Determination of equivalent current sources from spherical cap harmonic models of geomagnetic field variations

A new technique for continuation of the ground magnetic field caused by ionospheric currents to the ionosphere in spherical geometry is presented that makes use of elementary ionospheric current systems, which were introduced by Amm (1997) in extension of an earlier work by Fukushima (1976). The measured ground magnetic disturbance is expanded in terms of the ground magnetic effect of a spatial distribution of such elementary current systems. Using a matrix inversion technique, the scaling factors for each elementary current system, and therefrom the ionospheric equivalent currents are calculated. The technique can be applied to both global and local scales. Its advantages compared to the common field continuation techniques with Fourier (local scale), spherical cap (local to medium scale), or spherical (global scale) harmonic expansions are: 1) No fixed limitation of the spectral content has to be given for the whole analysis area, as it has to be done for the other techniques by truncation of a series expansion.2) The locations of the elementary current systems can be chosen freely, such that they are most suitable with respect to the available measurement sites or the type of current system to be analysed. Results of the new technique are discussed in comparison to results of the spherical cap harmonic expansion method for a model of a Cowling channel.

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“…The equations for the equivalent currents in terms of the SCHA expansion can be found in Haines and Torta (1994). In Fig.…”

Section: Application Examplementioning

confidence: 99%

Ionospheric disturbance magnetic field continuation from the ground to the ionosphere using spherical elementary current systems

2014

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“…Haines and Torta (1994) introduced a technique called spherical cap harmonic analysis, which enables the separation of the external and internal potentials based on a regional analysis of the Sq field. The spherical cap harmonic analysis is similar to the normal spherical harmonic analysis, but it does not analyze a global field.…”

Section: Spherical Harmonic Analysismentioning

confidence: 99%

Sq and EEJ—A Review on the Daily Variation of the Geomagnetic Field Caused by Ionospheric Dynamo Currents

2016

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A record of the geomagnetic field on the ground sometimes shows smooth daily variations on the order of a few tens of nano teslas. These daily variations, commonly known as Sq, are caused by electric currents of several μA/m 2 flowing on the sunlit side of the Eregion ionosphere at about 90-150 km heights. We review advances in our understanding of the geomagnetic daily variation and its source ionospheric currents during the past 75 years. Observations and existing theories are first outlined as background knowledge for the nonspecialist. Data analysis methods, such as spherical harmonic analysis, are then described in detail. Various aspects of the geomagnetic daily variation are discussed and interpreted using these results. Finally, remaining issues are highlighted to provide possible directions for future work.

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“…Viljanen et al (2004), Ngwira et al (2009) and others have used the spherical elementary current system (SECS; Amm & Viljanen 1999) for interpolating the spatial variation of the magnetic field disturbance across the area of a power system. Magnetic field variations can also be fitted using spherical cap harmonic analysis (SCHA; Haines 1985;Haines & Torta 1994) providing an alternative method for interpolation across a power network. These techniques are appropriate when there are a sufficient number of magnetic recording sites to map the spatial structure of the magnetic field variations.…”

Section: Discussionmentioning

confidence: 99%

Methodology for simulation of geomagnetically induced currents in power systems

Boteler¹

2014

J. Space Weather Space Clim.

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To assess the geomagnetic hazard to power systems it is useful to be able to simulate the geomagnetically induced currents (GIC) that are produced during major geomagnetic disturbances. This paper examines the methodology used in power system analysis and shows how it can be applied to modelling GIC. Electric fields in the area of the power network are used to determine the voltage sources or equivalent current sources in the transmission lines. The power network can be described by a mesh impedance matrix which is combined with the voltage sources to calculate the GIC in each loop. Alternatively the power network can be described by a nodal admittance matrix which is combined with the sum of current sources into each node to calculate the nodal voltages which are then used to calculate the GIC in the transmission lines and GIC flowing to ground at each substation. Practical calculations can be made by superposition of results calculated separately for northward and eastward electric fields. This can be done using magnetic data from a single observatory to calculate an electric field that is a uniform approximation of the field over the area of the power system. It is also shown how the superposition of results can be extended to use data from two observatories: approximating the electric field by a linear variation between the two observatory locations. These calculations provide an efficient method for simulating the GIC that would be produced by historically significant geomagnetic storm events.

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Determination of equivalent current sources from spherical cap harmonic models of geomagnetic field variations

Cited by 71 publications

References 18 publications

Ionospheric disturbance magnetic field continuation from the ground to the ionosphere using spherical elementary current systems

Ionospheric disturbance magnetic field continuation from the ground to the ionosphere using spherical elementary current systems

Sq and EEJ—A Review on the Daily Variation of the Geomagnetic Field Caused by Ionospheric Dynamo Currents

Methodology for simulation of geomagnetically induced currents in power systems

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