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

References

• Maus S , Haak V . Magnetic field annihilators: invisible magnetization and the magnetic equator. Geophys J Int. 2003;155:509–513.
   Web of Science ®Google Scholar
• Gerhards C . On the unique reconstruction of induced spherical magnetizations. Inverse Prob. 2016;32:015002.
   Web of Science ®Google Scholar
• Baratchart L , Hardin DP , Lima EA , et al . Characterizing kernels of operators related to thin plate magnetizations via generalizations of Hodge decompositions. Inverse Prob. 2013;29:015004.
   Web of Science ®Google Scholar
• Lima EA , Weiss BP , Baratchart L , et al . Fast inversion of magnetic field maps of unidirectional planar geological magnetization. J Geophys Res Solid Earth. 2013;118:1–30.
   Web of Science ®Google Scholar
• Butler RF . Paleomagnetism: magnetic domains to geologic terranes. Electronic edition. Springer; 2004.
   Google Scholar
• Gubbins D , Ivers D , Masterton SM , et al . Analysis of lithospheric magnetization in vector spherical harmonics. Geophys J Int. 2011;187:99–117.
   Web of Science ®Google Scholar
• Vervelidou F , Lesur V , Morschhauser A , et al . On the accuracy of paleopole estimations from magnetic field measurements. Geophys J Int. 2017;211:1669–1678.
   Web of Science ®Google Scholar
• Vervelidou F , Lesur V , Grott M , et al . Constraining the date of the Martian dynamo shutdown by means of crater magnetization. J Geophys Res. 2017;122:2294–2311.
   Web of Science ®Google Scholar
• Baratchart L , Gerhards C . On the recovery of crustal and core contributions in geomagnetic potential fields. SIAM J Appl Math. 2017;77:1756–1780.
   Web of Science ®Google Scholar
• Michel V . Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the earth’s gravitational field at satellite height. Inverse Prob. 2005;21:997–1025.
   Web of Science ®Google Scholar
• Michel V , Fokas AS . A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods. Inverse Prob. 2008;24:045019.
   Web of Science ®Google Scholar
• Runcorn SK . An ancient lunar magnetic dipole field. Nature. 1975;253:701–703.
   Web of Science ®Google Scholar
• Backus GE . Application of a non-linear boundary-value problem for Laplaces equation to gravity and geomagnetic intensity measurements. Q J Mech Appl Math. 1968;21:195–221.
   Web of Science ®Google Scholar
• Freeden W , Gervens T , Schreiner M . Constructive approximation on the sphere (with applications to geomathematics). Oxford: Oxford Science Publications, Clarendon Press; 1998.
   Google Scholar
• Backus G , Parker R , Constable C . Foundations of geomagnetism. Cambridge: Cambridge University Press; 1996.
   Google Scholar
• Freeden W , Schreiner M . Spherical functions of mathematical geosciences. Berlin, Heidelberg: Springer; 2009.
   Google Scholar
• Gerhards C . Locally supported wavelets for the separation of spherical vector fields with respect to their sources. Int J Wavel Multires Inf Process. 2012;10:1250034.
   Web of Science ®Google Scholar
• Baratchart L , Dang P , Qian T . Hardy-hodge decomposition of vector fields in ℝn . Trans Am Math Soc. 2017.
   PubMed Web of Science ®Google Scholar
• Edmonds AR . Angular momentum in quantum mechanics. Princeton (NJ): Princeton University Press; 1957.
   Google Scholar
• Fengler M . Vector spherical harmonic and vector wavelet based non-linear galerkin scheme for solving the incompressible Navier-Stokes equation on the sphere [PhD thesis]. University of Kaiserslautern; 2005.
   Google Scholar
• Freeden W , Gutting M . Special functions of mathematical (geo-)physics. Applied and numerical harmonic analysis. Basel: Birkhäuser; 2013.
   Google Scholar
• James RW . The Adams and Elsasser dynamo integrals. Proc R Soc London. 1973;331:469–478.
   Google Scholar
• Anzengruber SW , Ramlau R . Morozov’s discrepancy principle for Tikhonov-type functionals with nonlinear operators. Inverse Prob. 2010;26:025001.
   Web of Science ®Google Scholar
• Freeden W . Multiscale modelling of spaceborne geodata. Stuttgart: Teubner; 1999.
   Google Scholar
• Lu S , Pereverzyev S . Multiparameter regularization in downward continuation of satellite data. In: Freeden W , Nashed MZ , Sonar T , editors. Handbook of geomathematics. 2nd ed. Berlin, Heidelberg: Springer; 2015.
   Google Scholar
• Driscoll JR , Healy MH Jr . Computing fourier transforms and convolutions on the 2-sphere. Adv Appl Math. 1994;15:202–250.
   Web of Science ®Google Scholar
• Hesse K , Womersley RS . Numerical integration with polynomial exactness over a spherical cap. Adv Comput Math. 2012;36:451–483.
   Web of Science ®Google Scholar