Theory and Practice of Geophysical Data Inversion
Proceedings of the 8th International Mathematical Geophysics Seminar on Model Optimization in Exploration Geophysics 1990
Published on 6. December 2012
VIII, 376 pages
978-3-322-89417-5 (ISBN)
Description
The contributions to this volume cover a wide spectrum of recent developments in geophysical data inversion, including basic mathematics and general theory, numerical methods, as well as computer implementation of algorithms. Most of the papers are motivated by problems arising from geophysical research and applications both on a global scale and with respect to local geophysical surveys, underlining the increasing importance of geophysical exploration methods in various fields, such as structural geology, prospecting for mineral and energy resources, hydro geology, geotechnology, environmental protection and archaeology. The first section of the book deals with basic mathematics and general theory underlying geophysical data inversion. Papers presented here are concerned with stabilization algorithms to solve ill-posed inverse problems, sensitivity of kernel function estimations to random data errors and reduction of errors in inverse modelling of response functions by linear constraints, numerical procedures for approximating the solution to boundary value problems, accuracy and stability of inverse ill-posed problems constituted by problems of moments, and fast Fourier transforms for solving potential field problems. The second section contains papers on gravity and magnetics, dealing with the solvability of the inverse gravimetric problem for sources represented by point masses and other elementary, solution of the inverse problem in cases of nonuniformly distributed data as obtained by palaeomagnetic studies, satellite observations, and surface projections of buried archaeological targets by inverse filtering of geomagnetic data.
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Andreas Vogel
Theory and Practice of Geophysical Data Inversion
Proceedings of the 8th International Mathematical Geophysics Seminar on Model Optimization in Exploration Geophysics 1990
Book
01/1992
Vieweg+Teubner Verlag
€53.49
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Content
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.
