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<p>This study develops a comprehensive numerical model to characterize the spatiotemporal response of soil electric fields to lightning strikes, explicitly accounting for two critical pedophysical factors: the frequency dependence (FD) of electrical parameters and spatial heterogeneity arising from depth-dependent nonlinear conductivity. The lightning return stroke is simulated using the Modified Transmission Line with Exponential decay (MTLE) model, driven by a double Heidler base current function. The computational framework is based on a two-dimensional axisymmetric formulation, wherein the soil electric field is solved in the frequency domain via the full-wave Finite Element Method (FEM), with temporal solutions subsequently recovered through inverse Fourier transformation. The model’s reliability is rigorously validated against both the Sommerfeld integral method and the finite-difference time-domain (FDTD) approach. Systematic analysis reveals that the FD effect significantly influences the peak response and spatial distribution of the electric field, with the vertical component exhibiting substantially greater attenuation than the horizontal counterpart. Notably, for subsequent return strokes, FD induces a maximum attenuation of 40.25% in the vertical electric field intensity, corresponding to an amplitude decrease of 290.57 V/m at observation point (25, 0). Furthermore, parametric simulations demonstrate that increasing surface conductivity or reducing the thickness of the heterogeneous soil layer effectively suppresses FD-induced attenuation, offering practical insights for lightning protection and soil characterization in mountainous terrains.</p>

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Spatially heterogeneous soil model incorporating frequency-dependent electrical parameters for capturing lightning-induced electric field responses

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Pingping Rao,
  • Xia Shen,
  • Jiaxiang Wang,
  • Xiao Jin,
  • Jifei Cui

摘要

This study develops a comprehensive numerical model to characterize the spatiotemporal response of soil electric fields to lightning strikes, explicitly accounting for two critical pedophysical factors: the frequency dependence (FD) of electrical parameters and spatial heterogeneity arising from depth-dependent nonlinear conductivity. The lightning return stroke is simulated using the Modified Transmission Line with Exponential decay (MTLE) model, driven by a double Heidler base current function. The computational framework is based on a two-dimensional axisymmetric formulation, wherein the soil electric field is solved in the frequency domain via the full-wave Finite Element Method (FEM), with temporal solutions subsequently recovered through inverse Fourier transformation. The model’s reliability is rigorously validated against both the Sommerfeld integral method and the finite-difference time-domain (FDTD) approach. Systematic analysis reveals that the FD effect significantly influences the peak response and spatial distribution of the electric field, with the vertical component exhibiting substantially greater attenuation than the horizontal counterpart. Notably, for subsequent return strokes, FD induces a maximum attenuation of 40.25% in the vertical electric field intensity, corresponding to an amplitude decrease of 290.57 V/m at observation point (25, 0). Furthermore, parametric simulations demonstrate that increasing surface conductivity or reducing the thickness of the heterogeneous soil layer effectively suppresses FD-induced attenuation, offering practical insights for lightning protection and soil characterization in mountainous terrains.