Open AccessTime‐domain, spherical harmonic‐finite element approach to transient three‐dimensional geomagnetic induction in a spherical heterogeneous Earth
Author(s) -
Velímský Jakub,
Martinec Zdeněk
Publication year - 2005
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2005.02546.x
Subject(s) - earth's magnetic field , spherical harmonics , discretization , mathematical analysis , piecewise , finite element method , galerkin method , piecewise linear function , physics , electromagnetic induction , discontinuous galerkin method , mathematics , geophysics , geometry , magnetic field , quantum mechanics , electromagnetic coil , thermodynamics
SUMMARY We introduce a time‐domain method to solve the problem of geomagnetic induction in a heterogeneous Earth excited by variations of the ionospheric and magnetospheric currents with arbitrary spatiotemporal characteristics. The problem is formulated in the integral sense. The Galerkin discretization is based on the vector spherical harmonic functions and piecewise linear finite elements in the angular and radial directions, respectively. A semi‐implicit time integration scheme is employed. The method is validated against semi‐analytical (SA) solutions for conductivity models consisting of multiple eccentrically nested homogeneous spheres.