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Evaluation of time history distribution characteristics of lightning electromagnetic field in heterogeneous soil

  • Research Article - Applied Geophysics
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Abstract

Existing underground lightning electromagnetic field predictive methods are only relevant to conductivity distributions that are homogeneous or layered. In order to expand the scope of application of lightning electromagnetic field computation, the effect of heterogeneous soil conductivity on the electromagnetic field of lightning return is examined in depth. The current distribution in the lightning return channel is characterized by the dual Heidler discharge channel base current and MTLE return model. Using the full-wave finite element approach, a two-dimensional axisymmetric model is created. The time distribution characteristics of the lightning electromagnetic field in a soil with heterogeneous conductivity are evaluated. According to the research, the lightning electromagnetic field's, horizontal electric field, vertical electric field, and azimuthal magnetic field components are negatively, bipolarly, and positively distributed in the subsurface, respectively. The horizontal electric field dominates the subterranean electromagnetic field. The high conductivity of the soil has a significant attenuation effect on the high-frequency components of the lightning electromagnetic field's three electromagnetic components. The initial response of the horizontal electric field of a nonhomogeneous soil is dependent on the conductivity at the surface of soil, followed by a gradual dependence on the conductivity in deeper soil sections. The subsurface distribution of vertical electric and azimuthal magnetic fields tend to stratify in response to a nonhomogeneous drop in soil conductivity.

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Abbreviations

b :

Depth of nonhomogeneous change of soil conductivity

\(\sigma_{1}\) :

Conductivity at the soil surface

\(\sigma_{2}\) :

Conductivity at the soil bottom

\(\lambda\) :

Current height decay constant

v :

Return-stroke wavefront speed

u :

Heaviside function

I 0i :

Current peak

\(\tau_{i1}\) :

Time coefficients of wave head

\(\tau_{i2}\) :

Time coefficients of wave tail

n i :

Current waveform steepness factor

\(\eta_{i}\) :

Current peak correction factor

Z :

Channel height

L :

Model width

H :

Total soil thickness

h :

Nonhomogeneous layer thickness

\(\sigma_{0}\) :

Conductivity of air and lightning return channels

\(\varepsilon_{0}\) :

Relative permittivity of air and lightning return channels

\(\varepsilon_{1}\) :

Relative permittivity of nonhomogeneous layer

\(\varepsilon_{2}\) :

Relative permittivity of bottom soil

\(\mu_{0}\) :

Relative magnetic permeability

A :

Magnetic vector potential

\(\mu_{0}^{\prime }\) :

Vacuum permeability

\(\mu_{r}\) :

Relative permeability

\(\varepsilon_{0}^{\prime }\) :

Vacuum permittivity

\(\varepsilon_{r}\) :

Relative permittivity

\(J_{s}\) :

Surface current density

\(n\) :

Unit normal vector directed from soil to air

\(\delta\) :

Channel width

\(\Delta t\) :

Time steps

\(E_{r}\) :

Horizontal electric field component

\(E_{z}\) :

Vertical electric field component

\(H_{\varphi }\) :

Azimuthal magnetic field component

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Acknowledgements

The Authors gratefully acknowledge the financial support for this work provided by the National Natural Science Foundation of China (No. 42077435). In addition, the authors would take this opportunity to thank the editors and the anonymous reviewers for their valuable comments and suggestions in improving this paper.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Yuanbing Xiang, Pingping Rao, Weikang Feng & Peihao Ouyang

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  1. Yuanbing Xiang
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  2. Pingping Rao
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  4. Peihao Ouyang
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Correspondence to Pingping Rao.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Edited by Dr. Mario Zarroca Hernández (ASSOCIATE EDITOR) / Prof. Gabriela Fernández Viejo (CO-EDITOR-IN-CHIEF).

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Xiang, Y., Rao, P., Feng, W. et al. Evaluation of time history distribution characteristics of lightning electromagnetic field in heterogeneous soil. Acta Geophys. 72, 793–805 (2024). https://doi.org/10.1007/s11600-023-01100-w

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