Inverse Magnetometry: Mollifier Magnetization Distribution from Geomagnetic Field Data (Lecture Notes in Geosystems Mathematics and Computing)

Preface
	Goal of the Book
	Structure of the Book
	Acknowledgments
Contents
1 Introductory Remarks
	1.1 Cycle of Measurement and Mathematical Modeling
	1.2 Specific Problems in Inverse Potential Field Recovery
2 Basics of Magnetic Field Theory and Magnetization
	2.1 Magnetometric Methods: Historical Stages
	2.2 Essential Constituents of the Earth\'s Magnetic Field
	2.3 Maxwell Equations and Law of Biot–Savart
	2.4 Gauss Representation
3 Dipole Potential Based Magnetometry
	3.1 Magnetometric Measurements
	3.2 Localized Currents
	3.3 Vector Potential Representation Involving Magnetization
	3.4 Dipole Potentials
	3.5 Gravito-Magneto Combined Potential Relation
	3.6 Susceptibility and Permeability
4 Inverse Magnetometry
	4.1 Ill-Posedness and Regularization Methods
	4.2 Direct and Inverse Problem Formulation
	4.3 Heuristic Perception of the Ill-Posedness
	4.4 Magnetic Primary and Secondary Field
	4.5 Born Approximation
5 Multi-Scale Inverse Mollifier Magnetometry
	5.1 Mollifier Philosophy
	5.2 Mollifier Framework
	5.3 Multi-Scale Mollifier Approximation
	5.4 Multi-Scale Mollifier Divergence of the Magnetization
	5.5 Mollifier Wavelet Inversion Using Pre-Information
	5.6 Mollifier Reproducing Kernel Hilbert Space Structure
	5.7 Mollifier Spline Inversion Interpolation and Smoothing
	5.8 Mollifier Finite Pointset Wavelet Inversion
	5.9 Mollifier Born Optimization
6 Test Demonstrations
	6.1 Marmousi-Model
	6.2 Bavarian Molasse Area
7 Concluding Remarks
	7.1 Methodological Aspects
	7.2 Geodisciplinary Aspects
	7.3 Numerical Valuation
List of Symbols
	List of Symbols
References
Index