Theory and Practice of Geophysical Data Inversion : Proceedings of the 8th International Mathematical Geophysics Seminar on Model Optimization in Exploration Geophysics 1990

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. Front Matter....Pages I-VIII Front Matter....Pages 1-1 Effective Numerical Methods for Solving Implicit Ill-Posed Inverse Problems....Pages 3-19 On the Data Error Influence in Determining a Specific Response Function....Pages 21-34 Approximating the Solution to the Cauchy Problem and the Boundary Value for the Laplace Equation....Pages 35-48 On Numerical Integration Differentiation of Fractional Order: a Systems Theory Approach....Pages 49-71 Recent Results in the Study of the Moment Problem....Pages 73-84 On the Structure of Uniqueness in Linear Inverse Source Source Problems....Pages 85-98 Fast Algorithm for Solving Potential Field Problems....Pages 99-106 Front Matter....Pages 107-107 Solving Inverse Problems for Potential Fields for Nonuniform Data with Error....Pages 109-119 The Applicability of Two-dimensional Inversion Filters in Magnetic Prospecting for Buried Antiquities....Pages 121-144 Front Matter....Pages 145-145 Resolving Resistive Layers using Joint Inversion of LOTEM and MT Data....Pages 147-158 An Analysis of the Broad Spectrum Apparent Complex Resistivity Method....Pages 159-176 Front Matter....Pages 177-177 An Efficient Algorithm for Impedance Reconstruction by the Modified Gelfand-Levitan Inverse Method....Pages 179-190 Imaging of the Earth by Iterative Reconstruction Methods....Pages 191-210 Reverse-time Migration of Crosshole Data Using Tomographic Velocities....Pages 211-230 From Radon to Kirchhoff Migration....Pages 231-242 An Integral Equation Method for Seismic Modelling and Inversion....Pages 243-264 Inverse Scattering for Goupillaud Horizontally Layered Earth Model....Pages 265-282 Spectral Analysis of Blast Vibrations from Large Explosions....Pages 283-308 Optimization Approach to the Earthquake Source Inverse Problem....Pages 309-323 Front Matter....Pages 325-325 Reconstruction of the Surface Temperature History by the Least-Squares Inversion Theory....Pages 327-332 Front Matter....Pages 333-333 Empirical Covariance Functions between Seismic, Density and Gravity Data — an Important Constraint in 3D Gravimetric-Seismic Stochastic Inversion....Pages 335-360 Iterative Simultaneous Inversion of Gravity and Seismic Traveltime Data: I — Formulas....Pages 361-374 Back Matter....Pages 375-376