A New Approximate Method for Lightning-Radiated ELF/VLF Ground Wave Propagation over Intermediate Ranges

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>d</mml:mi></mml:math> (km) dependence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msup><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1.32</mml:mn></mml:mrow></mml:msup></mml:math>.