Green functions of the earth at borehole sensor installation depths for surface point load

• Published in: Papers in Meteorology and Geophysics Vol. 48; no. 4; pp. 89 - 100
• Main Author: Kamigaichi, Osamu
• Format: Journal Article
• Language: English
• Published: Japan Meteorological Agency / Meteorological Research Institute 1998
• Subjects: Boreholes; Displacement; Earth; Green's functions; Mathematical analysis; Mathematical models; Nonuniformity; Sensors
• ISSN: 0031-126X; 1880-6643
• DOI: 10.2467/mripapers.48.89

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.