A new subseismic governing system of equations and its expansions

Abstract

By appealing to the subseismic approximation (SSA), we establish a new system of two first-order partial differential equations involving displacement field only, which govern the normal modes of a rotating self-gravitating stratified compressible inviscid liquid core. To treat a slightly ellipsoidal Earth model we use a coordinate transformation method which introduces modified spheroidal and toroidal fields so as to avoid trouble with the validity of Taylor expansions near a surface of discontinuity in material properties. The governing equations are expanded in these modified spheroidal and toroidal fields, so that the governing partial differential equations in three-dimensional space become systems of ordinary differential equations in one-dimensional space. As one application of the new subseismic governing system of equations (SGSE) and its expansions, we make an analytical study of the effects of the liquid core on the Chandler wobble (CW) and free core nutation (FCN) using an Earth model which consists of a much simplified mantle and inner core and a more realistic liquid outer core. The results show that the periods of the CW and FCN are independent of the structure of the Earth's liquid core when the radial variation of ellipticity of isopycnal surfaces in the liquid outer core is neglected. As a second application of the SGSE we calculate eigenperiods of some gravity/inertia modes for both non-rotating and rotating stably spherically stratified liquid core with a rigid mantle and inner core. This computation shows the advantage of the new SGSE over the subseismic wave equation (SSWE).