On the unique reconstruction of induced spherical magnetizations. (7th December 2015)

• Record Type: Journal Article
• Authors: Gerhards, Christian
• Is Part Of: Inverse problems. Volume 32:Number 1(2016:Jan.)
• Publication Date: 2015-12-07
• Subjects: spherical Hardy–Hodge decomposition -- potential theory -- spherical magnetization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/1/015002
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Recovering spherical magnetizations m from magnetic field data in the exterior is a highly non-unique problem. A spherical Hardy–Hodge decomposition supplies information on what contributions of the magnetization m are recoverable but it does not supply geophysically suitable constraints on m that would guarantee uniqueness for the entire magnetization. In this paper, we focus on the case of induced spherical magnetizations and show that uniqueness is guaranteed if one assumes that the magnetization is compactly supported on the sphere. The results are based on ideas presented in (Baratchart et al 2013 Inverse Problems 29 015004 ) for the planar setting.