著者
山川 宜男
出版者
公益社団法人 日本地震学会
雑誌
地震 第2輯 (ISSN:00371114)
巻号頁・発行日
vol.8, no.2, pp.84-98, 1955-10-20 (Released:2010-03-11)
参考文献数
7
被引用文献数
18

Japanese seismologists succeeded in explaining the push-pull distribution of the initial motion of earthquakes by assuming two types stress distribution on the sphere which covers the hypocenter. Type A is the combination of hydrostatic pressure and pressure with distribution expressed in spherical harmonic P2(cosθ). Type B is the distribution of pressure expressed in P21(cosθ)cosφ. Generally the polar axis of these spherical harmonics does not coincide with vertical axis. On this point, Y. Sato obtained the formulae which express the transformation of the spherical harmonics by the rotation of coordinate system. According to his result, P2(cosθ0)=P2(cosθ)(1/4+3/4cos2χ)+P21(cosθ)cos(φ-φ)(1/2sin2χ)+P22(cosθ)cos2(φ-φ)(1/8-1/8cos2χ)P21(cosθ0)cosφ0=[sinφA21-cosφB21]where A21=P21(cosθ)sin(φ-φ)cosχ+P22(cosθ)sin2(φ-φ)(1/2sinχ)B21=P2(cosθ)(3/2sin2χ)-P21(cosθ)cos(φ-φ)cos2χ-P22(cosθ)cos2(φ-φ)(1/4sin2χ)where (φ, φ, χ) is Euler angles which express the rotation of the coordinate.In this paper, we calculated the strain produced in a semi-infinite elastic solid when hydrostatic pressure and pressure with distribution expressed in spherical harmonics P2(cosθ), P21(cosθ)cosφ, P22(cosθ)cos2φ were applied at the interior spherical cavity.The deformations expressed in cylindrical coordinate (R, φ, z) at the surface of semiinfinite elastic solid are as follows:—(1) The case in which hydrostatic pressure -P is appliedUR=3a3P/4μR/(f2+R2)3/2, Uφ=0, Uz=-3a3P/4μf/(f2+R2)3/2(2) The case of -PP2(cosθ)UR=3a3P/46μ[-5P/(f+R23/2)+18f2R/(f2+R2)5/2], Uφ=0, Uz=-3a3P/46μ[-5f/(f2+R23/2)+18f3/(f2+R2)5/2](3) The case of -PP21(cosθ)cosφUR=54a3P/23μcosφ[-f((f2+R2)3/2+f3(f2+R2)5/2], Uφ45a5P/184μsinφf(R2+f2)5/2, Uz=45a5P/184μsinφf(R2+f2)5/2(4) The case of -PP22(cosθ)cos2φUR=9a3P/23μcos2φ[4f/R3-4f2/R3(R2+f2)1/2+5R(f2+R2)3/2-2f2/R(R2+f2)3/2-6f2R

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ちなみに面倒な計算で大きく貢献したのは山川(1955) 。これ追っかけるのはかなり大変だった遠い記憶が... https://t.co/FI2461bcNY

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