We examined geomagnetic field observations at low and middle latitudes in the Northern Hemisphere during a 50-min interval (12 May 1999), characterized by a complex behaviour of the solar wind dynamic pressure. For the entire interval, the aspects of the geomagnetic response can be organized into four groups of events which show common characteristics for the H and D components, respectively. The correspondence between the magnetospheric field and the ground components reveals different aspects of the geomagnetic response in different magnetic local time (MLT) sectors. For the H component, the correspondence is highly significant in the dusk and night sectors; in the dawn and prenoon sectors it shows a dramatic change across a separation line that extends approximately between (6 MLT, 35°) and (13 MLT, 60°). For the D component, the correspondence has significant values in the dawn and prenoon regions. We propose a new approach to the experimental data analysis which reveals that, at each station, the magnetospheric field has a close correspondence with the geomagnetic field projection along an axis (M1) that progressively rotates from north/south (night events) to east/west orientation (dawn events). When projected along M1, the geomagnetic signals can be interpreted in terms of a one-dimensional pattern that mostly reflects the field behaviour observed at geostationary orbit. Several features appear more evident in this perspective, and the global geomagnetic response to the SW pressure variations appears much clearer than in other representations. In particular, the MLT dependence of the geomagnetic response is much smaller than that one estimated by previous investigations. A clear latitudinal dependence emerges in the dusk sector. The occurrence of low frequency waves at ~2.8mHz can be interpreted in terms of global magnetospheric modes driven by the SW pulse. This event occurred in the recovery phase after the day the SW almost disappeared (11 May 1999): in this sense our results suggest a rapid recovery of almost typical magnetospheric conditions soon after a huge expansion. Overshoot amplitudes, greater than in other cases, are consistent with a significant reduction of the ring current.