Open AccessSH Waves in a Transversely Isotropic Medium – III Transradially Isotropic Sphere
Author(s) -
Sato R.,
Lapwood E. R.,
Singh Kehar
Publication year - 1971
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1971.tb03591.x
Subject(s) - radius , isotropy , cylinder , perpendicular , physics , wavefront , transverse isotropy , wavelength , optics , geometry , point source , phase velocity , isotropic solid , phase (matter) , spheres , classical mechanics , mathematics , quantum mechanics , computer security , computer science , astronomy
Summary We consider waves and rays in a sphere which is transradially isotropicat any point the phase velocity along the radius is V v and in directions perpendicular to a radius is V H . We show that, for waves whose length is short compared with the radius of the sphere, we can describe rays and wavefronts travelling from a source in diametrial planes by the same ‘angle stretching’technique as for a transradially isotropic cylinder (Part II). But here the technique is valid only as a shortwave approximation, whereas in a cylinder the ‘angle stretching’method is exact for all wavelengths. We derive a short‐wave approximation for the displacement at any point of the sphere following an impulsive twist at an internal point. We also discuss the modification of periods of normal modes of oscillation of the sphere, as compared with a uniform sphere in which the shear velocity is V v . As would be expected, the periods are shortened or lengthened according as V H > V v .