Ground-based observations of geomagnetic field (B field) are usually a superposition of signatures from different source current systems in the magnetosphere and ionosphere. Fluctuating B fields generate geoelectric fields (E fields), which drive geomagnetically induced currents (GIC) in technological conducting media at the Earth's surface. We introduce a new Fourier integral B field model of east/west directed line current systems over a one-dimensional multilayered Earth in plane geometry. Derived layered-Earth profiles, given in the literature, are needed to calculate the surface impedance, and therefore reflection coefficient in the integral. The 2003 Halloween storm measurements were Fourier transformed for B field spectrum Levenberg-Marquardt least squares inversion over latitude. The inversion modeled strengths of the equatorial electrojets, auroral electrojets, and ring currents were compared to the forward problem computed strength. It is found the optimized and direct results match each other closely and supplement previous established studies about these source currents. Using this model, a data set of current system magnitudes may be used to develop empirical models linking solar wind activity to magnetospheric current systems. In addition, the ground E fields are also calculated directly, which serves as a proxy for computing GIC in conductor-based networks.