Electromagnetic Fields Radiated by Lightning Return Stroke Over Lossy Ground With Rock Formation

Abstract

Electromagnetic fields radiated by a lightning return stroke over lossy ground are calculated by finite difference time domain method in a two-dimensional cylindrical coordinate system. The considered ground model contains a rock formation for which four different geometries are defined: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rectangle</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">triangle</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">circle,</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random</i> . Two electrical conductivities that are very low and very high compared to the conductivity of the ground are defined for the rock formation. Different scenarios are examined by computing horizontal electric field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{E}}_{\boldsymbol{r}}}$</tex-math></inline-formula> , vertical electric field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{E}}_{\boldsymbol{z}}}$</tex-math></inline-formula> , and azimuthal magnetic field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{H}}_{\boldsymbol{\varphi }}}$</tex-math></inline-formula> for both conductivities. In addition to the effect of different geometries, effects of spatial averaging, changing position of rock, different return stroke propagation speeds, observation points at different heights and different horizontal range distances are investigated adopting both first and subsequent return stroke currents as the source. The results show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{E}}_{\boldsymbol{z}}}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{H}}_{\boldsymbol{\varphi }}}$</tex-math></inline-formula> fields are not much affected by geometry and conductivity change. However, for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{E}}_{\boldsymbol{r}}}$</tex-math></inline-formula> component, performances of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rectangle</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">triangle</i> geometries are close to each other and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random</i> one shows closest performance to that of the case when there is no rock inside the ground. On the other hand, the field values decrease as the rock conductivity increases for both stroke types.