Effects of Density Stratification on the Frequencies of the Inertial-Gravity Modes of the Earth’s Fluid Core

sayyid quthb;

The Earth’s outer core is a rotating ellipsoidal shell of compressible, stratified and self gravitating fluid. As such, in the treatment of geophysical problems a realistic model of this body needs to be considered. In this work, we consider compressible and stratified fluid core models with different stratification parameters, related to the local Brunt-Vaisala frequency, in order to study the effects of the core’s density stratification on the frequencies of some of the inertial-gravity modes of this body. The inertial-gravity modes of the core are free oscillations with periods longer than 12 hr. Historically, an incompressible and homogeneous fluid is considered to study these modes and analytical solutions are known for the frequencies and the displacement eigenfunctions of a spherical model. We show that for a compressible and stratified spherical core model the effects of non-neutral density stratification may be significant, and the frequencies of these modes may change from model to model. For example, for a spherical core model the frequency of the spin-over mode, the (2, 1, 1) mode, is unaffected while that of the (4, 1, 1) mode is changed from−0.410 for the Poincar´e core model to−0.434,−0.447 and −0.483 for core models with the stability parameter β = −0.001,−0.002 and −0.005, respectively, a maximum change of about 18 per cent when β =−0.005. Our results also show that for small stratification parameter, |β| ≤ 0.005, the frequency of an inertialgravity mode is a nearly linear function of β but the slope of the line is different for different modes, and that the effects of density stratification on the frequency of a mode is likely related to its spatial structure, which remains the same in different Earth models. We also compute the frequencies of some of the modes of the ‘PREM’ (spherical shell) core model and show that the frequencies of these modes may also be significantly affected by non-zero β.