Free oscillations of the earth-like planets in the presence of magnetic field

Abstract

we study the free oscillations of a non-rotating earth-like planet in the presence of a force free magnetic field. The model consists of a solid inner core, a liquid outer core and a solid mantle which is spherically symmetric. The lagrangian displacements are decomposed into scaloidal, poloidal and toroidal components using a gauged version of Helmholtz theorem. These components are identified, with P- , g and t- modes, respectively. The normal modes of the model are determined using a Rayleigh-Ritz variational technique. The consequence of the presence of the solid parts and the magnetic field is the emergence of pure t- oscillations. The magnetic field, in addition to exciting t- modes, couples the everpresent p- and g -modes together. As an application of the model, the real seismic data of the earth is used to calculate eigenvalues and eigenvectors for different modes.

Keywords

• planets
• oscillation
• earth
• magnetic field
• magnetohydrodynamics
• waves