On the Strain Produced in a Semi-infinite Elastic Solid by an Interior Source of Stress

Abstract

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 AA is the combination of hydrostatic pressure and pressure with distribution expressed in spherical harmonic P2 (cos 6). Type B is the distribution of pressure expressed in P21(cos e) cos b. 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 (cos eo)=P2 (cos 6)(4+4 cos 2X)+P91(cos 6) cos (cb-cb)(1 sin 2) +P22(cose)cos2(q-cb)(1-1cos2) 8 8 P21(cos 6o) cos qo=[sin q A21-=cos P B21] where A21=P21 (cos 6) sin (q S-cb) cos X+P22 (cos 6) sin 2(b-b)(1 sin X) B21=P2 (cos 6)(-sin 2)-P21(cos 6) cos (q-b) cos 2x-P92 (cos 61 cos 2(h--cLl-sin 2v Euler angles where (c,b, x) 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 (cos 6), P21(cos 6) cos q, P(cos 6) cos 2b were applied at the interior spherical cavity.