Heikki Vanhamaki

One-dimensional upward continuation of the ground magnetic field disturbance using spherical elementary current systems

Ionospheric equivalent currents are defined as spherical sheet currents, which reproduce the observed magnetic disturbances below the ionosphere. One way of determining these currents is to place several so called spherical elementary current systems (SECS) in the ionospheric height and to solve an inversion problem for the amplitudes of these systems. In previous studies this method has been applied to two-dimensional data sets, having both latitudinal and longitudinal spatial coverage (2D SECS method). In this paper a one-dimensional variant of this method (1D SECS) is developed. The 1D SECS method can be used even in those situations where the data set is one dimensional, e.g. with one meridionally aligned magnetometer chain. The applicability of the 1D SECS method is tested using both synthetic and real data. It is found that in real situations the errors in the 1D SECS results are 5—10% in current density profiles and ~5% in integrated currents, when compared to the results of the more accurate 2D SECS method.

Deriving the geomagnetically induced electric field at the Earth’s surface from the time derivative of the vertical magnetic field

We present a new method for estimating the geomagnetically induced electric field at the Earth’s surface directly from the time derivative of the vertical magnetic field, without any need for additional information about the Earth’s electric conductivity. This is a simplification compared to the presently used calculation methods, which require both the magnetic variation field and ground conductivity model as input data. The surface electric field is needed e.g. in modeling Geomagnetically Induced Currents (GIC) that flow in man-made conductor systems, such as gas and oil pipelines or high-voltage power grids. We solve the induced electric field directly from Faraday’s law, by representing the magnetic variation field in terms of external equivalent current and taking time derivative of the associated vector potential. This gives an approximative solution, where the divergence-free part of the electric field is reproduced accurately (at least in principle), but the curl-free part related to lateral variations in ground conductivity is completely neglected. We test the new calculation method with several realistic models of typical ionospheric current systems, as well as actual data from the Baltic Electromagnetic Array Research (BEAR) network. We conclude that the principle of calculating the (divergence-free part of the) surface electric field from time derivative of the vertical magnetic field is sound, and the method works reasonably well also in practice. However, practical applications may be rather limited as the method seems to require data from a quite dense and spatially extended magnetometer network.