Recent analytical investigations of electromagnetic ground wave propagation over inhomogeneous earth models

Wait, James R.

doi:10.1109/proc.1974.9570

Cited by 49 publications

(25 citation statements)

References 41 publications

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“…The lightning flash is assumed to strike on the ocean surface (the first section), and the observation point is near the interface (the second section), as shown in Figure 1. When the fields propagate from the ocean surface to the land section, the attenuation function along the mixed path is given by Wait and Walters [1963a, 1963b] and Wait [1974, 1998]:

W (0, d, j ω) = W_{2} (0, d, j ω) - {([], \frac{d γ_{0}}{2 π})}^{1 / 2} [{normalΔ}_{1} - {normalΔ}_{2}] \int_{0}^{d - d l} \frac{W_{2} ((), 0, d - x, j ω) W_{1} ((), 0, x, j ω)}{{((), x ((), d - x))}^{1 / 2}} d x

γ_{0} = j ω \sqrt{μ_{0} ε_{0}}

where W (0, d , jω ) is the total attenuation function along the mixed path, W 1 (0, d , jω ) and W 2 (0, d , jω ) are the attenuation functions of the first section and second section, respectively, which are given as below [ Wait , 1998; Hill and Wait , 1980]:

W_{n} (0, d, j ω) = 1 - j \sqrt{π p_{n}} exp (- p_{n}) e r f c (j \sqrt{p_{n}})

p_{n} = - \frac{j ω d}{2 c} {normalΔ}_{n}^{2}

<...>

…”

Section: Attenuation Function For the Rough Ocean‐land Mixed Propagatmentioning

confidence: 99%

Numerical simulation of the lightning electromagnetic fields along a rough and ocean‐land mixed propagation path

et al. 2012

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[1] In this paper we analyze the propagation effect of a rough and ocean-land mixed path on the lightning vertical electric field and azimuthal magnetic field by using Barrick's formulations and Wait's formulations. When the lightning-radiated electromagnetic fields propagate from the rough ocean surface to the finitely conducting land section, it is noted that the effect of the rough land section on the fields is much more than that of the rough ocean surface. The propagation effect of a small land section with a few tens of meters length on the electromagnetic spectrum over 2 MHz has to be taken into account, and the lower land conductivity results in a more field attenuation. The lightning fields undergo a sudden decrease near the interface from the ocean to the land section, and the propagation effect of the mixed path on the lightning fields within 10 MHz is primarily caused by the rough land section.

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W (0, d, j ω) = W_{2} (0, d, j ω) - {([], \frac{d γ_{0}}{2 π})}^{1 / 2} [{normalΔ}_{1} - {normalΔ}_{2}] \int_{0}^{d - d l} \frac{W_{2} ((), 0, d - x, j ω) W_{1} ((), 0, x, j ω)}{{((), x ((), d - x))}^{1 / 2}} d x

γ_{0} = j ω \sqrt{μ_{0} ε_{0}}

W_{n} (0, d, j ω) = 1 - j \sqrt{π p_{n}} exp (- p_{n}) e r f c (j \sqrt{p_{n}})

p_{n} = - \frac{j ω d}{2 c} {normalΔ}_{n}^{2}

<...>

…”

Section: Attenuation Function For the Rough Ocean‐land Mixed Propagatmentioning

confidence: 99%

Numerical simulation of the lightning electromagnetic fields along a rough and ocean‐land mixed propagation path

et al. 2012

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show abstract

“…W (0, d , jω ) is the attenuation function along the mixed propagation path. For a mixed propagation path, two different attenuation functions are given by Wait [1974] and Wait and Walters [1963a, 1963b]:

W (0, d, j ω) = W_{1} (0, d, j ω) - {[\frac{d γ_{0}}{2 π}]}^{1 / 2} [{normalΔ}_{2} - {normalΔ}_{1}] \int_{0}^{d l} \frac{W_{1} (0, d - x, j ω) W_{2} (0, x, j ω)}{{true(x true(d - x true) true)}^{1 / 2}} d x

W (0, d, j ω) = W_{2} (0, d, j ω) - {[\frac{d γ_{0}}{2 π}]}^{1 / 2} [{normalΔ}_{1} - {normalΔ}_{2}] \int_{0}^{d - d l} \frac{W_{2} (0, d - x, j ω) W_{1} (0, x, j ω)}{{true(x true(d - x true) true)}^{1 / 2}} d x

γ_{0} = j ω \sqrt{μ_{0} {italicε}_{0}}

where W 1 (0, d , jω ) and W 2 (0, d , jω ) are the attenuation functions for the first and second sections, respectively:

W_{n} (0, d, j ω

…”

Section: The Simplified Formula For a Mixed Propagation Pathmentioning

confidence: 99%

Examination of the Cooray‐Rubinstein (C‐R) formula for a mixed propagation path by using FDTD

Zhang

Fan

et al. 2012

J. Geophys. Res.

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[1] In this paper we extend the Cooray-Rubinstein (C-R) formula into a mixed propagation path (vertically stratified conductivity) and estimate the lightning horizontal electric fields over the mixed path, and we have examined its accuracy at distances of 100 m to 1000 m from the lightning channel by using finite difference time domain (FDTD). When the ground conductivity near the observation point is less than that near the strike point, it is noted that the C-R formula predicts a satisfactory accuracy in the initial several microseconds after the beginning of the return stroke. However, when the ground conductivity near the observation point is larger than that near the strike point, the initial negative excursion predicted by the C-R formula is underestimated, and the error increases with the increase of the difference between the two sections conductivity.

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“…It may >e mentioned that Wait [7][8][9][10][11][12] has done considerable work on the asymptotic calculation of the surface fields which are diffracted past an impedance discontinuity as at Q and Q of Figure 1. Indeed, some of his work [7,g,12] has bee; helpfbl in the asymptotic analysis of the currents which exist on a curved impedance boundary.…”

Section: Impedancementioning

confidence: 99%

Radiation by Sources on Perfectly Conducting Convex Cylinders with an Impedance Surface Patch.

Ersoy

Pathak²

1980

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Recent analytical investigations of electromagnetic ground wave propagation over inhomogeneous earth models

Cited by 49 publications

References 41 publications

Numerical simulation of the lightning electromagnetic fields along a rough and ocean‐land mixed propagation path

Numerical simulation of the lightning electromagnetic fields along a rough and ocean‐land mixed propagation path

Examination of the Cooray‐Rubinstein (C‐R) formula for a mixed propagation path by using FDTD

Radiation by Sources on Perfectly Conducting Convex Cylinders with an Impedance Surface Patch.

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