Theory and Practice of Geophysical Data Inversion

Dr. Andreas Vogel leitet das wissenschaftliche Institut für Presseforschung und Medienberatung in Köln.

1. Basic Mathematics and General Theory.- Effective Numerical Methods for Solving Implicit Ill-Posed Inverse Problems.- On the Data Error Influence in Determining a Specific Response Function.- Approximating the Solution to the Cauchy Problem and the Boundary Value Problem for the Laplace Equation.- On Numerical Integration/Differentiation of Fractional Order: a Systems Theory Approach.- Recent Results in the Study of the Moment Problem.- On the Structure of Uniqueness in Linear Inverse Source Problems.- Fast Algorithm for Solving Potential Field Problems.- 2. Gravity and Magnetics.- Solving Inverse Problems for Potential Fields for Nonuniform Data with Error.- The Applicability of Two-dimensional Inversion Filters in Magnetic Prospecting for Buried Antiquities.- 3. Geoelectrics and Electromagnetics.- Resolving Resistive Layers using Joint Inversion of LOTEM and MT Data.- An Analysis of the Broad Spectrum Apparent Complex Resistivity Method.- 4. Seismics.- An Efficient Algorithm for Impedance Reconstruction by the Modified Gelfand-Levitan Inverse Method.- Imaging of the Earth by Iterative Reconstruction Methods.- Reverse-time Migration of Crosshole Data using Tomographic Velocities.- From Radon to Kirchhoff Migration.- An Integral Equation Method for Seismic Modelling and Inversion.- Inverse Scattering for Goupillaud Horizontally Layered Earth Model.- Spectral Analysis of Blast Vibrations from Large Explosions.- Optimization Approach to the Earthquake Source Inverse Problem.- 5. Geothermics.- Reconstruction of the Surface Temperature History by the Least-squares Inversion Theory.- 6. Joint Inversion of Geophysical Data.- Empirical Covariance Functions between Seismic, Density and Gravity Data - an Important Constraint in 3D Gravimetric-Seismic Stochastic Inversion.-Iterative Simultaneous Inversion of Gravity and Seismic Traveltime Data: I - Formulas.