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Aspherical correction for free vibration of elastically anisotropic solid by means of theXYZ algorithm

Authors:	Hitoshi Oda

Institution:	(1) Department of Earth Sciences, Okayama University, 700 Okayama, Japan

Abstract:	By applying the perturbation theory to theXYZ algorithm (a kind of variational method), the difference f in free vibration frequencies between sphere and ellipsoid was approximated as $\delta f = \Psi _x \varepsilon _x + \Psi _y \varepsilon _y + \Psi _z \varepsilon _z$ , where i and _i (i = x,y andz) (i=x, y andz) are aspherical coefficients and asphericities of the ellipsoid, respectively. We developed an analytic method to compute the aspherical coefficients719-4 by using theXYZ algorithm. A numerical example was given for an ellipsoidal olivine, and an attempt was made to estimate the asphericities of the specimen by a least-squares method, based on the relationship between frequency shift and asphericity.

Keywords:	Free vibration elastic anisotropy asphericity XYZ algorithm RST
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