Open AccessFree oscillations of elastically anisotropic spheres and ellipsoids
Author(s) -
Oda H.,
Hirao J.,
Suzuki I.,
Visscher W. M.,
Anderson O. L.
Publication year - 1994
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1994.tb03984.x
Subject(s) - ellipsoid , isotropy , spheres , anisotropy , physics , degenerate energy levels , classical mechanics , mathematical analysis , mathematics , optics , quantum mechanics , astronomy
SUMMARY The free oscillations of elastically anisotropic spheres are computed here using a Rayleigh‐Ritz method developed by Mochizuki (1988). The computation of eigenfrequencies was made for elastic spheres with orthorhombic, tetragonal, cubic and isotropic crystal symmetries, and how the degenerate eigenfrequencies split due to the elastic anisotropy has been shown. A perturbation theory combined with the Rayleigh‐Ritz method was presented to compute shifts in and splits of eigenfrequencies due to deformation of an elastic sphere into an ellipsoid. The frequency shifts are expressed by δω=φ x E x +φ y E y +φ z E z , where E j and φ j (j = x, y, z) are, respectively, asphericities and aspherical coefficients of the ellipsoid. This equation was used not only to compute the free‐oscillation frequencies of an elastically anisotropic ellipsoid, but also to determine the asphericities of an olivine ellipsoid from observed resonant frequencies.