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A recently developed technique for reconstructing approximately two-dimensional (∂/∂z≈0), time-stationary magnetic field structures in space is applied to two magnetopause traversals on the dawnside flank by the four Cluster spacecraft, when the spacecraft separation was about 2000km. The method consists of solving the Grad-Shafranov equation for magnetohydrostatic structures, using plasma and magnetic field data measured along a single spacecraft trajectory as spatial initial values. We assess the usefulness of this single-spacecraft-based technique by comparing the magnetic field maps produced from one spacecraft with the field vectors that other spacecraft actually observed. For an optimally selected invariant (z)-axis, the correlation between the field components predicted from the reconstructed map and the corresponding measured components reaches more than 0.97. This result indicates that the reconstruction technique predicts conditions at the other spacecraft locations quite well. </p><p style="line-height: 20px;"> The optimal invariant axis is relatively close to the intermediate variance direction, computed from minimum variance analysis of the measured magnetic field, and is generally well determined with respect to rotations about the maximum variance direction but less well with respect to rotations about the minimum variance direction. In one of the events, field maps recovered individually for two of the spacecraft, which crossed the magnetopause with an interval of a few tens of seconds, show substantial differences in configuration. By comparing these field maps, time evolution of the magnetopause structures, such as the formation of magnetic islands, motion of the structures, and thickening of the magnetopause current layer, is discussed.<br><br> <b>Key words.</b> Magnetospheric physics (Magnetopause, cusp, and boundary layers) – Space plasma physics (Experimental and mathematical techniques, Magnetic reconnection)