The horizontal electric field from the lightning return-stroke channel is evaluated by the electromagnetic field equations of moving charges in this paper. When a lightning flash strikes the ground, the charges move upward the lightning channel at the return-stroke speed, thereby producing the electromagnetic fields. According to the electromagnetic field equations of moving charges, the detained charges, uniformly moving charges, and decelerating (or accelerating) charges in each segment of the channel generate electrostatic fields, velocity fields, and radiation fields, respectively. The horizontal component of the sum is the horizontal electric field over the perfectly conducting ground. For the real soil with finite conductivity, the Wait formula is used here for the evaluation of the horizontal electric field over the realistic soil. The proposed method can avoid the oscillation of the fields in the long distance by the FDTD method and the singularity problem of the integral equation by the Sommerfeld integral method. The influences of the return-stroke speed, distance, and soil conductivity on the horizontal electric field are also analyzed by the proposed method. The conclusions can be drawn that the horizontal electric field decreases with the increasing of the return-stroke speed; the negative offset increases with the increasing of horizontal distance and with the decreasing of the soil conductivity, thereby forming the bipolar waveform. These conclusions will be practically valuable for the protection of lightning-induced overvoltage on the transmission lines.

Studying underground propagation effects of lightning electromagnetic fields in different geological environments will contribute to more reasonable designs for protecting underground cables and electronic equipment. In this paper, we have analyzed influences of different geological environments, depths and soil water content on underground propagation of lightning electromagnetic fields in detail by using the finite difference time domain (FDTD) method in the 2-D cylindrical coordinate system to calculate components of underground electromagnetic fields at a horizontal distance of 200 m, including vertical electric field E z, horizontal electric field E r and azimuthal magnetic field H φ. The results show that the underground electric field is predominantly horizontal. Propagation of lightning electromagnetic fields in wet clay and wet limestone environment changes significantly compared to freshwater environment. Attenuation is larger with depth in wet clay and wet limestone, while propagation is unaffected in freshwater. When water content in soils ranges from 5% to 25%, the vertical electric field has the largest attenuation and the azimuthal magnetic field has the least attenuation. The electromagnetic fields in clay are most sensitive to changes in water content.

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