D region tomography: A technique for ionospheric imaging using lightning-generated sferics and inverse modeling

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McCormick, Jackson C.
Cohen, Morris B.
Romberg, Justin
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The $D$ region of the ionosphere (60$-$90 km altitude) is a plasma layer which is highly variable on timescales from fractions of a second to many hours and on spatial scales up to many hundreds of kilometers. VLF and LF (3$-$30 kHz, 30$-$300 kHz) radio waves are guided to global distances by reflections between the ground and the $D$ region. Therefore, information about the current state of the ionosphere is encoded in received VLF/LF signals. VLF transmitters, for example, have been used in the past for ionospheric remote sensing with ionospheric disturbances manifesting as perturbations in amplitude and/or phase. The return stroke of lightning is an impulsive VLF radiator, but unlike VLF transmitters, lightning flashes are spread broadly in space allowing for much greater spatial coverage of the $D$ region compared to VLF transmitters. Furthermore, sferics provide a broadband spectral advantage over the narrowband transmitters. The challenge is that individual lightning-generated waveforms, or `sferics', vary due to uncertainty in the time/location information, $D$ region ionospheric variability, and the uniqueness of each lightning flash. In part, this thesis describes a technique to mitigate this variability to produce stable high-SNR sferic measurements. Using a propagation model, the received sferics can be used to infer an electron density ionospheric profile that is interpreted as an average along the path from lighting stroke to receiver. We develop a new model for the electron density vs altitude which is a natural extension of the Wait and Spies 2-parameter model. We call this new model the `split' model after the fact that the $D$ region seems to commonly split into two exponentially increasing electron density portions. The split model is described by 4 parameters: $h'$, $\beta$, $s_\ell$, and $\Delta h$ respectively indicating the height, slope, split location, and split magnitude. We introduce the $D$ region tomography algorithm. The path-averaged electron density inferences are related to a 4-dimensional image specified by latitude, longitude, altitude, and time. For a given time window and altitude, we can produce a 2D slice where the electron density is specified everywhere, even where there is not a transmitter-receiver path. Sparse and nonuniform spatial and temporal coverage of the ionosphere leads to artifacts and bias with produced images. We address these problems through sparse optimization techniques and a smoothness constraint using the discrete cosine transform.
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