Geophysical Data Inversion Methods and Applications : Proceedings of the 7th International Mathematical Geophysics Seminar held at the Free University of Berlin, February 8-11, 1989

This monograph contains a selection of papers presented at the Seventh Inter­ national Seminar on Model Optimization in Exploration Geophysics held at the Free University of Berlin, February 8-11, 1989. The papers presented here cover the different methods of synthetic and real data sets. The volume covers a wide spectrum of the subject from basic mathematics, general theory and computer implementation of methods to their practical applications. The first section of the book deals with the basic mathematics and general theory underlying geophysical data inversion. Papers presented here include those dealing with the solution of ill-posed inverse problems, constraint strategies in optimization, spherical spline approximation and the use of integral transforms in geophysical data inversion. The second section contains papers on the inversion of gravity and magnetic data. These papers cover such topics as the use of singular v;alue decomposition and space domain iterative inversion techniques in the study of gravity and magnetic anomalies. Also included here are papers dealing with the stochastic and statistical modelling of potential fields, mass density distribution inside the earth and the mapping of archeological sites through the inversion of magnetic field data.

1. Basic Mathematical and General Theory.- Regularization and Cross Validation Methods for Nonlinear, Implicit, Ill-posed Inverse Problems.- Active Constraint Strategies in Optimization.- Robust Prediction and an Alternative Iteration Scheme for Ill-posed Problems.- Recovering the Orientation Distribution Function with Maximum Entropy from Experimental Pole Distribution Functions.- Cooperative Approach to Solving Inverse Problems in Integral Geophysics (Theoretical Aspects).- Spherical Spline Approximation and Its Application in Physical Geodesy.- Impedance Scattering Theory and Geophysical Problems.- Boundary Element Analysis of Inverse Problems of Linear Viscoelasticity.- Obtaining Materic Bodies through Concentration and Optimization of a Linear Functional.- The Mellin Transform — Its Properties and Applications in Geophysics.- 2. Gravity and Magnetics.- Optimisation of Magnetic Anomalies via Singular Value Decomposition.- A Statistical Approach to Depth Determination from Gravity Gradients.- Space Domain Iterative Inversion and its Application to the Western Anatolian Grabens.- The Elliptical Current Loop Model of Earth Magnetic and Paleomagnetic Field Sources.- The Influence of the Core-mantle Boundary Irregularities on the Mass Density Distribution Inside the Earth.- The Solution of the Inverse Gravity Problem of the Earth with a Homogeneous Ellipsoid Model.- Stochastic Modelling of Potential Fields for Geological Objects with Complex Internal Structure.- Secular Variation based on Archaeomagnetic Data from Ukraine and Bulgaria.- Can the Geophysical Maps over Buried Ancient Sites Reveal Specific Structures, if Correlated to Predetermined Signals?.- Study of Geomagnetic Field Reversals using the Mellin Transform.- 3. Electrics and Electromagnetics.- A Correlation between the Different Models of Resistivity Sounding Data to Discover a New Fresh Water Field in El Sadat City, Western Desert of Egypt.- Fluid Penetration and Formation Temperature Estimation by Inversion of Borehole Measurements.- Interpolation of Induced Polarisation Transients by the Generalized Cole-Cole Relaxation Model.- On the Solution of 2.5D Electromagnetic Field Problems.- 4. Seismics.- Automated Basic Static Corrections.- Fast Radon Transform and Velocity Analysis Applications.- An Optimizational Method for Solving the Inverse Dynamic Problem for the Wave Equation in the Class of Vertically Inhomogeneous Media: Numerical Modeling.- In-depth Parameter for Inversion in Terms of the Type of Stratification.- A Systems Theory Model for Inversion of the Abel Transform.- Numerically-Analytical Method for Calculation of Theoretical Seismograms in Layered-Inhomogeneous Media.- Weighting Factors in the Inversion of Seismic Data.- Algorithm for Calculation of Seismic Wave Field Propagation in the Medium with Curvilinear Free Surface.- Numerical Inversion of Travel Time Observations by Boundary Value Problem Methods.- The Multichannel Constrained Wiener Filter.- 5. Joint Inversion of Geophysical Data and Geothermics.- A Study of the Subsurface Model of Base Metal Mineralization using Complex Geophysical Exploration in Wadi El Khadra Prospect, Kingdom of Saudi Arabia.- Estimation of the Source Model Parameters for Thermal Anomalies in South Silesia.