Spatial Resolution in Inverse Problems: The EZIE Satellite Mission

Inverse modeling has become one of the primary methods for studying ionospheric electrodynamics, especially when using magnetic field measurements from below the ionosphere. We present a method for quantifying the spatial resolution in an inverse model for non-uniformly sampled spatial data. This method provides a tool for assessing if a model can resolve the physical phenomena of interest. We quantify the spatial resolution for the Spherical Elementary Current System basis functions to model the ionospheric dynamics. Our results apply to models with spatially confined model parameters, unlike spherical harmonics where the model parameters describe the amplitude of global surface functions. The method is demonstrated for the upcoming Electrojet Zeeman Imaging Explorer cubesat mission which will provide spatially distributed remote sensing measurements of the magnetic field in the mesosphere. We show that, including measurements from a single ground magnetometer can significantly improve the spatial resolution. However, the impact of including a ground magnetometer depends on the relative position of the station with respect to the mesospheric measurements. In addition, a method for reducing two regularization parameters to one is presented. Reducing the amount of regularization parameters simplifies the optimization problem and facilitates a fair comparison between the models with and without a ground magnetometer.