Abstract
A new approximate method for lightning-radiated extremely low-frequency (ELF) and very low-frequency (VLF) ground wave propagation over intermediate ranges is presented in this paper. In our approximate method, the original field attenuation function is divided into two factors in frequency domain representing the propagation effect of the ground conductivity and Earth’s curvature, and both of them have clearer formulations and can more easily be calculated rather than solving a complex differential equation related to Airy functions. 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 0.0%, −3.3%, and −8.7% for the earth conductivity of 4 S/m, 0.01 S/m, and 0.001 S/m, respectively. We also find that Earth’s curvature has much more effect on the field propagation at the intermediate ranges than the finite ground conductivity, and the lightning-radiated ELF/VLF electric field peak value (V/m) at the intermediate ranges yields a propagation distance d (km) dependence of d−1.32.
Highlights
Lightning-radiated very low-frequency (VLF) (3–30 kHz) and low-frequency (LF) (30–300 kHz) signals can propagate along a spherical earth with finite conductivity at an intermediate distance of hundreds to a couple of thousand kilometers, and the observed lightning-radiated electromagnetic field signal would be significantly attenuated and distorted due to the propagation effects (e.g., Wait [1,2,3,4], Shao and Jacobson [5], and Zhang et al [6,7,8,9])
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 extremely low-frequency (ELF) and VLF bands, and the higher frequency component is attenuated rapidly as the propagation distance increases
We present a new approximate method for lightning-produced ELF/VLF ground wave propagation over intermediate ranges, which is validated by using Newton–Raphson root-finding method presented by Shao and Jacobson [5] for propagation path with different ground conductivities; we found our approximate method could predict the field peak and waveform rise time with satisfactory accuracy
Summary
Lightning-radiated very low-frequency (VLF) (3–30 kHz) and low-frequency (LF) (30–300 kHz) signals can propagate along a spherical earth with finite conductivity at an intermediate distance of hundreds to a couple of thousand kilometers, and the observed lightning-radiated electromagnetic field signal would be significantly attenuated and distorted due to the propagation effects (e.g., Wait [1,2,3,4], Shao and Jacobson [5], and Zhang et al [6,7,8,9]). In 1980, Hill and Wait [15] generalized the previous computation methods of the attenuation function and presented an approximate method to calculate the ground wave attenuation function for arbitrary surface impedance along the spherical earth surface. In their method, different approximate formulas were used according to the phases of normalized surface impedance and a fourth-order Runge-Kutta formula had to be used to obtain the roots of differential equations. In 1993, Maclean and Wu [16] presented a Taylor series method to compute the attenuation function, and International Journal of Antennas and Propagation the roots of the complex differential equation were approximated by a Taylor series in their method
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