Reconstruction of the Lightning Return-Stroke Current from the Radiated Magnetic Field

This paper presents a new method to solve the inverse problem of reconstructing the lightning return-stroke current from measurements of the radiated magnetic field. Although the lightning channel is still assumed to be straight, vertical and at a known distance from the sensors measuring the fields, no model or channel-base measurement of the current is required, so that, unlike previous approaches to this kind of inverse problem, several assumptions on the current propagation along the channel can be dropped. The method is formulated in the frequency domain and is based on a double Fourier series representation of the unknown current as a function of two variables, i.e., the vertical coordinate and the frequency. The theoretical investigation results in an inversion algorithm, which is tested against simulated data in order to obtain some examples of current reconstruction.