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Integral Transforms of Geophysical Fields serve as one ofthe major tools for processing and interpreting geophysicaldata. In this book the authors present a unified treatmentof this theory, ranging from the techniques of the transfor-mation of 2-D and 3-D potential fields to the theory of se-paration and migration of electromagnetic and seismicfields. Of interest primarily to scientists and post-gradu-ate students engaged in gravimetrics, but also useful togeophysicists and researchers in mathematical physics.
List of contents
I Cauchy-Type Integrals in the Theory of a Plane Geopotential Field.- 1 Cauchy-Type Integral.- 2 Representation of Plane Geopotential Fields in the Form of the Cauchy-Type Integral.- 3 Techniques for Separation of Plane Fields.- 4 Analytical Continuation of a Plane Field.- II Cauchy-Type Integral Analogs in the Theory of a Three-Dimensional Geopotential Field.- 5 Three-Dimensional Cauchy-Type Integral Analogs.- 6 Application of Cauchy Integral Analogs to the Theory of a Three-Dimensional Geopotential Field.- 7 Analytical Continuation of a Three-Dimensional Geopotential Field.- III Stratton-Chu Type Integrals in the Theory of Electromagnetic Fields.- 8 Stratton-Chu Type Integrals.- 9 Analytical Continuation of the Electromagnetic Field.- 10 Migration of the Electromagnetic Field.- IV Kirchhoff-Type Integrals in the Elastic Wave Theory.- 11 Kirchhoff-Type Integrals.- 12 Continuation and Migration of Elastic Wave Fields.- Appendix A Space Analogs of the Cauchy-Type Integrals and the Quaternion Theory.- A.1 Quaternions and Operations Thereon.- A.2 Monogenic Functions.- A.3 Quaternion Notation of Space Analogs of the Cauchy-Type Integral.- Appendix B Green Electromagnetic Functions for Inhomogeneous Media and Their Properties.- B.1 Field Equations.- B.2 Lorentz Lemma for an Inhomogeneous Medium.- B.3 Reciprocal Relations.- B.4 Integral Representations of the Electric and Magnetic Fields.- B.5 Some Formulas and Rules of Operations on Dyadic Tensor Functions.- B.6 Tensor Statements of the Ostrogradsky-Gauss Theorem.- References.
