The proximity effect on the induced geoelectric field at the interface of different conductivity structures with lateral variations during geomagnetic storms

The induced geoelectric fields and telluric currents generated during geomagnetic storms will be distorted by lateral variations of the Earth conductivity.The power system located at the coastal area near the coastline or at the interface of different continental plates is more sensitive to this distortion.So far the"coast effect"has been considered as the most important effect for GIC research which explains the geoelectric field enhancement at the inland near the coast.Analytical methods such as plane wave method or complex image method cannot be used to model the conductivity structure with lateral variations or calculate the geoelectric field near the conductivity horizontal interface. Numerical methods are useful tools to analyze complicated electromagnetic field problems.In this paper,a thin sheet current with infinite width located at100 km above the Earth′s surface is assumed to represent the source of geomagnetic variations and is harmonic with the amplitude of 1A/m at different frequencies.Three Earth conductivitystructures are modelled where the basic model is horizontal uniform for results comparisons.The second structure has the same exact thicknesses and conductivity values with the basic one on one side and five times greater values on the other side to represent conductivity varying from low to high.Similar structure representing conductivity from high to low can be obtained by assuming five times lower values on the other side.The Galerkin finite element method is applied to analyze the case where the induced telluric currents are flowing parallel to the conductivity interface and four-node quadrilateral element is chosen to mesh the conductivity regions.The computational results show that the abrupt changes of conductivities have influences on the induced telluric currents,which can be classified as proximity effect and skin effect.The proximity effect shows that the geoelectric field and the induced current density decrease when the conductivity varies from low to high.The minimum of geoelectric field occurs at the interface.The geoelectric fields decrease 15%,38%,and 27% separately when the frequencies are0.03 Hz,0.003 Hz and 0.0005 Hz.This trend can be characterized by horizontal extent which is defined by the distance to the interface where the value becomes 1/e(=0.368)times reference value which is the difference compared to uniform structure.The horizontal extents under three frequencies are 26 km,106km,and 256 km.While for the case when the conductivity varies from high to low,the skin effect governs geoelectric fields at the interface by increasing 37%,40%,and 27% at these three frequncies.The corresponding horizontal extents are 35 km,164 km,and 283 km separately.The geoelectric field variations then increase or decrease GIC in the power systems located at the basic conductivity structure side and the mechanism is different with the impact of "coast effect".These trends and effects can be observed not only at the Earth′s surface but also under the surface till the depth of 150 km.There is need to emphasize again that for GIC research in power systems,especially for those systems at coastal areas,geoelectric field and GIC should be determined taken the extension directions of transmission line and coast into consideration.Both of the proximity effect and skin effect should be considered along with coast effect in research of GIC impacts during geomagnetic disturbances.The Galerkin finite element method applied in this paper is a suitable method when modelling the more complicated conductivity structure with 3D variations.Boundary conditions discussed in this paper can be varied depending on different modelling techniques and the scales of conductivity structure models.