A technique is developed for analyzing remote measurements made by a single spacecraft of two dimensional disturbances in the ambient magnetosheath or magnetospheric magnetic field, caused, for example, by flux transfer events or pressure pulses. The methodology is based on a recent linear theory for isentropic field-aligned MHD flow over gently sloping two-dimensional obstacles (Sonnerup et al., 1992). Using only magnetic field measurements, the analysis technique can provide information about the orientation and actual cross-sectional shape of the event, as well as information about the spacecraft trajectory relative to the bulge. If three-dimensional plasma velocity measurements are also available, the technique provides the velocity and size of the event as well, and it allows one to determine whether the current sources causing the disturbance were in fact located on the side of the spacecraft trajectory facing the magnetopause. Analysis of two sample events, one recorded by the spacecraft AMPTE/IRM (Active Magnetospheric Particle Tracer Explorer/Ion Release Module) in the magnetosheath and the other by AMPTE/CCE (Charge Composition Explorer) in the magnetosphere, indicates that the bulges on the magnetopause surface causing the magnetic field and flow perturbations for these events did not have the semicircular cross section suggested in previous work; instead they had a more elongated shape, the dimension tangential to the magnetopause being substantially larger than that normal to it. The calculated invariant axes of the two events were found to differ substantially from the corresponding minimum variance directions of the measured magnetic field. The IRM event was found to move at a speed of 227 km/s away from the subsolar region. For the CCE event, plasma flow data were not available, but it was deduced indirectly that the event moved at a speed of about 90 km/s, presumably away from the subsolar region. ¿ American Geophysical Union 1993