A generalization of the minimum variance analysis method

In order to determine the normal direction of the magnetopause, the minimum variance analysis technique is frequently used: it is applied to the magnetic field data of a magnetopause crossing observed by a satellite, and provides the direction along which the magnetic field variation is minimum. In this study we propose a method to extend naturally the framework of the minimum variance analysis so that it includes all continuity conditions across a planar magnetopause, so that we could use all physical quantities observed by the spacecraft. We first extend it to the electric field: we discuss how to determine the normal direction and the speed of the magnetopause along the normal by using both the magnetic and electric field data. We next discuss the full extension to all continuity conditions across the magnetopause. Finally, we discuss how to extend our method further so that it can deal with the magnetopause which is accelerating. A discussion of application to observations will appear separately.