Potential field extrapolation using three components of a solar vector magnetogram with a finite field of view

Abstract

The potential magnetic field from a finite planar boundary is extrapolated into the upper hemisphere using information from all three magnetic field components. The method determines, first, the transverse field associated with the observed normal magnetic intensity. Then by subtraction, the method determines the associated transverse magnetic field observed in the interior (i.e., in the field of view) of the magnetogram which is due to the normal flux exterior to the field of view of the magnetogram. Inverting this information gives an approximation to the exterior normal flux. The combination of the observed normal flux of the interior and the approximation of the exterior normal flux is employed to calculate the potential field. The formulation of the problem results in an ill-posed integral inversion problem in which a regularized solution is obtained using the singular value decomposition (SVD) technique in conjunction with an appropriate Tikhonov-Phillips filter. The technique can be applied to correcting potential field calculations which are influenced by out-of-view fluxes, e.g., for a high spatial resolution vector magnetogram with a small field of view in which there is no supporting exterior data. The problem studied is also important in providing a regularized solution of the Cauchy potential problem. The method provides a much larger range of convergence than the method of Gary and Musielak (1992), and, in fact, is stable in the total upper hemisphere.