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Integral Transforms of Geophysical Fields serve as one of the major tools for processing and interpreting geophysical data. They permit the solution of a wide range of geophysical problems, including the construction of images of geophysical sections as well as field filtering and separation. In this book the authors present a unified treatment of this theory, ranging from the techniques of the transformation of 2-D and 3-D potential fields to the theory of separation and migration of electromagnetic and seismic fields, thereby paving the way to the solution of direct and inverse geophysical problems. Written primarily for scientists and post-graduate students engaged in gravimetrics, this book should also be useful to geophysicists and researchers in mathematical physics.
List of contents
Contents: Cauchy-Type Integrals in the Theory of a Plane Geopotential Field: Cauchy-Type Integral. Representation of Plane Geopotential Fields in the Form of the Cauchy-Type Integral. Techniques for Separation of Plane Fields. Analytical Continuation of a Plane Field.- Cauchy-Type Integral Analogs in the Theory of a Three-dimensional Geopotential Field: Three-dimensional Cauchy-Type Integral Analogs. Application of Cauchy Integral Analogs to the Theory of a Three-Dimensional Geopotential Field. Analytical Continuation of a Three-Dimensional Geopotential Field.- Stratton-Chu Type Integrals in the Theory of Electromagnetic Fields: Stratton-Chu Type Integrals. Analytical Continuation of the Electromagnetic Field. Migration of the Electromagnetic Field.- Kirchhoff-type Integrals in the Elastic Wave Theory: Kirchhoff-type Integrals. Continuation and Migration of Elastic Wave Fields.- Appendix A: Space Analogs of the Cauchy-Type Integrals and the Quaternion Theory.-
Appendix B: Green Electromagnetic Functions for Inhomogeneous Media and Their Properties.- References.- Subject Index.
