闪电放电产生的频谱范围从几赫兹到几十兆赫兹，但是多数电磁场能量集中在低频和甚低频区。建立了一种新的更简便的近似解析算法来计算中远距离闪电回击电磁场。该近似算法将电磁波沿不同性质复杂地表传播的衰减函数在频域上分化为电导率衰减和地表曲率衰减两个函数的卷积，这样衰减函数物理意义更为明确，避开了和原来复杂的高震荡艾里函数有关的微分方程求解过程，计算过程大幅简化。通过繁琐繁杂但高精度的牛顿迭代求解法验证，证明了本文近似算法能很好的计算中距离闪电回击辐射场的幅值、波头时间等参量，在地面电导率为4 S·m-1，0.01 S·m-1和0.001 S·m-1时近似算法的最大误差分别为0.2%，3.3%和8.7%。简化后使得计算效率大大提高，同时通过精度对比，发现提出的近似算法精度是比较理想的。因此，该研究结果更加方便有效地解决了远距离雷电电磁波传播和放电参量的反演。此外计算发现地球曲面对中距离电磁场的传播具有明显的影响。比如，在地球曲面的影响下1 500 km处闪电回击ELF/VLF辐射电磁场的幅值仅仅为平坦地表情况的30%~40%，500 km处闪电回击ELF/VLF辐射电磁场的幅值仅仅为平坦地表情况的75%~80%。
Lightning discharges can radiate electromagnetic waves over a wide frequency range from a few Hz to many tens of MHz, but most of the electromagnetic energy is radiated in the ELF and VLF bands.A new approximate method for lightning-radiated extremely low-frequency (ELF) and very low-frequency (VLF) ground wave propagation over intermediate ranges (within 1500 km) was presented in this paper.In our approximate method the field attenuation function was divided into two factors in frequency domain representing the propagation effect of the earth conductivity and curvature, respectively, and these two attenuation factors have more clear and simple expressions in frequency domain, which can be easily calculated by multiplying them rather than solving complex differential equation related to Airy functions.The method was validated by using Newton-Raphson root-finding method for propagation path with different earth conductivities, we found our approximate method could predict the field peak and waveform rise time with a satisfactory accuracy.The comparison results show that our new approximate method can predict the lightning-radiated field peak value over the intermediate range with a satisfactory accuracy within maximum errors of 0.2%, 3.3% and 8.7% for the earth conductivity of 4 S·m-1, 0.01 S·m-1 and 0.001 S·m-1, respectively.So, the research result has solved it in a more efficient way.We also found that the earth curvature has much more effect on the field propagation at the intermediate ranges than the earth finite conductivity.For example, the lightning-produced field peak of ELF/VLF frequency propagating over a spherical-earth is just about 30%~40% of that propagating over a planar-earth at a distance of 1500 km, and 75%~80% for a distance of 500 km.we should pay more attenuation to the effect of earth curvature, for example, the current moment peak value predicted from the measured far field peak will be underestimated when using a far-field-current relationship at the assumed planar earth.
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