A D‐Region Ionospheric Imaging Method Using Sferic‐Based Tomography

Abstract

We present a tomographic imaging technique for the D‐region electron density using a set of spatially distributed very low frequency (VLF) remote sensing measurements. The D‐region ionosphere plays a critical role in many long‐range and over‐the‐horizon communication systems; however, it is unreachable by most direct measurement techniques such as balloons and satellites. Fortunately, the D region, combined with Earth’s surface, forms what is known as the Earth‐Ionosphere waveguide (EIWG) allowing VLF and low frequency (LF) radio waves to propagate to global distances. By measuring these signals, we can estimate a path measurement of the electron density, which we assume to be a path‐averaged electron density profile of the D region. In this work, we use path‐averaged inferences from lightning‐generated radio atmospherics (sferics) with a tomographic inversion to produce 3D models of electron density over the Southeastern United States and the Gulf of Mexico. The model begins with two‐dimensional great circle path observations, each of which is parameterized so it includes vertical profile information. The tomography is then solved in 2 dimensions (latitude and longitude) at arbitrarily many altitude slices to construct the 3D electron density. We examine the model’s performance in the synthetic case and determine that we have an expected percent error better than 10% within our area of interest. We apply our model to the 2017 ‘Great American Solar Eclipse’ and find a clear relationship between sunlight percentage and electron density at different altitudes.

Unifying VLF Transmitter and Sferic Modeling Efforts Via Tomography

“…Additionally, it is capable of producing 3D electron density maps instead of path averages. In comparison to a similar technique only using sferics (Richardson et al., 2023), a significant improvement is observed during periods with limited lightning. We show the model is capable of producing quiet‐time maps of electron density during both daytime and nighttime.…”

“…In the sferic‐only case, Richardson et al. (2023) used the following system of equations $$$\vec{e}={\boldsymbol{L}}^{-1}\boldsymbol{A}\vec{B}$$$ where $$\vec{e}$$ represents the vector containing each path's electron density at a single altitude, L is the diagonal matrix containing the path lengths, A contains the contribution of the DCT basis functions to each path, and $$\vec{B}$$ is the unknown containing the DCT coefficients being solved for. The DCT basis function set consists of 2D cosines with varying frequencies, starting at DC and gradually increasing.…”

“…In their study, Richardson et al. (2023) selected their α value by sweeping over a large search space on a test day then applying the optimal α value to new days. The same approach is used in this study.…”

“…Richardson et al. (2023) provided a method for generating spatially varied electron density slices which will be used here. Their method utilizes many 2D (latitude and longitude) Gaussians with randomly selected amplitude and standard deviation.…”

“…Instead, this work relies on path averages taken from existing VLF‐transmitter‐based and sferic‐based modeling approaches. This idea has been explored in the sferic‐only case (Richardson et al., 2023); however, the work presented here goes a step further to incorporate VLF transmitters. Here, we present comparisons between the sferic‐only method and the new unified approach, and examine the shortcomings of the sferic‐only approach.…”