Use of VLF transmissions in the location and mapping of lightning-induced ionisation enhancements (LIEs)
Lightning-induced ionisation enhancements (LIEs) are usually produced by short (~ 1 s) bursts of energetic electrons precipitated from the radiation belts in the process of amplifying whistlers. During their short life (~ 30 s) LIEs diffract or otherwise modify stable transmissions of VLF waves propagating in the two-dimensional Earth-ionosphere waveguide. This causes perturbations (‘Trimpis’) on the same time scale in the phase and amplitude of these VLF waves. Unless the LIEs are large (> 100 km) and smoothly varying (e.g., Gaussian distribution of ionisation enhancement) in the horizontal directions, the LIEs need not be on the great circle path (GCP) from VLF transmitter to receiver to produce Trimpis. Large and smooth LIEs produce ‘GCP Trimpis’, while small or structured LIEs produce ‘echo Trimpis’. The two can usually be distinguished, if Trimpi phase and amplitude are monitored and if the Trimpis are observed at several frequencies or on two or more spaced receivers simultaneously.
If only GCP Trimpis are considered, the causative LIEs can be located and mapped by geometric optics using a network of receivers of sufficient density (spacing ~ 100 km) and a few transmitters. Provided all Trimpis are identified as GCP, their mere detection is sufficient for location. This is equivalent to locating the LIE ‘shadows’ cast onto arrays of spaced receivers by two or more transmitters. If this GCP identification is not made, or is just assumed, location and mapping (size estimation) errors can be quite large. At VLF (λ ~ 15 km) this geometric optics approach cannot be used to study the horizontal fine structure of LIEs since LIEs producing GCP Trimpis have no fine structure.
Small or structured LIEs cast a diffraction pattern onto an array of spaced receivers. If both the phase and amplitude perturbation of echo Trimpis are measured at each receiver of the array, holographic techniques can be used to reconstruct the two-dimensional map or image of the causative LIEs. It is shown that, for a single system of one transmitter and a receiver array, this allows high resolution (~ 10 km) in the azimuthal dimension only. Equally high resolution in both horizontal dimensions can be achieved with two orthogonal systems. This technique works equally well on GCP Trimpis to map the causative LIEs (which are large and structureless) without incurring location errors thereby.