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S U M M A R YWe 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.

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We perform a reanalysis of hourly mean magnetic data from ground‐based observatories spanning 1997–2009 inclusive, in order to isolate (after removal of core and crustal field estimates) the spatiotemporal morphology of the external fields important to mantle induction, on (long) periods of months to a full solar cycle. Our analysis focuses on geomagnetically quiet days and middle to low latitudes. We use the climatological eigenanalysis technique called empirical orthogonal functions (EOFs), which allows us to identify discrete spatiotemporal patterns with no a priori specification of their geometry—the form of the decomposition is controlled by the data. We apply a spherical harmonic analysis to the EOF outputs in a joint inversion for internal and external coefficients. The results justify our assumption that the EOF procedure responds primarily to the long‐period external inducing field contributions. Though we cannot determine uniquely the contributory source regions of these inducing fields, we find that they have distinct temporal characteristics which enable some inference of sources. An identified annual‐period pattern appears to stem from a north‐south seasonal motion of the background mean external field distribution. Separate patterns of semiannual and solar‐cycle‐length periods appear to stem from the amplitude modulations of spatially fixed background fields.

S U M M A R YA novel time-domain approach to the global electromagnetic induction problem is applied to vector magnetometer data observed by the CHAMP satellite. Data recorded during 11 storm events in 2001-2003 are processed track by track, yielding time-series of spherical harmonic coefficients. The data are then interpreted in terms of 1-D layered electrical conductivity models. The inversion is performed by full search of model parametric space which yields sensitivity of misfit with respect to conductivities of layers and positions of interfaces. In the upper 50 km the inversion solidly recovers a conductive layer corresponding to averaged surface conductance. The conductivity of the lower mantle is established at 6 S m −1 assuming the upper-lower mantle interface is fixed at the seismic-based 670 km boundary. However, the satellite data favour the models with a large jump around 1000 km to unrealistic conductivity values exceeding 10 3 S m −1 . The resolution of the method in the resistive upper mantle sandwiched between conductive crust and lower mantle is poor. Nevertheless, an upper bound of 0.01 S m −1 is suggested by the data. A conductivity increase in the transition zone is not observed.