On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere

DOI10.1080/17415977.2018.1438426zbMath1460.65022arXiv1608.01216OpenAlexW2790769086MaRDI QIDQ4988509

Christian Gerhards

Publication date: 17 May 2021

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.01216

zbMATH Keywords

uniquenesssusceptibilitymagnetic dipolesinverse magnetization problemdecomposition of spherical vector fields

Mathematics Subject Classification ID

Inverse problems in geophysics (86A22) Spherical harmonics (33C55) Numerical integration (65D30) Geo-electricity and geomagnetism (86A25) Inverse problems for integral equations (45Q05)

Related Items (3)

Relation between Hardy components for locally supported vector fields on the sphere ⋮ A brief note on the computation of silent from nonsilent contributions of spatially localized magnetizations on a sphere ⋮ Unique reconstruction of simple magnetizations from their magnetic potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical integration with polynomial exactness over a spherical cap
• Special functions of mathematical (geo-)physics
• Spherical functions of mathematical geosciences. A scalar, vectorial, and tensorial setup
• Computing Fourier transforms and convolutions on the 2-sphere
• On the unique reconstruction of induced spherical magnetizations
• LOCALLY SUPPORTED WAVELETS FOR THE SEPARATION OF SPHERICAL VECTOR FIELDS WITH RESPECT TO THEIR SOURCES
• A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods
• On the Recovery of Core and Crustal Components of Geomagnetic Potential Fields
• Hardy-Hodge decomposition of vector fields in ℝⁿ
• Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions
• Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators
• Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the Earth's gravitational field at satellite height
• A Nonlinear Galerkin Scheme Involving Vector and Tensor Spherical Harmonics for Solving the Incompressible Navier--Stokes Equation on the Sphere
• APPLICATION OF A NON-LINEAR BOUNDARY-VALUE PROBLEM FOR LAPLACE'S EQUATION TO GRAVITY AND GEOMAGNETIC INTENSITY SURVEYS

This page was built for publication: On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere