A physical derivation of the horizontal electric field under the ground associated with lightning return strokes

We derive expressions for the lightning return stroke horizontal electric field and the azimuthal magnetic field under the ground assuming that the fields impinging on the ground can be represented as a sum of plane waves, each being diffracted into the ground with approximately the same angle. The results we obtain are equivalent to those presented by Cooray, who derived approximate expressions by mathematical manipulation of Banister's expressions. We use experimental magnetic fields at ground level from strikes to the 553-m tall CN-Tower to calculate the horizontal electric field and azimuthal magnetic field under the ground at different depths and for different ground conductivities.