The complex image approximation for induction in a multilayered Earth

Thomson, David J.; Weaver, J. T.

doi:10.1029/ja080i001p00123

Cited by 64 publications

(57 citation statements)

References 18 publications

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“…(A2) is valid for any layered Earth conductivity, if a general definition of the complex depth is used. The complex image approximation is generally valid when |pv| 3 1 where v is the wave number of the horizontal field variations (Thomson and Weaver, 1975;Boteler and Pirjola, 1998). Now, the second term in the right-hand side of Eq.…”

Section: Appendix Amentioning

confidence: 99%

The role of 3-D geomagnetic induction in the determination of the ionospheric currents from the ground geomagnetic data

Pulkkinen¹,

Engels

2005

Ann. Geophys.

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Abstract. The geomagnetic field variations measured at the surface of the Earth are composed of both internal and external parts. The external field arises from the sources in the magnetosphere and ionosphere, whereas the internal field is generated by the currents induced within the Earth. The internal part may in some situations comprise a notable part of the measured total field and thus a blind usage of geomagnetic field recordings potentially produces significant errors to estimated ionospheric currents. In this paper the role of geomagnetic induction in auroral ionospheric studies is investigated by modeling the induction using simultaneously the realistic ionospheric source and a realistic three-dimensional Earth conductivity structure.The modeling results imply that the effects of the lateral ground conductivity anomalies on ionospheric equivalent current patterns are, though clearly detected, less severe than anticipated for fields varying with periods from 5 to 120 min. However, the amplification of the determined currents caused by induction is significant, leading to an overestimation of up to 30% of the main current flow intensities, with the overestimation increasing sharply when moving away from the region of the main flow.In addition to the 3-D modeling, a simple method is introduced to help estimate the internal contribution to the measured variations of the I L index (local variant of the AL index). A test with the 26 June 1998 substorm event indicates that the method can help to extract the internal contribution from the I L index.

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Section: Appendix Amentioning

confidence: 99%

The role of 3-D geomagnetic induction in the determination of the ionospheric currents from the ground geomagnetic data

Pulkkinen¹,

Engels

2005

Ann. Geophys.

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“…A sophisticated computation technique with layered conductivity structures is the complex image method (CIM) (Lindell et al, 2000; Thomson and Weaver, 1975;Wait and Spies, 1969), which, in a generalised form, allows for including realistic 3-D models of ionospheric currents (Pirjola and Viljanen, 1998). It allows for use of closed-form formulas, thus making computations much faster than with the exact Fourier integrals.…”

Section: Introductionmentioning

confidence: 99%

Fast computation of the geoelectric field using the method of elementary current systems and planar Earth models

Viljanen¹,

Pulkkinen²,

Amm³

et al. 2004

Ann. Geophys.

105

106

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Abstract. The method of spherical elementary current systems provides an accurate modelling of the horizontal component of the geomagnetic variation field. The interpolated magnetic field is used as input to calculate the horizontal geoelectric field. We use planar layered (1-D) models of the Earth's conductivity, and assume that the electric field is related to the local magnetic field by the plane wave surface impedance. There are locations in which the conductivity structure can be approximated by a 1-D model, as demonstrated with the measurements of the Baltic Electromagnetic Array Research project. To calculate geomagnetically induced currents (GIC), we need the spatially integrated electric field typically in a length scale of 100 km. We show that then the spatial variation of the electric field can be neglected if we use the measured or interpolated magnetic field at the site of interest. In other words, even the simple plane wave model is fairly accurate for GIC purposes. Investigating GIC in the Finnish high-voltage power system and in the natural gas pipeline, we find a good agreement between modelled and measured values, with relative errors less than 30% for large GIC values.

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“…To address this need, CIM is derived here from EIT expressions formulated for planar impedance surfaces associated with arbitrary layered conductivity profiles. The derivation ultimately results in a generalization of the classical CIM formulation by [16] and of the extended CIM by [17] by inclusion of volume currents having arbitrary orientation with respect to the ionospheric plane.…”

Section: Introductionmentioning

confidence: 99%

“…The classical CIM as formulated by [16] is able to handle only divergence-free source currents confined to a plane. [17] extended the classical CIM to situations having more general volume currents by means of source equivalence to be discussed in detail later in the paper.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Source Equivalence and Extension of the Complex Image Method for Geophysical Applications

Pulkkinen¹,

Viljanen²,

Pirjola³

et al. 2009

PIER B

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Abstract-In this work, source equivalence and computation of the reflected (induced) electromagnetic field in geophysical situations are studied. It is shown that the application of Huygens' principle allows for full generalization of Fukushima's equivalence theorem that applies only for magnetic field. The source equivalence is revisited for a vertical line current element, and it is shown that the equivalent charge required to replace the original source by a planar equivalent source together with the surface charge associated with the reflected field generates a purely vertical total electric field on the ground. Consequently, if the magnetic field and horizontal components of the total electric field on the ground are of interest, only equivalent currents need to be considered. The classical Complex Image Method (CIM) is derived from the exact image theory for planar impedance surfaces. The classical CIM is extended by considering a divergence-free source current that may have components also perpendicular to the ground plane. The extension is seen to generate a complex image charge not present in the classical CIM. Further, a generalized application of the extended CIM to geophysical situations having divergence-free volume source currents is introduced. The application involves decomposition of the source into linear current elements and rotations, translations and reflections of the electromagnetic field expressions associated with each element. The validity of the new approach is verified for an example of external current system and ground model setup by means of comparisons to results obtained from exact formulation by [18].

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The complex image approximation for induction in a multilayered Earth

Cited by 64 publications

References 18 publications

The role of 3-D geomagnetic induction in the determination of the ionospheric currents from the ground geomagnetic data

The role of 3-D geomagnetic induction in the determination of the ionospheric currents from the ground geomagnetic data

Fast computation of the geoelectric field using the method of elementary current systems and planar Earth models

Electromagnetic Source Equivalence and Extension of the Complex Image Method for Geophysical Applications

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