Comparing two models of the Earth's magnetosphere

The existence of a multiplicity of models of the Earth's magnetosphere raises the question: when are two of them equivalent in representing the real magnetosphere? The isomorphism of any two models of the Earth's magnetosphere is defined in terms of magnetic field characteristics. To assess to what degree empirical models are isomorphic with physical ones, two magnetospheres are compared: the magnetosphere of Mead and Fairfield 1975] and the physical magnetosphere proposed by Buneman, 1993]. Parameters realizing the isomorphism are found for the Buneman magnetosphere and the distribution in space of magnetic field characteristics are presented for both models.