The effect of finitely conducting ground on the signature of lightning generated vertical electric fields at ground level was evaluated by numerical solution of Sommerfeld's integrals. Results are presented for distances between 10 m to 1 km from the lightning channel and for ground conductivities in the range of 0.01 and 0.001 S/m. The results obtained from the exact theory are compared with the predictions of several approximate theories available in the literature. Based on that comparison the limits of validity of these approximate theories are obtained.
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Vernon Cooray (2008) studied this question.
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