We investigate the storm-scale morphology of the magnetospheric magnetic field as well as underlying distributions of electric currents, equatorial plasma pressure, and entropy for four steady magnetospheric convection (SMC) events that occurred during the May 2000 and October 2011 magnetic storms. The analysis is made using the empirical geomagnetic field model TS07D, in which the structure of equatorial currents is not predefined and it is dictated by data. The model also combines the strengths of statistical and event-oriented approaches in mining data for the reconstruction of the magnetic field. The formation of a near-Earth minimum of the equatorial magnetic field in the midnight sector is inferred from data without ad hoc assumptions of a special current system postulated in earlier empirical reconstructions. In addition, a new SMC class is discovered where the minimum equatorial field is substantially larger and located closer to Earth. The magnetic field tailward of the minimum is also much larger, and the corresponding area of accumulated magnetic flux may occupy a very short tail region. The equatorial current and plasma pressure are found to be strongly enhanced far beyond geosynchronous orbit and in a broad local time interval covering the whole nightside region. This picture is consistent with independent recent statistical studies of the SMC pressure distributions, global MHD, and kinetic Rice Convection Model-Equilibrium (RCM-E) simulations. Distributions of the flux tube volume and entropy inferred from data reveal different mechanisms of the magnetotail convection crisis resolution for two classes of SMC events.