Integral Transforms in Geophysics

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.