Ray-theoretical relations between intrinsic and apparent dissipation factors in the Earth

Abstract

Summary. A ray-theoretical approach is successfully employed for obtaining the relations between the intrinsic dissipation factors of P- and S-waves, Qα and Qβ, and the apparent dissipation factors of toroidal and spheroidal oscillations, QTor and QSphThese are given in quite simple forms and are expressed, to zero-order approximatiom which neglects the effect of reflection of waves at an interface and/or at a free surface), as where α and β are the P- and S-wave velocities and the integrals are evaluated long the surface to surface P- and S-rays. Some numerical comparisons support the validity of these formulae for higher modes of toroidal and radial oscillations of a realistic earth model. A first-order approximation reveals that the existence of a discontinuity in an earth induces a systematic fluctuation in normal-mode Q values for any given phase velocity as a function of frequency (or radial mode number).