Application of linear inverse theory to a line current model of substorm current systems

The geomagnetic components from eight low-latitude ground stations and the ATS 1 satellite are studied for substorms occurring on December 24 and 25, 1967, and on August 15, 1968. A simple, four-parameter, field-aligned line current model is employed, and the linear inverse problem is constructed to determine the set of model parameters that best fit the data. A straightforward review of linear inversion theory is included in the theory section. The four model parameters are the magnitude of the current, the L shell on which the current flows, and the azimuthal positions of the eastern and western portions of the circuit. Both growth phases and expansion phases are treated. The best fits to the ground and satellite data are shown to be independent of the L parameter for values of L ≳ 3.5 when only ground data are treated and for values of L ≳ 8.5 when satellite data are included. The four-parameter model, although it produces good qualitative fits to expansion phase data, is unable to fit the data within 2 standard deviations of the error in the observations. The model is able to fit the growth phase of one substorm within 1 standard deviation. In one substorm with an apparent growth phase a better fit of the data during the expansion phase was obtained by combining the line current model of the growth phase with an additional four-parameter line current model.