3.1 ELF and VLF sferic recordings

Electromagnetic recordings of lightning radiated pulses, or ``sferics'' in the frequency range 30 Hz to 25 kHz were made using wide (10$^3$) dynamic range impedance-matched receivers and air-core loop antennae, generally far from the source lightning. Such an instrument is sensitive to the rate of change of the horizontal magnetic field at the ground. An alternative method for recording lightning sferics is to measure the vertical electric field using a pair of parallel conducting plates or a vertical monopole antennae.

Sferic data are primarily used to identify the time and polarity of cloud-to-ground lightning, and also to infer the vertical currents flowing in the lightning. While the onset polarity of a sferic in vertical electric field data always unambiguously indicates whether lightning is positive or negative cloud-to-ground, this information is also determined for our loop antenna (i.e., horizontal magnetic field) if the loop orientation and the approximate direction to the lightning (with precision adequate to specify the quadrant of the signal arrival azimuth angle) are known. In the cases shown in this work, the precise locations of cloud-to-ground lightning were available from the National Lightning Detection Network.

The lightning radiated spectrum peaks in the ELF and VLF (3 Hz to 30 kHz) radio bands [Uman, 1987, p. 119]. Because the Earth-ionosphere cavity is bounded by a highly conducting ground and the conducting ionosphere at these frequencies, electromagnetic pulses from lightning may propagate long distances in modes analogous to the modes (TE, TM, and TEM) of an ideal parallel-plate waveguide [e.g., Inan and Inan, 1999, p. 739]. In the imperfect (lossy and anisotropic) waveguide of the ground and ionosphere, all three mode families contribute to the horizontal magnetic field and vertical electric field at higher frequencies [Cummer, 1997, p. 32]; however below $\sim$1.5 kHz, only the TEM mode propagates. This frequency corresponds to the TE and TM lowest mode cutoff frequency, equal to $c/2h$ in the ideal waveguide, where $c$ is the speed of light and $h$ is the separation of the conducting plates.

Techniques were recently developed for remotely sensing $D$ region properties using TE and TM modes in lightning sferics [Cummer et al., 1998a] and for deducing vertical source current moments using the TEM mode at frequencies below 1.5 kHz [Cummer and Inan, 2000]. The latter technique is used in Section 5.2. Horizontal currents at cloud heights are inefficient at exciting the TEM mode in the Earth-ionosphere waveguide since the radiation pattern of a horizontal antenna above conducting ground exhibits a null at low elevation angles [Jordan and Balmain, 1968, p. 641-644]. As a result, horizontal current determination for frequencies below $\sim$1.5 kHz is not possible using long-range receivers.

Sferics were recorded in digital format on magnetic tape or in triggered snapshots onto compact disks. The antenna gains were deduced from their geometric properties and the receiver was calibrated by injecting known currents into the preamplifer while it was connected to a lumped `dummy' load having the same input impedance as the actual loop used for measurements. Sferic waveform magnitudes shown in this work are expressed as magnetic field amplitudes $B$ which correspond to the measured $\partial B /\partial t$ in an electromagnetic wave in free space.