <0.01 degree range, spherical green functions and their Boussinesq approximations coincide well except for those including radial displacement, both at depth=0 and ≠0, but diverge at large θ due to the earth's nonuniformity and surface curvature. Atmospheric coefficients for areal and volume strain show scale dependence reflecting the earth's inner structure and the relative magnitude of installation and skin depths. |
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| AbstractList | Green functions of the earth at borehole sensor installation depths (0 to 962.5m, at each 68.75m) for the surface vertical point load were calculated using spherical earth model 1066A. Correct calculation requires both eigen functions and Legendre functions whose order n exceeds 1 million. Green function behavior at depth=0 and depth≠0 are significantly different, especially at a short distance from the loading point. In the θ (angular distance) <0.01 degree range, spherical green functions and their Boussinesq approximations coincide well except for those including radial displacement, both at depth=0 and ≠0, but diverge at large θ due to the earth's nonuniformity and surface curvature. Atmospheric coefficients for areal and volume strain show scale dependence reflecting the earth's inner structure and the relative magnitude of installation and skin depths. Green functions of the earth at borehole sensor installation depths (0 to 962.5m, at each 68.75m) for the surface vertical point load were calculated using spherical earth model 1066A. Correct calculation requires both eigen functions and Legendre functions whose order n exceeds 1 million. Green function behavior at depth=0 and depth[ne]0 are significantly different, especially at a short distance from the loading point. In the [thetas] (angular distance) <0.01 degree range, spherical green functions and their Boussinesq approximations coincide well except for those including radial displacement, both at depth=0 and [ne]0, but diverge at large [thetas] due to the earth's nonuniformity and surface curvature. Atmospheric coefficients for areal and volume strain show scale dependence reflecting the earth's inner structure and the relative magnitude of installation and skin depths. Green functions of the Earth at borehole sensor installation depths (0 to 962.5m, at each 68.75 m) for the surface vertical point load were calculated using spherical Earth model 1066A. Correct calculation requires both eigen functions and Legendre functions whose order n exceeds 1 million. Green function behavior at depth = 0 and nonzero depth are significantly different, especially at a short distance from the loading point. In the theta (angular distance) less than 0.01 degree range, spherical green functions and their Boussinesq approximations coincide well, except for those including radial displacement, both at zero and nonzero depth, but diverge at large theta due to the Earth's nonuniformity and surface curvature. Atmospheric coefficients for areal and volume strain show scale dependence reflecting the Earth's inner structure and the relative magnitude of installation and skin depths. (Author) Green functions of the Earth at borehole sensor installation depths (0 to 962.5 m, at each 68.75 m) for the surface vertical point load were calculated using spherical Earth model 1066A. Correct calculation requires both eigen functions and Legendre functions whose order n exceeds 1 million. Green function behavior at depth=0 and depth [not equal to] 0 are significantly different, especially at a short distance from the loading point. In the theta (angular distance) <0.01 degree range, spherical green functions and their Boussinesq approximations coincide well except for those including radial displacement, both at depth=0 and [not equal to] 0 but diverge at large theta due to the Earth's nonuniformity and surface curvature. Atmospheric coefficients for areal and volume strain show scale dependence reflecting the Earth's inner structure and the relative magnitude of installation and skin depths. |
| Author | Kamigaichi, Osamu |
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| CitedBy_id | crossref_primary_10_1093_gji_ggab216 crossref_primary_10_1007_s00024_021_02831_x crossref_primary_10_1029_2019JB018088 crossref_primary_10_1002_2017GL075615 crossref_primary_10_1177_108128650200700501 crossref_primary_10_1029_2012JB009657 |
| Cites_doi | 10.1111/j.1365-246X.1993.tb06988.x 10.1016/0031-9201(81)90046-7 10.1111/j.1365-246X.1995.tb03546.x 10.4294/jpe1952.26.13 10.4294/jpe1952.22.123 10.1029/RG010i003p00761 10.1016/B978-0-12-460811-5.50010-6 10.1098/rsta.1975.0025 10.1111/j.1365-246X.1961.tb06815.x 10.1111/j.1365-246X.1988.tb01119.x |
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| References | Kamigaichi, O., 1987: Physical consideration on the correction methods of volumetric strain and tilt data for the effects of atmospheric pressure change. Q. J. Seismol. (Kenshin Jiho), 50, 41-49 (in Japanese). Tsuruoka, H., M. Ohtake, and H. Sato, 1995: Statistical test of the tidal triggering of earthquake: contribution of the ocean tide loading effect. Geophys. J. Int., 122, 183-194. Dziewonski, A. M. and D. L. Anderson, 1981: Preliminary reference earth model. Phys. Earth. Planet. Inter., 25, 297-356. Takemoto, S., T. Yamamoto, A. Mukai, and T. Sato, 1992: Loading effects of oceanic tides on tidal strain measurements. J. Geodetic Soc. of Japan, 38, 211-219 (in Japanese). Saito, M., 1974: Some problems of static defomation of the earth. J. Phys. Earth, 22, 123-140. Saito, M., 1988: DISPER80: A subroutine package for the calculation of seismic normal-mode solutions. Seismol. Algorithms, pp.293-319 Takeuchi, H. and M. Saito, 1972: Seismic surface waves. Meth. Comput. Phys., 11, pp.217-295. Farrell, W. E., 1972: Deformation of the earth by surface loads. Rev. Geophys. Space Phys., 10, 761-797. Gilbert, F. and A. M. Dziewonski, 1975: An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra. Phil. Trans. R. Soc. Lond., Ser. A, 278, 187-269. Saito, M., 1978: Relationship between tidal and load Love numbers. J. Phys. Earth, 26, 13-16. Endo, T. and S. Okubo, 1982: Partial derivatives of the green function. Proc. 58th J. Geodet. Soc., 105-106 (in Japanese). Nihei, S., K. Sato, and O. Kamigaichi, 1987: Observation by borehole volume strainmeters (I) - Summary from 1976 to 1986. Q. J. Seismol., 50, 65-88 (in Japanese). Alterman, Z., H. Jarosch, and C. L. Pekeris, 1961: Propagation of Rayleigh waves in the earth. Geophys. J. R. Astr. Soc., 4, 219-241. Okubo, S., 1988: Asymptotic solutions to the static defomation of the earth - I. Spheroidal mode. Geophys. J. Int., 92, 39-51. Sun, W. and S. Okubo, 1993: Surface potential and gravity changes due to internal dislocation in a spherical earth - I. Theory for a point dislocation. Geophys. J. Int., 114, 569-592. Sato, T. and H. Hanada, 1984: A program for the computation of oceanic tidal loading effects ‘GOTIC’. Publ. Int. Lat. Obs. Mizusawa, 18, 29-47. 11 12 14 15 (16) 1995; 122 (13) 1993; 114 1 2 3 4 5 6 7 8 9 10 |
| References_xml | – reference: Nihei, S., K. Sato, and O. Kamigaichi, 1987: Observation by borehole volume strainmeters (I) - Summary from 1976 to 1986. Q. J. Seismol., 50, 65-88 (in Japanese). – reference: Takeuchi, H. and M. Saito, 1972: Seismic surface waves. Meth. Comput. Phys., 11, pp.217-295. – reference: Alterman, Z., H. Jarosch, and C. L. Pekeris, 1961: Propagation of Rayleigh waves in the earth. Geophys. J. R. Astr. Soc., 4, 219-241. – reference: Dziewonski, A. M. and D. L. Anderson, 1981: Preliminary reference earth model. Phys. Earth. Planet. Inter., 25, 297-356. – reference: Farrell, W. E., 1972: Deformation of the earth by surface loads. Rev. Geophys. Space Phys., 10, 761-797. – reference: Saito, M., 1974: Some problems of static defomation of the earth. J. Phys. Earth, 22, 123-140. – reference: Sato, T. and H. Hanada, 1984: A program for the computation of oceanic tidal loading effects ‘GOTIC’. Publ. Int. Lat. Obs. Mizusawa, 18, 29-47. – reference: Saito, M., 1978: Relationship between tidal and load Love numbers. J. Phys. Earth, 26, 13-16. – reference: Kamigaichi, O., 1987: Physical consideration on the correction methods of volumetric strain and tilt data for the effects of atmospheric pressure change. Q. J. Seismol. (Kenshin Jiho), 50, 41-49 (in Japanese). – reference: Saito, M., 1988: DISPER80: A subroutine package for the calculation of seismic normal-mode solutions. Seismol. Algorithms, pp.293-319 – reference: Tsuruoka, H., M. Ohtake, and H. Sato, 1995: Statistical test of the tidal triggering of earthquake: contribution of the ocean tide loading effect. Geophys. J. Int., 122, 183-194. – reference: Endo, T. and S. Okubo, 1982: Partial derivatives of the green function. Proc. 58th J. Geodet. Soc., 105-106 (in Japanese). – reference: Okubo, S., 1988: Asymptotic solutions to the static defomation of the earth - I. Spheroidal mode. Geophys. J. Int., 92, 39-51. – reference: Takemoto, S., T. Yamamoto, A. Mukai, and T. Sato, 1992: Loading effects of oceanic tides on tidal strain measurements. J. Geodetic Soc. of Japan, 38, 211-219 (in Japanese). – reference: Sun, W. and S. Okubo, 1993: Surface potential and gravity changes due to internal dislocation in a spherical earth - I. Theory for a point dislocation. Geophys. J. Int., 114, 569-592. – reference: Gilbert, F. and A. M. Dziewonski, 1975: An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra. Phil. Trans. R. Soc. Lond., Ser. A, 278, 187-269. – ident: 3 – volume: 114 start-page: 569 issn: 0956-540X issue: 3 year: 1993 ident: 13 doi: 10.1111/j.1365-246X.1993.tb06988.x – ident: 12 – ident: 11 – ident: 2 doi: 10.1016/0031-9201(81)90046-7 – volume: 122 start-page: 183 issn: 0956-540X issue: 1 year: 1995 ident: 16 doi: 10.1111/j.1365-246X.1995.tb03546.x – ident: 14 – ident: 10 doi: 10.4294/jpe1952.26.13 – ident: 9 doi: 10.4294/jpe1952.22.123 – ident: 4 doi: 10.1029/RG010i003p00761 – ident: 15 doi: 10.1016/B978-0-12-460811-5.50010-6 – ident: 5 doi: 10.1098/rsta.1975.0025 – ident: 6 – ident: 7 – ident: 1 doi: 10.1111/j.1365-246X.1961.tb06815.x – ident: 8 doi: 10.1111/j.1365-246X.1988.tb01119.x |
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| Snippet | Green functions of the earth at borehole sensor installation depths (0 to 962.5m, at each 68.75m) for the surface vertical point load were calculated using... Green functions of the Earth at borehole sensor installation depths (0 to 962.5 m, at each 68.75 m) for the surface vertical point load were calculated using... Green functions of the Earth at borehole sensor installation depths (0 to 962.5m, at each 68.75 m) for the surface vertical point load were calculated using... |
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| SubjectTerms | Boreholes Displacement Earth Green's functions Mathematical analysis Mathematical models Nonuniformity Sensors |
| Title | Green functions of the earth at borehole sensor installation depths for surface point load |
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